Efficient orthonormal aberration coefficient estimation for wavefront sensing over variable non-circular pupils of the Hobby-Eberly Telescope

Hanshin Lee, Michael Hart, Gary J. Hill, Marc D. Rafal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Wavefront sensing (WFS) is one of the key elements for active alignment of the new Wide-Field Corrector (WFC), as it tracks sidereal motion, with respect to the fixed Hobby-Eberly Telescope (HET) primary mirror. During a track, part of the 10m-pupil of the WFC can lie outside the primary periphery and be clipped off. An additional field-dependent central obscuration by the holes and baffles of the WFC leads to complex pupil geometries. The combination of these is a complicated dynamically varying non-circular telescope pupil. This unique problem to the WFS on the HET needs to be dealt with by choosing an appropriate set of orthonormal aberration polynomials during wavefront reconstruction. In this paper, three ways of computing orthonormal aberration polynomials and their coefficients are discussed. These are based on the Gram-Schmidt (GS) process, but differ in the way of computing key integrals during the GS process. The first method analytically computes the integrals, where a computer algebra program is used. The second uses the Gaussian quadrature over triangulated pupil geometries that approximate the true pupil shape. The last uses indirect numerical estimates of the integrals, which turned out to be natural by-products of the usual least-square Zernike polynomials fit. It is shown that the first method is limited to cases of simple pupil shapes, while the second can be applied to more general pupil shapes. However, when dealing with complicated dynamically varying non-circular pupils, the last method can be vastly more efficient than the second and enables the possibility of estimating orthonormal aberration coefficient on the fly. Also noticed is that the last method naturally takes into account the pixelation effect of pupil geometries due to pixel-based imaging sensors (e.g. CCDs). With these benefits, the last method can be used as a viable tool in real-time wavefront analysis over dynamically changing pupils as in the Hobby- Eberly Telescope, which is otherwise vastly inefficient with analytic methods used in past studies.

Original languageEnglish (US)
Title of host publicationModeling, Systems Engineering, and Project Management for Astronomy IV
DOIs
StatePublished - Nov 8 2010
Externally publishedYes
EventModeling, Systems Engineering, and Project Management for Astronomy IV - San Diego, CA, United States
Duration: Jun 27 2010Jul 1 2010

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume7738
ISSN (Print)0277-786X

Conference

ConferenceModeling, Systems Engineering, and Project Management for Astronomy IV
CountryUnited States
CitySan Diego, CA
Period6/27/107/1/10

Keywords

  • Hobby-Eberly Telescope
  • Phase Retrieval
  • Segmented mirror
  • Surface figure

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Lee, H., Hart, M., Hill, G. J., & Rafal, M. D. (2010). Efficient orthonormal aberration coefficient estimation for wavefront sensing over variable non-circular pupils of the Hobby-Eberly Telescope. In Modeling, Systems Engineering, and Project Management for Astronomy IV [77381L] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 7738). https://doi.org/10.1117/12.857140