Analytical representation of integrals relevant to coherent imaging
Authors:
J. M. Pimbley and S. D. Silverstein
Journal:
Quart. Appl. Math. 47 (1989), 263-272
MSC:
Primary 94A99; Secondary 30E20, 92A07
DOI:
https://doi.org/10.1090/qam/998100
MathSciNet review:
998100
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Abstract: This work presents and evaluates three classes of definite integrals which can arise in the signal processing analysis of coherent imaging systems. All integrals yield to the method of contour integration in the complex plane. Such a treatment requires physically reasonable constraints on the beam divergence, apodizing function of the phased array. The physical foundation of the three integral classes is described in the text.
S. D. Silverstein, Coherence and speckle reduction in compounded correlated phased arrays: Synthetic aperture radar, J. Opt. Soc. Amer. A, vol. 3, 1925–1934 (Nov. 1986)
S. D. Silverstein and M. O’Donnell, Speckle reduction using correlated mixed-integration techniques, Proc. SPIE Int. Symp. on Pattern Recog. and Acoustic Imaging, Vol. 768, 168–172 (Feb. 1987)
M. O’Donnell and S. D. Silverstein, Optimum displacement for compound image generation in medical ultrasound, to be published in IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control (1988)
S. D. Silverstein and M. O’Donnell, Theory of frequency and temporal compounding in coherent imaging: Speckle suppression and image resolution, J. Opt. Soc. Amer. A, vol. 5, 101–113 (January 1988)
- George F. Carrier, Max Krook, and Carl E. Pearson, Functions of a complex variable: Theory and technique, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222256
- George Arfken, Mathematical methods for physicists, Academic Press, New York-London, 1966. MR 0205512
S. D. Silverstein, Coherence and speckle reduction in compounded correlated phased arrays: Synthetic aperture radar, J. Opt. Soc. Amer. A, vol. 3, 1925–1934 (Nov. 1986)
S. D. Silverstein and M. O’Donnell, Speckle reduction using correlated mixed-integration techniques, Proc. SPIE Int. Symp. on Pattern Recog. and Acoustic Imaging, Vol. 768, 168–172 (Feb. 1987)
M. O’Donnell and S. D. Silverstein, Optimum displacement for compound image generation in medical ultrasound, to be published in IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control (1988)
S. D. Silverstein and M. O’Donnell, Theory of frequency and temporal compounding in coherent imaging: Speckle suppression and image resolution, J. Opt. Soc. Amer. A, vol. 5, 101–113 (January 1988)
G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a complex variable, McGraw-Hill, New York, 1966
G. Arfken, Mathematical methods for physicists, Academic Press, New York, 1970
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Article copyright:
© Copyright 1989
American Mathematical Society
