# Tilt-then-Blur or Blur-then-Tilt? Clarifying the Atmospheric Turbulence Model

arXiv: https://arxiv.org/abs/2207.06377 · HTML: https://mlsanity.com/paper/2207.06377/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2022.

## Built on by (most cited first, 17 of 17)

- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [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)
- [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)
- [Double Blind Imaging with Generative Modeling](https://mlsanity.com/paper/2503.21501/) (2025)
- [Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis](https://mlsanity.com/paper/2603.01398/) (2026)
- [Optical aberrations in autonomous driving: Physics-informed parameterized temperature scaling for neural network uncertainty calibration](https://mlsanity.com/paper/2412.13695/) (2024)
- [GSTurb: Gaussian Splatting for Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2602.22800/) (2026)
- [High-Quality and Efficient Turbulence Mitigation with Events](https://mlsanity.com/paper/2603.20708/) (2026)

## Abstract (arXiv)

Imaging at a long distance often requires advanced image restoration algorithms to compensate for the distortions caused by atmospheric turbulence. However, unlike many standard restoration problems such as deconvolution, the forward image formation model of the atmospheric turbulence does not have a simple expression. Thanks to the Zernike representation of the phase, one can show that the forward model is a combination of tilt (pixel shifting due to the linear phase terms) and blur (image smoothing due to the high order aberrations). Confusions then arise between the ordering of the two operators. Should the model be tilt-then-blur, or blur-then-tilt? Some papers in the literature say that the model is tilt-then-blur, whereas more papers say that it is blur-then-tilt. This paper clarifies the differences between the two and discusses why the tilt-then-blur is the correct model. Recommendations are given to the research community.