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Title: Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry

Abstract

There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this paper, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish the height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. Finally, the new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.

Authors:
 [1];  [2];  [3]; ORCiD logo [4];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States); Sichuan Univ., Chengdu (China)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States); Chinese Academy of Sciences (CAS), Shanghai (China); Univ. of Chinese Academy of Sciences, Beijing (China)
  4. Nanjing Univ. of Science and Technology (China)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1392297
Alternate Identifier(s):
OSTI ID: 1363851
Report Number(s):
BNL-114238-2017-JA
Journal ID: ISSN 0003-6935
Grant/Contract Number:
SC0012704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Applied Optics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 18; Journal ID: ISSN 0003-6935
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; algorithms; distortion; interpolation; optical components; polarization mode dispersion; reconstruction algorithms

Citation Formats

Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, and Idir, Mourad. Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry. United States: N. p., 2017. Web. doi:10.1364/AO.56.005139.
Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, & Idir, Mourad. Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry. United States. doi:10.1364/AO.56.005139.
Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, and Idir, Mourad. Wed . "Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry". United States. doi:10.1364/AO.56.005139.
@article{osti_1392297,
title = {Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry},
author = {Huang, Lei and Xue, Junpeng and Gao, Bo and Zuo, Chao and Idir, Mourad},
abstractNote = {There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this paper, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish the height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. Finally, the new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.},
doi = {10.1364/AO.56.005139},
journal = {Applied Optics},
number = 18,
volume = 56,
place = {United States},
year = {Wed Jun 14 00:00:00 EDT 2017},
month = {Wed Jun 14 00:00:00 EDT 2017}
}

Journal Article:
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  • Here in this work, a model based method is applied to phase measuring deflectometry, which is named as modal phase measuring deflectometry. The height and slopes of the surface under test are represented by mathematical models and updated by optimizing the model coefficients to minimize the discrepancy between the reprojection in ray tracing and the actual measurement. The pose of the screen relative to the camera is pre-calibrated and further optimized together with the shape coefficients of the surface under test. Simulations and experiments are conducted to demonstrate the feasibility of the proposed approach.
  • The correspondence residuals due to the discrepancy between the reality and the shape model in use are analyzed for the modal phase measuring deflectometry. Slope residuals are calculated from these discrepancies between the modal estimation and practical acquisition. Since the shape mismatch mainly occurs locally, zonal integration methods which are good at dealing with local variations are used to reconstruct the height residual for compensation. Finally, results of both simulation and experiment indicate the proposed height compensation method is effective, which can be used as a post-complement for the modal phase measuring deflectometry.
  • Accuracy of Shack-Hartmann type wavefront sensors depends on the shape and layout of the lenslet array that samples the incoming wavefront. It has been shown that an array of gratings followed by a focusing lens provide a substitution for the lensslet array. Taking advantage of the computer generated holography technique, any arbitrary diffraction grating aperture shape, size or pattern can be designed with little penalty for complexity. In the present work, such a holographic technique is implemented to design regular hexagonal grating array to have zero dead space between grating patterns, eliminating the possibility of leakage of wavefront during themore » estimation of the wavefront. Tessellation of regular hexagonal shape, unlike other commonly used shapes, also reduces the estimation error by incorporating more number of neighboring slope values at an equal separation.« less
  • In this paper, we describe the development of a zonal wavefront sensor that comprises an array of binary diffraction gratings realized on a transparent sheet (i.e., polyester film) followed by a focusing lens and a camera. The sensor works in a manner similar to that of a Shack-Hartmann wavefront sensor. The fabrication of the array of gratings is immune to certain issues associated with the fabrication of the lenslet array which is commonly used in zonal wavefront sensing. Besides the sensing method offers several important advantages such as flexible dynamic range, easy configurability, and option to enhance the sensing framemore » rate. Here, we have demonstrated the working of the proposed sensor using a proof-of-principle experimental arrangement.« less