1. Introduction

The impact of atmospheric aerosols on climate and air quality is receiving increasing attention, which results in requirements for improved measurements of aerosol spatial distribution and optical properties. Lidar technique has played a very important role in the atmospheric aerosol remote sensing realm in recent years [1–13 ]. By virtue of a spectroscopic filter, high-spectral-resolution lidar (HSRL) can separate the narrowband Mie scattering spectrum induced by aerosols from the broadened Rayleigh scattering spectrum induced by the atmospheric molecules (Cabannes scattering) [2–11 ]. This kind of spectral discrimination is the crucial point for HSRLs to realize straightforward quantitative retrieval of aerosol optical properties such as backscatter coefficient, extinction coefficient, lidar ratio, etc., without reliance on some a prior assumptions compared with standard backscatter lidars. The available spectroscopic filters in current HSRL instruments can be divided into two categories, that is, the atomic/molecular absorption filter and the interferometric filter. The typical representative of the first category is the well-known iodine absorption filter, which has great advantages in aspects of filtering stability, large acceptance angle, and high suppression against aerosol backscattering [3, 5, 7, 8 ]. Yet, it can only work at 532 nm wavelengths, and there is no flexibility in lidar wavelength selection. The Fabry-Perot interferometer (FPI), as one of the most popular members among the second category of spectroscopic filters, is simple and can be engineered to any wavelength readily, but is limited by the small acceptance angle [2, 9, 14 ]. Typically, it requires a very large aperture to accept low divergence incident light in order to obtain the narrow spectral discrimination needed for the HSRL technique. Recently, a Mach-Zehnder interferometer (MZI) is also developed to detect the aerosol optical properties in HSRL through fringe analysis technique [15, 16 ], which is different from the above-mentioned spectroscopic filters in principle.

A new type of interferometric filter, field-widened Michelson interferometer (FWMI), is considered very potential to be an alternative to these spectroscopic filters above. Historically, the FWMI was firstly employed as an analog birefringent filter in the Michelson Doppler Imager on the Solar and Heliospheric Observatory (SOHO) mission in 1980 [17]. Then great attentions are paid to the FWMI with the success of the wind imaging interferometer WINDII, where, the FWMI plays the role of Fourier transform spectroscopy to analyze the scattering spectrum [18]. Subsequently, more works were done to further optimize the field widening characteristic of such an interferometer in order to improve the detection performance of wind and temperature on the upper atmosphere [19–22 ].

Inspired by these previous applications, the concept of FWMI can be readily extended to the HSRL realm as a new generation of spectral discrimination filters [10, 23, 24 ]. Like the FPI, the FWMI can be engineered to filter at an arbitrary wavelength, but it offers better angular acceptance characteristics due to the refractivity and dimension matched optical interference arms, allowing the input beam (and device aperture) to be much smaller. Moreover, another remarkable superiority of the FWMI is the better spectral discrimination ability than the FPI. This is because the spectral rejection band of the FWMI is much flatter than the sharp Airy function of the FPI spectral transmission. Also, the relatively loose alignment requirement, small size (thus light weight), less sensitivity to glass surface flatness, etc. are other reasons for us to develop this new kind of spectroscopic filter for HSRL applications.

However, because of essentially distinctive principles between HSRL applications and these previous applications (such as WINDII and SOHO), many new studies should be made to investigate the design and specification requirements of the FWMI as the spectroscopic filter of HSRL. Relevant investigations in these aspects are insufficient so far. Moreover, the development of the FWMI spectroscopic filter is much more complicate than the iodine absorption filter and the FPI filter in aspects such as optical configuration, fabrication, assembling, controlling, operation demand, etc. The concomitant capital and time costs for FWMI development are thus considerable. All the status quo limits the progress in the practicability and popularization of the FWMI in the HSRL technique.

We have made plenty of theoretical researches about FWMI applications in HSRL technique [10, 11, 23, 25 ]. Guided by these works, a prototype FWMI intended for our 532 nm ground-based polarized HSRL system is established. In this paper, we will describe the practical development about our FWMI, with the technical focus on its design, experimental optimization and comprehensive potential evaluation approaches. These works lay the solid foundation for the development of future FWMI-based HSRL instrument. It is expected that this paper can be a good beginning for the HSRL community to propel the development of the FWMI spectroscopic filter, in both theoretical and experimental levels.

2. Practical design of the FWMI

The structure of the developed prototype FWMI intended for our ground-based HSRL is shown in Fig. 1 . It consists of a solid glass arm and an air gap arm, both arms connected to two adjacent surfaces of a beam splitter. The end of solid arm is finely polished and well coated to achieve a ∼100% high reflection mirror 2 (M2). The air gap arm is composed of another high reflection mirror (M1) attached to a three axes piezoelectric transducer (PZT). Here, the PZT is used to change the length of the air gap within a small range, and adjust the parallelism between the air-arm and solid-arm end mirrors, which provides great convenience for tuning the FWMI to the laser wavelength and obtaining good wavefront compensation over the whole effective aperture of the FWMI.

 

Fig. 1 Practical structure of our developed prototype FWMI for ground-based HSRLs.

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To realize field widening of the interferometer, the refractivity and lengths of its two arms should be matched. In HSRL applications, it is better to tilt the FWMI at a small angle with respect to the incident beam to keep the back-propagating light from contaminating the signal that should be received by other channels. The basic requirement for field widening angle is determined by the divergent angle of the input beam, and the tilted placement condition would increase this requirement apparently. To avoid consuming a part of the widened angle on the tilt configuration, the design process of our FWMI takes the tilted angle into consideration as well. First, we should choose proper glass material to compose the solid arm. The determination of glass type can be arbitrary in theory, but it may be limited by the realistic glass processing technique, glass length, cost, and so on. Then, calculate the lengths of the arms by solving two linear equations, which are called the fixed optical path difference (FOPD) condition and the field-widening condition, respectively (general theory can be found in our previous work in [25]). The FOPD condition is

The FOPD of the FWMI is an important parameter that should be determined before calculating the arm lengths using Eqs. (1) and (2) . It straightforwardly relates to the free spectral range (FSR) of the interferometer ($FOPD=c/FSR$). As is known, the contribution of the spectroscopic filter in HSRL is to block the aerosol Mie scattering signal while transmit the molecular Cabannes scattering signal as much as possible. The bandwidth of the molecular spectrum is nearly 2.8 GHz for the wavelength of 532 nm at atmospheric temperature close to 300 K while that of the aerosol signal is eventually the same as the transmitted laser (~100 MHz). In order to optimize the spectral discrimination, the FSR of the FWMI should be matched to the bandwidths of the aerosol and molecular scattering spectrums. For the FWMI operating at the wavelength of 532 nm, the suggested FSR is 3 GHz based on the optimal estimation approach in [25], and it corresponds to an FOPD of 100 mm. Such an FSR can produce a satisfactory balance between a good transmission to the molecular scattering and a good spectral discrimination, and generally this balance would not change obviously because the molecular transmittance of the FWMI is relatively insensitive to the bandwidth of the molecular spectrum over the range of conditions in the atmosphere.

We employ H-ZF52 in Chengdu glass category (CDGM glass) as the solid glass arm due to its large refractivity (which can ensure a small arm length) and mature processing technique. Introducing the refractive indices of H-ZF52 ($n_1=1.8584@532nm$) and air ($n_{\text{2}}=1.0002@532nm$) along with the pre-chosen tilted placement angle $({\theta }_t={1.5}^{\circ })$into the design formulas, lengths of the solid glass arm and air gap are obtained to be 37.876 mm and 20.3821 mm, respectively. The cube beam splitter is a 50%:50% non-polarized one with the size of one inch, and well coated to reduce the light reflection at the interfaces of different optical mediums. In fact, the beam splitter and the solid arm are built together with the same glass material, in order to reduce the cemented surface. In the interferometer, all the optical surfaces are finely polished to ensure the flatness less than $1/15\lambda$ and parallelism better than 1 minute of arc.

The simulated OPD variation of this FWMI with respect to the incident angle is shown in Fig. 2 . For comparative purpose, we also draw a plot corresponding to the result using the previous field widening concept as in WINDII [18]. It can be seen that the proposed design equations can obtain better field widening characteristic than the previous ones. Actually, the proposed design asks for setting the first-order derivative of the OPD with regard to the chosen tilted angle to zero. This process introduces another local extremum for the OPD curve at the tilted angle ($\theta$ = ${\theta }_t$) while through the previous field widening method, only one extremum at the normal incidence ($\theta$ = 0) exists. The inset plot in Fig. 2 gives the detailed information of the area in the blue dashed box. Due to the introduced two local extremums from the proposed design, the flat area in the OPD curve becomes enlarged (in spite of some ripple), thus the overall variation trend of the OPD is slower. Furthermore, the proposed design method is also more beneficial to the tilted application of the FWMI. We can see that if operated with a tilted angle, the FWMI designed by the previous method would not work at the local extremum of the OPD curve any more while the one designed through the proposed method is still so. Thus, the local variation of the OPD for the FWMI from the proposed design at the operated tilted angle is also much smaller than that from the previous design method.

 

Fig. 2 Theoretical OPD variation of the FWMI with respect to the incident angle. The red plot is the design result using our proposed field widening method, and the green one is that using the previous field widening concept as in WINDII.

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From the design results above, we see that the developed FWMI is of compact and simple structure, which would contribute to the system robustness and fabrication convenience (such as keep good surface figures, refractivity homogeneity of the arms, operation stability, etc.). Also, its theoretical field widening characteristic is very satisfactory through the proposed design method. In the following sections, we will introduce the experimental approaches to optimize and estimate the practical potential of the developed FWMI, before deploying it in our HSRL instrument.

3. Experimental setup for simultaneous optimization and comprehensive potential evaluation of the FWMI

Although the air gap length of the FWMI can be calculated theoretically, it is not an easy task to achieve an air gap with the calculated length precisely at assembly time. Also, evaluating the comprehensive potential of the FWMI is another practical tricky problem. These two matters can be resolved simultaneously via the proposed experimental approach here.

The experimental system shown in Fig. 3 is set up. As is known, in the HSRL technique the frequency of the laser transmitter is the fundamental spectral reference for the system design and operations of these spectrum-related components. In order to reveal the real potential of the FWMI as much as possible, the experimental evaluation conditions, such as the testing spectrum, temperature, etc., should be same as that when the FWMI practically operates in the HSRL instrument. Therefore, we provisionally use the laser that has been intended for our HSRL transmitter to act as the light source in this estimation experiment, which is actually a commercial injection-seeded frequency-doubled pulsed Nd:YAG laser with the single pulse energy of 270 mJ at the 532 nm. We employ a set of wedge mirrors to split the transmitted laser in order to attenuate the obtained laser power in the experiment. An adjustable stop 1 is then used to intercept the marginal area of the beam spot. Subsequently, the beam goes through a pinhole space filter to smooth the laser energy distribution. The space-filtered laser is next collimated by an aplanatic lens L1, whose focal length is four times larger than that of the convergent lens in the pinhole space filter. It can be seen that this configuration is equivalent to a beam expander with $4\times$ amplification, which can accomplish the space filtering, beam expanding and collimation at the same time. Another aplanatic lens L2 is employed to convert the plane collimated beam into the divergent spherical laser. The diameter of the stop 1 can be adjusted to change the laser spot size that strikes the lens L2, resulting in a controllable divergent angle for the generated spherical laser wavefront. When the divergent spherical beam exits from the output port of the FWMI, the interferogram is generated and converged onto a CCD detector (located in the focal plane of L3) after passing through the adjustable stop 2 and an imaging lens L3. Note that, the FWMI here is slightly off-axis placed by about 1.5 degree, in order to produce the same tilted usage condition as expected in our HSRL operation. The stop 2 here is also intended to choose the desired incident angular range that goes into the CCD, providing more flexibility for adjusting the effective divergent angle and controlling the illumination energy. Interferograms can be captured and processed to analyze the performance of the developed FWMI. Notice, the CCD should be configured into the external trigger mode and the trigger source should be chosen as the synchronizing voltage signal during the laser pulse is generated. This allows the interferogram from every single laser pulse to be recorded.

 

Fig. 3 Schematic of experimental setup for simultaneous assembly optimization and potential evaluation of the FWMI. Note that, the FWMI is slightly off-axis placed by about 1.5 degree in order to produce the same tilted usage condition as expected in HSRL operation.

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4. Experimental approach and results

4.1 FWMI assembly optimization

As is described before, the solid glass arm of the FWMI is optically built to the cube beam splitter while the air gap arm is composed of the high reflection mirror M1 mounted with the PZT. The position of the M1 should be fixed properly to realize the field widening. Since the full trip of the PZT is always very limited (30$\mu m$ in our case), it is of significance to assemble the M1 to the desirable position accurately enough in advance, and then finely adjust its position through the PZT in order to implement the optimal field widening performance. Figures 4(a)-4(g) shows several typical interferograms sequentially captured during the manual moving of the M1 towards the cube beam splitter under the illumination of about 3.5 degree half divergent angular range. The moving step here is set to several centimeters intentionally to interpret the field widening phenomenon. It can be seen that the number of the interference fringe becomes smaller and smaller with M1 approaching some position, and starts to increase again when M1 further leaves away this position. This phenomenon straightforwardly manifests the implementation process of the field widening, and provides a heuristic reference for the FWMI assembly. When an interferogram with less than one fringe over the whole aperture like Fig. 4(d) is obtained, it demonstrates that the current position of M1 is very closed to the ideal one. Nevertheless, the situation can be further improved by finely transiting M1 through the PZT until the interferogram with the least fringe number is generated. However, it is not possible to discover the number variation of the interference fringe directly when the M1 is finely tuned. Therefore, we adopt the fringe analysis technique in the interferometry realm to quantify the phase variation over the whole interferogram aperture. Here, the accurate phase-shifting demodulation approach such as the 4-step algorithm [26, 27 ] is suggested since the PZT can help to accomplish records of the phase-shifting interferograms easily. We can drive the PZT to tune M1 with a special moving step such as 1$\mu m$ around the possible optimal position straightforwardly inferred from the fringe number. At each new position, 4 frames of interferograms are captured according to the requirements of the 4-step phase-shifting algorithm, and the wavefront is demodulated to represent the OPD variation of the FWMI among the whole divergent angular range of the incident beam in the current configuration. From the concept of the field widening, it is understandable that the best M1 location can be identified where the demodulated wavefront has the smallest peak-to-valley (PV) value and root-mean-square (RMS) value. It should be noticed that if the PV and RMS values of the wavefronts are always varied monotonously during the transition of the PZT, it means that the best position of the M1 cannot be obtained in the limited moving range of the PZT. An assistant micro whole shift of the M1 and PZT should be needed in this case. The direction of this shift can be judged clearly by the overall shape of the demodulated wavefront figure (the pit shape or the protrusion shape). If the shapes of the demodulated wavefront are always the same as that when the M1 is apparently far away the ideal location, the shift direction should be towards the beam splitter; otherwise, the direction should be opposite. Repeat this adjustment and demodulation until the PV and RMS of the demodulated wavefront reach the smallest values we can realize. Then the current M1 position would be the optimal one for realizing the FWMI assembly.

 

Fig. 4 Several typical interferograms sequentially captured during the manual moving of the M1 toward the cube beam splitter under the illumination of about 3.5 degree half divergent angular range. The moving step here is set to several centimeters intentionally to interpret the field widening phenomenon.

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According to the theoretical calculation from Eq. (1), the air gap length deviation of about 3$\mu m$ from the theoretically optimal one would not bring about obvious field widening characteristic variation. This fact also reveals the characteristic of relative insensitivity of the field widening technique to M1 position. Therefore, we choose the optimization step of 1$\mu m$ in our experiment. Actually, to save the searching time of the optimal position, we can use a larger optimization step of M1 firstly to determine an approximately optimal position of M1, and then diminish the step to our desired positioning accuracy when the approximately optimal position is found.

In the wavefront demodulation process above, the determination of effective apertures and centers of the recorded interferograms is helpful for estimating the angular dependence of the OPD for the developed FWMI intuitively since the pixel positions relative to the fringe center of an interferogram have corresponding relationships with the beam incident angles. A simple but useful approach, which is based on the fringe modulations to automatically complete the aperture partition and center identification of the interferogram, is described here. We firstly demodulate the originally captured interferograms by the 4-step phase-shifting algorithm directly. We know that, except for the desired wavefront information, the fringes modulation map can also be obtained from this demodulation algorithm. In the effective area of an interferogram, the obtained modulations are remarkably large while the area with near zero modulations is considered as the useless part. Therefore, a modulation threshold can be used to transform the modulation map into a binary image. Morphologic open operation is employed to smooth the edge and eliminate the isolated parts of this binary image subsequently. At last, the edge of this binary image can be determined through a common edge extraction method such as the Prewitt operator. At this time, it is convenient to obtain a mathematical description about the effective image area via circle fitting the extracted image edge in a least square sense. The pixel center of the fitted circle is the fringe center, and the coverage area of the circle is the effective aperture of the interferogram. With the calculated effective aperture and fringe center, we can move the useless part of these originally recorded interferograms, and the information corresponding to the whole divergent range of the incident beam is identified.

4.2 Field widening characteristic evaluation

After the FWMI is optimized through the above approach, we can also obtain its field widening characteristic simultaneously. In our lidar construction, the FOV and effective diameter of the telescope receiver aperture is designed to be 0.1 mrad and 280 mm, respectively. Since the FOV Aperture Product (FAP) of an HSRL is constant from the perspective of geometrical optics (which actually represents the etendue of the whole optical system), the FOV of the incident beam into the FWMI is about 0.1 degree if the bean diameter is constrained to 10 mm. In the field widening characteristic evaluation experiment, we adjust the two stops properly to produce a laser beam with half divergent angle of 1.5 degree, which is much larger for all possible incident angles that the FWMI may practically encounter in HSRL. This estimation can make enough allowance for revealing the real performance of the FWMI. By the four-step phase-shifting method, the corresponding wavefront passing through the FWMI is demodulated as shown in Fig. 5 . It can be seen that the PV and RMS values of the wavefront are about 0.04$\lambda$ and 0.008$\lambda$ respectively in this case.

 

Fig. 5 Field widening characteristic of the developed FWMI with respect to the incident angular range from zero to 1.5 degree. The x-y coordinates adopt the pixels to denote the wavefront angular aperture just for simplicity. The central pixel corresponds to zero divergent angle, and the edge pixels for 1.5 degree divergent angle. The corresponding divergent angle of any other pixel is proportional to the pixel distance relative to the central pixel.

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From Fig. 3, we can see that the testing light in this experiment can be equivalent to a point source because of the aplanatic lens L2. This fact means that the light ray with different incident angle hits different aperture position of the FWMI. Thus, the effect from the interferometer imperfections, such as glass surface figure imperfection, the inhomogeneity of glass refractive index, etc., on the field widening performance presented in Fig. 5 is minimized, which makes the measured field widening results more convincing. From the experimental results, we notice that the practical field widening characteristic of the developed FWMI is not as good as the theoretically designed one because the measured PV value of the FWMI OPD variation with respect to the angular range from zero to 1.5 degree is slightly larger than the expected value in Fig. 2 within the same angular range. However, considering that the theoretical PV is the limited value we can realize practically, the ultimate field widening performance of the developed FWMI is satisfactory since the realized PV value of the transmitted wavefront does not differ much from the perfect one. This result is estimated to be enough for good spectral discrimination within large FOV in HSRL application, as will be discussed in section 4.5.

4.3 Cumulative wavefront distortion evaluation

As just pointed out above, the setup shown in Fig. 3 is proposed to optimize the FWMI assembly and estimate the field widening characteristic simultaneously. The testing light there is a divergent spherical wave with the desired divergent angle actually. This point-like light source is beneficial to decoupling the effect on the field widening characteristic estimation from the fabrication defects of the FWMI. However, good field widening performance is only one basic requirement for the developed FWMI. The wavefront distortion induced by some fabrication defects of the interferometer is also an important index to determine its spectral discrimination potential. In order to evaluate the cumulative wavefront distortion caused by these practical fabrication imperfections, we need to remove the aplanatic lens L2 in above experimental setup, and illuminate the FWMI using plane wave with large beam diameter. Similar phase-shifting technique can be performed to measure the cumulative wavefront distortion caused by the FWMI.

Figure 6 shows the measured cumulative wavefront distortion of the developed FWMI from its central area of 70% of the total aperture (i.e., about 18 mm diameter). The PV and RMS values for the distorted wavefront from this area are 0.087$\lambda$ and 0.016$\lambda$, respectively. Although all optical surfaces are finely polished to ensure the flatness less than 1/15$\lambda$, but it can be seen from Fig. 6 that the total wavefront distortion is also considerable even only considering 70% of the total aperture. For lager optical aperture of the FWMI, the induced wavefront distortion is also larger. We infer that the wavefront distortion may mainly come from the gluing of the beam splitter, which is difficult to be controlled via the conventional commercial gluing technique in China. Fortunately, it is not necessary for us to use the full aperture of the FWMI in the HSRL operation. The good field widening performance of the FWMI can mitigate the aperture requirement for the spectral filtering greatly due to the FAP effect, as illustrated in section 4.2. For example, if the incident beam diameter can be compressed to 10 mm, then its divergent angle should reach about 0.16 degree based on the lidar design parameters as mentioned in section 4.2. This divergent angle is completely in the field widening range of the developed FWMI. Hence, the FWMI would be expected to work well in this case. However, the traditional FPI spectral filter could not be qualified for the spectral filtering in the same situation since the divergent angle is a little bit large for it. In other words, the FPI spectral filter should employ the large effective aperture to compensate its small acceptable angle while it is unnecessary for the FWMI to do so because of its good field widening ability (general, it can be estimated that the aperture of the FPI should be more than 10 times larger than that of FWMI in order to greatly alleviate the performance degrading induced by its large angular dependence). This is one of the advantages of the FWMI spectral filter compared with the FPI spectral filter in HSRL. In our FWMI utility, 70% of the total aperture is far enough to process the entire lidar return beam. From the testing result in Fig. 6, the cumulative wavefront distortion induced by these partial areas of the developed FWMI seems acceptable, although exceeding our expectation a little. If some advanced glass processing technique such as fluid jet polishing can be employed, we can realize much smaller wavefront distortion within even larger optical aperture. The effects from the cumulative wavefront distortion on the practical spectral discrimination performance of the FWMI will be analyzed later in section 4.5.

 

Fig. 6 Cumulative wavefront distortion of the developed FWMI from its central aperture with area of 70% of the total aperture.

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4.4 Stability evaluation

In real operation of the FWMI, we should tune the valley of its spectral function to the laser centroid frequency, that is, the so-called frequency locking. In addition, we enclose the FWMI in a hermetical temperature-controlled chamber with temperature stability of about 0.1 Celsius to minimize the thermal effect. However, such temperature stability is not enough to ensure long-term working of the FWMI. Considering the simultaneous requirements for frequency locking and temperature stability enhancement, we have developed an automatic closed-loop servo system to compensate the relative frequency shift between HSRL laser transmitter and the FWMI based on advanced and novel optical heterodyne technique (a detailed description of this locking system will be presented in [28]). During operation of this frequency locking system, any frequency unlocking (maybe caused by PZT position drift, temperature drift, and small transient vibration) will be converted into an error signal, which is fed back into the PZT controller to tune back the FWMI. The sign of error signal is related to the frequency unlocking direction directly. For example, if the frequency is left-shifted, the error signal may be positive; otherwise, it should be negative. Also, the amplitude of error signal is proportional to the quantity of relative frequency shift between the FWMI and laser transmitter. Once the FWMI is properly tuned, the error signal would be zero. Figure 7(a) shows an experimental calibration curve between the error signal and the relative frequency shift by scanning the PZT with 1 nm step manually. We can see that the sensitivity of the error signal to the frequency shift is 61.02 mV/nm through the linear fitting estimation. Figure 7(b) shows the locking test of the FWMI. At point $A$, the locking system is turned on, and the FWMI is quickly tuned to the locking state at point B with the time less than 1 second. Note that, due to the DC offset of 70 mV from locking electrics, the locking point corresponds to 70 mV error signal rather than zero in the practical experiment. To test the robustness of the locking, we introduce an external perturbation by tapping the FWMI intentionally at point C. It can be seen that the FWMI can recover locking rapidly. According to our test, the standard deviation of the error signal during the long-period locking state more than 1 hour is estimated to be 145.4 mV, corresponding to 2.4 nm locking accuracy. Considering the 3 GHz FSR of the FWMI, the frequency locking accuracy for the developed interferometer should be about 27 MHz, which may be the best result we can realize at this stage because the PZT position drift for long-term operation is ~1 nm. This locking technique seems very robust and can work continually for several hours.

 

Fig. 7 Frequency locking performance of the developed FWMI.

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We should mention that although the real-time frequency locking can enhance the stability of the FWMI extremely, the locking signal may mix with the science signal from the atmospheric backscattering. There are two good ways which can solve this problem well. The first approach is to lock the interferometer to fundamental wavelength of the HSRL laser transmitter. For example, if the FWMI is locked to 1064 nm seed laser, then it would be also resonant at higher harmonics such as 532 nm and 355 nm. In this approach, the locking signal and the science signal have completely different optical frequency components, so we can separate them easily by dichromic mirror and commercial interference filter. The second approach is to lock the FWMI using a laser reference that has the same wavelength but perpendicular polarization direction with respect to the HSRL laser transmitter. Then we can separate the science signal from the locking signal through polarization selective optics such as polarized beam splitter, polarized crystal, etc. The first approach is very applicable to the development of HSRL at 532 nm and 355 nm while if near-infrared HSRL (1064 nm) is required, the second approach would be a practical solution.

4.5 Discussion

Via the proposed experimental approach in this paper, the developed FWMI can be assembled optimally and its performance characteristic can be estimated flexibly and simultaneously.

The optimization process is very important to promote the potential of the FWMI. As is mentioned previously, it is difficult to mount the reflection mirror M1 of the FWMI precisely to compose the air gap arm with the calculated length. In fact, it is unnecessary to do so as well. Because the solid glass arm itself does not have the precise dimension and refractivity as are in the theoretical calculation because of the fabrication and processing imperfections, the calculated length for the air gap would not produce the best field widening performance obviously. There is no doubt that only the air gap length determined from experimental methods can match to the practical solid glass arm specifications more reasonably.

The field widening characteristic and the cumulative wavefront distortion are two critical indexes that determine the performance of the developed FWMI. But always, it is troublesome to examine them separately because both of them induce wavefront variation of the FWMI. To decouple these two factors, we use the divergent spherical wave from point-source laser produced by an aplanatic lens for estimating the field widening characteristic and the collimated plane wave with large beam aperture for estimating the cumulative wavefront distortion. Based on the experimental results, the OPD variation of the FWMI among the whole divergent angular range from zero to 1.5 degree is about 0.04$\lambda$. Also, we demonstrate that it is preferable to employ the central area of 70% of total aperture of the FWMI as the effective optical area because the RMS value of cumulative wavefront distortion from this area conforms to the expectation of $\text{0}\text{.01}\lambda$ calculated according to our tolerance budget [25]. Introducing the tested field widening characteristic, the cumulative wavefront distortion and the stability of the developed FWMI into our comprehensive evaluation model in [25], we can estimate the spectral discrimination ratio (SDR, defined as the attenuation ratio of aerosol signal to molecular signal in [25] to reveal the comprehensive potential of any type of spectroscopic filter in HSRL application) of the FWMI to be about 75 when the divergent angle of incident beam is 1.5 degree. In the practical design of our lidar system, the divergent angle of the lidar returning signal should be smaller than 0.5 degree, in which case, the SDR would increase to 86 from these experimental data. According to our earlier study in [11], a large SDR contributes to high measurement accuracy and reducing the retrieval dependence on the aerosol loading condition as for HSRL technique. A SDR about 100 is very excellent for HSRL retrieval, and a larger SDR would not bring about remarkable promotion for the retrieval accuracy further; a SDR larger than 50 can be considered as acceptable which has the ability to ensure ~15% accuracy for observing relatively heavy aerosol loading such as thin cloud [11]. Therefore, the as-built FWMI possesses the good potential to be deployed in our HSRL project from these experimental data. For comparisons, we would like to mention that, the SDR of an FPI etalons is difficult to be made larger than 10 from the study in [23] (actually, it is really true for the reported FPI-based HSRL so far [2]). Therefore, the accuracy of FPI-based HSRL for detecting the aerosols and cloud with large scattering ratio (such as water cloud) may be not so good compared to the FWMI-based HSRL. This is also one of the reasons for us to develop the FWMI technique. Of course, the superiority of the iodine cell based HSRL for detecting heavy aerosol loading is incomparable since its SDR is rather high.

5. Conclusion and future work

We develop a new type of interferometric spectroscopic filter, i.e., the FWMI, which is intended to act as the spectral discriminator in HSRL technique. The design process of the developed FWMI is described in detail. The experimental approach which can realize the optimized FWMI assembly and estimate its comprehensive characteristic simultaneously is proposed. After the optimization process, the PV and RMS values of the measured OPD variation for the developed prototype FWMI are 0.04$\lambda$ and 0.008$\lambda$ respectively when the half divergent angle of the incident beam is as much as 1.5 degree. Also, from the testing, we find that it is preferable to employ the central area of 70% of total aperture of the FWMI as the effective optical area because the RMS value of cumulative wavefront distortion from this area is closed to our tolerance budget 0.01$\lambda$. Through an active locking technique, the frequency of the FWMI can be locked to the laser transmitter with accuracy of 27 MHz for more than one hour. From these experimental characterizations, the SDR for the developed FWMI is evaluated to be larger than 86 if the divergent angle of incident beam is smaller than 0.5 degree. All these results demonstrate the great potential of the developed FWMI as the spectroscopic discriminator for HSRLs, as well as the feasibility of the proposed design and optimization process.

Our future work is to build a 532 nm polarized HSRL instrument employing this developed FWMI, and the comprehensive instrument calibration concerning the total optical efficiency, the instrument depolarization, the systematic coefficient, etc., would be the main topic in the next development stage.

At last, we should emphasize again that the FWMI technique can be built to any wavelength based on the technical contents proposed in this paper. As far as we know, no near-infrared HSRL is reported so far, which may be due to the lack of proper spectroscopic filter and the weaker Rayleigh scattering. Because of these advantages described above, it is expected that the proposed FWMI technique would be very promising to provide a convenient solution for building HSRL systems working at near-infrared wavelength (typically 1064 nm). UV-VIS-NIR (ultraviolet, visible and near-infrared) multi-wavelength HSRLs will provide more comprehensive understanding to the atmospheric aerosol and cloud for scientific community.