Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis

Junwei Zeng; Dong Liang; Sheng-Jun Huang; Kun Zhan; Songcan Chen

cs.CVMar 2, 2026

Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis

Authors: Junwei Zeng, Dong Liang, Sheng-Jun Huang, Kun Zhan, Songcan Chen

Organizations: Nanjing University of Aeronautics and Astronautics · School of Information Science and Engineering, Lanzhou University

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 & tables

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.

Distance (m)	Focal length (m)	F-number	$C_{n}^{2}$ ( $10^{-14}\,\text{m}^{-2/3}$ )	Height (m)	Wind speed (m/s)	Exposure-time (ms)
[30,100]	[0.1,0.3]	{2.8,4}	[50,300]	{4,50}	[1,3]	[0.5,8]
[30,100]	[0.1,0.3]	{2.8,4,5.6}	[200,500]	{100,200}	[3,5]	[0.5,8]
[100,200]	[0.2,0.5]	{2.8,4,5.6}	[5,50]	{200,400}	[1,4]	[1,20]
[100,200]	[0.2,0.5]	{2.8,4,5.6,8}	[20,100]	{4,50}	[2,6]	[0.5,10]
[200,400]	[0.3,0.5]	{2.8,4,5.6,8}	[2,30]	{50,100}	[2,5]	[1,20]
[200,400]	[0.3,0.5]	{4,5.6,8,11}	[10,40]	{10,50}	[3,6]	[1,20]

Table 1: Parameter sampling ranges for ET-Turb dataset generation. Notation:

[a,b]

denotes uniform sampling from continuous interval;

\{v_{1},\ldots,v_{n}\}

denotes uniform sampling from discrete set. All 12 configurations are sampled with equal probability.

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 $\frac{f\mathbf{v}_{w}t}{L}$ .

Training Dataset	TSR-WGAN [ 23 ]		TMT [ 55 ]		DATUM [ 53 ]		MambaTM [ 54 ]
Training Dataset	NIQE $\downarrow$	BRISQUE $\downarrow$	NIQE $\downarrow$	BRISQUE $\downarrow$	NIQE $\downarrow$	BRISQUE $\downarrow$	NIQE $\downarrow$	BRISQUE $\downarrow$
TMT-dynamic [ 55 ]	4.231	52.502	4.361	58.581	4.219	54.921	4.217	55.062
ATSyn-dynamic [ 53 ]	4.224	54.462	4.483	59.707	4.308	59.126	4.247	56.876
ET-Turb	4.190	50.981	4.221	56.691	4.204	54.070	4.212	55.050

Table 2: Quantitative comparison of turbulence mitigation models trained on different synthetic datasets and evaluated on real turbulence data. Models trained on ET-Turb dataset achieve consistently lower NIQE and BRISQUE scores (lower is better), confirming superior realism and generalization capability compared to TMT-Dynamic [ 55 ] dataset and ATSyn-Dynamic [ 53 ] dataset.

Panel of Figure 5 — Figure 5: Visual comparison of turbulence mitigation results on real data for MambaTM [ 54 ] 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 [ 55 ] dataset and ATSyn-Dynamic [ 53 ] dataset.

Panel of Figure 6 — Figure 6: Visual ablation study on exposure modeling strategies for real turbulence restoration. The continuous ET-MTF formulation produces more natural textures and stable structures compared to fixed or binary exposure approaches.

Exposure Strategy	NIQE $\downarrow$	BRISQUE $\downarrow$
ET-Turb ( $\tau=1$ ms)	4.355	55.457
ET-Turb (MTF ${}_{\text{SE/LE}}$ )	4.297	55.123
ET-Turb (MTF ${}_{\text{ET}}$ )	4.212	55.050

Table 3: Ablation study on exposure modeling strategies within the ET-Turb synthesis pipeline. Comparing fixed (

\tau=1

ms), binary (MTF

{}_{\text{SE/LE}}

), and continuous (MTF

{}_{\text{ET}}

) exposure formulations demonstrates that continuous modeling yields the best perceptual quality on MambaTM [ 54 ] .

Panel of Figure 7 — Figure 7: ET-Turb-Real dataset composition: multi-camera systems and diverse scene distribution. Real-world turbulence data is collected across three different imaging devices, providing comprehensive coverage of diverse environmental and anthropogenic scenes such as urban landscapes, entertainment venues, industrial infrastructure, traffic scenarios, and commercial establishments.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Method	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
TSR-WGAN [ 23 ]	18.90	0.5927	0.5608
TMT [ 55 ]	24.97	0.7507	0.3807
DATUM [ 53 ]	22.85	0.6436	0.4700
MambaTM [ 54 ]	23.77	0.6658	0.4490

Appendix

Table 4: Quantitative evaluation on the ET-Turb test set. TMT [ 55 ] achieves the best performance across all metrics, highlighting the effectiveness of its component-wise training strategy.

	Trained on ET-Turb			Trained on ATSyn-Dynamic [ 53 ]
Method	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Noise-input	20.57 (↓1.36%)	0.58 (↓9.38%)	0.57 (↑16.33%)	20.57 (↓1.36%)	0.58 (↓9.38%)	0.57 (↑16.33%)
TMT [ 55 ]	21.22 (↓0.38%)	0.66 (↓1.49%)	0.51 (↑2.21%)	21.19 (↓0.42%)	0.66 (↓2.94%)	0.51 (↑2.37%)
DATUM [ 53 ]	22.43 (↓0.80%)	0.61 (↓4.69%)	0.51 (↑2.89%)	22.14 (↓1.07%)	0.62 (↓7.46%)	0.53 (↑8.16%)
MambaTM [ 54 ]	22.12 (↓1.07%)	0.64 (↓1.54%)	0.52 (↑4.49%)	22.10 (↓1.34%)	0.63 (↓4.55%)	0.52 (↑8.33%)

Appendix

Table 5: Robustness evaluation under exposure-dependent Gaussian noise added to the ET-Turb test set. Models trained on ET-Turb and ATSyn-Dynamic [ 53 ] are compared.

	$r_{0}$ ±10%			wind speed within 10-20m/s
Method	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Input	20.71 (↓0.07%)	0.78 (↓0.14%)	0.34 (↑0.25%)	20.43 (↓0.51%)	0.76 (↓2.07%)	0.36 (↑1.88%)
TMT [ 55 ]	21.20 (↓0.06%)	0.83 (↓0.14%)	0.33 (↑0.12%)	20.83 (↓0.82%)	0.80 (↓1.19%)	0.36 (↑2.22%)
DATUM [ 53 ]	22.27 (↓0.11%)	0.79 (↓0.17%)	0.33 (↑0.18%)	21.75 (↓0.87%)	0.76 (↓1.48%)	0.36 (↑2.37%)
MambaTM [ 54 ]	21.57 (↓0.06%)	0.78 (↓0.13%)	0.36 (↑0.00%)	21.19 (↓0.60%)	0.75 (↓1.23%)	0.38 (↑1.99%)

Appendix

Table 6: Sensitivity analyses with respect to

r_{0}

and wind speed. The Fried parameter

r_{0}

is perturbed by

\pm

10%, while wind speed is increased from the training range (1–10 m/s) to 10–20 m/s.

Figure 8: Text recognition accuracy on the turbulence-text dataset [ 55 ] , evaluated using ASTER [ 44 ] .

Figure 9: Brightness distribution statistics of ET-Turb.

Methods	Hardie	Chimitt	Lau	P2S	Ours
Sec./frame	119.63	5.88	3.13	0.35	3.24

Appendix

Table 7: Processing time for a

256^{2}

frame.

Panel of Figure 11 — Figure 11: Visualization of the turbulence synthesis pipeline across six parameter configurations. Each row corresponds to a distinct set of physical parameters from Tab. 11 . The columns show: (a) original undistorted image, (b) tilt with color-coded displacement field, (c) exposure-dependent blur, and (d) final synthesized turbulence combining both degradation components.

Panel of Figure 12 — Figure 12: Generation of turbulent images under varying intensities and exposure-time using our data synthesis method. As the exposure-time and turbulence intensity increase, the degree of blur becomes more pronounced. The associated parameter set is distance = 500 m, focal length = 300 mm, F-number = 8, height = 50 m, and wind speed = 5 m/s.

Panel of Figure 13 — Figure 13: Real-world turbulence mitigation results. Models trained on ET-Turb dataset demonstrate strong generalization to real atmospheric turbulence, successfully restoring fine details such as text and license plates while maintaining varying degrees of color fidelity.

Panel of Figure 14 — Figure 14: Qualitative comparison of state-of-the-art turbulence mitigation methods trained on ET-Turb dataset. Each row corresponds to a specific method, showing results from two representative test scenes (left and right).

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