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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 5 — May. 1, 1994
  • pp: 1667–1673

Wave-front curvature sensing from a single defocused image

Paul Hickson  »View Author Affiliations


JOSA A, Vol. 11, Issue 5, pp. 1667-1673 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001667


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Abstract

The possibility of sensing the curvature and the slope of a distorted wave front from a single defocused star image is investigated. The suggested technique is similar to the differential curvature-sensing method of Roddier [ R&D note 87-3 ( National Optical Astronomy Observatories, Tucson, Ariz., 1987)] but uses only a single sensor at a point either before or after the focus. The signal-to-noise ratio that is achievable with such a sensor is ultimately limited by atmospheric scintillation to a value of the order of Q r 0 2 / λ z 0, where r0 is Fried’s correlation scale, λ is the wavelength, and z0 is the root-mean-square distance through the atmosphere, weighted by the refractive-index structure constant Cn2. At the best astronomical sites, with an optimal adaptive-optics system, a value of Q 50 should be achievable. Adaptive-optics systems that use such a sensor should be capable of achieving an increase in the effective atmospheric correlation scale of a factor of Q 6 / 5; hence a single-image curvature sensor should be practical whenever D / r 0 Q 6 / 5. This condition is shown to hold at good astronomical sites even for telescopes as large as 8 m and wavelengths as short as 0.5 μm. In addition to optical and mechanical simplicity, the single-image sensor offers the advantage of reduced detector read noise and potentially higher efficiency compared with those from a differential system.

© 1994 Optical Society of America

History
Original Manuscript: December 7, 1992
Revised Manuscript: November 17, 1993
Manuscript Accepted: November 18, 1993
Published: May 1, 1994

Citation
Paul Hickson, "Wave-front curvature sensing from a single defocused image," J. Opt. Soc. Am. A 11, 1667-1673 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-5-1667

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