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 disks 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 disks, this article 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.

中文翻译：

---

从球面天线的经典波展开导出的恒星散斑和相关函数

迈克尔逊相位和 Hanbury Brown-Twiss 强度恒星干涉测量法分别需要用恒星辐射的场的一阶和二阶相关函数的表达式来表示它们的直径和测量的准单色波长。尽管我们的太阳和大多数其他恒星在光学波长下都是球形的，但之前对散斑和相关函数的确定将恒星建模为圆盘而不是球体，因为可用于平面表面部分相干场的数学工具。然而，由于大多数恒星的形状确实像球体而不是圆盘，本文将恒星建模为球形天线，由薄表面层（光球层）内随机分布的不相关体积源组成。直接使用时域场，散斑图案和相关函数的独立、直接、详细的推导基于一种新颖的、角对称的、球模展开，其系数由假定的恒星辐射的朗伯性质和球面汉克尔函数的均匀渐近行为决定. 一阶空间平均和时间平均相关函数被证明是相同的，归一化的二阶相关函数等于一加一阶相关函数的平方。