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Abstract
The optical scale bar with calibrated or measured internal point-to-point length has many applications in coordinate measurements. In this paper, the virtual optical scale bar with two retroreflectors is constructed by the absolute distance measurement based on pulse-to-pulse interferometry. The temporal and dispersive coherence could be utilized to determine the adjustable internal length of multiple pulse-to-pulse intervals with high precision. The proposed scheme was combined with a pellicle beamsplitter to minimize systematic error. The influence of its thickness on precision is also discussed and calibrated in detail. Besides, a femtosecond mode-locked pulse laser with 100-MHz repetition rates was employed in our system to develop an optical scale bar and verify the feasibility of the proposed method. The sub-micron precision could be realized by temporal coherence with a piezo-driven stage or a simplified non-polarized scheme of dispersed coherence. It shows that this method could achieve a flexible and high-precision virtual optical scale bar for further practical applications.
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1. Introduction
Large-scale manufacturing and coordinate measurement have broadband applications in the industrial field, such as precision engineering with aerospace assembly and shipbuilding [1,2]. The optical scale bar is a flat and lightweight linear bar in several sizes with a determined distance between two points, which is commonly utilized in photogrammetry [3,4], multi-station theodolites [5], and indoor global positioning stations (iGPS) [6]. The optical scale bar in photogrammetry with reflective targets or coded targets performs as a traceable calibrated reference in single photogrammetry for calibration or stereo photogrammetry for corresponding connection of two photographs, and the precision of point-to-point distance of the scale bar would finally influence the coordinate measurement [7]. Besides, the optical scale bar with cooperative targets in multi-station theodolites and iGPS could also provide the orientation parameters with one distance measurement and multiple angular measurements, which is an optimization method for the procedure of calibrations [5,8]. Additionally, in the coordinate measurements with laser trackers, a point-based rigid which could also be regarded as multiple scale bars and typically utilized for the relocation and enhancing the precision of coordinate measurement in the large workspace [9]. However, up to now, the optical scale bar has always been made of metal materials or invar steel with unchangeable length, and the precision of point-to-point distance would be lost during the long-term abrasion and has to be recalibrated, which would be inflexible in practice. Although the laser tracker could measure the distance between two points with the module of absolute distance measurement (ADM), the precision is still limited by the angular measurement error from its amplification effect and low efficiency from single-point measurement. A typical application of optical scale bar is shown in Fig. 1.
Fig. 1. Typical applications of optical scale bar for calibration of orientation parameters with cooperative targets, P1 - P6: measured points.
The ADM technique with fast progress provides the possibility for the establishment of a virtual optical scale bar between two points with high precision. Among them, the electronic distance measurement (EDM) with the synthetic wavelength interferometry (SWI) [10], frequency-scanning interferometry (FSI) [11,12], and multi-wavelength interferometry (MWI) [13,14] are representative researches. Since the year of 2000, various principles have been developed by the inherent advantages of the optical frequency comb by combining with the traditional ranging technique [15], e.g. the pulse-to-pulse interferometry (both temporal [16] and dispersive [17,18] interferometry), the SWIs with inter-mode beats [19,20], the MWIs [21], and comb-based FSI [22], etc. Generally, the pulse-to-pulse interferometry with single-comb based on temporal and dispersive coherence can realize a high-accuracy and long-distance measurement only with the reference and measurement pulses overlapped or coherence with each other, and there is a compromise between the effective measurement range (with dead-zones) and accuracy. Besides, the dual-comb system with slightly different repetition rates by employing asynchronous optical sampling (ASOPS) permits the fast distance measurement (up to kHz), high accuracy (up to sub-$\mu$m), and without large dead-zone [23,24], but the system complexity comes from the construction of two optical frequency combs [25]. As another equivalent approaches, the dynamic optical sampling by cavity tuning (OSCAT) with stabilized fiber or large dynamic cavity tuning [26,27] and the method of switching repetition rates [28] also could be potential single-comb solutions, but up to now, the complicated system and its dynamic range are unsatisfactory for practical applications. Consequently, as a relatively traceable and straightforward system, when the repetition frequency is locked to an atomic clock, the pulse-to-pulse interferometry has broadened applications in the calibrations of gauge blocks and baselines [29,30]. Although the dynamic range of the scale bar is limited, the measurement workspace could be extended by the coordinate measurement method in which the optical scale bar would be a desirable reference and promise the overall precision. With the development of high-repetition-rate combs such as electro-optic [31] and microresonator combs [32,33], the dead zone has the potential to be eliminated by increasing the scanning range of pulses.
Commonly, an optical beamsplitter that produces two reflected beams for a single input beam is involved in the interferometer for guiding the laser beam back and forth between two retroreflectors [34,35]. The scheme of the plate beamsplitters (1-3 mm on sizes) or the cube beamsplitters (typically is larger than 5 mm) are normally employed in these interferometers. However, the thickness of the beamsplitter would be adding an extra systematic error in the internal point-to-point length. In [35], the cube beamsplitter is calibrated previously in an interferometer with a tandem low-coherence laser, but the measuring length is only around 100 mm limited by the low coherence, which is not suitable for the demand of practical large-scale measurements. Besides, the “ghost image" or the secondary reflection, especially for the high-power pulsed laser reflected from the front or rear surface, would severely interfere with the measurement process. In this paper, a virtual optical scale bar is proposed by the pulse-to-pulse interferometry with a femtosecond pulse laser with 100-MHz repetition rates. The high-precision temporal or dispersive coherence as two promising optional approaches would determine the internal length between the two retroreflectors. The optical scheme involves a pellicle beamsplitter with micron thickness, and the thin and stretched optical-grade nitrocellulose membrane could operate without “ghost images" and chromatic aberrations on the measurements, although caution in handling protected mounting should be required. A balanced interferometer is designed here to evaluate the systematic errors from the thickness of the pellicle beamsplitter, the experimental results are also compared with an opposing confocal laser probe technique. Additionally, a simple system with a dispersed interferometer is also proposed.
The remaining sections are organized as follows: Section 2 introduces the principle of virtual scale bar by the temporal or dispersive pulse-to-pulse interferometry, and the systematic errors from the thickness of the pellicle beamsplitter are analyzed by numerical simulations; in Section 3, we perform the experiments in both polarized and non-polarized pulse-to-pulse interferometers, and the method for determination of the distance and the repeatability are also presented; in Section 4, the thickness of pellicle beamsplitter is evaluated by a balanced dispersive interferometer which is also comparing with the opposing confocal laser probe technique, afterward, the uncertainty budget is summarized. In the end, the discussion and further work are concluded in Section 5.
2. Experimental principle
Figure 2 illustrates an proof-of-concept experimental scheme for determining and evaluating the length of a virtual optical scale-bar. This system combines with a balanced interferometer and an unbalanced interferometer to measure the absolute length difference between the two hollow retroreflectors positioned on both sides of the beamsplitter. The femtosecond pulses are emitted from the laser sources (C-Fiber, Menlo Systems), collimated by a collimator (F280APC-1550, Thorlabs), and amplified by an EDFA. Its repetition rate of 100 MHz is feedback controlled by repetition rate synchronization electronics (RRE-SYNCRO, Menlo Systems) and locked to a rubidium atomic clock (8040C, Symmetricom). The polarization could be rotated by a half-wave plate (AHWP10M-1600, Thorlabs) to adjust the split ratio after being optimized by a polarizer (LPNIR050-MP2, Thorlabs). The optical beam is split into two parts which one part goes into the reference arm, and the other part transmits into the measurement arm. The reference target attached on a piezo-driven stage (PZT, P-622.1CD, PI) was coarsely adjusted by a translation stage (P-521.DD1, PI). The measurement beam is split vertically by a pellicle beamsplitter (BP145B3, Thorlabs), and the optical beams would be reflected back and forth between two hollow retroreflectors (UBBR1-1S, Newport). A roughly tape measurement previously determines the positions of the two retroreflectors to promise coherence, and the two are both with a direct screw mount to the optical platform. When the optical beams pass the front surface of the pellicle beamsplitter, half of the beam would be reflected towards PBS after a quarter-wave plate (AQWP10M-1600, Thorlabs) and interference with reference beam for detection. Two detected options are provided for evaluating the length measurements: the one is the temporal coherence detected by a photodetector (PDB450C, Thorlabs) and recorded by the oscilloscope (MDO4054C, Tektronix), the other is the dispersive interference recorded by the optical spectrum analyzer (OSA, AQ6370D, Yokogawa) after collected by a multi-mode fiber.
Fig. 2. The optical arrangement for a virtual optical scale bar by pulse-to-pulse interferometry, BS: Beamsplitter, PBS: Polarizing beamsplitter, RRE: Repetition rate synchronization electronics, EDFA: Erbium co-doped fiber amplifiers, OSA: Optical spectrum analyzer.
The geometric length between PBS and pellicle beamsplitter is $L_1$. The right part of the point-to-point length is $L_2$, and the left part is $L_3$. The refractive index of air is noted as $n_1$, and the refractivity of the pellicle beamsplitter is given as $n_2$. Firstly, the optical beam length measured from PBS to Retroflector2 is $2n_1(L_1 + L_2)$, and it is approximately equal to the length of the reference arm with Retroflector1. After that, the reflected beam by Retroreflector2 passes the pellicle beamsplitter where beam traps block the other. The optical beam would be back and forth between the pellicle beamsplitter and Retroreflector3. Meanwhile, half of the beam would be reflected into the detected module. The second detected optical length could be expressed as $2n_1(L_1 + 2L_2 + L_3)$, where $L_{3}=L_{3}^{\prime }+L_{b}\left (n_{2} / n_{1}\right )$ and $L_{b}$ is the geometric distance as the optical beam passing through the beamsplitter. Supposed that the first detection beam is the initial point, the point-to-point optical length of $n_1(L_2 + L_3)$ could be obtained from the difference between the two measurements.
The thickness of the pellicle beamsplitter could be ignored for simplifying analysis. However, it has to be considered in practice when the requirement for the relative accuracy is better than $10^{-6}$. The geometrical error from the pellicle beamsplitter is analyzed in Fig. 3(a). The thickness of the pellicle beamsplitter is assumed as $L_t$, and $L_{b}=L_{t} / \cos \theta _{2}$. The incident angle is $\theta _1$ and the refracted angle is $\theta _2$ ($\theta _1>\theta _2$). The total geometric length between the Retroreflector2 and Retroreflector3 is expressed as $L=L_{3}^{\prime }+L_{2}+L_{b} n_{2} / n_{1}$. The horizontal component of the point-to-point length is $L_h = L + L_b[\cos (\theta _1-\theta _2) - n_2/n_1]$ and the vertical component is $L_v=L_b\sin (\theta _1-\theta _2)$. Finally, the error from the thickness could be calculated from $L_{err} = L' - L = \sqrt {{L_h}^{2} + {L_v}^{2}} - L$. The refractive index of the membrane material is around 1.5, and the group refractive index of air is ignored for calculation. The incident angle is assumed as 45 degrees, and the thickness of the pellicle beamsplitter is supposed as 2 $\mu$m and 4 $\mu$m, respectively. Figures 3(b)-(c) show the simulated relative errors when the point-to-point length ranges up 90 m. The relative errors of the length measurement will reach below the order of $10^{-7}$ as the distance increases, which indicates the influence of the inserted thickness is limited. Besides, the thickness of the pellicle beamsplitter results in almost fixed impacts. The absolute error is 1.232 $\mu$m at 2 $\mu$m and 2.463 $\mu$m at 4 $\mu$m. The absolute error could be regarded as a systematic error with minor changes since it would be converged. If desired, this error could also be compensated into the experimental results by the previous calibration, which would be introduced in Section 4.1.
Fig. 3. (a) The geometric analysis of the pellicle beamsplitter with exaggerated description in optical scale bar, The relative systematic errors: (b) the thickness of 2 $\mu$m, (c) the thickness of 4 $\mu$m.
3. Experimental results
The calculated length in the pulse-to-pulse interferometry could be expressed as
where the $n_g$ is the group refraction index of air and $f_{r}$ is the repetition frequency of laser source. The integer part $N$ could be measured coarsely by a ranging method with lower accuracy which is better than half of the pulse-to-pulse interval, and the fractional part $\Delta$ could be both derived by the temporal and dispersive interference. $c$ is the speed of light. Three independent experiments are proposed here for evaluating the feasibility of the virtual optical scale bar. At first, a temporal coherence method is proposed here for evaluation of the internal length measurement, and the intensity monitoring signal of the PZT is utilized as a reference for the determination of the fractional parts. It could be given as where the $V_{p1}$ and $V_{p2}$ represent the corresponding voltage of the monitor signal at the peak position of the envelope from the temporal coherence patterns. The $V_{max}$ and $V_{min}$ are the maximum and minimum voltage of the smoothed monitor signal, which is recorded from a 16-bits sensor resolution, respectively. The consecutive temporal coherence patterns and the monitoring signal of the piezo-driven stage are recorded at the same time by an oscilloscope with different channels for promising the time synchronization, which is shown in Fig. 4(a) and Fig. 5. $L_{s}$ is the scanning range of the PZT, which could be feedback controlled by a closed-loop. The envelope of the temporal coherence patterns is extracted by the modified Gaussian curve fitting, which has already been introduced in [36]. The fine scanning range of PZT in our experiments is 250 $\mu$m. The output power here is measured by a benchtop power meter and is 6.2 mW after a polarizer. The sampling point is 1 Mpts, and the sampling rate is 250 kS/s. The typical extraction of the envelope of the coherence patterns is also presented in Fig. 4(b). The experimental results of measured distance and the environmental parameters of temperature and humidity are given in Fig. 4(c) and (d), respectively, and the measured pressure is 100.92 kPa. The group refractive index of air is calculated by the modified Edlén equation [37]. The average value of the distance measurement is 1498456.70 $\mu$m, and the standard deviation (STD) is 475.92 nm with the corresponding relative precision of $3.18 \times 10^{-7}$. The thickness of the pellicle beamsplitter is ignored in the experiments of this section.However, the internal distance with high precision around or better than $10^{-6}$ is challenging to compare with a commercial instrument such as laser trackers and photogrammetry, for example. One has to be attempted here to simultaneously measure and compare the distance by temporal and dispersive coherence. The EDFA is applied here with the output power around 13.4 mW after a polarizer, and the I/O trigger output of the controller of translation stage (C-863 Mercury Controller, PI) would perform as a reference signal for calculating the fractional distance in temporal coherence. The scanning temporal coherence patterns are recorded as given in Fig. 6(a), and the typically extracted envelope is also shown in Fig. 6(b). In dispersive interferometry, the spectrum interference signal is collected by the OSA as Fig. 6(c) and contains the phase difference between the measurement path and the reference path. The dispersed interference intensity could be obtained by the fast Fourier transformation (FFT), and the single side-band spectrum of the AC peaks is shown in Fig. 6(d). Then every single AC peak is band-passed filtered, and inverse Fourier transformed (iFFT). After that, the wrapped phase and the unwrapped phase are extracted. The fractional distance can be calculated from the derivative of the unwrapped phase as
where $\nu$ represents the optical frequency, and $d\varphi /d\nu$ is the derivative of the unwrapped phase to the optical frequency. Our proposed dispersed coherence method has already been successfully demonstrated in the absolute angular measurement in [38]. The dispersive interferogram is acquired with 32768 sampling points, and wavelength ranges from 1520 nm to 1640 nm.Fig. 4. (a) The coherence patterns and the monitoring signal from the piezo-driven stage, (b) The typical extraction of envelope of coherence patterns, (c) The experimental results with 60 measurements, (d) The environmental parameters recorded by a data logger (TSP01, Thorlabs).
Fig. 5. Photographic illustration of the optical scale bar by the pulse-to-pulse interferometry with temporal coherence detection based on the proposed scheme in Fig. 2.
Fig. 6. (a) The temporal coherence patterns with the reference signal, (b) The typical extraction of the envelope of coherence patterns, (c) The dispersed coherence patterns, (d) The single side-band AC spectrum of the FFT in the dispersed interferometry.
Figures 7(a) and (b) show the results of comparison experiments by the temporal and dispersive methods, and the averaging results and standard deviation are also summarized in Table 1. In the temporal methods, the main error of the fractional distance measurement comes from the precision of the positioning of the scanning translation stage. Fortunately, the scanning range could be calibrated and calculated by the dispersive interferometer in the comparing experimental scheme. The Retroreflector2 and Refroreflector3 keep still, and the beginning point (Position1) and the endpoint (Position2) of the scanning are measured successively. As depicted in Fig. 7(c), The scanning range is measured 30 times, and the interval between the two measurements is 1.998962 mm when the nominal scanning range is 2 mm. The calibrated results are also shown in Fig. 7(a). Besides, three retroreflectors would coherence with each other, generating three corresponding independent peaks in the FFT spectrum. The measured distance could be calculated by the phase information of Peak2 or the difference of Peak1 and Peak3. As given in Fig. 6(d), the signal-to-noise ratio of Peak1 is higher than the others, which might lead to a better precision of the distance difference between Peak1 and Peak3 (0.78 $\mu$m) in Table 1. The comparing results conclusively are within in $10^{-6}$ between the temporal coherence and dispersive coherence methods.
Fig. 7. (a) The experimental results from the temporal coherence methods, (b) The experimental results of the dispersive interferometer by iFFT of different peaks, (c) The calculation of the scanning range in the temporal coherence by the dispersive interferometer.
Table 1. Comparison of the internal length measurement by the temporal and dispersive coherence methods
The dispersive interferometry could be realized by a more straightforward optical arrangement, using no time-delay line of mechanical scanning. The proposed approach here employs a differential dispersive interferometer for measuring the internal length of two targets by the non-polarized scheme. In Fig. 8(a), the first detection beam is collected by the OSA, and then the second detection beam transmits forth and back during the two 1.5" retroreflectors (LTBP-A-Z-RS-HA, MetrologyWorks) commonly utilized for the laser trackers. The target mount could be compatible with the other spherical targets such as the theodolite sphere and the photogrammetry sphere. Eventually, the length difference between the first and second detection is the measured length by dispersive coherence. The internal length is coarsely calibrated by a laser tracker (AT901, Leica) as 1.49820734 m in a precise mode. The tracker head and the targets are approximately settled in a line to avoid the errors from the angular encoder of the laser tracker. Additionally, a fiber beam isolator (IO-H-1550APC, Thorlabs) is connected before collimating to prevent the optical beam feedback to the laser cavity for protection. The recorded data by the OSA is 40 times from 1450 nm to 1650 nm. The typically dispersed interferogram is shown in Fig. 8(b), and its FFT spectrum is also presented in Fig. 8(c). One of the retroreflectors is slightly moved to determine the sign of the fractional measured distance, which could also be replaced by the slight adjustment of the repetition rates. Besides, multiple peaks in the FFT spectrum present numerous times of the measured distance since the optical beams reflect back and forth repeatably. In Table 2, the difference between the distance of Peak1 and results of the laser tracker is 8.45 $\mu$m, and the error might come from the ranging ability of the laser tracker, the thickness of the beamsplitter, the centering of retroreflectors, the ball roundness, and the reflector mount, etc. The simplified optical scheme is more compact and easy to implement multiple branches reconfigured strategy as [34] which would have the potential to be applied in future industrial applications.
Fig. 8. (a) The simplified dispersive interferometer for the internal length measurement, (b) The spectral interferograms recorded by the OSA, (c) The single side-band AC spectrum of the FFT for the detected dispersed interferogram, (d) The distance measurement from iFFT of different peaks.
Table 2. Calculated results of the simplified scheme by the dispersive interferometry
4. Calibrations and discussions
4.1 Thickness calibration
In Section 2, the error from the thickness of the pellicle beamsplitter would convergence as the measured internal length increases. Moreover, it could be ignored when the measured distance is larger than around 20 m, but it is noteworthy at around 1.5 m. As depicted in Figures 9(a) and (b), a balanced interferometer is also presented for determining the thickness of the pellicle beamsplitter based on the proposed design of Fig. 2, and the calibrated methods by dispersive interferometer is similar as the [17]. The thickness could be calculated by the difference of fractional distance before and after inserting into a pellicle beamsplitter. After insertion, the pellicle beamsplitter would be adjusted to ensure the return light is highest while the angle to the front surface is perpendicular. The thickness of the beamsplitter could be given as
where $\Delta _2$ is the fractional distance after insertion and the $\Delta _1$ is before insertion. $n_2$ is the refractive index of the inserted materials, and $n_1$ is the group refractive index of air. The repeatability for 20 consecutive calibrations of dispersive coherence is summarized in Table 3. The refractive index of the pellicle beamsplitter (BP145B3, Thorlabs) is coarsely supposed as 1.5. In addition, the other two optical window plates (N-BK7, WG11010, and UVFS, WG41050, Thorlabs) are measured by this system for verifying the feasibility in Table 3, and the group refractive index of N-BK7 is around 1.5231 and is 1.4673 for the UVFS (in Table 2 in [17]). The experimental results lie in the nominal parameters which the manufacturer provides. To further evaluate the accuracy, the thickness of the pellicle beamsplitter is also measured by the opposing confocal laser probe technique, which is presented in Figs. 9(c) and (d). Two commercial chromatic confocal sensor heads (OP2-Fc and CDS-500, THINKFOCUS) are utilized in this system, including a broadband light source and a spectrometer. This sensing technique is also detailed introduced in [39], and the thickness of the pellicle beamsplitter is measured in five different positions over 50 times (see the inset of Fig. 9(d)). The averaging value is 3.22 $\mu$m, and the difference with the results by the dispersive interferometer is within the level of sub-microns. The error from the thickness of the pellicle beamsplitter of 3.64 $\mu$m is 2.24 $\mu$m (1.98 $\mu$m for the thickness of 3.22 $\mu$m). After calibration, the measured internal distance above is 1498213.55 $\mu$m, and the difference between the laser tracker is decreased to 6.21 $\mu$m.Fig. 9. (a) The experimental scheme for the calibration of the thickness of pellicle beamsplitter, (b) The photograph of the experimental platform with optical beamlines based on the reconfigured proposed scheme in Figs. 2, (c) and (d) The comparison calibration by the opposing confocal laser probe technique.
Table 3. Comparison of the calibrations of the pellicle beamsplitter and optical windows by balanced dispersive interferometry.
Table 4. Uncertainty budget for the optical scale bar with pulse-to-pulse interferometry, where N represents the normal distribution and R is the rectangular distribution.
4.2 Uncertainty budget
From Eq. (1), the measurement uncertainty can be calculated as
In Eq. (5), the first term is related to the measurement and calculation of the group refractive index which is resolved from the modified Edlén equation [37] which the contribution is $1\times 10^{-8}L$ from the equations. The temperature and humidity are measured by the data logger (TSP01, Thorlabs), and the pressure is measured by the compensator and sensors (XC-80, Renishaw). The measurement uncertainty of temperature, air pressure and humidity are 0.5 K, 100 Pa, and 2%, respectively, corresponding contribution of $2.67\times 10^{-7}L$, $1.51\times 10^{-7}L$, and $1.50\times 10^{-8}L$. The uncertainty of the CO$_2$ measurement is assumed as 60 ppm, and the corresponding contribution is $4.88\times 10^{-9}L$. The second term comes from the stability of the repetition rate of the femtosecond pulse laser. In our experiments, the repetition rates of 100 MHz is traced and locked to the Rb clock (8040C, Symmetricom), and monitored by a frequency counter (53230A, Agilent) by a one-hour measurement. The standard deviation of the monitoring is 0.15 mHz, and the corresponding contribution is $7.5\times 10^{-13}L$ which could be ignored in the measurements. Taking the simplified dispersed interferometer, for example, the standard deviation from the pulse-to-pulse alignment is around 0.74 $\mu$m, and the contribution to the uncertainty of the fractional distance measurement. Consequently, by combining the individual uncertainty above, the combined expanded uncertainty from the pulse-to-pulse interferometry is $[\rm (0.74\mu m)^{2}$ + $(6.15\times 10^{-7}L)^{2}]^{1/2}$($k=2$). However, in practice, the measurement of the optical scale bar has to consider the geometric error from the retroreflectors and their mounts. For instance, the geometric error from the centering of optics is 3 $\mu$m and the roundness of the ball is around 1.5 $\mu$m (e.g. Leica RRR No. 575784), and the precision of the positioning by the mount is assumed as 1.5 $\mu$m which is controlled by the ability of machining. The error from the calibration of the thickness of the pellicle beamsplitter is assumed as 1 $\mu$m. In this case, the combined expanded uncertainty of the measurement therefore is $[\rm (7.65\mu m)^{2}$ + $(6.15\times 10^{-7}L)^{2}]^{1/2}$($k=2$). The uncertainty budget is presented in Table 4.
5. Conclusion and future improvements
In this paper, the method for a virtual optical scale bar was proposed and demonstrated by the pulse-to-pulse interferometry, and the internal point-to-point distance could be measured by temporal and dispersive coherence method combining with a pellicle beamsplitter. The thickness of the pellicle beamsplitter is analyzed by the numerical simulation, and it is also calibrated with consistent results by the balanced dispersive interferometer and opposite confocal laser probe technique. In our experiments, a combining system is designed for comparing the precision of the internal distance measurement by the temporal and dispersed detection. Besides, a simplified dispersed interferometer is demonstrated without a mechanical delay line. The experimental result is also compared with a laser tracker, and the residual deviation mainly comes from the geometric error of the retroreflectors and their mounts by the uncertainty analyzed. In future work, the proposed method would be carried out with a high-repetition-rate optical frequency comb for eliminating the dead zones. In addition, a multi-branch internal distances measurement would be designed for a re-configurable framework with multiple optical scale bars only by one laser source as the assumption of [34], and it would have a wider application in the coordinate measurement such as photogrammetry and multi-theodolite for example.
Funding
National Key Research and Development Program of China (2019YFB2006103); National Institute of Metrology, China (AKY1902, AKYZZ2103).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. W. T. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large-scale metrology–an update,” CIRP Ann. 51(2), 587–609 (2002). [CrossRef]
2. W. Gao, S.-W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. Lu, W. Knapp, A. Weckenmann, W. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015). [CrossRef]
3. T. Luhmann, “Close range photogrammetry for industrial applications,” ISPRS J. Photogramm. Remote. Sens. 65(6), 558–569 (2010). [CrossRef]
4. J. Baqersad, P. Poozesh, C. Niezrecki, and P. Avitabile, “Photogrammetry and optical methods in structural dynamics–a review,” Mech. Syst. Signal. Process. 86, 17–34 (2017). [CrossRef]
5. F. Miao, B. Wu, C. Peng, G. Ma, and T. Xue, “Dynamic calibration method of the laser beam for a non-orthogonal shaft laser theodolite measurement system,” Appl. Opt. 58(33), 9020–9026 (2019). [CrossRef]
6. Z. Wang, L. Mastrogiacomo, F. Franceschini, and P. Maropoulos, “Experimental comparison of dynamic tracking performance of igps and laser tracker,” Int J Adv Manuf Technol 56(1-4), 205–213 (2011). [CrossRef]
7. N. Kochi, Photogrammetry, Handbook of Optical Metrology: Principles and Applications (Chemical Rubber Company, 2008).
8. Z. Zhao, J. Zhu, B. Xue, and L. Yang, “Optimization for calibration of large-scale optical measurement positioning system by using spherical constraint,” J. Opt. Soc. Am. A 31(7), 1427–1435 (2014). [CrossRef]
9. A. Wan, J. Xu, D. Miao, and K. Chen, “An accurate point-based rigid registration method for laser tracker relocation,” IEEE Trans. Instrum. Meas. 66(2), 254–262 (2016). [CrossRef]
10. M. Astrua, M. Pisani, and M. Zucco, “Traceable 28 m-long metrological bench for accurate and fast calibration of distance measurement devices,” Meas. Sci. Technol. 26(8), 084008 (2015). [CrossRef]
11. H. Pan, X. Qu, and F. Zhang, “Micron-precision measurement using a combined frequency-modulated continuous wave ladar autofocusing system at 60 meters standoff distance,” Opt. Express 26(12), 15186–15198 (2018). [CrossRef]
12. Y. Shang, J. Lin, L. Yang, Y. Liu, T. Wu, Q. Zhou, and J. Zhu, “Precision improvement in frequency scanning interferometry based on suppression of the magnification effect,” Opt. Express 28(4), 5822–5834 (2020). [CrossRef]
13. K. Meiners-Hagen, T. Meyer, G. Prellinger, W. Pöschel, D. Dontsov, and F. Pollinger, “Overcoming the refractivity limit in manufacturing environment,” Opt. Express 24(21), 24092–24104 (2016). [CrossRef]
14. K. Meiners-Hagen, T. Meyer, J. Mildner, and F. Pollinger, “SI-traceable absolute distance measurement over more than 800 meters with sub-nanometer interferometry by two-color inline refractivity compensation,” Appl. Phys. Lett. 111(19), 191104 (2017). [CrossRef]
15. N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photon. 5(4), 186–188 (2011). [CrossRef]
16. J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004). [CrossRef]
17. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006). [CrossRef]
18. M. Cui, M. Zeitouny, N. Bhattacharya, S. Van Den Berg, and H. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011). [CrossRef]
19. K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000). [CrossRef]
20. N. R. Doloca, K. Meiners-Hagen, M. Wedde, F. Pollinger, and A. Abou-Zeid, “Absolute distance measurement system using a femtosecond laser as a modulator,” Meas. Sci. Technol. 21(11), 115302 (2010). [CrossRef]
21. G. Wang, Y.-S. Jang, S. Hyun, B. J. Chun, H. J. Kang, S. Yan, S.-W. Kim, and Y.-J. Kim, “Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser,” Opt. Express 23(7), 9121–9129 (2015). [CrossRef]
22. N. Kuse and M. Fermann, “Frequency-modulated comb lidar,” APL Photon. 4(10), 106105 (2019). [CrossRef]
23. I. R. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3(6), 351–356 (2009). [CrossRef]
24. H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014). [CrossRef]
25. R. Zhang, Z. Zhu, and G. Wu, “Static pure strain sensing using dual–comb spectroscopy with fbg sensors,” Opt. Express 27(23), 34269–34283 (2019). [CrossRef]
26. H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett. 41(10), 2366–2369 (2016). [CrossRef]
27. M. I. Kayes and M. Rochette, “Precise distance measurement by a single electro-optic frequency comb,” IEEE Photonics Technol. Lett. 31(10), 775–778 (2019). [CrossRef]
28. D. R. Carlson, D. D. Hickstein, D. C. Cole, S. A. Diddams, and S. B. Papp, “Dual-comb interferometry via repetition rate switching of a single frequency comb,” Opt. Lett. 43(15), 3614–3617 (2018). [CrossRef]
29. D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express 19(6), 4881–4889 (2011). [CrossRef]
30. D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a helium–neon interferometer,” Precis. Eng. 37(3), 694–698 (2013). [CrossRef]
31. R. Yang, F. Pollinger, K. Meiners-Hagen, J. Tan, and H. Bosse, “Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair,” Opt. Lett. 39(20), 5834–5837 (2014). [CrossRef]
32. P. Trocha, M. Karpov, D. Ganin, M. H. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018). [CrossRef]
33. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative kerr solitons in optical microresonators,” Science 361, 6402 (2018). [CrossRef]
34. J. Muelaner, W. Wadsworth, M. Azini, G. Mullineux, B. Hughes, and A. Reichold, “Absolute multilateration between spheres,” Meas. Sci. Technol. 28(4), 045005 (2017). [CrossRef]
35. A. Winarno, S. Masuda, S. Takahashi, H. Matsumoto, and K. Takamasu, “Noncontact method of point-to-point absolute distance measurement using tandem low-coherence interferometry,” Meas. Sci. Technol. 29(2), 025006 (2018). [CrossRef]
36. Y. Liu, L. Yang, Y. Guo, J. Lin, P. Cui, and J. Zhu, “Optimization methods of pulse-to-pulse alignment using femtosecond pulse laser based on temporal coherence function for practical distance measurement,” Opt. Lasers. Eng. 101, 35–43 (2018). [CrossRef]
37. G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified edlén’s formulae,” Metrologia 35(2), 133–139 (1998). [CrossRef]
38. X. Liang, J. Lin, L. Yang, T. Wu, Y. Liu, and J. Zhu, “Simultaneous measurement of absolute distance and angle based on dispersive interferometry,” IEEE Photonics Technol. Lett. 32(8), 449–452 (2020). [CrossRef]
39. J. Li, Y. Zhao, H. Du, X. Zhu, K. Wang, and M. Zhao, “Adapative modal decomposition based overlapping-peaks extraction for the thickness measurement in chromatic confocal microscopy,” Opt. Express 28(24), 36176–36187 (2020). [CrossRef]
