Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis

TL;DR

This work revisits the modulation transfer function (MTF) formulation and proposes a novel Exposure-Time-dependent MTF (ET-MTF) that models blur as a continuous function of exposure-time, and derives a tilt-invariant point spread function (PSF) from the ET-MTF that provides a comprehensive and physically accurate characterization of turbulence-induced blur.

Abstract

Atmospheric turbulence significantly degrades long-range imaging by introducing geometric warping and exposure-time-dependent blur, which adversely affects both visual quality and the performance of high-level vision tasks. Existing methods for synthesizing turbulence effects often oversimplify the relationship between blur and exposure-time, typically assuming fixed or binary exposure settings. This leads to unrealistic synthetic data and limited generalization capability of trained models. To address this gap, we revisit the modulation transfer function (MTF) formulation and propose a novel Exposure-Time-dependent MTF (ET-MTF) that models blur as a continuous function of exposure-time. For blur synthesis, we derive a tilt-invariant point spread function (PSF) from the ET-MTF, which, when integrated with a spatially varying blur-width field, provides a comprehensive and physically accurate characterization of turbulence-induced blur. Building on this synthesis pipeline, we construct ET-Turb, a large-scale synthetic turbulence dataset that explicitly incorporates continuous exposure-time modeling across diverse optical and atmospheric conditions. The dataset comprises 5,083 videos (2,005,835 frames), partitioned into 3,988 training and 1,095 test videos. Extensive experiments demonstrate that models trained on ET-Turb produce more realistic restorations and achieve superior generalization on real-world turbulence data compared to those trained on other datasets. The dataset is publicly available at: github.com/Jun-Wei-Zeng/ET-Turb.

Figures (13)

• Figure 1: Imaging results under atmospheric turbulence with different exposure-time. Short-exposure (e.g., 1 ms) primarily exhibits turbulence-induced tilt as turbulence state is effectively frozen. In contrast, long-exposure (e.g., 40 ms) integrates multiple turbulent states over time, resulting in significantly stronger blur.
• Figure 2: Overview of the proposed exposure-time-dependent turbulence synthesis pipeline. The exposure-time $\tau$ is treated as a continuous input parameter to both the ET-MTF and blur-width field formulations. By systematically varying $\tau$, our pipeline generates turbulence-degraded images with physically consistent blur characteristics from the input tilt image.
• Figure 3: Comparison of MTF formulations at short and long-exposure limits. ET-MTF shows a smooth evolution of the MTF as exposure-time varies between the short and long-exposure limits.
• Figure 4: Temporal evolution of turbulence degradation under Taylor's frozen-flow hypothesis in video synthesis. We construct an extended turbulence degradation field along the wind direction $\mathbf{v}_w$. Temporal correlation between frames is achieved by displacing this field over time using the shift $\frac{f \mathbf{v}_w t}{L}$.
• Figure 5: Visual comparison of turbulence mitigation results on real data for MambaTM zhang2025learning models trained on different synthetic datasets. Models trained on ET-Turb dataset produce sharper and more natural restorations with fewer artifacts compared to those trained on TMT-Dynamic zhang2024imaging dataset and ATSyn-Dynamic zhang2024spatio dataset.