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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 21 — Jul. 20, 2013
  • pp: 5235–5246

Cramer–Rao bounds for intensity interferometry measurements

Richard Holmes, Brandoch Calef, D. Gerwe, and P. Crabtree  »View Author Affiliations

Applied Optics, Vol. 52, Issue 21, pp. 5235-5246 (2013)

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The question of signal-to-noise ratio (SNR) in intensity interferometry has been revisited in recent years, as researchers have realized that various innovations can offer significant improvements in SNR. These innovations include improved signal processing. Two such innovations, the use of positivity and the use of knowledge of the general shape of the object, have been proposed. This paper investigates the potential gains offered by these two approaches using Cramer–Rao lower bounds (CRLBs). The CRLB on the variance of the positivity-constrained maximum likelihood (ML) estimate is at best 1/4 of the variance of the unconstrained estimator. This is compared to the positivity-constrained ML estimator, which delivers a best-case variance reduction of only (11/π)/2=34.1%. The gains offered by prior knowledge depend on the quality of such information, as might be expected from optimal weighting of such data with the measured data. Furthermore, biases are induced by the application of constraints, and these biases can eliminate some or all of the advantage of lower variances, as found when considering the total root-mean-square error. A form of CRLB for variance is presented that properly incorporates prior information.

© 2013 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(030.6600) Coherence and statistical optics : Statistical optics
(100.2980) Image processing : Image enhancement
(350.1270) Other areas of optics : Astronomy and astrophysics
(100.3175) Image processing : Interferometric imaging
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:
Imaging Systems

Original Manuscript: January 23, 2013
Revised Manuscript: May 4, 2013
Manuscript Accepted: May 30, 2013
Published: July 18, 2013

Richard Holmes, Brandoch Calef, D. Gerwe, and P. Crabtree, "Cramer–Rao bounds for intensity interferometry measurements," Appl. Opt. 52, 5235-5246 (2013)

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