First-Order Statistics of Speckle Intensity

doi:10.1117/3.100010.ch3

Book: Simulating Speckle with Python

Author(s): Joseph W. Goodman

Published: 2024

https://doi.org/10.1117/3.100010.ch3

Author Affiliations +

Abstract

In the optical region of the spectrum, detectors are unable to follow the ultra-fast cycles of the optical field amplitude, but rather, they respond to incident power or intensity, averaged over some response time of the detector and some finite area of the detector element. For that reason, in studying speckle in the optical region of the spectrum, the intensity statistics of random phasor sums are of much greater interest than amplitude statistics. We now turn our attention to simulating the intensity statistics of random phasor sums. The Python code used in the previous chapter for various amplitude cases can be reused with small changes. Instead of calculating the length of the random phasor sums, we must calculate the squared length of those sums, for the squared length corresponds to intensity. Accordingly, we modify the previous code to calculate intensity statistics. We will compare the analytical results with histograms in the various cases we consider.