Abstract

The paper discusses the influence of the geometry of a Hartmann-(Shack) wavefront sensor on the total error of modal wavefront reconstruction. A mathematical model is proposed, which describes the modal wavefront reconstruction in terms of linear operators. The model covers the most general case and is not limited by the orthogonality of decomposition basis or by the method chosen for decomposition. The total reconstruction error is calculated for any given statistics of the wavefront to be measured. Based on this estimate, the total reconstruction error is calculated for regular and randomised Hartmann masks. The calculations demonstrate that random masks with non-regular Fourier spectra provide absolute minimum error and allow to double the number of decomposition modes.

© 2005 Optical Society of America

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Appl. Opt.

Computers Elect. Engng

M. C. Roggemann, �??Optical perfomance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,�?? Computers Elect. Engng 18, 451�??466 (1992).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Y. Carmon and E. N. Ribak, �??Phase retrieval by demodulation of a Hartmann-Shack sensor,�?? Opt. Commun. 215, 285�??288 (2003).
[CrossRef]

Opt. Express

Optical Engineering

N. Roddier, �??Atmospheric wavefront simulation using Zernike polynomials,�?? Optical Engineering 29, 1174 �?? 1180 (1990).

Other

B. Patterson, �??Circular and Annular Zernike Polynomials, Mathematica® Package,�?? <a href="http://library.wolfram.com/infocenter/MathSource/4483/"> http://library.wolfram.com/infocenter/MathSource/4483/</a>(2002). UK Astronomy Technology Centre.

G.-m. Dai, �??Modified Hartmann-Shack Wavefront Sensing and Iterative Wavefront Reconstruction,�?? in Adaptive Optics in Astronomy, vol. 2201 of Proceedings of SPIE, (SPIE, 1994), pp. 562 �?? 573.

I. Ghozeil, Optical Shop Testing, chap. Hartmann and Other Screen Tests, 2nd ed. (JohnWiley & Sons, Inc., New York, 1992), pp. 367 �?? 396

R. K. Tyson, Principles of adaptive optics, 2nd ed. (Academic Press, Boston, 1998).

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