OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 3 — Mar. 1, 1999
  • pp: 533–548

Power series evaluation of covariances for turbulence-induced phase distortions including outer scale and servo lag effects

Brent L. Ellerbroek  »View Author Affiliations


JOSA A, Vol. 16, Issue 3, pp. 533-548 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000533


View Full Text Article

Enhanced HTML    Acrobat PDF (424 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Power series formulas are developed to efficiently compute the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. These covariances may be used to evaluate and optimize the predicted performance of adaptive optical (AO) systems. The power series formulas apply when one or both of the phase distortions is temporally filtered by the closed-loop impulse response function of the AO control loop, thereby allowing the effects of a finite servo bandwidth to be included in AO system performance modeling without the introduction of additional numerical integrations. Results are presented for the Kolomogorov turbulence spectrum with an infinite outer scale, as well as for the case of a finite outer scale with the von Kármán turbulence spectrum. Amplitude scintillation effects are neglected. The Taylor, or frozen flow, hypothesis is used to model the temporal behavior of the turbulence, by using a fixed windspeed profile w(z) and a random wind direction profile θw(z) for which the mean values of the quantities cos[kθw(z)] and sin[kθw(z)] can be computed. The resulting formulas for the covariances are weighted integrals of the refractive-index structure constant Cn2(z), where the weighting functions are power series in from one to three indices depending on the choices made regarding the atmospheric turbulence spectrum and the direction of the wind. The integral with respect to z may also be evaluated analytically, provided that (i) the Cn2(z) profile is a sum of terms of the form zp exp(-cz) and (ii) the phase distortion profiles are not temporally filtered.

© 1999 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.7060) Atmospheric and oceanic optics : Turbulence

History
Original Manuscript: August 24, 1998
Manuscript Accepted: November 2, 1998
Published: March 1, 1999

Citation
Brent L. Ellerbroek, "Power series evaluation of covariances for turbulence-induced phase distortions including outer scale and servo lag effects," J. Opt. Soc. Am. A 16, 533-548 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-3-533

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited