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

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]
  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:
Report Number(s):
BNL-113806-2017-JA
Journal ID: ISSN 0143-8166
Grant/Contract Number:
AC02-98CH10886
Type:
Accepted Manuscript
Journal Name:
Optics and Lasers in Engineering
Additional Journal Information:
Journal Volume: 91; Journal ID: ISSN 0143-8166
Publisher:
Elsevier
Research Org:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Contributing Orgs:
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)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; shape reconstruction from gradient; wavefront reconstruction; splines
OSTI Identifier:
1354706