# Eight models for coherence of radiation from incoherent sources and coherence of sunlight

## TL;DR

This paper develops and compares eight models for the coherence of quasi-monochromatic light from spherical incoherent sources, providing analytical and numerical tools to understand coherence properties in various geometries and sizes.

## Contribution

It introduces eight new models for incoherent source coherence, simplifies calculations, and identifies the ball model as most suitable for solar image analysis.

## Key findings

- Far-field transverse coherence forms beyond source size
- Wide angle coherence described by Bessel functions
- Ball model best matches solar limb darkening observations

## Abstract

Eight models for the coherence of the quasi-monochromatic light from spherical incoherent sources are constructed by placing incoherent monopole and dipole sources on the surface of a sphere, inside a ball and on a plane circular disk. All models allow relatively simple numerical calculations of coherence functions for arbitrary source sizes and positions of observation points. We show that the far-field regime for transverse coherence is formed at the distances larger than the source size, regardless of the wavelength. Wide angle far field coherences have simple analytical representations in terms of the spherical and cylindrical Bessel functions. For very large sources the main and few first lobes of coherence function is well represented by paraxial approximation, which reduces the number of models to three. Based on the solar images corresponding to these three models the ball model emerges as the most appropriate. Ball model can be modified to match the limb darkening observations.

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Source: https://tomesphere.com/paper/1904.05944