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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 264–275

Imaging a class of non-Gaussian fields beyond the diffraction limit

Stanley J. Reeves  »View Author Affiliations

JOSA A, Vol. 16, Issue 2, pp. 264-275 (1999)

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In standard intensity imaging, apart from the availability of prior information about an image, the resolution is limited by the width of the aperture. The region of support of the autocorrelation of the pupil function is the measured spatial-frequency bandwidth of the imaging system, and thus the size of the pupil function determines the resolution limit. This relationship between the size of the pupil function and the resolution limit is generally taken to describe a fundamental limit for resolution. Contrary to conventional wisdom, the resolution is actually limited only for fields with zero higher-order cumulants. For fields with nonvanishing higher-order cumulants, higher resolution can be obtained by integrating higher powers of instantaneous intensity in the image plane and combining these images appropriately. The result is that resolution is limited only by the time required for the integral of the higher power of intensity to approximate the expected value. These claims are demonstrated, and the variance of the integrated intensity-squared image as a function of the temporal spectrum and integration time is analyzed. Simulations are provided that show imaging of spatial-frequency information outside the support of the pupil function autocorrelation for non-Gaussian fields.

© 1999 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(110.2990) Imaging systems : Image formation theory

Original Manuscript: May 1, 1998
Revised Manuscript: August 17, 1998
Manuscript Accepted: October 19, 1998
Published: February 1, 1999

Stanley J. Reeves, "Imaging a class of non-Gaussian fields beyond the diffraction limit," J. Opt. Soc. Am. A 16, 264-275 (1999)

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