Semi-analytic simulation of optical wave propagation through turbulence

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with one phase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.