Raman lidar at 355 nm using low dead time photon counting for atmospheric aerosol measurements.

Photon counting is an effective way to enhance the dynamic range of the data acquisition system (DAQ) in Raman lidars. However, there exists a deficiency of relatively high dead times among current options, which necessitates an additional calibration procedure for the nonlinearity of the photon counting signal, thus leading to unanticipated errors. A field programmable gate array (FPGA)-based photon counting module has been proposed and implemented in a Raman lidar, offering two operational channels. Through observational experiments, it was determined that this module has an overall dead time of 1.13 ns taking advantage of the high-speed amplifier/discriminator pair and the logic design, a significant improvement compared to the 4.35 ns of a commercially used Licel transient recorder within the same counting rate range. This notably low dead time implies that its output maintains sufficient linearity even at substantially high counting rates. As a result, the need for a dead time calibration procedure prior to signal integration with the analog signal is eliminated, reducing uncertainty in the final integrated signal, and even in the retrieval result. The backscattering result of the comparison between this module and a transient recorder indicates that a more precise performance can be acquired benefiting from this hardware upgrading.

Multi-slice ptychographic imaging with multistage coarse-to-fine reconstruction.

The ability to image 3D samples with optical sectioning is essential for the study of tomographic morphology in material and biological sciences. However, it is often hampered by limitations of acquisition speed and equipment complexity when performing 3D volumetric imaging. Here, we propose, to the best of our knowledge, a new method for 3D reconstruction from a minimum of four intensity-only measurements. The complementary structured patterns provided by the digital micromirror device (DMD) irradiate the outermost layer of the sample to generate the corresponding diffraction intensities for recording, which enables rapid scanning of loaded patterns for fast acquisition. Our multistage reconstruction algorithm first extracts the overall coarse-grained information, and then iteratively optimizes the information of different layers to obtain fine features, thereby achieving high-resolution 3D tomography. The high-fidelity reconstruction in experiments on two-slice resolution targets, unstained Polyrhachis vicina Roger and freely moving C. elegans proves the robustness of the method. Compared with traditional 3D reconstruction methods such as interferometry-based methods or Fourier ptychographic tomography (FPT), our method increases the reconstruction speed by at least 10 times and is suitable for label-free dynamic imaging in multiple-scattering samples. Such 3D reconstruction suggests potential applications in a wide range of fields.

Optical Aberration Calibration and Correction of Photographic System Based on Wavefront Coding.

The image deconvolution technique can recover potential sharp images from blurred images affected by aberrations. Obtaining the point spread function (PSF) of the imaging system accurately is a prerequisite for robust deconvolution. In this paper, a computational imaging method based on wavefront coding is proposed to reconstruct the wavefront aberration of a photographic system. Firstly, a group of images affected by local aberration is obtained by applying wavefront coding on the optical system's spectral plane. Then, the PSF is recovered accurately by pupil function synthesis, and finally, the aberration-affected images are recovered by image deconvolution. After aberration correction, the image's coefficient of variation and mean relative deviation are improved by 60% and 30%, respectively, and the image can reach the limit of resolution of the sensor, as proved by the resolution test board. Meanwhile, the method's robust anti-noise capability is confirmed through simulation experiments. Through the conversion of the complexity of optical design to a post-processing algorithm, this method offers an economical and efficient strategy for obtaining high-resolution and high-quality images using a simple large-field lens.

Quantitative phase imaging based on wavefront correction of a digital micromirror device.

The strong need in materials and biological science has prompted the development of high-speed quantitative phase imaging. However, for phase retrieval applying digital micromirror devices (DMDs), the accuracy of the retrieved phase will be disturbed by the DMD-induced aberrations. Here, we propose a phase retrieval method based on measuring and correcting errors caused by phase non-uniformity of the device. Using only four binary amplitude masks and corresponding diffraction intensities, the proposed method achieves rapid convergence and high-quality reconstruction. The experiments prove the practical feasibility for general samples and the effective improvement of the retrieved phase accuracy.

Quantitative phase and amplitude imaging with an efficient support constraint.

High-speed quantitative phase and amplitude imaging methods have led to numerous biological discoveries. For general samples, phase retrieval from a single-diffraction pattern has been an algorithmic and experimental challenge. Here we present a quantitative phase and amplitude imaging method applying an efficient support constraint to yield a rapid algorithmic convergence due to the removal of the twin image and spatial shift ambiguities. Compared to previous complex-valued imaging, our method is lenslet-free and relies neither on assumption based on sample sparsity nor interferometric measurements. Our method provides a robust method for imaging in materials and biological science, while its rapid imaging capability will benefit the investigation of dynamical processes.

Relationship between the effective attenuation coefficient of spaceborne lidar signal and the IOPs of seawater.

Multiple scattering is an inevitable effect in spaceborne oceanic lidar because of the large footprint size and the high optical density of seawater. The effective attenuation coefficient klidar in the oceanic lidar equation, which indicates the influence of the multiple scattering effect on the formation of lidar returns, is an important parameter in the retrieval of inherent optical properties (IOPs) of seawater. In this paper, the relationships between klidar of the spaceborne lidar signal and the IOPs of seawater are investigated by solving the radiative transfer equation with an improved semianalytic Monte Carlo model. Apart from the geometric loss factors, klidar is found to decrease exponentially with the increase of depth in homogeneous waters. klidar is given as an exponential function of depth and IOPs of seawater. The mean percentage errors between klidar calculated by the exponential function and the simulated ones in three typical stratified waters are within 0.5%, proving the effectiveness and applicability of this klidar-IOPs function. The results in this paper can help researchers have a better understanding of the multiple scattering effect of spaceborne lidar and improve the retrieval accuracy of the IOPs and the chlorophyll concentration of case 1 water from spaceborne lidar measurements.

Generalized high-spectral-resolution lidar technique with a multimode laser for aerosol remote sensing.

High-spectral-resolution lidar (HSRL) is a powerful tool for atmospheric aerosol remote sensing. The current HSRL technique often requires a single longitudinal mode laser as the transmitter to accomplish the spectral discrimination of the aerosol and molecular scattering conveniently. However, single-mode laser is cumbersome and has very strict requirements for ambient stability, making the HSRL instrument not so robust in many cases. In this paper, a new HSRL concept, called generalized HSRL technique with a multimode laser (MML-gHSRL), is proposed, which can work using a multimode laser. The MML-gHSRL takes advantage of the period characteristic of the spectral function of the interferometric spectral discrimination filter (ISDF) thoroughly. By matching the free spectral range of the ISDF with the mode interval of the multimode laser, fine spectral discrimination for the lidar return from each longitudinal mode can be realized. Two common ISDFs, i.e., the Fabry-Perot interferometer (FPI) and field-widened Michelson interferometer (FWMI), are introduced to develop the MML-gHSRL, and their performance is quantitatively analyzed and compared. The MML-gHSRL is a natural but significant generalization for the current HSRL technique based on the IDSF. It is potential that this technique would be a good entrance to future HSRL developments, especially in airborne and satellite-borne aerosol remote sensing applications.

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.

Design of the interferometric spectral discrimination filters for a three-wavelength high-spectral-resolution lidar.

We address design of the interferometric spectral discrimination (ISD) filters for a specific three-wavelength high-spectral-resolution lidar (HSRL) in this paper. Taking into account the strong dependence of the transmittance of the ISD filters on the incident angle of light ray, the optical path of the receiving channel with an ISD filter in HSRL is analyzed. We derive the lidar equation with the angular distribution of backscatter signal, through which Monte Carlo (MC) simulations are then carried out to obtain the optimal parameters of the ISD filters for the HSRL at 1064 nm, 532 nm and 355 nm, respectively. Comparing the retrieval errors of the MC simulations based on different ISD filters, the configuration and parameters of the best ISD filter at each wavelength are determined. This paper can be employed as a theoretical guidance during the design of a three-wavelength HSRL with ISD filters.

Frequency locking of a field-widened Michelson interferometer based on optimal multi-harmonics heterodyning.

A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.

Defects evaluation system for spherical optical surfaces based on microscopic scattering dark-field imaging method.

In the field of automatic optical inspection, it is imperative to measure the defects on spherical optical surfaces. So a novel spherical surface defect evaluation system is established in this paper to evaluate defects on optical spheres. In order to ensure the microscopic scattering dark-field imaging of optical spheres with different surface shape and radius of curvature, illumination with variable aperture angle is employed. In addition, the scanning path of subapertures along the parallels and meridians is planned to detect the large optical spheres. Since analysis shows that the spherical defect information could be lost in the optical imaging, the three-dimensional correction based on a pin-hole model is proposed to recover the actual spherical defects from the captured two-dimensional images. Given the difficulty of subaperture stitching and defect feature extraction in three-dimensional (3D) space after the correction, the 3D subapertures are transformed into a plane to be spliced through geometric projection. Then, methods of the surface integral and calibration are applied to quantitatively evaluate the spherical defects. Furthermore, the 3D panorama of defect distribution on the spherical optical components can be displayed through the inverse projective reconstruction. Finally, the evaluation results are compared with the OLYMPUS microscope, testifying to the micrometer resolution, and the detection error is less than 5%.

Aspheric subaperture stitching based on system modeling.

Instead of various mathematical stitching algorithms, an aspheric subaperture stitching interferometric method relying on modern computer modeling technique is presented. Based on our previously reported non-null annular subaperture stitching interferometry (NASSI), a simultaneous reverse optimizing reconstruction (SROR) method based on system modeling is proposed for full aperture figure error reconstruction. All the subaperture measurements are simulated simultaneously with a multi-configuration model in a ray tracing program. With the multi-configuration model, full aperture figure error would be extracted in form of Zernike polynomials from subapertures wavefront data by the SROR method. This method concurrently accomplishes subaperture retrace error and misalignment correction, requiring neither complex mathematical algorithms nor subaperture overlaps. Experiment results showing the validity of SROR method are presented.

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.

Quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating.

A compact quadriwave lateral shearing interferometer (QWLSI) with strong adaptability and high precision is proposed based on a novel randomly encoded hybrid grating (REHG). By performing the inverse Fourier transform of the desired ±1 Fraunhofer diffraction orders, the amplitude and phase distributions of the ideally calculated quadriwave grating can be obtained. Then a phase chessboard is introduced to generate the same phase distribution, while the amplitude distribution can be achieved using the randomly encoding method by quantizing the radiant flux on the ideal quadriwave grating. As the Faunhofer diffraction of the REHG only contains the ±1 orders, no order selection mask is ever needed for the REHG-LSI. The simulations and the experiments show that the REHG-LSI exhibits strong adaptability, nice repeatability, and high precision.

General measurement of optical system aberrations with a continuously variable lateral shear ratio by a randomly encoded hybrid grating.

A general lateral shearing interferometry method to measure the wavefront aberrations with a continuously variable shear ratio by the randomly encoded hybrid grating (REHG) is proposed. The REHG consists of a randomly encoded binary amplitude grating and a phase chessboard. Its Fraunhofer diffractions contain only four orders which are the ±1 orders in two orthogonal directions due to the combined modulation of the amplitude and phase. As a result, no orders selection mask is needed for the REHG and the shear ratio is continuously variable, which is beneficial to the variation of sensitivity and testing range for different requirements. To determine the fabrication tolerance of this hybrid grating, the analysis of the effects of different errors on the diffraction intensity distributions is carried out. Experiments have shown that the testing method can achieve a continuously variable shear ratio with the same REHG, and the comparison with a ZYGO GPI interferometer exhibits that the aberration testing method by the REHG is highly precise and also has a good repeatability. This testing method by the REHG is available for general use in testing the aberrations of different optical systems in situ.

Determination of aspheric vertex radius of curvature in non-null interferometry.

Traditional spherical radius of curvature interferometry is not valid for an aspheric vertex radius of curvature (VROC) due to the obstacle in identifying null positions (cat's eye or confocal position). Simultaneous optimization for multiconfiguration of an interferometer model is proposed to retrieve the actual aspheric VROC from its biased nominal value. This procedure works out the contradiction between VROC deviation and positioning error and even surface figure error, independent of absolute positioning by cat's eye or confocal position. In this method, the aspheric VROC and surface figure can be measured simultaneously, which facilitates the test process remarkably in practical optical shop testing. Furthermore, the parent VROC of a hollow aspheric (annular surface) also can be determined in this method. The performance of the proposed method is validated by experiments.

Reverse optimization reconstruction of aspheric figure error in a non-null interferometer.

Aspheric non-null testing, as an alternative to the traditional null testing, achieves more flexible measurements. However, figure-error reconstruction in non-null tests has always been difficult due to the presence of retrace error. A novel method with reverse optimization is proposed for aspheric figure-error reconstruction in a non-null interferometer. It is a generalized and effective approach based on system modeling and polynomial fitting. An optimization function is set with polynomial coefficients of the desired figure error as variables and those of the detected experimental wavefront as optimization targets. Through the reverse optimization process with iterative ray tracing, the optimal solutions can be extracted and the desired figure error is reconstructed with a simple fitting procedure. Numerical simulations verifying the high accuracy of the proposed method are presented with error considerations. A set of experiments has also been carried out to demonstrate the validity and repeatability of this method.

Non-null annular subaperture stitching interferometry for steep aspheric measurement.

A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching ideal and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. In this way, relatively large overlapping areas can be obtained for adjustment errors correction while the error accumulation would be decreased. With the reverse optimization reconstruction (ROR) method for retrace error correction, the figure error of each subaperture can be retrieved accurately. Therefore, the testing accuracy and efficiency are thus increased. The dynamic test range is extended as well. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with those of the Zygo interferometer.

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.