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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1067–1083

Resolution of synthetic-aperture imaging through turbulence

Thomas J. Karr  »View Author Affiliations

JOSA A, Vol. 20, Issue 6, pp. 1067-1083 (2003)

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A theory is developed for the resolution of an optical synthetic-aperture imaging system viewing an object through an inhomogeneous refractive medium. The inhomogeneities of the propagation medium create errors in the phase history data with resultant space-variant image effects, including geometric distortions and broadening of the impulse response or point-spread function. I relate the intensity-impulse response to the usual wave structure function. I determine the modulation transfer function for synthetic apertures of any size and exposure time, valid whenever the optical bandwidth is small compared with the carrier frequency, and derive the resolution for monostatic and bistatic synthetic apertures, valid whenever the real sampling aperture is small compared with the medium’s coherence length. The results take the same form as the well-known turbulence-limited resolution of incoherent, real-aperture imaging with short exposure. Turbulence-limited synthetic-aperture resolution is somewhat better than incoherent real-aperture resolution under the same conditions. Autofocus processing improves synthetic-aperture resolution beyond this limit, and adaptive correction of higher-order phase history errors would improve it further.

© 2003 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6600) Coherence and statistical optics : Statistical optics
(110.2990) Imaging systems : Image formation theory
(110.4100) Imaging systems : Modulation transfer function
(280.6730) Remote sensing and sensors : Synthetic aperture radar

Original Manuscript: September 1, 2002
Revised Manuscript: November 27, 2002
Manuscript Accepted: November 27, 2002
Published: June 1, 2003

Thomas J. Karr, "Resolution of synthetic-aperture imaging through turbulence," J. Opt. Soc. Am. A 20, 1067-1083 (2003)

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  28. We have chosen to chirp the local oscillator signal. This measurement process is known as dechirp-on-receive or stretch processing. The same result can be obtained by interfering sE(t)with a monochromatic optical wave and then dechirping the electronic beat signal from the optical detector either by mixing with a chirped electrical LO signal or by digital filtering.
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