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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 8 — Aug. 30, 2004
  • pp: 1445–1451

Statistical properties of the Strehl ratio as a function of pupil diameter and level of adaptive optics correction following atmospheric propagation

Jeffrey B. Shellan  »View Author Affiliations

JOSA A, Vol. 21, Issue 8, pp. 1445-1451 (2004)

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The propagation of an optical beam through atmospheric turbulence produces wave-front aberrations that can reduce the power incident on an illuminated target or degrade the image of a distant target. The purpose of the work described here was to determine by computer simulation the statistical properties of the normalized on-axis intensity—defined as (D/r0)2 SR—as a function of D/r0 and the level of adaptive optics (AO) correction, where D is the telescope diameter, r0 is the Fried coherence diameter, and SR is the Strehl ratio. Plots were generated of (D/r0)2 〈SR〉 and σSR/SR, where 〈SR〉 and σSR are the mean and standard deviation, respectively, of the SR versus D/r0 for a wide range of both modal and zonal AO correction. The level of modal correction was characterized by the number of Zernike radial modes that were corrected. The amount of zonal AO correction was quantified by the number of actuators on the deformable mirror and the resolution of the Hartmann wave-front sensor. These results can be used to determine the optimum telescope diameter, in units of r0, as a function of the AO design. For the zonal AO model, we found that maximum on-axis intensity was achieved when the telescope diameter was sized so that the actuator spacing was equal to approximately 2r0. For modal correction, we found that the optimum value of D/r0 (maximum mean on-axis intensity) was equal to 1.79Nr+2.86, where Nr is the highest Zernike radial mode corrected.

© 2004 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(230.4040) Optical devices : Mirrors

Original Manuscript: October 28, 2003
Revised Manuscript: February 20, 2004
Manuscript Accepted: February 20, 2004
Published: August 1, 2004

Jeffrey B. Shellan, "Statistical properties of the Strehl ratio as a function of pupil diameter and level of adaptive optics correction following atmospheric propagation," J. Opt. Soc. Am. A 21, 1445-1451 (2004)

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  16. In our computations the mean phase gradient was computed over all SAs that were at least 50% illuminated. For cases where the SA was fully illuminated, this computation is equivalent to taking the difference between the mean phases along opposite SA edges (average G tilt). The matrix inversion needed for the least-squares reconstructor was implemented by Matlab’s pseudoinverse algorithm pinv.
  17. The computer runs described in this paper took approximately two full weeks to complete on a 1.2-GHz machine, so it was impractical to increase significantly the number of phase-screen realizations or the phase grid point resolution.

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