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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 8 — Aug. 1, 1998
  • pp: 2097–2106

Optimal modal wave-front compensation for anisoplanatism in adaptive optics

Matthew R. Whiteley, Byron M. Welsh, and Michael C. Roggemann  »View Author Affiliations

JOSA A, Vol. 15, Issue 8, pp. 2097-2106 (1998)

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We examine how modal aberration measurements degraded by turbulence-induced anisoplanatism may be used to optimally conjugate atmospheric phase aberrations. By examining the form of the aperture-averaged mean square residual phase error, we show that atmospheric compensation is suboptimal when the measured coefficients from off-axis or finite-altitude guide stars are applied directly. The optimal compensation is obtained only when conjugate phase coefficients are estimated, given the guide-star measurements and knowledge of the spatial correlation of the on-axis and measured phase coefficients, by use of a minimum-mean-square-error (MMSE) estimator. The form of this estimator is outlined, thus motivating the need to quantify the spatial cross correlation of the Zernike coefficients of the phase aberrations. With a knowledge of the modal cross correlation, we show that wave-front compensation performance can be enhanced by use of the MMSE estimator over use of the beacon measurements directly for all orders of correction. For high-order off-axis natural-guide-star correction, equivalent imaging performance is obtained at a beacon offset 10% larger than when beacon measurements are used directly. For high-order laser-guide-star correction, equivalent imaging performance is obtained at laser-guide-star altitudes 20% lower when the MMSE estimator is employed.

© 1998 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics

Original Manuscript: November 26, 1997
Revised Manuscript: April 14, 1998
Manuscript Accepted: April 16, 1998
Published: August 1, 1998

Matthew R. Whiteley, Byron M. Welsh, and Michael C. Roggemann, "Optimal modal wave-front compensation for anisoplanatism in adaptive optics," J. Opt. Soc. Am. A 15, 2097-2106 (1998)

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