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Title: Spline based least squares integration for two-dimensional shape or wavefront reconstruction

Abstract

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.

Authors:
 [1];  [2];  [3];  [4];  [1]
+ Show Author Affiliations
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II); Sichuan Univ., Chengdu (China). School of Aeronautics and Astronautics
  3. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II); Chinese Academy of Sciences (CAS), Shanghai (China). Shanghai Inst. of Applied Physics; Univ. of Chinese Academy of Sciences, Beijing (China)
  4. Nanjing Univ. of Science and Technology (China). Jiangsu Key Lab. of Spectral Imaging and Intelligence Sense
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Contributing Org.:
Sichuan Univ., Chengdu (China); Chinese Academy of Sciences (CAS), Shanghai (China); Univ. of Chinese Academy of Sciences, Beijing (China); Nanjing Univ. of Science and Technology (China)
OSTI Identifier:
1354706
Report Number(s):
BNL-113806-2017-JA
Journal ID: ISSN 0143-8166
Grant/Contract Number:  
AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Optics and Lasers in Engineering
Additional Journal Information:
Journal Volume: 91; Journal ID: ISSN 0143-8166
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; shape reconstruction from gradient; wavefront reconstruction; splines

Citation Formats

Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, and Idir, Mourad. Spline based least squares integration for two-dimensional shape or wavefront reconstruction. United States: N. p., 2016. Web. doi:10.1016/j.optlaseng.2016.12.004.
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Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, & Idir, Mourad. Spline based least squares integration for two-dimensional shape or wavefront reconstruction. United States. https://doi.org/10.1016/j.optlaseng.2016.12.004
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Huang, Lei, Xue, Junpeng, Gao, Bo, Zuo, Chao, and Idir, Mourad. Wed . "Spline based least squares integration for two-dimensional shape or wavefront reconstruction". United States. https://doi.org/10.1016/j.optlaseng.2016.12.004. https://www.osti.gov/servlets/purl/1354706.
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@article{osti_1354706,
title = {Spline based least squares integration for two-dimensional shape or wavefront reconstruction},
author = {Huang, Lei and Xue, Junpeng and Gao, Bo and Zuo, Chao and Idir, Mourad},
abstractNote = {In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.},
doi = {10.1016/j.optlaseng.2016.12.004},
journal = {Optics and Lasers in Engineering},
number = ,
volume = 91,
place = {United States},
year = {Wed Dec 21 00:00:00 EST 2016},
month = {Wed Dec 21 00:00:00 EST 2016}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.optlaseng.2016.12.004
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Works referenced in this record:

Framework for gradient integration by combining radial basis functions method and least-squares method
journal, January 2013

Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction
journal, January 2006

Improvement of high-order least-squares integration method for stereo deflectometry
journal, January 2015

  • Ren, Hongyu; Gao, Feng; Jiang, Xiangqian
  • Applied Optics, Vol. 54, Issue 34
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Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms
journal, January 2012

  • Dai, Fengzhao; Tang, Feng; Wang, Xiangzhao
  • Applied Optics, Vol. 51, Issue 21
  • DOI: 10.1364/AO.51.005028

Improvement of least-squares integration method with iterative compensations in fringe reflectometry
journal, January 2012

Wave-front estimation from wave-front slope measurements
journal, January 1980

Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry
journal, January 2013

  • Li, Guanghui; Li, Yanqiu; Liu, Ke
  • Journal of the Optical Society of America A, Vol. 30, Issue 7
  • DOI: 10.1364/JOSAA.30.001448

Phase estimates from slope-type wave-front sensors
journal, January 1978

Shape reconstruction from gradient data
journal, January 2008

  • Ettl, Svenja; Kaminski, Jürgen; Knauer, Markus C.
  • Applied Optics, Vol. 47, Issue 12
  • DOI: 10.1364/AO.47.002091

Optimal wave-front estimation
journal, January 1977

Wave-front reconstruction for compensated imaging
journal, January 1977

A 2 D high accuracy slope measuring system based on a Stitching Shack Hartmann Optical Head
journal, January 2014

  • Idir, Mourad; Kaznatcheev, Konstantine; Dovillaire, Guillaume
  • Optics Express, Vol. 22, Issue 3
  • DOI: 10.1364/OE.22.002770

Least-squares method for data reconstruction from gradient data in deflectometry
journal, January 2016

  • Ren, Hongyu; Gao, Feng; Jiang, Xiangqian
  • Applied Optics, Vol. 55, Issue 22
  • DOI: 10.1364/AO.55.006052

Modal wavefront reconstruction from its gradient
journal, January 2015

Wavefront reconstruction with the adaptive Shack–Hartmann sensor
journal, January 2005

Comparison of two-dimensional integration methods for shape reconstruction from gradient data
journal, January 2015

Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements
journal, January 1977

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    Works referencing / citing this record:

    Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry
    journal, December 2017

    • Zhang, Zonghua; Wang, Yuemin; Huang, Shujun
    • Sensors, Vol. 17, Issue 12
    • DOI: 10.3390/s17122835

    A Calibration Method for System Parameters in Direct Phase Measuring Deflectometry
    journal, April 2019

    • Deng, Xiaoting; Gao, Nan; Zhang, Zonghua
    • Applied Sciences, Vol. 9, Issue 7
    • DOI: 10.3390/app9071444

    Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry
    journal, January 2017

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