Direct synthesis of partially coherent fields at the outputs of $ABCD$ optical systems

We develop a method to directly synthesize partially coherent fields at the outputs of
$ABCD$
optical systems. This new method has the potential to result in significant computational savings over evaluating four-dimensional Collins formula (also known as the generalized Huygens-Fresnel integral) and even the traditional simulation approach, in which a stochastic field realization is synthesized in the source plane and then propagated through the
$ABCD$
system using fast Fourier transforms. We derive this direct synthesis method by applying Collins formula and the superposition rule for genuine partially coherent fields. We then discuss the conditions under which using it provides significant computational savings. Lastly, we demonstrate the technique by applying it to synthesize Schell-model and non-uniformly correlated random field instances at the output of a simple optical system. We compare sample moments of the field to those computed using the traditional simulation approach to validate our direct synthesis method.