Zhongtao Cheng

Retrieval and analysis of a polarized high-spectral-resolution lidar for profiling aerosol optical properties

Taking advantage of the broad spectrum of the Cabannes-Brillouin scatter from atmospheric molecules, the high spectral resolution lidar (HSRL) technique employs a narrow spectral filter to separate the aerosol and molecular scattering components in the lidar return signals and therefore can obtain the aerosol optical properties as well as the lidar ratio (i.e., the extinction-to-backscatter ratio) which is normally selected or modeled in traditional backscatter lidars. A polarized HSRL instrument, which employs an interferometric spectral filter, is under development at the Zhejiang University (ZJU), China. In this paper, the theoretical basis to retrieve the aerosol lidar ratio, depolarization ratio and extinction and backscatter coefficients, is presented. Error analyses and sensitivity studies have been carried out on the spectral transmittance characteristics of the spectral filter. The result shows that a filter that has as small aerosol transmittance (i.e., large aerosol rejection rate) and large molecular transmittance as possible is desirable. To achieve accurate retrieval, the transmittance of the spectral filter for molecular and aerosol scattering signals should be well characterized.

Dark-field microscopic image stitching method for surface defects evaluation of large fine optics

One of the challenges in surface defects evaluation of large fine optics is to detect defects of microns on surfaces of tens or hundreds of millimeters. Sub-aperture scanning and stitching is considered to be a practical and efficient method. But since there are usually few defects on the large aperture fine optics, resulting in no defects or only one run-through line feature in many sub-aperture images, traditional stitching methods encounter with mismatch problem. In this paper, a feature-based multi-cycle image stitching algorithm is proposed to solve the problem. The overlapping areas of sub-apertures are categorized based on the features they contain. Different types of overlapping areas are then stitched in different cycles with different methods. The stitching trace is changed to follow the one that determined by the features. The whole stitching procedure is a region-growing like process. Sub-aperture blocks grow bigger after each cycle and finally the full aperture image is obtained. Comparison experiment shows that the proposed method is very suitable to stitch sub-apertures that very few feature information exists in the overlapping areas and can stitch the dark-field microscopic sub-aperture images very well.

Effects of spectral discrimination in high-spectral-resolution lidar on the retrieval errors for atmospheric aerosol optical properties.

This paper presents detailed analysis about the effects of spectral discrimination on the retrieval errors for atmospheric aerosol optical properties in high-spectral-resolution lidar (HSRL). To the best of our knowledge, this is the first study that focuses on this topic comprehensively, and our goal is to provide some heuristic guidelines for the design of the spectral discrimination filter in HSRL. We first introduce a theoretical model for retrieval error evaluation of an HSRL instrument with a general three-channel configuration. The model only takes the error sources related to the spectral discrimination parameters into account, while other error sources not associated with these focused parameters are excluded on purpose. Monte Carlo (MC) simulations are performed to validate the correctness of the theoretical model. Results from both the model and MC simulations agree very well, and they illustrate one important, although not well realized, fact: a large molecular transmittance and a large spectral discrimination ratio (SDR, i.e., ratio of the molecular transmittance to the aerosol transmittance) are beneficial to promote the retrieval accuracy. More specifically, we find that a large SDR can reduce retrieval errors conspicuously for atmosphere at low altitudes, while its effect on the retrieval for high altitudes is very limited. A large molecular transmittance contributes to good retrieval accuracy everywhere, particularly at high altitudes, where the signal-to-noise ratio is small. Since the molecular transmittance and SDR are often trade-offs, we suggest considering a suitable SDR for higher molecular transmittance instead of using unnecessarily high SDR when designing the spectral discrimination filter. These conclusions are expected to be applicable to most of the HSRL instruments, which have similar configurations as the one discussed here.

Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique

A phase unwrapping algorithm for interferometric fringes based on the unscented Kalman filter (UKF) technique is proposed. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the UKF process. Simulations indicate that the proposed algorithm has better accuracy than some widely employed phase unwrapping approaches in the same noise condition. Also, the time consumption of the algorithm is reasonably acceptable. Applications of the algorithm in our different optical interferometer systems are provided to demonstrate its practicability with good performance. We hope this algorithm can be a practical approach that can help to reduce the systematic errors significantly induced by phase unwrapping process for interferometric measurements such as wavefront distortion testing, surface figure testing of optics, etc.

Field-widened Michelson interferometer for spectral discrimination in high-spectral-resolution lidar: theoretical framework

A field-widened Michelson interferometer (FWMI) is developed to act as the spectral discriminator in high-spectral-resolution lidar (HSRL). This realization is motivated by the wide-angle Michelson interferometer (WAMI) which has been used broadly in the atmospheric wind and temperature detection. This paper describes an independent theoretical framework about the application of the FWMI in HSRL for the first time. In the framework, the operation principles and application requirements of the FWMI are discussed in comparison with that of the WAMI. Theoretical foundations for designing this type of interferometer are introduced based on these comparisons. Moreover, a general performance estimation model for the FWMI is established, which can provide common guidelines for the performance budget and evaluation of the FWMI in the both design and operation stages. Examples incorporating many practical imperfections or conditions that may degrade the performance of the FWMI are given to illustrate the implementation of the modeling. This theoretical framework presents a complete and powerful tool for solving most of theoretical or engineering problems encountered in the FWMI application, including the designing, parameter calibration, prior performance budget, posterior performance estimation, and so on. It will be a valuable contribution to the lidar community to develop a new generation of HSRLs based on the FWMI spectroscopic filter.

Interferometric filters for spectral discrimination in high-spectral-resolution lidar: performance comparisons between Fabry–Perot interferometer and field-widened Michelson interferometer

Thanks to wavelength flexibility, interferometric filters such as Fabry-Perot interferometers (FPIs) and field-widened Michelson interferometers (FWMIs) have shown great convenience for spectrally separating the molecule and aerosol scattering components in the high-spectral-resolution lidar (HSRL) return signal. In this paper, performance comparisons between the FPI and FWMI as a spectroscopic discrimination filter in HSRL are performed. We first present a theoretical method for spectral transmission analysis and quantitative evaluation on the spectral discrimination. Then the process in determining the parameters of the FPI and FWMI for the performance comparisons is described. The influences from the incident field of view (FOV), the cumulative wavefront error induced by practical imperfections, and the frequency locking error on the spectral discrimination performance of the two filters are discussed in detail. Quantitative analyses demonstrate that FPI can produce higher transmittance while the remarkable spectral discrimination is one of the most appealing advantages of FWMI. As a result of the field-widened design, the FWMI still performs well even under the illumination with large FOV while the FPI is only qualified for a small incident angle. The cumulative wavefront error attaches a great effect on the spectral discrimination performance of the interferometric filters. We suggest if a cumulative wavefront error is less than 0.05 waves RMS, it is beneficial to employ the FWMI; otherwise, FPI may be more proper. Although the FWMI shows much more sensitivity to the frequency locking error, it can outperform the FPI given a locking error less than 0.1 GHz is achieved. In summary, the FWMI is very competent in HSRL applications if these practical engineering and control problems can be solved, theoretically. Some other estimations neglected in this paper can also be carried out through the analytical method illustrated herein.

Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting

In experiments of inertial confinement fusion (ICF), the thickness uniformity of capsule and the density uniformity of deuterium-tritium (DT) ice are both key to successful ignition, while the cross-grating lateral shearing interferometer (CGLSI), which is accurate and insensitive to disturbance, can be employed to test the density distribution of DT ice precisely. In this paper, a wavefront retrieval method for CGLSI based on differential Zernike polynomial fitting is presented. Fast Fourier Transform technique (FFT) is employed to get the frequency spectrum of the interferogram obtained by CGLSI. By performing Inverse Fast Fourier Transform (IFFT) of the +1 order spectrum in both X and Y directions, it is possible to extract shearing wavefronts from the interferogram in both two orthogonal directions. Utilizing differential Zernike polynomial fitting method, we are capable of integrating two shearing wavefronts in both X and Y directions together and retrieving the wavefront under testing. In the process of solving Zernike coefficients, the characteristics of differential Zernike orthogonal polynomials should be taken fully into account in mathematical modeling. To avoid the retrieval error introduced due to matrix mutation, the determination of discrete grid number and aperture shape must be in line with the theory that Zernike polynomials are orthogonal over a unit circle as well. The result of simulation analysis shows that the wavefront retrieval method for CGLSI based on differential Zernike polynomial fitting is correct and accurate, and the root-mean-square error of this method is less than λ/15.

Field-widened Michelson interferometer for spectral discrimination in high-spectral-resolution lidar: practical development.

A field-widened Michelson interferometer (FWMI), which is intended as the spectroscopic discriminator in ground-based high-spectral-resolution lidar (HSRL) for atmospheric aerosol detection, is described in this paper. The structure, specifications and design of the developed prototype FWMI are introduced, and an experimental approach is proposed to optimize the FWMI assembly and evaluate its comprehensive characteristic simultaneously. Experimental results show that, after optimization process, the peak-to-valley (PV) value and root-mean-square (RMS) value of measured OPD variation for the FWMI are 0.04λ and 0.008λ respectively among the half divergent angle range of 1.5 degree. 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. The practical spectral discrimination ratio (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. This paper is expected to provide a good entrance for the lidar community in future HSRL developments using the FWMI technique.

Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations

Abstract. A pattern recognition model for aerosol classification with atmospheric backscatter lidars is proposed and studied in detail. The theoretical framework and the implementation process of the proposed model are presented. Computer simulations have been carried out to verify the practicability and robustness of this model. The k-fold cross-validation method is employed in the process of classifier designing to choose the proper decision rule, which is mainly based on statistical pattern recognition theory. At the same time, the validity of the model is evaluated. The generalized self-validation is also carried out in the computer simulations to verify the stability of the model. The analysis of the performances in reduced status, especially the instance of application to Cloud-Aerosol Lidar with Orthogonal Polarization, demonstrates the generalization ability and performance of this model.

Sparse microdefect evaluation system for large fine optical surfaces based on dark-field microscopic scattering imaging

It is considered challenging to evaluate the sparse microdefects of large optical surfaces because the microdefects are usually of microns while the test samples are of hundreds of millimeters. Most of the existing methods encounter problems such as uncertainty and inefficiency in eyeballing, inconsequence between laser source and international standard, limitation of detecting area, qualitative but not quantitative nor standard measurement of defects, etc. In this paper, a dark-field microscopic scattering imaging system for microdefects evaluation is introduced. The principle of the proposed surface microdefect evaluation system will be presented and the experiment results on evaluating numerous of test samples will be given.