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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 5 — May. 1, 2012
  • pp: 722–733

Accommodation of speckle in object-based phasing

Glenn A. Tyler  »View Author Affiliations

JOSA A, Vol. 29, Issue 5, pp. 722-733 (2012)

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This work addresses the physical basis of the measurement process for object-based phasing of an array of telescopes. In this regard an enhanced least-squares estimator that is capable of differentiating among three families of array aberrations in an object-based phasing system is developed. In a system of this nature the system to be phased illuminates the object of interest and the return radiation is detected. Telescope aberrations, atmospheric aberrations, and speckle-induced aberrations are all reported by the estimator to facilitate correction of telescope and atmospheric aberrations. This is accomplished by proper handling of the unobservable modes and recognizing that the five global aberrations—telescope array piston, atmospheric array piston and tilt, and speckle array piston and tilt—cannot be measured accurately so they need to be projected out of the estimated piston commands. Except for these relatively benign array aberrations, the disturbances for all three families of array aberrations are estimated exactly. An interesting feature of the speckle array aberrations is that a synthetic aperture is developed that is almost twice as large as the array of telescopes under consideration.

© 2012 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(030.6140) Coherence and statistical optics : Speckle

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: October 25, 2011
Revised Manuscript: January 5, 2012
Manuscript Accepted: January 6, 2012
Published: April 19, 2012

Glenn A. Tyler, "Accommodation of speckle in object-based phasing," J. Opt. Soc. Am. A 29, 722-733 (2012)

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  4. This is a “fast” way to obtain the correct result. Here the derivative is with respect to pT assuming that pT is independent of p. In actuality, the derivative of the scalar nTn is taken with respect to the elements of p resulting in a set of multiple equations with multiple unknowns. When this process is completed Eq. (29) is obtained.
  5. It is well known that the quantity H0 is equivalent to the pseudoinverse of G. This is the solution with minimum norm. Although the result expressed in Eq. (38) could be determined immediately, the process illustrated here provides significant insight into what will be required in the next section to obtain an appropriate estimator. For this application a naive application of Eq. (38) will result in a deficient estimator.
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