skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors

Abstract

Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for “Calibrate, and then Stitch”, calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for “Stitch, and then Calibrate”, stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in $x$- and y-directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexiblemore » option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.« less

Authors:
ORCiD logo; ; ORCiD logo; ; ; ; ORCiD logo; ; ;
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:
1561346
Alternate Identifier(s):
OSTI ID: 1570670
Report Number(s):
BNL-212190-2019-JAAM
Journal ID: ISSN 1094-4087; OPEXFF
Grant/Contract Number:  
SC0012704
Resource Type:
Published Article
Journal Name:
Optics Express
Additional Journal Information:
Journal Name: Optics Express Journal Volume: 27 Journal Issue: 19; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Huang, Lei, Wang, Tianyi, Nicolas, Josep, Vivo, Amparo, Polack, François, Thomasset, Muriel, Zuo, Chao, Tayabaly, Kashmira, Wook Kim, Dae, and Idir, Mourad. Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors. United States: N. p., 2019. Web. doi:10.1364/OE.27.026940.
Huang, Lei, Wang, Tianyi, Nicolas, Josep, Vivo, Amparo, Polack, François, Thomasset, Muriel, Zuo, Chao, Tayabaly, Kashmira, Wook Kim, Dae, & Idir, Mourad. Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors. United States. doi:10.1364/OE.27.026940.
Huang, Lei, Wang, Tianyi, Nicolas, Josep, Vivo, Amparo, Polack, François, Thomasset, Muriel, Zuo, Chao, Tayabaly, Kashmira, Wook Kim, Dae, and Idir, Mourad. Wed . "Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors". United States. doi:10.1364/OE.27.026940.
@article{osti_1561346,
title = {Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors},
author = {Huang, Lei and Wang, Tianyi and Nicolas, Josep and Vivo, Amparo and Polack, François and Thomasset, Muriel and Zuo, Chao and Tayabaly, Kashmira and Wook Kim, Dae and Idir, Mourad},
abstractNote = {Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for “Calibrate, and then Stitch”, calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for “Stitch, and then Calibrate”, stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in $x$- and y-directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexible option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.},
doi = {10.1364/OE.27.026940},
journal = {Optics Express},
number = 19,
volume = 27,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1364/OE.27.026940

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Stitching methods at the European Synchrotron Radiation Facility (ESRF)
journal, May 2016

  • Vivo, A.; Lantelme, B.; Baker, R.
  • Review of Scientific Instruments, Vol. 87, Issue 5
  • DOI: 10.1063/1.4950745

High-speed noncontact profiler based on scanning white-light interferometry
journal, January 1994


Stitching Interferometry: A Flexible Solution for Surface Metrology
journal, January 2003


Determination and compensation of the “reference surface” from redundant sets of surface measurements
journal, May 2013

  • Polack, François; Thomasset, Muriel
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 710
  • DOI: 10.1016/j.nima.2012.10.134

Iterative algorithm for subaperture stitching interferometry for general surfaces
journal, January 2005

  • Chen, Shanyong; Li, Shengyi; Dai, Yifan
  • Journal of the Optical Society of America A, Vol. 22, Issue 9
  • DOI: 10.1364/JOSAA.22.001929

LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
journal, January 2011

  • Fong, David Chin-Lung; Saunders, Michael
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 5
  • DOI: 10.1137/10079687X

Relative angle determinable stitching interferometry for hard x-ray reflective optics
journal, April 2005

  • Mimura, Hidekazu; Yumoto, Hirokatsu; Matsuyama, Satoshi
  • Review of Scientific Instruments, Vol. 76, Issue 4
  • DOI: 10.1063/1.1868472

Iterative algorithm for three flat test
journal, January 2007


Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates
journal, January 2012

  • Chen, Shanyong; Liao, Wenlin; Dai, Yifan
  • Applied Optics, Vol. 51, Issue 17
  • DOI: 10.1364/AO.51.003817

Principles of interference microscopy for the measurement of surface topography
journal, January 2015


Surface shape determination with a stitching Michelson interferometer and accuracy evaluation
journal, February 2019

  • Polack, F.; Thomasset, M.; Brochet, S.
  • Review of Scientific Instruments, Vol. 90, Issue 2
  • DOI: 10.1063/1.5061930

Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null
journal, January 2010


Stitching techniques for measuring X-ray synchrotron mirror topography
journal, February 2019

  • Vivo, A.; Barrett, R.; Perrin, F.
  • Review of Scientific Instruments, Vol. 90, Issue 2
  • DOI: 10.1063/1.5063339

Stitching interferometry for synchrotron mirror metrology at National Synchrotron Light Source II (NSLS-II)
journal, January 2020


Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors
journal, December 2009

  • Su, Peng; Burge, James H.; Parks, Robert E.
  • Applied Optics, Vol. 49, Issue 1
  • DOI: 10.1364/AO.49.000021

Absolute planarity with three-flat test: an iterative approach with Zernike polynomials
journal, January 2008


Two-dimensional stitching interferometry based on tilt measurement
journal, January 2018


Self-Calibration: Reversal, Redundancy, Error Separation, and ‘Absolute Testing’
journal, January 1996


Error reductions for stitching test of large optical flats
journal, July 2012


One-dimensional angular-measurement-based stitching interferometry
journal, January 2018


Completeness condition for unambiguous profile reconstruction by sub-aperture stitching
journal, January 2018

  • Nicolas, Josep; Ng, May Ling; Pedreira, Pablo
  • Optics Express, Vol. 26, Issue 21
  • DOI: 10.1364/OE.26.027212