Seeing through a turbulent atmosphere has been one of the biggest challenges for ground-to-ground long-range incoherent imaging systems. The literature is very rich that can be dated back to Andrey Kolmogorov in the late 40’s, followed by a series of major developments by David Fried, Robert Noll, among others, during the 60’s and 70’s. However, even though we have a much better understanding of the atmosphere today, there remains a gap from the optics theory to image processing algorithms. In particular, training a deep neural network requires an accurate physical forward model that can synthesize training data at a large scale. Traditional wave propagation simulators are not an option here because they are computationally too expensive --- a 256x256 gray scale image would take several minutes to simulate.  

In this talk, I will discuss the lessons I learned over the past few years and present some of my own work. I will start by giving a brief introduction of the classical split-step propagation model that has been the backbone of many numerical wave simulators. Then I will present two new simulators my students and I invented at Purdue:

- Collapsed phase-over-aperture model (our first-generation simulator): The idea is to compress the propagation path into a single phase-screen where each pixel on the phase screen is modeled through a Zernike expansion over the aperture. To enable spatial correlations of the aberrations, we invented a mirroring technique that brings the multi-aperture angle-of-arrival model from the image plane to the object plane. With additional numerical inventions, we offer 20x speed-up compared to the traditional split-step propagation.

- Phase-to-Space transform (our second-generation simulator): The idea is to rewrite the spatially varying steps in the first-generation model by introducing a spatially invariant basis expansion. We overcome the difficulty of translating from the Zernike coefficients to the new basis coefficients via the phase-to-space transform we invented. Our phase-to-space transform is implemented via a shallow neural network. By combining with the collapsed model, we offer 1000x speed-up compared to the traditional split-step propagation.

As an image processing / computer vision person, I will explain the turbulence physics using the language we are familiar with. I will discuss the potential benefits of the new simulators for future deep learning algorithms on this topic.