Simulation of laser speckle patterns generated by random rough surfaces

Laser speckle patterns typically occur when a laser beam with a narrow spectral linewidth is reflected by small-scale rough surfaces. These intensity patterns are of great interest for active imaging techniques such as gated-viewing, optical coherence tomography, or any other measurement techniques involving laser illumination. In addition to turbulence effects, surface roughness elevation plays an important role in this process. This paper presents the 2D simulation of isotropic small-scale rough surfaces with the corresponding objective speckle patterns, caused only by the reflection of laser light by those surfaces. In addition, laser speckles generated from sea surfaces, whose structures are anisotropic due to the effect of wind, are also shown. The numerical procedure for the simulation of the (material/sea) surface roughness is based on Fast Fourier Transform (FFT). Our method can simulate surfaces with given power spectral density or auto-covariance function (ACF). The most common are the Gaussian and exponential ACF's. Thereby, the root-mean-square (rms) of surface heights and the correlation length are the main roughness descriptors for surfaces. A surface realization, using a fractal power-law for the spectral density, is also shown. For the simulation of the sea surface roughness, the main input parameters for the wave power spectrum are wind speed, wind direction and fetch. The simulation of the speckle patterns comprises the free-space propagation of a Gaussian-shaped laser beam in forward direction, the subsequent reflection at the rough surface, which introduces fluctuations in the wave phase, and the backward propagation of the reflected laser beam. The method is similar to that of the laser beam propagation in a turbulent atmosphere that uses a 2D spatial field of phase fluctuations (phase screens), whereas here, only a single 2D phase screen is considered that defines the reflective medium.