http://arxiv.org/abs/1910.08113
Michelson phase and Hanbury Brown-Twiss intensity stellar interferometry require expressions for the speckle patterns and the first and second order correlation functions, respectively, of the fields radiated by stars in terms of their diameters and measured quasi-monochromatic wavelengths. Although our sun and most other stars are spherical in shape at optical wavelengths, all previous determinations of speckle and correlation functions have modeled stars as circular discs rather than spheres because of the mathematical tools available for incoherent fields on planar surfaces, and the absence of closed-form expressions for the prerequisite Green’s function on a spherical surface. However, with the incentive that most stars are indeed shaped like spheres and not discs, the present paper avoids the direct use of surface Green’s functions by modeling a star as a spherical antenna composed of a random distribution of uncorrelated volume sources within a thin surface layer (photosphere and chromosphere). Without using van Cittert-Zernicke, central limit, or moment theorems, a self-contained, straightforward, detailed derivation of speckle patterns and correlation functions is given based on angularly symmetric spherical mode expansions with coefficients determined by the assumed Lambertian nature of the star’s radiation and the uniform asymptotic behavior of the spherical Hankel functions.
A. Yaghjian
Mon, 21 Oct 19
44/54
Comments: 14 pages, 1 figure
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