Point diffraction interferometer based on a silicon nitride waveguide spherical wave source.

A point diffraction interferometer based on silicon nitride waveguide (WG-PDI), adopting a silicon nitride waveguide spherical wave source (WG-SWS) with Si substrate and SiO2 cladding, is proposed for spherical surface testing. The WG-SWS is used to overcome the drawbacks of the existing spherical wave sources, which can generate high accuracy and high numerical aperture spherical reference wave. In this paper, the theory of the WG-PDI is described, and the possible errors introduced by the device are analyzed. In addition, the lateral deviation between the curvature center of the test wave and the curvature center of the reference wave cannot be eliminated in the reflected configuration of the pinhole diffraction interferometer. After analyzing the influence of the systematic error introduced by the lateral deviation, the semi-reflective film was coated on the output facet of the waveguide spherical wave source to realize point diffraction interference without lateral deviation. Finally, the surface error of a spherical surface was measured by WG-PDI. The experimental results agree well with those measured by the ZYGO interferometer.

Solving optimal carrier frequencies of a CGH null compensator through a double-constrained searching method based on iterative ray-tracings.

Interferometry based on a computer-generated hologram (CGH) null compensator is a general method for high-precision metrology of aspherics. Because the most commonly used CGHs are the Ronchi type with only two quantization steps, tilt and defocus carrier frequencies must always be introduced to separate the disturbing diffraction orders (DDOs). Determining the amount of carrier frequencies is a pivotal but difficult issue in the CGH design process. Previous studies have only drawn qualitative conclusions or obtained some approximate results under specific conditions. This paper proposes a double-constrained searching method based on iterative ray-tracings, which can directly and accurately give the optimal combination of tilt and defocus carrier frequencies, as long as the aspheric under test is a concave one and has an analytical expression. The optimal carrier frequencies solved by the proposed method will minimize the line density of the CGH on the premise of separating all DDOs, which will reduce the cost and difficulty of fabrication as much as possible. The proposed method is almost error-free and holds a clear advantage over the previous methods in terms of versatility. Several typical design examples are presented to verify the feasibility and versatility of the proposed method. Its accuracy is also verified through making comparisons of the ray-tracing results between another method and Zemax models based on these examples.

Fast path planning algorithm for large-aperture aspheric optical elements based on minimum object depth and a self-optimized overlap coefficient.

In the procedure of surface defects detection of large-aperture aspheric optical elements, it is necessary to scan the surface of the element to achieve full coverage inspection. Since the curvature of the aspherical element is constantly changing from the center to the edge, it is of great difficulty to carry out efficient path planning. In addition, the machine vision system is a microscopic system with limited depth of field, and the sub-aperture imaging of aspherical elements has a visual depth along the object side. When the object depth is greater than the depth of field, out-of-focus blur will generate, so the object depth needs to be as small as possible. In response to these problems, this paper proposes a fast path planning algorithm based on the minimum object depth of a sub-aperture. To ensure minimum object depth, the machine vision system collects images along the normal direction of the sub-aperture plane. To address the problem of the surface curvatures of aspheric elements being different and the overlap coefficient difficult to determine, this paper proposes an image processing based overlap coefficient self-optimization algorithm. When scanning with full coverage of elements, there is only one connected domain in the horizontal projection image of all sub-apertures. According to this premise, the overlap coefficient is optimized through an image processing method to obtain a local optimal path planning strategy. According to the obtained path planning strategy, combining the component parameters and mechanical structure, the mapping matrix of the path planning algorithm transplanted to the detection system is calculated. Through computer programming, automatic sub-aperture acquisition is realized, and the self-edited sub-aperture stitching program is applied to reconstruct the collected sub-apertures. Our algorithm can complete path planning within 5 s, and the experimental results show that the maximum stitching misalignment error of the collected sub-apertures is no more than four pixels, and the average is one pixel. The reconstruction accuracy satisfies the needs of subsequent image processing and digital quantization.

Reference wave source based on silicon nitride waveguide in point diffraction interferometer.

Reference wave source (RWS) is the key component of the point diffraction interferometer, which determines the quality of the reference wave. The silicon nitride waveguide RWS is proposed to efficiently overcome the drawbacks of the existing RWSs, aimed at providing a spherical reference wave with high numerical aperture (NA) and high accuracy. The waveguide RWS consists of the straight waveguide, the bend waveguide, and the Y-branch edge coupler. The straight waveguide determines the accuracy and the NA of the reference wave, whereas the latter two determine the light transmittance of the RWS. Simulation results show that the peak-to-valley (PV) and the rms of the deviation from an ideal spherical wave are 2.86×10-4λ (λ=532nm) and 4.83×10-5λ, respectively, and the maximum light transmittance could reach 24%. Experiment results show that the NA of the reference wave reaches up to 0.58, its spot has a good circular symmetry, and its intensity has Gaussian distribution. Although the light transmittance is only 0.2%, it is expected to improve with the development of experimental conditions and waveguide fabrication technology.

Simulation of a machine vision system for reflective surface defect inspection based on ray tracing.

A complete simulation of a machine vision system aimed at defect inspection on a reflective surface is proposed by ray tracing. The simulated scene is composed of the camera model, surface reflectance property, and light intensity distribution along with their corresponding object geometries. A virtual reflective plane geometry with scratches of various directions and pits of various sizes is built as the sample. Its realistic image is obtained by Monte Carlo ray tracing. Compared to the pinhole camera model, the camera model with a finite aperture emits more rays to deliver physical imaging. The bidirectional reflectance distribution function is applied to describe the surface reflectance property. The illustrated machine vision system captures a number of images while translating the light tubes. Then the image sequence obtained by experiment or simulation is fused to generate a well-contrasted synthetic image for defect detection. A flexible fusion method based on differential images is introduced to enhance the defect contrast on a uniform flawless background. To improve detection efficiency, defect contrast of synthetic images obtained by various fusion methods is evaluated. Influence of total image number, light tube width, and fusion interval is further discussed to optimize the inspection process. Experiments on car painted surfaces have shown that the simulated parameters can instruct the setup of the optical system and detect surface defects efficiently. The proposed simulation is capable of saving great effort in carrying out experimental trials and making improvements on reflective surface defect inspection.

Classification between digs and dust particles on optical surfaces with acquisition and analysis of polarization characteristics.

In the automatic detection for surface defects of optical components, the digs and dust particles exhibit similar features: point-like shape and variable intensity reflectivity. On this condition, these two types with entirely different damages are easily confused so that misjudgments will be induced. To solve this problem, a polarization-characteristics-based classification method of digs and dust particles (PCCDD) is proposed based on the polarimetric imaging technique and dark-field imaging technique. First, a dark-field imaging system equipped with a polarization state generator (PSG) and a polarization state analyzer (PSA) is employed to measure and establish normalized Mueller matrices' datasets of digs and dust particles. And by a nonlinear global search combined with a separability evaluation method, the optimal number of acquisitions and corresponding polarization measurement states of the PSG and the PSA are obtained, as well as the parameters of classification function. Then, multiple polarization images are acquired under the optimal states to extract a multidimensional feature description that relates only to the polarization characteristics of the defect; this subsequently acts as the input vector of the classifier to finally achieve the classification. This method takes full advantage of both the difference in polarization properties between digs and dust particles and the characteristic that the polarization properties of digs are relatively invariant while those of dust particles have a large variability. The classification process involves only simple matrix operations. Compared to the traditional discrimination method based on intensity images, the features obtained by this method have a higher separability. Experiments show that the classification accuracy reaches over 90%. This method can be further applied to the recognition and discrimination of other defects in the field of surface defects' detection.

High-precision calibration method for shear ratio based on the shearing wavefront feature extraction of a phase plate.

A new method based on the shearing wavefront feature extraction (SWFE) of a phase plate is proposed to accurately estimate the shear ratio of the system. The relationship between the shear ratio of a quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating (REHG) and the measurement sensitivity, dynamic range, and wavefront retrieval accuracy is analyzed to provide a theoretical guidance for practical application. The simulation result of the SWFE method shows that the relative error of the shear ratio value is about 1.8×10-3, within the acceptable range of the system. In the experiment, two fused quartz phase plates etched with step change edge grooves were introduced to calibrate the shear ratio of the REHG wavefront diagnosis system. Then, the etching depths of these two phase plates and the figure error of a spherical surface were characterized by the REHG. A comparison with a ZYGO GPI interferometer exhibits that the testing results by the REHG are highly precise, which further confirms the effectiveness of the SWFE method in the shear ratio calibration. This shear ratio calibration method is available for similar kind of shearing interferometric wavefront sensor.

Characterization of the pinhole diffraction based on the waveguide effect in a point diffraction interferometer.

The nearly ideal spherical wavefront generated by pinhole diffraction is the key factor determining the achievable accuracy in point diffraction interferometers (PDIs), as it is employed as the reference wavefront. A comprehensive characterization of the diffraction of a pinhole at the operating-wavelength scale that is normally adopted in PDI is given. The incident light is coupled into the pinhole, which functions as a cylindrical waveguide, and is diffracted in the end. The field in the pinhole is analyzed based on mode theory and the diffraction wave in the far field is derived from the field equivalence principle. The diffraction wave is characterized by the light transmittance, the polarization, and the wavefront aberration, which are all determined by the properties of the mode in the pinhole. The diameter of the pinhole should not be smaller than 0.6λ to make the transmittance sufficient. With a linearly polarized incident light, the diffraction wave is elliptically polarized, and the wavefront aberration is dominated by the astigmatic component. The method explicitly reveals the physical mechanism of pinhole diffraction. The analytic solutions are fast to compute, easy to analyze, and intuitively show the diffractive properties of the pinhole. The conclusions are significant for insight into the nature of pinhole diffraction and provide theoretical reference for analysis of numerical results and the design of PDI systems.

Comprehensive design and calibration of an even aspheric quarter-wave plate for polarization point diffraction interferometry.

A polarization point diffraction interferometry (PPDI) system, adopting a specially designed even aspheric quarter-wave plate (EAQWP) in the test path, is proposed for low-reflectivity and high-numerical-aperture spherical surface testing. In terms of the low-reflectivity mirror measurement, the obtained poor fringes contrast, which can significantly affect the measurement accuracy, can be improved by the polarization characteristic of the EAQWP. Simultaneously, the wavefront distortion, especially larger in high-numerical apperture (NA) measurement, can be greatly reduced attributable to the even aspheric surface design instead of the plane. In addition, the pose error introduced by EAQWP is demonstrated in detail, and a difference restoration model is built to calibrate it. Consequently, the location of the EAQWP is fixed in the test path after calibrating the pose error, having no need to be adjusted with the change of the spherical mirror under test, which facilitates the system alignment in practical optical shop testing. Ultimately, the surface error of a spherical mirror with a low-reflectivity of 0.04 and a high NA of 0.5 is measured with PPDI. The experimental results are validated to be in good agreement with that of a ZYGO interferometer.

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.

Minimizing cross-axis sensitivity in grating-based optomechanical accelerometers.

Cross-axis sensitivity of single-axis optomechanical accelerometers, mainly caused by the asymmetric structural design, is an essential issue primarily for high performance applications, which has not been systematically researched. This paper investigates the generating mechanism and detrimental effects of the cross-axis sensitivity of a high resoluion single-axis optomechanical accelerometer, which is composed of a grating-based cavity and an acceleration sensing chip consisting of four crab-shaped cantilevers and a proof mass. The modified design has been proposed and a prototype setup has been built based on the model of cross-axis sensitivity in optomechanical accelerometers. The characterization of the cross-axis sensitivity of a specific optomechanical accelerometer is quantitatively discussed for both mechanical and optical components by numerical simulation and theoretical analysis in this work. The analysis indicates that the cross-axis sensitivity decreases the contrast ratio of the interference signal and the acceleration sensitivity, as well as giving rise to an additional optical path difference, which would impact the accuracy of the accelerometer. The improved mechanical design is achieved by double side etching on a specific double-substrate-layer silicon-on-insulator (SOI) wafer to move the center of the proof mass to the support plane. The experimental results demonstrate that the modified design with highly symmetrical structure can suppress the cross-axis sensitivity significantly without compromising the sensitivity and resolution. The cross-axis sensitivity defined by the contrast ratio of the output signal drops to 2.19% /0.1g from 28.28%/0.1g under the premise that the acceleration sensitivity of this single-axis optomechanical accelerometer remains 1162.45V/g and the resolution remains 1.325µg.

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.

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.

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.

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.

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.