GaussianSchelltype

Gaussian Schell-model type, commonly referred to as the Gaussian Schell-model (GSM), is a statistical model for partially coherent optical fields. It describes quasi-monochromatic beams whose spatial intensity and coherence have Gaussian profiles. The GSM is one of the simplest and most widely used models for partially coherent light, applicable to laser sources, thermal beams, and synchrotron radiation.

At a reference plane, the cross-spectral density W(r1, r2) factorizes as W(r1, r2) = sqrt(I(r1) I(r2)) μ(|r1 - r2|), where I(r) is the intensity distribution and μ is the complex degree of coherence normalized to μ(r, r) = 1. In the GSM, I(r) is Gaussian, I(r) = I0 exp(-|r|^2 / w^2), and μ(Δr) = exp(-|Δr|^2 / 2 σ_c^2). Thus the cross-spectral density is Gaussian in both coordinates, characterized by the beam width w and the coherence width σ_c.

Propagation properties: The GSM is closed under paraxial propagation and common optical transformations; the width w and the coherence width σ_c transform in a way that preserves the Gaussian form, described by simple ABCD-like rules. This allows analytic expressions for intensity and degree of coherence after propagation through free space, lenses, or other linear optical systems.

Applications and context: The GSM is widely used to model partially coherent lasers, thermal beams, and X-ray or synchrotron radiation sources. It provides a practical compromise between fully coherent and completely incoherent models, enabling tractable analysis of interference, imaging performance, and coherence properties in a variety of optical systems.