A comparison of g(1)(\tau), g(3/2)(\tau), and g(2)(\tau), for radiation from harmonic oscillators in Brownian motion with coherent background

TL;DR

This paper compares different correlation functions of radiation from harmonic oscillators in Brownian motion, providing expressions for chaotic radiation and analyzing their signal-to-noise ratios relevant to astrophysical observations.

Contribution

It introduces a comprehensive comparison of g(1), g(3/2), and g(2) correlation functions for chaotic radiation modeled by harmonic oscillators in Brownian motion, including signal-to-noise analysis.

Findings

Signal-to-noise ratio for g(1) scales linearly with |g(1)(τ)|.

Signal-to-noise ratio for g(2) scales with the square of |g(1)(τ)|.

Derived expressions for Rician chaotic radiation in astrophysical contexts.

Abstract

We compare the field-field g(1)(\tau), intensity-field g(3/2)(\tau), and intensity-intensity g(2)(\tau) correlation functions for models that are of relevance in astrophysics. We obtain expressions for the general case of a chaotic radiation, where the amplitude is Rician based on a model with an ensemble of harmonic oscillators in Brownian motion. We obtain the signal to noise ratios for two methods of measurement. The intensity-field correlation function signal to noise ratio scales with the first power of |g(1)(\tau)|. This is in contrast with the well-established result of g(2)(\tau) which goes as the square of |g(1)(\tau)|.