Free-space Optical Diffraction and the Fisher Information

TL;DR

This paper reveals that free-space optical diffraction inherently reduces the Fisher information of the transverse intensity distribution, linking physical diffraction effects to information theory and parameter estimation.

Contribution

It establishes a fundamental relationship between diffraction and Fisher information using the transport-of-intensity approach in the paraxial regime.

Findings

Diffraction causes the intensity distribution to flatten during propagation.

Diffraction monotonically decreases Fisher information related to the intensity model.

The analysis connects optical physics with information-theoretic concepts.

Abstract

Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity distribution. By interpreting intensity as a probability density, we show that a) free-space diffraction will always act to flatten the intensity distribution as the beam propagates, and consequently b) diffraction will monotonically minimize the Fisher Information with respect to any parameterization of the intensity distribution model that depends on propagation distance.