Stellar speckle and correlation functions derived from classical wave expansions for spherical antennas. (arXiv:1910.08113v2 [astro-ph.IM] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Yaghjian_A/0/1/0/all/0/1">Arthur D. Yaghjian</a>
Michelson phase and Hanbury Brown–Twiss intensity stellar interferometry
require expressions for 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, previous determinations of
speckle and correlation functions have modeled stars as circular discs rather
than spheres because of the mathematical tools available for partially coherent
fields on planar surfaces. However, with the incentive that most stars are
indeed shaped like spheres and not discs, the present paper models a star as a
spherical antenna composed of a random distribution of uncorrelated volume
sources within a thin surface layer (photosphere). Working directly with the
time-domain fields, a self-contained, straightforward, detailed derivation of
speckle patterns and correlation functions is given based on a novel, angularly
symmetric, spherical mode expansion with coefficients determined by the assumed
Lambertian nature of the star’s radiation and the uniform asymptotic behavior
of the spherical Hankel functions. First order spatially averaged and
temporally averaged correlation functions are proven to be identical and the
normalized second order correlation function is shown to equal one plus the
square of the first order correlation function. The direct time-domain approach
reveals explicit expressions for the quasi-monochromatic wave-packet fields of
stellar radiation as well as new criteria for the validity of the far-field
approximation for the fields of incoherent sources that are much less
restrictive than the Rayleigh-distance criterion for coherent sources.
Michelson phase and Hanbury Brown–Twiss intensity stellar interferometry
require expressions for 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, previous determinations of
speckle and correlation functions have modeled stars as circular discs rather
than spheres because of the mathematical tools available for partially coherent
fields on planar surfaces. However, with the incentive that most stars are
indeed shaped like spheres and not discs, the present paper models a star as a
spherical antenna composed of a random distribution of uncorrelated volume
sources within a thin surface layer (photosphere). Working directly with the
time-domain fields, a self-contained, straightforward, detailed derivation of
speckle patterns and correlation functions is given based on a novel, angularly
symmetric, spherical mode expansion with coefficients determined by the assumed
Lambertian nature of the star’s radiation and the uniform asymptotic behavior
of the spherical Hankel functions. First order spatially averaged and
temporally averaged correlation functions are proven to be identical and the
normalized second order correlation function is shown to equal one plus the
square of the first order correlation function. The direct time-domain approach
reveals explicit expressions for the quasi-monochromatic wave-packet fields of
stellar radiation as well as new criteria for the validity of the far-field
approximation for the fields of incoherent sources that are much less
restrictive than the Rayleigh-distance criterion for coherent sources.
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