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Absolute distance measurement using laser interferometric wavelength leverage with a dynamic-sideband-locked synthetic wavelength generation

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Abstract

Absolute distance measurement with laser interferometry has the advantages of high precision and traceability to the definition of meter but its accuracy is primarily limited by the phase demodulation. Among kinds of absolute distance interferometric measurements, the multi-wavelength interferometry is widely used but seriously limited by the generation of suitable synthetic wavelength and the stability of adopted synthetic wavelength. Inspired by the mechanical lever, we hereby establish a principle of laser interferometric wavelength leverage (LIWL) for absolute distance measurement. By keeping the phase difference in two single wavelengths constant, LIWL achieves the measurement of large distance with respect to synthetic wavelengths by detecting nanometer displacement with respect to a single wavelength. The merit of LIWL is eliminating the influence of phase demodulation error. And a dynamic-sideband locking method based on a high-frequency electro-optic modulator is proposed, which can flexibly and quickly generate variable synthetic wavelengths from tens of kilometer to millimeter with high stability. Experimental setup was constructed and absolute distance measurements were performed. Experimental results show that a measurement range of 100 m with residual error of less than 15 µm has been achieved by comparing the LIWL system and an incremental laser interferometer.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Absolute distance measurement with large range has been paid increased attention in the applications of high-end equipment manufacturing, space mission, large-scale metrology and so on [15]. Laser interferometry has been the focus of research for distance measurement because of its high precision and traceability to the definition of meter [6,7]. However, the inherent ambiguity of single-wavelength interferometry limits the measuring range to half of the used wavelength. To overcome the ambiguity, multi-wavelength interferometry (MWI) was proposed by C. R. Tilford [8] and it has been rapidly developed in recent years [911]. In MWI, multiple laser wavelengths are used to generate a chain of decreasing synthetic wavelengths, where the maximum one covers the measuring range and the minimum one determines the resolution. To realize high precision absolute distance measurement with large range, the key issues in MWI are the generation of the required synthetic wavelength chain, the stability of the synthetic wavelengths, and the accuracy of phase demodulation corresponding to the synthetic wavelength.

To generate the synthetic wavelength chain, multiple laser sources with fixed wavelength can be employed in parallel [12], while the discrete spectra of the available laser sources make it difficult to generate required synthetic wavelengths to cope with different measuring distances. A wide and continuous spectral range can be acquired using an external cavity diode laser (ECDL), and it can be employed in sequence to obtain multiple wavelengths. For instance, C. Y. Yin proposed a changeable synthetic wavelength chain (CSWC) method for absolute length measurement in optical probes [13]. Using one ECDL, desired synthetic wavelengths determined by the measuring distance and the measurement uncertainty were created. S. H. Lu presented the variable synthetic wavelength interferometry (VSWI) to measure large step heights, and one ECDL was employed to synthesize a series of synthetic wavelengths in descending order [14]. However, the achieved measurement relative uncertainties are not better than 10−6 in CSWC and VSWI, and the maximum error source comes from the synthetic wavelength uncertainty which is determined by the individual uncertainty of the used wavelengths. That is because the frequency stability of a free-running ECDL is not better than 10−7, making it become the main contribution to the measurement uncertainty, and this contribution increases with the measuring distance. Therefore, it is necessary to take certain frequency stabilization methods to ensure the stability of the synthetic wavelength.

In MWI, the synthetic wavelength ΛS is described as ΛS=λ1λ2/|λ1-λ2|=cf, where λ1 and λ2 are laser wavelengths for generating the synthetic wavelength, Δf is the frequency difference between the two used wavelengths, and c is the speed of light in vacuum. To get synthetic wavelength with high stability, one way is stabilizing the individual used wavelengths to certain frequency references. It can be realized by locking the ECDL to the Fabry-Perot cavity [15] or the absorption lines of selected atoms or molecules [16]. However, the Fabry-Perot cavity with high stability requires precise control of the environment parameters, like temperature, sound and vibration, and it cannot trace to the definition of meter. The available absorption lines in nature are isolated discrete points, making it difficult to generate arbitrary synthetic wavelengths we need in MWI. Recently, optical frequency comb (OFC) has been used as a precision wavelength ruler for it can provide a few hundreds of thousands of narrow line width wavelengths over a broad optical spectral range [17,18]. S.W. Kim et al. employed an ECDL locked to the OFC for absolute length measurement in MWI, and the required multiple wavelengths were provided by sequentially tuning and phase-locking the ECDL to a set of pre-selected optical modes of the OFC [19,20]. Such methods will take a longer time for unlocking and locking ECDL to different modes. In addition, the uncertainty of the synthesized wavelength will be deteriorated by 1–2 orders of magnitude by stabilizing the individual used wavelengths to the frequency references. According to the definition of the synthetic wavelength, the uncertainty is only determined by the frequency difference between the used wavelengths, so directly stabilizing the frequency difference is a potential way to further reduce the uncertainty of the synthetic wavelength.

Another key issue in MWI is to demodulate the synthetic phase corresponding to the synthetic wavelength accurately. A common solution is demodulating the interference phase of the used wavelengths individually, and then make a difference to get the synthetic phase. To demodulate the interference phase of every laser wavelength with high precision, L. Hartmann et al. adopted the homodyne detection technique using a single frequency laser, and the measured phase was demodulated from a pair of quadrature interference signals obtained by a Fresnel rhombi [21]. While it is vulnerable to low frequency disturbances, and the laser power drift, unequal gain of the detectors and non-quadrature interference signals will result in nonlinear errors. N. Schuhler et al. adopted the heterodyne detection technique which uses a dual-frequency laser with two linearly polarized orthogonal beams, and the measured phase shift is carried on the beat signal of the dual-frequency laser [22,23]. The technique has advantages of fast response, immune to noise and inherent freedom from drift, however, the nonlinear errors contributed by frequency mixing and polarization mixing limit the precision of the phase demodulation. In our previous work, the phase generated carrier (PGC) homodyne detection technique which has simple optical configuration was used for absolute distance measurement [24]. In this technique, a high-frequency carrier phase signal is used to convert the measured phase signal onto the sidebands of the carrier frequency and its harmonics, making the phase demodulation have less sensitivity to the optical and electronic noises. Even so, no matter which phase detection technique is adopted, nonlinear errors in phase demodulation are always inevitable. Then, the operation of subtraction for getting the synthetic interference phase will amplify the nonlinear error, and the amplitude of the nonlinear error varies periodically when the synthetic interference phase changes in 0∼2π.

In this paper, we establish a principle of laser interferometric wavelength leverage (LIWL) to measure large distance with respect to synthetic wavelengths by detecting nanometer displacement with respect to a single wavelength. And we further propose an electro-optical modulator (EOM) based dynamic-sideband locking method to generate variable synthetic wavelengths with high stability. The principle of LIWL is deduced, its realization is revealed, and experiments are performed for verification.

2. Principle of the laser interferometric wavelength leverage

Figure 1 shows the principle schematic of LIWL. In Fig. 1(a), two orthogonal linearly polarized beams with fixed wavelength of λ1 and tunable wavelength of λ2 are combined at PBS1. The output beam of PBS1 is divided into two beams by BS. The reflected beam is incident on PBS2, where beam λ2 is reflected, beam λ1 transmits PBS2, directs to the reference M1, and then is reflected. The transmitted beam of BS is incident on the measurement M2 and then reflected. The reflected beams recombine at BS and generate interference signals of λ1 and λ2, which are split by PBS3 and detected by PD1 and PD2, respectively.

 figure: Fig. 1.

Fig. 1. Principle and schematic of the laser interferometric wavelength leverage. (a) Optical layout. (b) Phase difference with the tuning of λ2. (c) Conception of wavelength leverage.

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In Fig. 1(b), the phase difference Δφ between the interference signals of λ1 and λ2 can be expressed as

$$\Delta \varphi \textrm{ = }{\varphi _\textrm{1}}\textrm{ - }{\varphi _\textrm{2}}\textrm{ = }\frac{{4\pi }}{{{\lambda _1}}}({L + {L_\textrm{1}}} )- \frac{{4\pi }}{{{\lambda _2}}}L$$
where L1 represents the distance between PBS2 and M1, L represents the distance difference to be measured between BS to PBS2 and BS to M2, φ1 and φ2 represent the interference phases of wavelengths λ1 and λ2.

When wavelength λ2 is tuned to λ2λ2, the phase difference will change to Δφ'

$$\Delta \varphi ^{\prime}\textrm{ = }\frac{{4\pi }}{{{\lambda _\textrm{1}}}}({L + {L_\textrm{1}}} )- \frac{{4\pi }}{{{\lambda _\textrm{2}}\textrm{ + }\Delta {\lambda _2}}}L$$

To determine the distance difference L, M1 is moved a very small displacement Δl to make the phase difference equal to the initial Δφ again. That is

$$\Delta \varphi ^{\prime\prime}\textrm{ = }\frac{{4\pi }}{{{\lambda _\textrm{1}}}}({L + {L_\textrm{1}}\textrm{ + }\Delta l} )- \frac{{4\pi }}{{{\lambda _\textrm{2}}\textrm{ + }\Delta {\lambda _2}}}L$$

When Δφ " =Δφ, a one-to-one correspondence can be established between L and Δl

$$L \cdot \frac{1}{{{\Lambda _{\textrm{SS}}}}} = \Delta l \cdot \frac{1}{{{\lambda _1}}}$$
where ΛSS=(λ2λ2λ2λ2. It represents the self-synthetic wavelength constructed by the change of λ2.

The expression of Eq. (4) is similar to the mechanical leverage in mechanics, as shown in Fig. 1(c). Here, we call it the laser interferometric wavelength leverage (LIWL). Similar to the definitions of the five components of fulcrum, resistance, resistance arm, effort, and effort arm in the mechanical lever, in LIWL, L corresponds to the resistance, 1/ΛSS to the resistance arm, Δl to the effort, 1/λ1 to the effort arm, and phase difference Δφ keeping constant to the fulcrum.

Therefore, by moving M1 to keep Δφ constant and detecting the moved displacement Δl, the absolute long distance to be measured can be obtained

$$L = \frac{{{\Lambda _{\textrm{SS}}}}}{{{\lambda _1}}}\Delta l$$

Equation (5) indicates that a measured distance L in the range of ΛSS/2 can be achieved by detecting the displacement Δl in the range of λ1/2. For instance, when the frequency of laser 2 is changed by 1 MHz, ΛSS will be about 300 m, and when Δλ2 reaches 6 nm, ΛSS will decrease to 100 µm. Therefore, by tuning λ2 to construct a gradually decreasing variable self-synthetic wavelength, absolute distance measurement in hundreds of meters with micrometer-level accuracy can be realized.

Obviously, constructing a variable synthetic wavelength with high stability and providing a small displacement Δl with nanometer accuracy are essential for LIWL. Here, it should be emphasized that the key innovative of LIWL is to keep Δφ constant, which can eliminate the influence of the nonlinear error of single-wavelength phase demodulation on the phase of synthetic wavelength in most MWI.

3. Realization of LIWL for absolute distance measurement

3.1 Synthetic wavelength generation with EOM- based dynamic-sideband locking

Figure 2 shows the principle of proposed synthetic wavelength generation with dynamic- sideband locking. In Fig. 2(a), the first external cavity diode laser (ECDL1) is referenced to an optical frequency comb (OFC). Its output beam is split into two beams by a fiber splitter (FS1). The first beam of ECDL1 passes through a high-frequency EOM (EOMH) modulated by a sinusoidal signal and generates the corresponding sidebands with frequency of fsideband

$${f_{\textrm{sideband}}} = {f_1} + k \cdot {f_\textrm{r}}$$
where f1 is the original frequency of ECDL1, k indicates the order of sidebands, and k=0, ±1, ±2, …, and fr is the modulating frequency of the sinusoidal signal, which is generated by an adjustable phase-locked oscillator (PLO) and amplified by an amplifier (AMP).

 figure: Fig. 2.

Fig. 2. Principle of synthetic wavelength generation with dynamic-sideband locking. (a) Optical configuration of laser sources. (b) Schematic of the changes of f2 and fb with fr.

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Output beam of another external cavity diode laser (ECDL2) is also split into two parts by FS2. Sidebands of ECDL1 and one beam of ECDL2 are combined by a fiber combiner (FC) and detected by an avalanche photodiode (APD). The beat frequency signal is filtered, amplified, and then phase locked to the Rubidium clock signal (REF) by using a phase-locked loop (PLL). As Fig. 2(b) shown, the frequency of ECDL2 is offset-frequency locked to Nth sideband of ECDL1 and expressed as

$${f_2}\textrm{ = }{f_1} + N{f_\textrm{r}} + {f_\textrm{o}}\textrm{ = }{f_1} + {f_b}$$
where fo is the beat frequency between ECDL2 and the Nth sideband, and fb=Nfr+fo is the frequency difference between ECDL2 and ECDL1.

The second beams of ECDL1 and ECDL2 are combined into one orthogonal linearly polarized beam at a fiber polarization combiner (FPC) and acts as the light source for LIWL.

According to Eq. (6), if we adjust the modulating frequency fr, the frequencies of sidebands will change dynamically (Here, we call them dynamic sidebands). As Fig. 2(b) shown, once ECDL2 keeps locked to the Nth sideband of ECDL1 (e.g. N=5), f2 will change with the adjustment of fr. Denoting the ith modulating frequency as fr[i], then f2[i] and fb[i] can be expressed as

$${f_{2[i]}} = {f_1} + {f_{\textrm{b}[i]}} = {f_1} + N{f_{\textrm{r[}i\textrm{]}}} + {f_\textrm{o}}$$
$${f_{\textrm{b}[i]}} = N{f_{\textrm{r}[i\textrm{]}}} + {f_\textrm{o}}$$

Equations (8) and (9) indicate that both f2[i] and fb[i] can be adjusted by dynamically locking to the sideband. Therefore, by adopting the wavelength of λ2 before and after adjusting fr, we can construct a variable self-synthetic wavelength ΛSS[i] traced to Rubidium clock with high stability.

$${\Lambda _{\textrm{SS}[i]}} = \left|{\frac{{{\lambda_{\textrm{2[}i\textrm{]}}} \cdot {\lambda_{\textrm{2[}i - 1\textrm{]}}}}}{{{\lambda_{\textrm{2[}i\textrm{]}}} - {\lambda_{\textrm{2[}i - 1\textrm{]}}}}}} \right|\textrm{ = }\frac{c}{{N\Delta {f_{\textrm{r[}i\textrm{]}}}}}$$
where Δfr[i]=fr[i]-fr[i−1] is the changed amount of fr, and c is the light speed in vacuum. Obviously, the value of ΛSS[i] is determined by Δfr[i] and N.

According to Eq. (10), it is possible to flexibly construct a ΛSS[i] from tens of kilometer to millimeter by only setting different Δfr[i]. For example, the non-ambiguity range (NAR) of absolute distance measurement, i.e. ΛSS[i]/2, can be up to 300 m when Δfr[i] is set to 100 kHz, further to 3 km when Δfr[i] is set to 10 kHz or to 30 km when Δfr[i] is set to 1 kHz. While by setting Δfr[i] to 1GHz, NAR will decrease to 30 mm.

In addition, by adopting the frequency difference between ECDL1 and ECDL2, another variable synthetic wavelength ΛS[i] can be obtained

$${\Lambda _{\textrm{S[}i\textrm{]}}} = \left|{\frac{{{\lambda_1} \cdot {\lambda_{\textrm{2[}i\textrm{]}}}}}{{{\lambda_\textrm{1}} - {\lambda_{\textrm{2[}i\textrm{]}}}}}} \right|\textrm{ = }\frac{c}{{{f_{\textrm{b[}i\textrm{]}}}}}\textrm{ = }\frac{c}{{N{f_{\textrm{r[}i\textrm{]}}}\textrm{ + }{f_o}}}$$

By comparing Eq. (10) and Eq. (11), we can see that ΛS[i] will be much smaller than ΛSS[i] because fr[i] is much larger than Δfr[i]. Therefore, ΛSS[i] and ΛS[i] are used for coarse distance measurements and fine distance measurements, respectively.

Here, it should be emphasized that when constructing different synthetic wavelengths, ECDL2 always remains locked to the same sideband. This avoids the unlocking and locking operation of ECDL2 and will greatly reduce the adjusting time of synthetic wavelength.

3.2 Realization of an equivalent displacement Δl with an EOM

In Fig. 1(a), the purpose of moving M1 is to adjust the interference phase of wavelength λ1 to keep Δφ constant. The accuracy and stability of the displacement Δl is very important because its error will be magnified by a factor of ΛSS/λ1 when calculating the measured distance L. Generally, as Fig. 1(a) shows, PZT stage equipped with capacitive feedback sensors can provide a sub-micrometer displacement with repeatability of ±1nm. However, in the configuration of Fig. 1(a), partial optical path of beams λ1 and λ2 is not in common, which will make the tiny drift between PBS2 and M1 be magnified and result in larger measurement error. In addition, the mechanical movement of PZT stage might introduce some other errors, such as vibration, and thermal deformation.

Here, an EOM made of LiNbO3 crystal is adopted to generate an equivalent nanometer displacement. As shown in Fig. 3, due to the birefringent and linear electro-optic effects, when the orthogonal linearly polarized beam passes through the EOM, an induced phase difference between λ1 and λ2 will be generated

$$\Delta {\varphi _\textrm{e}}\textrm{ = }\frac{{2\pi WV}}{d}\left( {\frac{{n_\textrm{e}^3{\gamma_{33}}}}{{{\lambda_1}}} - \frac{{n_\textrm{o}^3{\gamma_{13}}}}{{{\lambda_2}}}} \right)$$
where V is the amplitude of the applied electric field, W and d are crystal's length and thickness, γ33 and γ13 are crystal's appropriate electro-optic coefficients, and ne and no are crystal's extraordinary index and ordinary index.

 figure: Fig. 3.

Fig. 3. Realization of the equivalent displacement with an EOM. (a) Optical layout. (b) Schematic of transverse electro-optic effect of crystal.

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As beam λ1 is p-polarization and beam λ2 is s-polarization, we define ${l_\textrm{P}} = {{n_e^3{\gamma _{33}}WV} / {2d}}$ and ${l_\textrm{S}} = {{n_o^3{\gamma _{13}}WV} / {2d}}$. Then, we can get

$$\Delta {\varphi _\textrm{e}}\textrm{ = }\frac{{4\pi }}{{{\lambda _1}}}{l_\textrm{P}} - \frac{{4\pi }}{{{\lambda _2}}}{l_\textrm{S}}\textrm{ = }\frac{{4\pi }}{{{\Lambda _\textrm{S}}}}{l_\textrm{S}}\textrm{ + }\frac{{4\pi }}{{{\lambda _1}}}({{l_\textrm{P}} - {l_\textrm{S}}} )$$

Usually, lS/lP is about 0.3∼0.5. Equation (13) indicates that the adjustment of Δφe (i.e. phase difference between λ1 and λ2) can be realized by changing the applied voltage V of EOM. In LIWL, the range of Δφ is from -π to π, which means lP and lS are in several hundred nanometers. Therefore, for distance measurement with ΛS larger than 1mm, the first term in Eq. (13) is small enough to be neglected. Then, (lP-lS) of the second term is equivalent to the nanometer displacement Δl provided by PZT.

4. Experiments and results

4.1 Experimental setup

Figure 4 shows the optical configuration and experimental setup of constructed LIWL for absolute distance measurement. As Fig. 4(a) shows, LIWL includes two sinusoidal phase modulating interferometers. The first one consisting of BS1, M1 and M2 is used for absolute distance measurement. The second one consisting of BS1, M1, BS3, BS2 and BS4 is used to measure the equivalent Δl and monitor the drift of optical path of BS1-M1. In the two interferometers, wavelengths λ1 and λ2 share the same optical path of BS1-M1 and their phases are modulated sinusoidally by EOM1 and EOM2. EOM3 is adopted to provide the equivalent displacement Δl to adjust the phase difference Δφ for LIWL. The interference phases of four detectors PD1, PD2, PD3, and PD4 are denoted as φm1, φm2, φr1, and φr2, respectively. The four phases are demodulated simultaneously with PGC algorithm realized by a FPGA-based (XC7K160T, Xilinx) high-speed signal processing board [25].

 figure: Fig. 4.

Fig. 4. Experimental setup of LIWL for absolute distance measurement. (a) Optical configuration of LIWL. (b) Constructed experimental setup.

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In the experiment, two same ECDL lasers (TLB6700, New Focus) with a tunable range of 765–781 nm are adopted. ECDL1 is locked to the OFC (FC1500-250, Menlo Systems) and then modulated by a high-frequency EOM (NIR-MPX800-LN-10, Ixblue) with modulating frequency about 12 GHz. This high-frequency modulating signal is provided by a programmable digital signal generator (LMS-183CX, Vaunix) with a frequency sweeping range of 6–18 GHz. ECLD2 is locked to the −4th sideband of ECDL1 with a beat frequency fo=60 MHz. The sinusoidal modulating signals of EOM1 and EOM2, the DC modulating signal of EOM3 are generated by FPGA board and amplified to a range of ±400 V with high-voltage amplifiers (ATA-2161, Aigtek). A 10 MHz Rubidium clock (STM-Rb, Sync-tech) with stability of 3.3×10−12 (relative Allan deviation in 1s) provides a global reference for the whole experimental system. By sweeping the frequency of the high-frequency EOM, four self-synthetic wavelengths ΛSS[i] from hundred meters to tens of millimeter and five synthetic wavelengths ΛS[i] with very small difference are generated. Table 1 shows one group of selected parameters and the generated synthetic wavelengths in the experiments.

Tables Icon

Table 1. Selected parameters and generated synthetic wavelengths

Figure 4(b) shows the experimental setup constructed on an 80 m underground granite air-bearing guide rail in the laboratory of National Institute of Metrology (NIM), China. To evaluate the performance of the proposed LIWL system, three He-Ne interferometers (Agilent 5519B, Keysight) configured in triangular were adopted to measurement the displacement of guide rail. The displacement results of three interferometers are used to calculate a corrected displacement with the smallest Abbe error, which corresponds to a virtual interferometer at the center of triangle [26]. Therefore, for accurate comparison, our LIWL was placed at position of the virtual interferometer. The target mirrors of our system and Agilent interferometers were mounted on the same slider of the guide rail, whose actual moving range is about 72 m. In the experiments, the ambient parameters (temperatures along the guide rail, pressure, relative humidity, and CO2 concentration) were measured to compensate the refractive index of air (nair) for our system and Agilent interferometers. The nair was determined by the modified Edlén equation [27]. Several experiments were carried out.

4.2 Resolution and stability of the equivalent displacement Δl

From Figs. 4(a) and 3(a), we can see that, the change in the phase difference Δφr=φr1-φr2 represents the phase change Δφe caused by the applied voltage change of EOM3. Therefore, the equivalent displacement can be obtained by Δl=δ(Δφr) × λ1/2π when changing the applied voltage. Here, δ(Δφr) is the variation of Δφr. Figure 5 shows the resolution and stability evaluation results of Δl. An equivalent displacement Δl with step of 0.5 nm can be achieved by increasing the applied voltage. And after the voltage stops increasing, the recorded fluctuation of Δl is less than ±0.21 nm in 140 s, with a standard deviation of 0.073 nm. This result shows that an accurate Δl can be provided for LIWL by adjusting the applied voltage of EOM.

 figure: Fig. 5.

Fig. 5. Resolution and stability evaluation results of the equivalent displacement Δl

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4.3 Stability of the frequency difference fb with dynamic-sideband locking

The stability of synthetic wavelength is determined by the stability of frequency difference fb between ECDL2 and the sideband of ECDL1. According to Eq. (9), the stability of fb is related to that of fr and fo, where fr can be further expressed as fr = K × fRb. Here, fRu is the frequency of Rubidium atomic clock, and K is the ratio of fr to fRb (for example, K=1200 for fr = 12 GHz). Therefore, by simultaneously recording fo and fRb, fb can be obtained. Fig. 6 shows the recorded experimental results in 4 hours. The fluctuation of fb is less than ±25 Hz, with a standard deviation of 5.97 Hz. And the relative Allan deviation of fb reaches 1.47×10−10 in 1s averaging time. These results indicate that the proposed dynamic-sideband-locked synthetic wavelength generation method can provide a variable synthetic wavelength with high stability.

 figure: Fig. 6.

Fig. 6. Stability experimental results of the frequency difference fb. (a) Fluctuation of fb. (b) Relative Allan standard deviation of fb.

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4.4 Absolute distance measurement

In the absolute distance measurement experiments, the modulating frequency is adjusted in sequence according to the values listed in Table 1, and the demodulated phases (normalized to 0–1) of four detectors are updated in real time. The distance measurement includes coarse results by LIWL method with four second-order ΛSS[i] and fine results by MWI with five first-order ΛS[i]. The detail measurement procedure is as following:

Step 1. Set the initial modulating frequency of high-frequency EOMH as fr[i], reset EOM3's applied voltage, i.e. V=0, calculate ΛS[i] with Eq. (11), record the initial phase difference ΦS[i]=φm1[i]- φm2[i].

Step 2. Sweep the modulating frequency from fr[i] to fr[i+1], the phase difference will change to ΦS[i+1]=φm1[i+1]- φm2[i+1]. Calculate ΛSS[i] with Eq. (10), record the reference phase difference Δφr[i]=φr1[i]-φr2[i].

Step 3. Increase the applied voltage of EOM3 to make the phase difference Φ' S[i+1] =φ 'm1[i+1]- φ 'm2[i+1] equal to the original ΦS[i], record the new Δφ ' r[i]=φ ' r1[i]-φ ' r2[i] when Φ ' S[i+1]S[i]. Then, obtain the equivalent displacement as Δl[i] =(Δφ ' r[i]- Δφr[i]) × λ1/2. According to LIWL method, the fractional part of measured distance can be calculated as Lɛ[i] = Δl[i] ×ΛSS[i]/λ1. Then, the coarse absolute distance can be determined as

$${L_{\textrm{c[}i\textrm{ + }1\textrm{]}}}\textrm{ = }\frac{{{\Lambda _{\textrm{SS[}i\textrm{ + }1\textrm{]}}}}}{2} \cdot \textrm{INT}\left[ {\frac{{2{L_{\textrm{c[}i\textrm{]}}}\textrm{ - 2}{L_{\varepsilon [i\textrm{ + }1\textrm{]}}}}}{{{\Lambda _{\textrm{SS[}i\textrm{ + }1\textrm{]}}}}}} \right] + {L_{\varepsilon [i\textrm{ + }1\textrm{]}}}$$
where i=0,1,2, Lc[0]= Lɛ[0], and the function INT[] returns the integral part of the argument.

Step 4. If i<2, update i = i+1 and repeat steps 1–3. Otherwise, stop and determine five fine absolute distance measurement results as

$${L_{\textrm{f[}j\textrm{]}}}\textrm{ = }\frac{{{\Lambda _{\textrm{S[}j\textrm{]}}}}}{2} \cdot \left( {\textrm{INT}\left[ {\frac{{2{L_{\textrm{c[3]}}}}}{{{\Lambda _{\textrm{S[}j\textrm{]}}}}}\textrm{ - }{\Phi _{\textrm{S}[j]}}} \right] + {\Phi _{\textrm{S}[j]}}} \right)$$
where j=0–4.

Step 5. Because the differences in five ΛS[j] are very small, we determine the final distance measurement result as $L\textrm{ = }\frac{1}{5}\sum\limits_{j = 0}^4 {{L_{\textrm{f[}j\textrm{]}}}}$.

Distance measurement repeatability, resolution, and comparison experiments were implemented to evaluate the performance of the constructed LIWL system. Firstly, the target retroreflector M2 was placed at a distance ∼52 m and 30 measurements were repeated. For each measurement, four coarse results Lc[i] and one final result L were recorded and shown in Fig. 7. From Figs. 7(a)–7(d) with the ΛSS[i] decreasing from ∼214 m to ∼61 mm, the distance measurement results become more and more accurate with standard deviations (STDs) decreasing from 120.1 mm to 27.9 µm. As expected, the measurement accuracy of the final result shown in Fig. 7(e) has been further improved, with fluctuation about 6 µm and STD about 1.8 µm. This result is reasonable for the five ΛS[j] being in a range of 6.7 mm to 6.0 mm.

 figure: Fig. 7.

Fig. 7. Repeat measurement results of a distance ∼52 m. (a)–(d) four coarse results. (e) the final results.

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Secondly, at a distance ∼52 m, M2 was driven to move forth and back with a moving step of 15 µm by a PZT stage (P-753.1CD, PI). After the PZT stage stops completely, five absolute distance measurements from coarse to fine were implemented. The experimental results shown in Fig. 8 indicate that the distance step of 15 µm can be obviously distinguished, and the distance resolution is better than 7.5 µm.

 figure: Fig. 8.

Fig. 8. Experimental results of distance resolution evaluation at a distance ∼52 m.

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At last, long distance measurement with a moving step of 5 m was performed. This experiment includes two part, first 0–70 m and second 60–100 m. In the first part, the offset distance is ∼3.3 m, and in the second part, the offset distance is ∼60 m by folding a fixed path of 20 m. The absolute distance results obtained by LIWL system (LADM) are compared with displacement results obtained by Agilent interferometer (LRDM) after removing the offset. Each experiment was conducted twice, and at each position, 15 consecutive data were recorded in 1.5 seconds. Figure 9 shows the difference of the averaged data between LIWI system and interferometer. It can be seen that, in the range of 0–70 m and the ranges of 60–100 m, the maximum residual errors are approximately 12.2 µm and 14.2 µm, respectively. All the experiments show that our LIWL system has realized a distance measurement range of 100 m with a residual error of less than 15 µm.

 figure: Fig. 9.

Fig. 9. Comparison experimental results. (a) Distance measurement from 3–73 m. (b) Distance measurement from 60–100 m.

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5. Discussions

According to Eq. (10), the measurement range (NAR) is determined by Δfr[i] and N, where Δfr[i] is limited by the frequency sweeping resolution of the signal generator driving the high-frequency EOM. Generally, 100Hz frequency step is available for most signal generator, which means that it is possible to construct a ΛSS[i] of 300 m, 3 km or more lager by setting N=5 and Δfr[i]=100 kHz, 10 kHz, etc. However, in such case, the coherence length of the laser source might be the key factor limiting the measurement distance. In our experiment, the linewidth of the ECDL is less than 200 kHz, corresponding to a maximal measurement distance of 497 m.

For the measurement uncertainty of the result L, it only depends on the fractional measurement of fine results Lf[i] because the integral fringe number of the synthetic wavelength ΛS[i] can be correctly determined. Therefore, the uncertainty of L is given according to Eq. (15) as

$$u(L )= \sqrt {{{\left( {L\frac{{u({{n_{\textrm{air}}}} )}}{{{n_{\textrm{air}}}}}} \right)}^2} + 2{{\left( {L\frac{{u({{\Lambda _\textrm{S}}} )}}{{{\Lambda _\textrm{S}}}}} \right)}^2} + {{\left( {\frac{{{\Lambda _\textrm{S}}}}{2}u({{\Phi _\textrm{S}}} )} \right)}^2}}$$

We can see that the first two terms are length-dependent, the third term is determined by the value of synthetic wavelength and phase demodulation error. Combining the uncertainties of the environmental parameters and the uncertainty of Edlén equation, the contribution of u(n)/n to u(L) is 2.3 × 10−8L[26]. In addition, the stability of the synthetic wavelength (equal to the stability of fb) has been tested and achieved a relative uncertainty of 1.47×10−10. Therefore, the contribution of uS)/ ΛS to u(L) is insignificant. Lastly, with the influences of electronic noise, crosstalk in multi-channel high-speed ADC, and the phase difference calculation, the uncertainty of ΦS is about 0.0005 (corresponding to 0.18°) in the experiment, which contributes 1.7 µm to u(L) for ΛS=6.7 mm. Assuming the measurement error is Gaussian distribution, the measurement expanded uncertainty U(L) is obtained with a coverage factor of k=2 as

$$U(L )= 2u(L )= 2\sqrt {{{({2.3 \times {{10}^{ - 8}}L} )}^2} + {{({1.7\mu \textrm{m}} )}^2}}$$

According to Eq. (17), the proposed LIWL method can achieve a measurement uncertainty of 4.1 µm at a measurement distance of 52 m, which agrees with the obtained results of measurement fluctuation being 6 µm and STD being 1.8 µm. In addition, a relative uncertainty of 5.7 × 10−8 at a measurement distance of 100 m can be achieved with LIWL method.

The main factor affecting the measurement uncertainty is the first term in Eq. (16), which is limited by the uncertainty of Edlén equation. Even if the uncertaintiy of environmental parameters is improved, this term will not be less than 1 × 10−8L. For the last term, the minimum synthetic wavelength ΛS plays a main role on it. In our method, if we increase the laser power of ECDL1 or the modulation depth of EOMH to generate more sidebands to lock ECDL2 to a higher one (e.g. N=8) and increase the modulating frequency fr (e.g. 20 GHz), a synthetic wavelength ΛS of 1.87 mm is theoretically attainable. In such case, the second term in Eq. (17) can be decreased to 0.47 µm and the final accuracy can be further improved.

6. Conclusion

In summary, we have demonstrated the principle of laser interferometric wavelength leverage (LIWL) for absolute distance measurement with the dynamic-sideband-locked synthetic wavelength generation. The high-frequency EOM-based dynamic-sideband locking method can flexibly generate variable synthetic wavelengths from hundreds meter to millimeter with a relative uncertainty of 1.47×10−10. Theoretical analysis and experiments have verified the feasibility of the proposed LIWL method. The results show that: 1) the residual error is less than 15 µm between the results of the LIWL system and those of Agilent interferometers in a measurement range of 100 m; 2) at the distance of 52 m, the measurement fluctuation and STD are 6 µm and 1.8 µm, respectively, and the distance resolution is better than better than 7.5 µm. These results indicate the proposed method has a great potential application in the fields of precision equipment manufacturing, space mission, length metrology, and so on.

Funding

National Natural Science Foundation of China (51527807, 51875530, 52035015); Natural Science Foundation of Zhejiang Province (2017R51006, LZ18E050003); National Key Research and Development Program of China (2016YFF0200405, 2018YFF0212703); Changjiang Scholar Program of Chinese Ministry of Education (IRT_17R98).

Acknowledgments

The authors thank the division of dimensional metrology of NIM for providing the comparison devices.

Disclosures

The authors declare no conflicts of interest.

References

1. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009). [CrossRef]  

2. Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016). [CrossRef]  

3. K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019). [CrossRef]  

4. R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016). [CrossRef]  

5. J. Dale, B. Hughes, A. J. Lancaster, A. J. Lewis, A. J. H. Reichold, and M. S. Warden, “Multi-channel absolute distance measurement system with sub ppm-accuracy and 20 m range using frequency scanning interferometry and gas absorption cells,” Opt. Express 22(20), 24869–24893 (2014). [CrossRef]  

6. G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012). [CrossRef]  

7. K. Zhu, B. Guo, Y. Lu, S. Zhang, and Y. Tan, “Single-spot two-dimensional displacement measurement based on self-mixing interferometry,” Optica 4(7), 729–735 (2017). [CrossRef]  

8. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16(7), 1857–1860 (1977). [CrossRef]  

9. S. Sharma, P. Eiswirt, and J. Petter, “Electro optic sensor for high precision absolute distance measurement using multiwavelength interferometry,” Opt. Express 26(3), 3443–3451 (2018). [CrossRef]  

10. Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolut distance measurement,” Opt. Express 26(5), 5747–5757 (2018). [CrossRef]  

11. G. Wu, L. Liao, S. Xiong, G. Li, Z. Cai, and Z. Zhu, “Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement,” Sci. Rep. 8(1), 4362 (2018). [CrossRef]  

12. J. E. Decker, J. R. Miles, A. A. Madej, R. F. Siemsen, K. J. Siemsen, S. D. Bonth, K. Bustraan, S. Temple, and J. R. Pekelsky, “Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry-application to absolute long gauge block measurement,” Appl. Opt. 42(28), 5670–5678 (2003). [CrossRef]  

13. C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002). [CrossRef]  

14. S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 3021382 (2002). [CrossRef]  

15. Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005). [CrossRef]  

16. C. C. Chan, W. Jin, H. L. Ho, D. N. Wang, and Y. Wang, “Improvement of measurement accuracy of fiber Bragg grating sensor systems by use of gas absorption lines as multi-wavelength references,” Electron. Lett. 37(12), 742–743 (2001). [CrossRef]  

17. J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010). [CrossRef]  

18. X. Xu, Z. Zhang, H. Zhang, H. Zhao, W. Xia, M. He, J. Li, J. Zhai, and H. Wu, “Long distance measurement by dynamic optical frequency comb,” Opt. Express 28(4), 4398–4411 (2020). [CrossRef]  

19. J. Jin, Y. J. Kim, Y. Kim, and S. W. Kim, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006). [CrossRef]  

20. S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009). [CrossRef]  

21. L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19(4), 045307 (2008). [CrossRef]  

22. N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. 31(21), 3101–3103 (2006). [CrossRef]  

23. Y. Salvadé, N. Schuhler, S. Lévêque, and S. L. Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008). [CrossRef]  

24. S. Zhang, Z. Xu, B. Chen, L. Yan, and J. Xie, “Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry,” Opt. Express 26(7), 9273–9284 (2018). [CrossRef]  

25. J. Xie, L. Yan, B. Chen, and Y. Lou, “Extraction of Carrier Phase Delay for Nonlinear Errors Compensation of PGC Demodulation in an SPM Interferometer,” J. Lightwave Technol. 37(13), 3422–3430 (2019). [CrossRef]  

26. J. Li, “Development of Indoor 80 m Large-scale Laser Comparator National Standard,” Doc thesis, Tianjin Univ. (2017).

27. K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994). [CrossRef]  

References

  • View by:

  1. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
    [Crossref]
  2. Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
    [Crossref]
  3. K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
    [Crossref]
  4. R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
    [Crossref]
  5. J. Dale, B. Hughes, A. J. Lancaster, A. J. Lewis, A. J. H. Reichold, and M. S. Warden, “Multi-channel absolute distance measurement system with sub ppm-accuracy and 20 m range using frequency scanning interferometry and gas absorption cells,” Opt. Express 22(20), 24869–24893 (2014).
    [Crossref]
  6. G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
    [Crossref]
  7. K. Zhu, B. Guo, Y. Lu, S. Zhang, and Y. Tan, “Single-spot two-dimensional displacement measurement based on self-mixing interferometry,” Optica 4(7), 729–735 (2017).
    [Crossref]
  8. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16(7), 1857–1860 (1977).
    [Crossref]
  9. S. Sharma, P. Eiswirt, and J. Petter, “Electro optic sensor for high precision absolute distance measurement using multiwavelength interferometry,” Opt. Express 26(3), 3443–3451 (2018).
    [Crossref]
  10. Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolut distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
    [Crossref]
  11. G. Wu, L. Liao, S. Xiong, G. Li, Z. Cai, and Z. Zhu, “Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement,” Sci. Rep. 8(1), 4362 (2018).
    [Crossref]
  12. J. E. Decker, J. R. Miles, A. A. Madej, R. F. Siemsen, K. J. Siemsen, S. D. Bonth, K. Bustraan, S. Temple, and J. R. Pekelsky, “Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry-application to absolute long gauge block measurement,” Appl. Opt. 42(28), 5670–5678 (2003).
    [Crossref]
  13. C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
    [Crossref]
  14. S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 3021382 (2002).
    [Crossref]
  15. Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
    [Crossref]
  16. C. C. Chan, W. Jin, H. L. Ho, D. N. Wang, and Y. Wang, “Improvement of measurement accuracy of fiber Bragg grating sensor systems by use of gas absorption lines as multi-wavelength references,” Electron. Lett. 37(12), 742–743 (2001).
    [Crossref]
  17. J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
    [Crossref]
  18. X. Xu, Z. Zhang, H. Zhang, H. Zhao, W. Xia, M. He, J. Li, J. Zhai, and H. Wu, “Long distance measurement by dynamic optical frequency comb,” Opt. Express 28(4), 4398–4411 (2020).
    [Crossref]
  19. J. Jin, Y. J. Kim, Y. Kim, and S. W. Kim, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
    [Crossref]
  20. S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
    [Crossref]
  21. L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19(4), 045307 (2008).
    [Crossref]
  22. N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. 31(21), 3101–3103 (2006).
    [Crossref]
  23. Y. Salvadé, N. Schuhler, S. Lévêque, and S. L. Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008).
    [Crossref]
  24. S. Zhang, Z. Xu, B. Chen, L. Yan, and J. Xie, “Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry,” Opt. Express 26(7), 9273–9284 (2018).
    [Crossref]
  25. J. Xie, L. Yan, B. Chen, and Y. Lou, “Extraction of Carrier Phase Delay for Nonlinear Errors Compensation of PGC Demodulation in an SPM Interferometer,” J. Lightwave Technol. 37(13), 3422–3430 (2019).
    [Crossref]
  26. J. Li, “Development of Indoor 80 m Large-scale Laser Comparator National Standard,” Doc thesis, Tianjin Univ. (2017).
  27. K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
    [Crossref]

2020 (1)

2019 (2)

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

J. Xie, L. Yan, B. Chen, and Y. Lou, “Extraction of Carrier Phase Delay for Nonlinear Errors Compensation of PGC Demodulation in an SPM Interferometer,” J. Lightwave Technol. 37(13), 3422–3430 (2019).
[Crossref]

2018 (4)

2017 (1)

2016 (2)

Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
[Crossref]

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

2014 (1)

2012 (1)

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

2010 (1)

J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

2009 (2)

S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

2008 (2)

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19(4), 045307 (2008).
[Crossref]

Y. Salvadé, N. Schuhler, S. Lévêque, and S. L. Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008).
[Crossref]

2006 (2)

2005 (1)

Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
[Crossref]

2003 (1)

2002 (2)

C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
[Crossref]

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 3021382 (2002).
[Crossref]

2001 (1)

C. C. Chan, W. Jin, H. L. Ho, D. N. Wang, and Y. Wang, “Improvement of measurement accuracy of fiber Bragg grating sensor systems by use of gas absorption lines as multi-wavelength references,” Electron. Lett. 37(12), 742–743 (2001).
[Crossref]

1994 (1)

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

1977 (1)

Abich, K.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Abou-Zeid, A.

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19(4), 045307 (2008).
[Crossref]

Abramovici, A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Amparan, B.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Baatzsch, A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Barr, D. C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Barranco, G. F.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
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K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
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Bize, M. P.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Bogan, C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Bonth, S. D.

Braxmaier, C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Burke, M. J.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Clark, K. C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Dahl, K.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Dale, J.

Dändliker, R.

Danzmann, K.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Davis, M. A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Decker, J. E.

Dickson, J. A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Downs, M. J.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

Dubovitsky, S.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Eckardt, A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Eiswirt, P.

Ester, T.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Estler, W. T.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

Flatscher, R.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Flechtner, F.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Floch, S. L.

Folkner, W. M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Forbes, A.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

Francis, S.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Galetto, M.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

Gilbert, M. S.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Gilles, F.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Goch, G.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

Gohlke, M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Grossard, N.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Guenther, B.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Guo, B.

Hager, P.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Härtig, F.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
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Hartmann, L.

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19(4), 045307 (2008).
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Hasebe, K.

Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
[Crossref]

Hauden, J.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

He, M.

Heine, F.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Heinzel, G.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
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Jang, Y. S.

Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
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Jin, J.

S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
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J. Jin, Y. J. Kim, Y. Kim, and S. W. Kim, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
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Jin, W.

C. C. Chan, W. Jin, H. L. Ho, D. N. Wang, and Y. Wang, “Improvement of measurement accuracy of fiber Bragg grating sensor systems by use of gas absorption lines as multi-wavelength references,” Electron. Lett. 37(12), 742–743 (2001).
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Kang, H. J.

Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Kaufer, M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
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Kim, Y.

S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
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J. Jin, Y. J. Kim, Y. Kim, and S. W. Kim, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
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Kim, Y. J.

J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
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S. Hyun, Y. J. Kim, Y. Kim, J. Jin, and S. W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
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J. Jin, Y. J. Kim, Y. Kim, and S. W. Kim, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
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Kim, Y. K.

Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. K. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Lee, J.

J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
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Lee, K.

J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
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Lee, S.

J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Nicklaus, K.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
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Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Peterek, M.

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Pierce, R.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Reavis, G.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Reiche, J.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Reichold, A. J. H.

Salvadé, Y.

Sanjuan, J.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Sato, T.

Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
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Schmitt, R. H.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
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Schuhler, N.

Schütze, D.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Seiter, C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Shaddock, D.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Shafir, E.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
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Sharma, S.

Sheard, B.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Siemsen, K. J.

Siemsen, R. F.

Sileo, M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Spero, R.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Spiers, G.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Stede, G.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Stephens, M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Sutton, A.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Y. Kurosaki, S. Maehara, K. Hasebe, Y. Ohta, T. Sato, M. Ohkawa, T. Maruyama, and T. Tsubokawa, “Frequency stabilization of a semiconductor laser using the spectrum of a Fabry-Perot etalon controlled by the Rb absorption line,” Proc. SPIE. 5710, 73–82 (2005).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Wang, R. T.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
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Wang, Y.

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Warden, M. S.

Ware, B.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Wegener, H.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Windisch, S.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Woodruff, C.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Wu, G.

Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolut distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

G. Wu, L. Liao, S. Xiong, G. Li, Z. Cai, and Z. Zhu, “Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement,” Sci. Rep. 8(1), 4362 (2018).
[Crossref]

Wu, H.

Xia, W.

Xie, J.

Xiong, S.

G. Wu, L. Liao, S. Xiong, G. Li, Z. Cai, and Z. Zhu, “Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement,” Sci. Rep. 8(1), 4362 (2018).
[Crossref]

Xu, G.

Xu, J.

C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
[Crossref]

Xu, X.

Xu, Y.

C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
[Crossref]

Xu, Z.

Yan, L.

Yin, C.

C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
[Crossref]

Zender, B.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

Zhai, J.

Zhang, H.

Zhang, S.

Zhang, Z.

Zhao, H.

Zhou, Q.

Zhu, K.

Zhu, Z.

Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolut distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

G. Wu, L. Liao, S. Xiong, G. Li, Z. Cai, and Z. Zhu, “Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement,” Sci. Rep. 8(1), 4362 (2018).
[Crossref]

Zimmermann, M.

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

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[Crossref]

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R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in large-scale metrology-review and future trends,” CIRP Ann. 65(2), 643–665 (2016).
[Crossref]

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C. C. Chan, W. Jin, H. L. Ho, D. N. Wang, and Y. Wang, “Improvement of measurement accuracy of fiber Bragg grating sensor systems by use of gas absorption lines as multi-wavelength references,” Electron. Lett. 37(12), 742–743 (2001).
[Crossref]

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S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 3021382 (2002).
[Crossref]

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[Crossref]

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C. Yin, Z. Chao, D. Lin, Y. Xu, and J. Xu, “Absolute length measurement using changeable synthetic wavelength chain,” Opt. Eng. 41(4), 746–750 (2002).
[Crossref]

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Phys. Rev. Lett. (1)

K. Abich, A. Abramovici, B. Amparan, A. Baatzsch, B. B. Okihiro, D. C. Barr, M. P. Bize, C. Bogan, C. Braxmaier, M. J. Burke, K. C. Clark, C. Dahl, K. Dahl, K. Danzmann, M. A. Davis, G. D. Vine, J. A. Dickson, S. Dubovitsky, A. Eckardt, T. Ester, G. F. Barranco, R. Flatscher, F. Flechtner, W. M. Folkner, S. Francis, M. S. Gilbert, F. Gilles, M. Gohlke, N. Grossard, B. Guenther, P. Hager, J. Hauden, F. Heine, G. Heinzel, M. Herding, M. Hinz, J. Howell, M. Katsumura, M. Kaufer, W. Klipstein, A. Koch, M. Kruger, K. Larsen, A. Lebeda, A. Lebeda, T. Leikert, C. C. Liebe, J. Liu, L. Lobmeyer, C. Mahrdt, T. Mangoldt, K. Nicklaus, R. Pierce, J. A. Ravich, G. Reavis, J. Reiche, J. Sanjuan, D. Schütze, C. Seiter, D. Shaddock, B. Sheard, M. Sileo, R. Spero, G. Spiers, G. Stede, M. Stephens, A. Sutton, J. Trinh, K. Voss, D. Wang, R. T. Wang, B. Ware, H. Wegener, S. Windisch, C. Woodruff, B. Zender, and M. Zimmermann, “In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer,” Phys. Rev. Lett. 123(3), 031101 (2019).
[Crossref]

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[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. Principle and schematic of the laser interferometric wavelength leverage. (a) Optical layout. (b) Phase difference with the tuning of λ2. (c) Conception of wavelength leverage.
Fig. 2.
Fig. 2. Principle of synthetic wavelength generation with dynamic-sideband locking. (a) Optical configuration of laser sources. (b) Schematic of the changes of f2 and fb with fr.
Fig. 3.
Fig. 3. Realization of the equivalent displacement with an EOM. (a) Optical layout. (b) Schematic of transverse electro-optic effect of crystal.
Fig. 4.
Fig. 4. Experimental setup of LIWL for absolute distance measurement. (a) Optical configuration of LIWL. (b) Constructed experimental setup.
Fig. 5.
Fig. 5. Resolution and stability evaluation results of the equivalent displacement Δl
Fig. 6.
Fig. 6. Stability experimental results of the frequency difference fb. (a) Fluctuation of fb. (b) Relative Allan standard deviation of fb.
Fig. 7.
Fig. 7. Repeat measurement results of a distance ∼52 m. (a)–(d) four coarse results. (e) the final results.
Fig. 8.
Fig. 8. Experimental results of distance resolution evaluation at a distance ∼52 m.
Fig. 9.
Fig. 9. Comparison experimental results. (a) Distance measurement from 3–73 m. (b) Distance measurement from 60–100 m.

Tables (1)

Tables Icon

Table 1. Selected parameters and generated synthetic wavelengths

Equations (17)

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Δ φ  =  φ 1  -  φ 2  =  4 π λ 1 ( L + L 1 ) 4 π λ 2 L
Δ φ  =  4 π λ 1 ( L + L 1 ) 4 π λ 2  +  Δ λ 2 L
Δ φ  =  4 π λ 1 ( L + L 1  +  Δ l ) 4 π λ 2  +  Δ λ 2 L
L 1 Λ SS = Δ l 1 λ 1
L = Λ SS λ 1 Δ l
f sideband = f 1 + k f r
f 2  =  f 1 + N f r + f o  =  f 1 + f b
f 2 [ i ] = f 1 + f b [ i ] = f 1 + N f r[ i ] + f o
f b [ i ] = N f r [ i ] + f o
Λ SS [ i ] = | λ 2[ i ] λ 2[ i 1 ] λ 2[ i ] λ 2[ i 1 ] |  =  c N Δ f r[ i ]
Λ S[ i ] = | λ 1 λ 2[ i ] λ 1 λ 2[ i ] |  =  c f b[ i ]  =  c N f r[ i ]  +  f o
Δ φ e  =  2 π W V d ( n e 3 γ 33 λ 1 n o 3 γ 13 λ 2 )
Δ φ e  =  4 π λ 1 l P 4 π λ 2 l S  =  4 π Λ S l S  +  4 π λ 1 ( l P l S )
L c[ i  +  1 ]  =  Λ SS[ i  +  1 ] 2 INT [ 2 L c[ i ]  - 2 L ε [ i  +  1 ] Λ SS[ i  +  1 ] ] + L ε [ i  +  1 ]
L f[ j ]  =  Λ S[ j ] 2 ( INT [ 2 L c[3] Λ S[ j ]  -  Φ S [ j ] ] + Φ S [ j ] )
u ( L ) = ( L u ( n air ) n air ) 2 + 2 ( L u ( Λ S ) Λ S ) 2 + ( Λ S 2 u ( Φ S ) ) 2
U ( L ) = 2 u ( L ) = 2 ( 2.3 × 10 8 L ) 2 + ( 1.7 μ m ) 2

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