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Signal-to-noise ratio of the bispectral analysis of speckle interferometry

Nakajima, Tadashi (1988) Signal-to-noise ratio of the bispectral analysis of speckle interferometry. Journal of the Optical Society of America A, 5 (9). pp. 1477-1491. ISSN 1084-7529. http://resolver.caltech.edu/CaltechAUTHORS:NAKjosaa88

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Abstract

Monte Carlo simulations of an atmospheric phase screen, based on a Kolmogorov spectrum of phase fluctuations, were performed. Speckle patterns produced from the phase screens were used to derive statistical properties of power spectra and bispectra of speckle interferograms. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of a heuristic treatment based on an interferometric picture of speckle pattern formation in deriving the attenuation factor and the signal-to-noise ratio of the bispectral modulation transfer function in the mid-spatial-frequency range. The derived modulation transfer function is also interpreted in terms of the signal-to-noise ratio at low light levels. A general expression of the signal-to-noise ratio of the bispectrum is derived as a function of the transfer functions of the telescope, the number of speckles, and the mean photon counts in the mid-spatial-frequency range.


Item Type:Article
Additional Information:© 1988 Optical Society of America Received February 8, 1988; accepted April 26, 1988 It is a pleasure to express my special thanks to A.C.S. Readhead for initial suggestions on simulations, which were essential to this work. I would also thank P.W. Gohram, S.R. Kulkarni, G. Neugebauer, and A.C.S. Readhead for valuable discussions and useful comments on the manuscripts of the paper. I thank the editor, J. C. Dainty, and an anonymous referee for informing me of recent literature that was not mentioned in the original manuscript. Finally, I acknowledge the financial support of National Science Foundation grant AST 86-13059 and the Schlumberger Fellowship. Note added in proof: While this paper was being processed, the author was informed by the editor that a recent work by Ayers et al. 27 had some overlap with the present paper. Ayers et al. obtained, by means of a different logical path, an expression for the SNR of the bispectrum in the mid-frequency range that is identical to Eq. (7.34) of this paper.
Record Number:CaltechAUTHORS:NAKjosaa88
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:NAKjosaa88
Alternative URL:http://www.opticsinfobase.org/abstract.cfm?URI=josaa-5-9-1477
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ID Code:2426
Collection:CaltechAUTHORS
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Deposited On:02 Nov 2006
Last Modified:29 Aug 2014 17:24

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