A fractal noise approach to three-dimensional optical turbulence simulation

We present a novel approach to simulating three-dimensional (3D) atmospheric optical turbulence. Unlike methods that use a series of two-dimensional phase screens to simulate 3D turbulence, this approach does not require vacuum propagation and provides a straightforward prescription to simulate turbulence of the desired character. In this method, we generate a continuous and differentiable 3D stochastic field of refractive-index fluctuations. Our approach is based on the Perlin noise approach that is used extensively in digital animation and video game design to model turbulent phenomena, such as flames or clouds. Although Perlin noise is used to model turbulence qualitatively, it has not previously been shown that it can accurately model atmospheric turbulence. Here we show that Perlin’s approach can be made physically accurate and, in particular, that the statistical and spectral properties of the generated noise agree with an empirically validated extension of Kolmogorov theory, modified to account for a finite outer scale. We provide a method to associate physical parameters, such as <i>C²_n</i>, with the simulated turbulence, and demonstrate that it is possible to generate turbulence with a specific <i>C²_n</i> profile. Furthermore, this approach is computationally efficient and can be extended to four dimensions to simulate time-dependent fluctuations.