# Real-Time Dense Field Phase-to-Space Simulation of Imaging through Atmospheric Turbulence

arXiv: https://arxiv.org/abs/2210.06713 · HTML: https://mlsanity.com/paper/2210.06713/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2022.

## Built on by (most cited first, 16 of 16)

- [FarSight: A Physics-Driven Whole-Body Biometric System at Large Distance and Altitude](https://mlsanity.com/paper/2306.17206/) (2023)
- [Physics-Driven Turbulence Image Restoration with Stochastic Refinement](https://mlsanity.com/paper/2307.10603/) (2023)
- [Spatio-Temporal Turbulence Mitigation: A Translational Perspective](https://mlsanity.com/paper/2401.04244/) (2024)
- [Person Recognition at Altitude and Range: Fusion of Face, Body Shape and Gait](https://mlsanity.com/paper/2505.04616/) (2025)
- [Deep Learning Techniques for Atmospheric Turbulence Removal: A Review](https://mlsanity.com/paper/2409.14587/) (2024)
- [Learning Phase Distortion with Selective State Space Models for Video Turbulence Mitigation](https://mlsanity.com/paper/2504.02697/) (2025)
- [Long-range Turbulence Mitigation: A Large-scale Dataset and A Coarse-to-fine Framework](https://mlsanity.com/paper/2407.08377/) (2024)
- [Turb-Seg-Res: A Segment-then-Restore Pipeline for Dynamic Videos with Atmospheric Turbulence](https://mlsanity.com/paper/2404.13605/) (2024)
- [Diffeomorphic Template Registration for Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2405.03662/) (2024)
- [EvTurb: Event Camera Guided Turbulence Removal](https://mlsanity.com/paper/2508.10582/) (2025)
- [NeRT: Implicit Neural Representations for General Unsupervised Turbulence Mitigation](https://mlsanity.com/paper/2308.00622/) (2023)
- [Source-free Domain Adaptation for Video Object Detection Under Adverse Image Conditions](https://mlsanity.com/paper/2404.15252/) (2024)
- [Reconstructing Satellites in 3D from Amateur Telescope Images](https://mlsanity.com/paper/2404.18394/) (2024)
- [Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis](https://mlsanity.com/paper/2603.01398/) (2026)
- [Atmospheric Turbulence Removal with Video Sequence Deep Visual Priors](https://mlsanity.com/paper/2402.19041/) (2024)
- [Restore What Matters: Lessons from Joint Restoration and Recognition](https://mlsanity.com/paper/2609.13791/) (2026)

## Abstract (arXiv)

Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave propagation which splits the propagation path into many segments and propagates every pixel in each segment individually via the Fresnel integral. This repeated evaluation becomes increasingly time-consuming for larger images. As a result, the split-step simulation is often done only on a sparse grid of points followed by an interpolation to the other pixels. Even so, the computation is expensive for real-time applications. In this paper, we present a new simulation method that enables real-time processing over a dense grid of points. Building upon the recently developed multi-aperture model and the phase-to-space transform, we overcome the memory bottleneck in drawing random samples from the Zernike correlation tensor. We show that the cross-correlation of the Zernike modes has an insignificant contribution to the statistics of the random samples. By approximating these cross-correlation blocks in the Zernike tensor, we restore the homogeneity of the tensor which then enables Fourier-based random sampling. On a 512×512 image, the new simulator achieves 0.025 seconds per frame over a dense field. On a 3840 × 2160 image which would have taken 13 hours to simulate using the split-step method, the new simulator can run at approximately 60 seconds per frame.