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Title: Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors

Abstract

Several techniques have been used with Shack-Hartmann wavefront sensors to determine the local wave-front gradient across each lenslet. In this article we introduce an iterative weighted technique which is specifically targeted for open-loop applications such as aberrometers and metrology. In this article the iterative centroiding technique is compared to existing techniques such as center-of-mass with thresholding, weighted center-of-gravity, matched filter and cross-correlation. Under conditions of low signal-to-noise ratio, the iterative weighted centroiding algorithm is demonstrated to produce a lower variance in the reconstructed phase than existing techniques. The iteratively weighted algorithm was also compared in closed-loop and demonstrated to have the lowest error variance along with the weighted center-of-gravity, however, the iteratively weighted algorithm removes the bulk of the aberration in roughly half the iterations than the weighted center-of-gravity algorithm. This iterative weighted algorithm is also well suited to applications such as guiding on telescopes.

Authors:
;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
908382
Report Number(s):
UCRL-JRNL-229735
TRN: US200722%%619
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Optics Express, n/a, no. 8, April 16, 2007, pp. 5147 - 5149; Journal Issue: 8
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; ALGORITHMS; SIGNAL-TO-NOISE RATIO; TELESCOPES

Citation Formats

Baker, K L, and Moallem, M M. Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors. United States: N. p., 2007. Web. doi:10.1364/OE.15.005147.
Baker, K L, & Moallem, M M. Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors. United States. doi:10.1364/OE.15.005147.
Baker, K L, and Moallem, M M. Wed . "Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors". United States. doi:10.1364/OE.15.005147. https://www.osti.gov/servlets/purl/908382.
@article{osti_908382,
title = {Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors},
author = {Baker, K L and Moallem, M M},
abstractNote = {Several techniques have been used with Shack-Hartmann wavefront sensors to determine the local wave-front gradient across each lenslet. In this article we introduce an iterative weighted technique which is specifically targeted for open-loop applications such as aberrometers and metrology. In this article the iterative centroiding technique is compared to existing techniques such as center-of-mass with thresholding, weighted center-of-gravity, matched filter and cross-correlation. Under conditions of low signal-to-noise ratio, the iterative weighted centroiding algorithm is demonstrated to produce a lower variance in the reconstructed phase than existing techniques. The iteratively weighted algorithm was also compared in closed-loop and demonstrated to have the lowest error variance along with the weighted center-of-gravity, however, the iteratively weighted algorithm removes the bulk of the aberration in roughly half the iterations than the weighted center-of-gravity algorithm. This iterative weighted algorithm is also well suited to applications such as guiding on telescopes.},
doi = {10.1364/OE.15.005147},
journal = {Optics Express, n/a, no. 8, April 16, 2007, pp. 5147 - 5149},
number = 8,
volume = ,
place = {United States},
year = {Wed Feb 28 00:00:00 EST 2007},
month = {Wed Feb 28 00:00:00 EST 2007}
}
  • We propose a simple and powerful algorithm to extend the dynamic range of a Shack-Hartmann wave-front sensor. In a conventional Shack-Hartmann wave-front sensor the dynamic range is limited by the f-number of a lenslet, because the focal spot is required to remain in the area confined by the single lenslet. The sorting method proposed here eliminates such a limitation and extends the dynamic range by tagging each spot in a special sequence. Since the sorting method is a simple algorithm that does not change the measurement configuration, there is no requirement for extra hardware, multiple measurements, or complicated algorithms. Wemore » not only present the theory and a calculation example of the sorting method but also actually implement measurement of a highly aberrated wave front from nonrotational symmetric optics.« less
  • The suitability of the Hartmann-Shack technique for the determination of the propagation parameters of a laser beam is faced against the well known caustic approach according to the ISO 11146 standard. A He-Ne laser (543 nm) was chosen as test beam, both in its fundamental mode as well as after intentional distortion, introducing a moderate amount of spherical aberration. Results are given for the most important beam parameters M{sup 2}, divergence, and beam widths, indicating an agreement of better than 10% and for adapted beam diameter <5%. Furthermore, the theoretical background, pros and cons, as well as some features ofmore » the software implementation for the Hartmann-Shack sensor are briefly reviewed.« less
  • Shack-Hartmann based Adaptive Optics system with a point-source reference normally use a wave-front sensing algorithm that estimates the centroid (center of mass) of the point-source image 'spot' to determine the wave-front slope. The centroiding algorithm suffers for several weaknesses. For a small number of pixels, the algorithm gain is dependent on spot size. The use of many pixels on the detector leads to significant propagation of read noise. Finally, background light or spot halo aberrations can skew results. In this paper an alternative algorithm that suffers from none of these problems is proposed: correlation of the spot with a idealmore » reference spot. The correlation method is derived and a theoretical analysis evaluates its performance in comparison with centroiding. Both simulation and data from real AO systems are used to illustrate the results. The correlation algorithm is more robust than centroiding, but requires more computation.« less
  • The analytic frequency responses of the traditional wavefront reconstructors of Hudgin, Fried, and Southwell are presented, which exhibit amplification or attenuation of the original signal at high spatial frequencies. To overcome this problem, a reconstructor with unity frequency response is developed based on a band-limited derivative calculation. The algorithm is both numerically and experimentally confirmed.