Completeness condition for unambiguous profile reconstruction by sub-aperture stitching

Nicolas, Josep; Ng, May Ling; Pedreira, Pablo; Campos, Juan; Cocco, Daniele

doi:10.1364/oe.26.027212

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

Journal Article · 15 October 2018 · Optics Express

DOI: https://doi.org/10.1364/oe.26.027212 · OSTI ID:1476845

^[1]; Ng, May Ling ^[2]; Pedreira, Pablo ^[1]; Campos, Juan ^[3]; Cocco, Daniele ^[2]

ALBA Synchrotron Light Source, Barcelona (Spain)
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Univ. Autonoma de Barcelona, Barcelona (Spain)

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.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FIS2015-66328-C3-1-R; FIS2015-66328-C3-2-R; AC02-76SF00515

OSTI ID:: 1476845

Alternate ID(s):: OSTI ID: 1490632

Journal Information:: Optics Express, Vol. 26, Issue 21; ISSN 1094-4087

Publisher:: Optical Society of America (OSA)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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Surface shape determination with a stitching Michelson interferometer and accuracy evaluation Polack, F.; Thomasset, M.; Brochet, S. Review of Scientific Instruments, Vol. 90, Issue 2 https://doi.org/10.1063/1.5061930	journal	February 2019