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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. 19, Iss. 3 — Mar. 1, 2002
  • pp: 444–457

Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, and A. Smith  »View Author Affiliations


JOSA A, Vol. 19, Issue 3, pp. 444-457 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000444


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Abstract

Quasi-monochromatic light will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of the illuminated object. Further information can be obtained if two colors of coherent light are used, provided that the colors are sufficiently close in wavelength that the interference is also measurable. It is shown that no more than two intensities of two speckle patterns and their interference are required to produce an unambiguous band-limited image of an object, to within an overall spatial translation of the image, in the absence of measurement errors and in the case where all roots of both fields and their complex conjugates are distinct. This result is proven with a root-matching technique, which treats the electric fields as polynomials in the pupil plane, the coefficients of which form the desired complex object. Several root-matching algorithms are developed and tested. These algorithms are generally slow and sensitive to noise. So motivated, several other techniques are applied to the problem, including phase retrieval, expectation maximization, and probability maximization in a sequel paper [J. Opt. Soc. Am. A 19, 458 (2002)]. The phase-retrieval and expectation-maximization techniques proved to be most effective for reconstructions of complex objects larger than 10 pixels across.

© 2002 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(120.6150) Instrumentation, measurement, and metrology : Speckle imaging

History
Original Manuscript: February 11, 2001
Revised Manuscript: July 13, 2001
Manuscript Accepted: July 16, 2001
Published: March 1, 2002

Citation
R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, and A. Smith, "Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors," J. Opt. Soc. Am. A 19, 444-457 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-3-444

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