# Simulating Anisoplanatic Turbulence by Sampling Inter-modal and Spatially Correlated Zernike Coefficients

arXiv: https://arxiv.org/abs/2004.11210 · HTML: https://mlsanity.com/paper/2004.11210/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2020.

## Built on by (most cited first, 27 of 27)

- [Accelerating Atmospheric Turbulence Simulation via Learned Phase-to-Space Transform](https://mlsanity.com/paper/2107.11627/) (2021)
- [Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Model](https://mlsanity.com/paper/2207.10040/) (2022)
- [OSDFace: One-Step Diffusion Model for Face Restoration](https://mlsanity.com/paper/2411.17163/) (2024)
- [FarSight: A Physics-Driven Whole-Body Biometric System at Large Distance and Altitude](https://mlsanity.com/paper/2306.17206/) (2023)
- [Dual Associated Encoder for Face Restoration](https://mlsanity.com/paper/2308.07314/) (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)
- [Augmentation of Atmospheric Turbulence Effects on Thermal Adapted Object Detection Models](https://mlsanity.com/paper/2204.08745/) (2022)
- [Real-World Atmospheric Turbulence Correction via Domain Adaptation](https://mlsanity.com/paper/2402.07371/) (2024)
- [A comparison of different atmospheric turbulence simulation methods for image restoration](https://mlsanity.com/paper/2204.08974/) (2022)
- [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)
- [Thermal to Visible Image Synthesis under Atmospheric Turbulence](https://mlsanity.com/paper/2204.03057/) (2022)
- [Effective Adapter for Face Recognition in the Wild](https://mlsanity.com/paper/2312.01734/) (2023)
- [Unsupervised Methods for Video Quality Improvement: A Survey of Restoration and Enhancement Techniques](https://mlsanity.com/paper/2507.08375/) (2025)
- [Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis](https://mlsanity.com/paper/2603.01398/) (2026)
- [How to Augment for Atmospheric Turbulence Effects on Thermal Adapted Object Detection Models?](https://mlsanity.com/paper/2405.06383/) (2024)
- [Turbulence Strength Cn2 Estimation from Video using Physics-based Deep Learning](https://mlsanity.com/paper/2408.16623/) (2024)
- [Broadband Wide Field of View Imaging with Computational Mirrors](https://mlsanity.com/paper/2605.00029/) (2026)
- [Impact of Atmospheric Turbulence and Pointing Error on Earth Observation](https://mlsanity.com/paper/2605.22268/) (2026)
- [D2Turb: Depth-Aware Simulation and Decoupled Learning for Single-Frame Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2605.27460/) (2026)
- [Restore What Matters: Lessons from Joint Restoration and Recognition](https://mlsanity.com/paper/2609.13791/) (2026)

## Abstract (arXiv)

Simulating atmospheric turbulence is an essential task for evaluating turbulence mitigation algorithms and training learning-based methods. Advanced numerical simulators for atmospheric turbulence are available, but they require evaluating wave propagation which is computationally expensive. In this paper, we present a propagation-free method for simulating imaging through turbulence. The key idea behind our work is a new method to draw inter-modal and spatially correlated Zernike coefficients. By establishing the equivalence between the angle-of-arrival correlation by Basu, McCrae and Fiorino (2015) and the multi-aperture correlation by Chanan (1992), we show that the Zernike coefficients can be drawn according to a covariance matrix defining the correlations. We propose fast and scalable sampling strategies to draw these samples. The new method allows us to compress the wave propagation problem into a sampling problem, hence making the new simulator significantly faster than existing ones. Experimental results show that the simulator has an excellent match with the theory and real turbulence data.