Numerical modeling of speckle fields: catching the visible and the invisible

The present paper deals with the numerical simulation of the diffracted field emanating from an optically rough surface illuminated by a spatially coherent white-light source. The colored speckle pattern which can be observed under these circumstances visualizes the 3D structure of the diffracted speckle field and, what’s more, it allows us appreciate the differences between diffraction regimes, i.e. Fresnel rather than Fraunhofer regime. In the paper the 3D structure of near- and far-field diffraction fully developed speckle fields will be explored by numerical simulation in the Mathematica™ environment, by using few highly-optimized functions implementing the Rayleigh-Sommerfeld formulation into the built-in FFT (Fast Fourier Transform) algorithm. In the applicability range of the Fresnel approximation, the dimensionless Fresnel number fully describes the diffraction regime and the results of the numerical simulation can be simply mapped into the physical world by the appropriate scaling parameters at diffraction plane and along the propagation direction.