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

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.
 [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:
Report Number(s):
Journal ID: ISSN 0003-6935
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Applied Optics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 18; Journal ID: ISSN 0003-6935
Optical Society of America (OSA)
Research Org:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; algorithms; distortion; interpolation; optical components; polarization mode dispersion; reconstruction algorithms
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1363851