Sub-aperture Scanning Research Articles

Circular Subaperture Stitching Interferometry Based on Polarization Grating and Virtual–Real Combination Interferometer

This paper presents a polarization grating based circular subaperture stitching interferometer. The system can be used for small F/# concave surface tests with a large F/# transmission sphere, where F/# is the ratio of focal length to aperture. A polarization grating was employed to deflect the incident beam for subaperture scanning by its axial rotation instead of a multi-axis motion-control system. Compared with the traditional subaperture stitching interferometric system, the system proposed in this paper is smaller in size and reduces the measurement error introduced by mechanical adjustment. Using a virtual interferometer model and a virtual-real combination algorithm to remove the retrace error, the full-aperture figure error can be directly obtained without the need for a complex stitching algorithm. The feasibility of the algorithm was verified, and the measurement error caused by the modeling error was analyzed by simulation. The capability of the polarization grating to scan subapertures was experimentally confirmed, and possible solutions to some engineering challenges were pointed out. The research in this paper has pioneering and guiding significance for the application of polarization grating in interferometry.

Scanning strategy for surface defects evaluation of large fine optical components

Defects, such as scratches and digs etc., play an important role in quality control of fine optical components. Dark field microscopic imaging has become one of the most commonly means for surface defects detection. However, the imaging field of view is very limited compared with the increasing aperture of the test parts and sub-aperture scanning is usually employed to increase the detection aperture while ensuring the system resolution. The problems that classic “S” Shape Sub-Aperture (SSSA) strategy faces are the high positioning accuracy requirement for the translation stage and the time-consuming processing of huge number of sub-apertures. Herein, a Sub-Region and Sub-Aperture (SRSA) scanning strategy is proposed. It divides the aperture of test part into sub-regions. Within each sub-region, classic scanning strategies and stitching methods can be employed the same time when next sub-region is being scanned. The whole aperture of the test part can be obtained when all the sub-regions are stitched together. Thus the positioning accuracy requirement of translation stage is reduced from the whole aperture to a sub-region while most of the sub-aperture stitching and processing time is covered within the scanning process. The relationship between the positioning accuracy of translation stage and the sizes of sub-aperture/sub-region is discussed in detail. Comparison experiments show the superiority of the proposed SRSA scanning strategy with which large-aperture, high precision scanning detection of large-aperture optical components can be accomplished efficiently and economically.

Error analysis and measurement methods of curved optical element surface defects dark-field imaging inspection system based on multi-axis kinematics

In surface defect dark-field inspection of the curved optical element, the camera field of view (FOV) is much smaller than the aperture of the element, so the images of different positions on the element surface, which are also called sub-aperture images, need to be collected and stitched to obtain the whole surface image of the element. It is usually achieved by controlling multi-axis motion guide rails to make relative motion between camera and optical element. During sub-aperture images collection, there is not only relative translation between camera and optical element, but also optical element spin and swing with its optical axis for curved optical element. The motion errors of each motion axis will make sub-aperture scanning path deviate its predetermined path. Hence, it will lead to the dislocation of the stitching image, and will cause defects break and dislocation in stitching image, which will largely affect the optical element surface quality quantitative evaluation. Since multi-axis kinematics (MAK) is a mathematical model which is often used to describe the motion of objects located in multi-axis system, such as numerical control machine and mechanical arm. The multi-axis kinematics error analysis (MAKEA) model is put forward in this paper and applied in the optical element surface defects dark-field imaging inspection system. The effect of all axis motion errors including optical axis motion errors to sub-aperture scanning path has been specifically simulated and analyzed. The simulation result indicates that the optical axis swing error caused by assembly is the main error of dark-field imaging system, whereupon a swing angle assembly error measurement (SAAEM) method by measuring the optical axis positions of different thickness spherical optical elements is proposed. By adjusting the motor of the element optical axis swing, the optical axis swing error can be compensated. The sub-aperture images stitching experiment is carried out to verify the validity of optical axis swing error compensation. Results show the situation of sub-aperture images stitching dislocation is improved. The root-mean-square-error (RMSE) of sub-aperture images scanning path after error compensation is nearly 1/20 of the RMSE before compensation.

High-precision automatic centering method for aspheric optical elements based on machine vision

In the machine vision inspection of large-aperture aspheric optical components, the limited field of view and micron-level detection accuracy requirements make sub-aperture scanning imaging indispensable. High-precision scanning depends on the alignment of the spin axis of the mechanical system and the optical axis of the component, so the component needs to be centered before scanning. In view of this problem, this paper proposes a high-precision automatic centering method (HPACM) for rotationally symmetric aspheric optical elements based on machine vision. The goal is to adjust two reference points on the optical axis to the mechanical spin axis, which are the sphere center of the upper surface vertex and the sphere center of the lower surface vertex imaged by the upper surface of the element respectively. Adjust the first point to the spin axis is the Eccentric Error Correction (EEC), and then adjust the second point to the spin axis is the tilt error correction (TEC). In EEC and TEC, the component rotates one circle around the spin axis. If there exists eccentric or tilt error, the crosshair on the image plane will move along a circular trajectory which center on the spin axis. Then use pixel coordinates of crosshair center extraction algorithm (PCCEA) to extract the pixel coordinates of the centers of the crosshair images during the circular motion, and apply the least squares circle fitting algorithm to obtain the trajectory circle of the crosshair centers. The center of the crosshair and the center of the track circle on the image plane correspond to the sphere center of the surface vertex and a point on the spin axis of the object side respectively, and the relative positions of these two points on the image plane can be converted to the object side according to the system parameters. Experimental results show that the proposed HPACM can correct the eccentric and tilt error to within 7um and 0.5’.

Topography measurement of helical grooves on a hemisphere based on stitching interference microscopy

Hemispherical bearings fabricated with helical grooves on the working surface show improved aerodynamic performance which depends to a large extent on the machining accuracy of the grooves. Topography measurement of the entire groove from macro to micro scale is thus important to evaluate the bearing performance. White light interference microscopy is widely used in topography measurement. However, subaperture stitching is necessary to extend the field of view (FOV) for large area measurement but limited to planar surfaces. This paper presents a method of interference microscopy combined with subaperture stitching. The long groove is divided into a series of subapertures with overlapping regions. Each subaperture meets the requirement of FOV and measurable slope limit of the microscope. We show that the helical curve is approximately located on a geodesic circle of the hemisphere. Accordingly a special fixture is designed with a rotary table to rotate the groove around the axis perpendicular to the geodesic circle. A four-axis scanning platform is integrated with the interference microscope. Based on the principle of minimal deviations in overlapping regions, six-degree-of-freedom motion error introduced in subaperture scanning is simultaneously corrected through an iterative stitching algorithm. It is experimentally verified by measuring a real part with helical grooves etched on a hemisphere bearing rotor. Complete high-resolution topography of the entire groove is reconstructed and the stitching map shows no overlap sliding effect, which is instructive for assessment of the machining error and further evaluation of the bearing performance.

Chromatic confocal sensor-based sub-aperture scanning and stitching for the measurement of microstructured optical surfaces.

The noncontact optical probe-based surface scanning is promising for the measurement of complex-shaped optical surfaces. In this study, by combining a chromatic confocal sensor and a planar nano-positioning stage, a sub-aperture scanning and stitching method is developed for the noncontact measurement of the microstructured optical surfaces, with the measured form accuracy being irrespective of the accuracy of the global scanning stage. After the scanning, the Gaussian process-based denoising is employed to remove the measurement noises, and a hybrid registration algorithm is proposed to achieve a 6-DOF alignment of any neighbored sub-apertures. For the registration, the differential evolution-based minimization is implemented to find a coarse transformation which then serves as the initial value for the iterative closest point-based fine registration. The hybrid method is beneficial in finding an optimal registration with a greatly reduced computation burden. Finally, the effectiveness of the developed measurement system, as well as the stitching algorithm, is comprehensively demonstrated through practically measuring a sinusoidal micro-grid surface.

Establishment and verification of diffraction BRDF model for scratched material surface

The surface reflectance at micro scale is mainly dominated by wave effect and cannot be explained by geometric ray model. In this paper, we use wave optics to analyze the incoherent reflectivity and gained important insights into the establishment of the diffraction BRDF model of scratched material surface. In order to confirm the model given, we improve the BRDF measurement method into the sub-aperture scanning Fourier transform system. The experimental data are in good agreement with the theoretical model. The proposed scratch diffraction BRDF model is more suitable to describe the actual physical process, and can provide theoretical basis for proposing detection scheme for scratches of different standards. The model can also be used to analyze the stray light of scratched material surface and the target characteristics of multi texture surface.

Establishment and verification of sub-aperture scanning Fourier transform system for scattered light measurements

We present sub-aperture scanning Fourier transform system, a method for fast Bidirectional reflection distribution function (BRDF) measurements. A single lens is used for Fourier transform, and the scattering light field is measured by sub aperture scanning of the Fourier transform lens. Through Fourier transform, a single measurement can obtain multi-angle scattering data, and sub-aperture scanning further expands the measurement angle range. Due to the full utilization of image detectors, once measurement can get 1944 points’ data inside 10°. Thus the system’s precision can get to 0.005°and the measurement time can shorten ten times. Finally, the method is verified by comparing the experimental data. Experimental results show that the relative error of this method is less than 1%. These results provide theoretical basis and technical support for the application of BRDF in sub aperture scanning Fourier transform system.

Confocal laser scanning and 3D reconstruction methods for the subsurface damage of polished optics

The subsurface damage (SSD) of optics is one of the key factors limiting the increase of energy density of high-power solid-state lasers. Because of the characteristics of small size, low density and wide distribution, it is difficult to detect the SSD of large polished optics with high-accuracy. Confocal laser scanning and three-dimensional (3D) reconstruction methods are proposed in this paper. 3D scanning in a small area is realized by a galvo and piezo stage, and sub-aperture scanning in a large area is realized by a XY stage. Sub-aperture images are stitched together to construct a volume data field, and then a modified Marching Cubes (MC) algorithm is used for 3D reconstruction. Simulations and experimental results show that the algorithm runs faster with low memory footprint, and morphologies of SSDs are displayed intuitively and accurately. The proposed methods provide quantitative evaluations such as the positions, depths and cross-sectional areas of SSDs.

哈特曼原理子口径斜率扫描检测及误差研究

哈特曼原理子口径斜率扫描检测及误差研究

Stitching test of large flats by using two orthogonally arranged wavefront interferometers.

The most challenging problem in the stitching test of large flats with a small-aperture interferometer is the accumulation effect of the second-order error. As it is approximately enlarged by the square of the ratio of full aperture size to subaperture size, a very small amount of the second-order error in the reference surface of a transmission flat can be accumulated and gets far from negligible when the subaperture is far smaller than the full aperture. We present here a solution by using two orthogonally arranged wavefront interferometers. One is responsible for a subaperture test and the other for the simultaneous measurement of relative tilts. Because the accumulation effect originates from the lateral shift of the second-order error, only the tilt along the subaperture scanning direction needs to be measured accurately. It is no longer determined by stitching optimization instead to avoid the error accumulation. Piston and tilt perpendicular to the scanning direction are still determined by stitching optimization. The method is experimentally verified and compared to the stitching test with the reference surface error calibrated out, both referenced to the full aperture test result obtained with a 24-inch interferometer.

Validation of simultaneous reverse optimization reconstruction algorithm in a practical circular subaperture stitching interferometer

We demonstrate the validity of the simultaneous reverse optimization reconstruction (SROR) algorithm in circular subaperture stitching interferometry (CSSI), which is previously proposed for non-null aspheric annular subaperture stitching interferometry (ASSI). The merits of the modified SROR algorithm in CSSI, such as auto retrace error correction, no need of overlap and even permission of missed coverage, are analyzed in detail in simulations and experiments. Meanwhile, a practical CSSI system is proposed for this demonstration. An optical wedge is employed to deflect the incident beam for subaperture scanning by its rotation and shift instead of the six-axis motion-control system. Also the reference path can provide variable Zernike defocus for each subaperture test, which would decrease the fringe density. Experiments validating the SROR algorithm in this CSSI is implemented with cross validation by testing of paraboloidal mirror, flat mirror and astigmatism mirror. It is an indispensable supplement in SROR application in general subaperture stitching interferometry.

Alignment methods for micron-scale surface defects automatic evaluation of large-aperture fine optics

A surface defect evaluation system can combine microscopic scattering dark-field imaging with sub-aperture scanning and stitching. Thousands of sub-apertures are involved; mechanical errors will cause stitching dislocation, leading to defect cracks. In this Letter, we propose standard line coordinate error adjustment dealing with consistency error between coordinates of the scanning and imaging system, and defocus depth estimation leveling method dealing with high-cleanliness fine optics defocuing caused by the surface which is not perpendicular to microscope’s optical axis. Experiments show defect cracks are effectively solved and the defocus of 420 mm×420 mm components can be controlled within depth of field 20 μm.

형상이차미분을 이용한 자유곡면 형상복원법

We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x- and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

Distortion correction in surface defects evaluating system of large fine optics

It is challenging to quantitate micron-scale defects on the surface of large optics. Based on microscopic scattering dark-field imaging, sub-aperture scanning and stitching, the Surface Defects Evaluating System (SDES) can spot and measure scratch and digs on large optics. In order to evaluate defects of down to sub-micron over apertures of hundreds of millimeters, high magnification zoom microscope and large format CCD camera are employed to balance between the efficiency and resolution. Unfortunately, large optical distortion in the sub-aperture images can be found, and feature recognition of defect images as well as mismatches of the sub-apertures stitching are greatly affected. In this paper, a distortion correction procedure based on the Brown–Conrady model is proposed. Grayscale surface fitting and bilinear interpolation techniques are employed to obtain better correction accuracy. A grids-patterned fused silica standard plate has been specifically made to calibrate the distortion. Comparison experiments indicate that the distortion in the SDES can be corrected by the proposed method very well.

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.

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析

大口径光学系统测试用双回转子孔径扫描装置设计与误差分析