Statistics of random optical field generated by a random walk with a finite number of steps

Classical stochastic electromagnetic field assumes that the number of steps is infinite, but in practice, the number of steps for random walk is limited, even though the number of steps is large. Therefore, the statistical properties of finite-step random phasor sums are different from those of classical ones. As an example, the negative exponential probability density function of classical intensity speckles is not suitable for speckles with limited steps. In some applications, including but not limited to synthetic-aperture radar (SAR) imagery, wireless communication and wavelet analysis, when the probability density function of the classical speckle is used to calculate, the acquired result is often biased, and can't provide appropriate estimation with reasonable accuracy. In this paper, we make the statistical analysis of the Stokes parameters of the random polarization phasor sums with a limited number of steps. The statical properties for the stochastic optical fields generated with a limited number of steps are presented with different applications in optical engineering.