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Title: Completeness condition for unambiguous profile reconstruction by sub-aperture stitching

Abstract

We describe the conditions required for a set of displaced sub-aperture measurements to contain sufficient information to reconstruct the stitched mirror profile removing all additive systematic errors of the measuring instrument, independent of the reference surface and of the guidance error of the linear stage used for the translation. We show that even-spaced stitching must be avoided and that the pitch error of the linear stage or the curvature of the reference must be measured, to avoid periodic errors and curvature errors in the reconstructed profile. We show that once these uncertainties are solved, the 1D profile can be reconstructed free of any additive systematic error. In conclusion, the theory is supported by computer simulations and by experimental results using two different instruments.

Authors:
ORCiD logo [1];  [2];  [1];  [3];  [2]
  1. ALBA Synchrotron Light Source, Barcelona (Spain)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Univ. Autonoma de Barcelona, Barcelona (Spain)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1476845
Alternate Identifier(s):
OSTI ID: 1490632
Grant/Contract Number:  
FIS2015-66328-C3-1-R; FIS2015-66328-C3-2-R; AC02-76SF00515
Resource Type:
Journal Article: Published Article
Journal Name:
Optics Express
Additional Journal Information:
Journal Volume: 26; Journal Issue: 21; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Nicolas, Josep, Ng, May Ling, Pedreira, Pablo, Campos, Juan, and Cocco, Daniele. Completeness condition for unambiguous profile reconstruction by sub-aperture stitching. United States: N. p., 2018. Web. doi:10.1364/oe.26.027212.
Nicolas, Josep, Ng, May Ling, Pedreira, Pablo, Campos, Juan, & Cocco, Daniele. Completeness condition for unambiguous profile reconstruction by sub-aperture stitching. United States. doi:10.1364/oe.26.027212.
Nicolas, Josep, Ng, May Ling, Pedreira, Pablo, Campos, Juan, and Cocco, Daniele. Mon . "Completeness condition for unambiguous profile reconstruction by sub-aperture stitching". United States. doi:10.1364/oe.26.027212.
@article{osti_1476845,
title = {Completeness condition for unambiguous profile reconstruction by sub-aperture stitching},
author = {Nicolas, Josep and Ng, May Ling and Pedreira, Pablo and Campos, Juan and Cocco, Daniele},
abstractNote = {We describe the conditions required for a set of displaced sub-aperture measurements to contain sufficient information to reconstruct the stitched mirror profile removing all additive systematic errors of the measuring instrument, independent of the reference surface and of the guidance error of the linear stage used for the translation. We show that even-spaced stitching must be avoided and that the pitch error of the linear stage or the curvature of the reference must be measured, to avoid periodic errors and curvature errors in the reconstructed profile. We show that once these uncertainties are solved, the 1D profile can be reconstructed free of any additive systematic error. In conclusion, the theory is supported by computer simulations and by experimental results using two different instruments.},
doi = {10.1364/oe.26.027212},
journal = {Optics Express},
issn = {1094-4087},
number = 21,
volume = 26,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1364/oe.26.027212

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

Figures / Tables:

Fig. 1 Fig. 1: Diagram representing the measurement process. The interferometer measures the distance at every point between the surface under test and a reference surface. The instrument (including the reference surface, have to be scanned along the SUT. Guidance error of such motion introduces a pitch and piston at every measurement.

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.