Free-space Optical Diffraction and the Fisher Information

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.