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Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis

Conference: CVPR 2026
arXiv: 2603.01398
Code: Available
Area: Scientific Computing
Keywords: Atmospheric Turbulence Synthesis, Exposure-Time Modeling, Modulation Transfer Function (MTF), Point Spread Function (PSF), Turbulence Image Restoration

TL;DR

Ours proposes the Exposure-Time dependent Modulation Transfer Function (ET-MTF), modeling exposure time as a continuous variable. A large-scale synthetic turbulence dataset, ET-Turb (5,083 videos, 2 million frames), is constructed, significantly improving the generalization of turbulence restoration models on real-world data.

Background & Motivation

Atmospheric turbulence introduces geometric distortion (tilt) and exposure-time-related blur through random fluctuations in the refractive index, severely affecting long-range imaging applications such as remote sensing, video surveillance, and astronomical observation. The performance of learning-based methods highly depends on the realism of training data, yet acquiring large-scale paired real-world turbulence data is extremely expensive, making synthetic datasets essential.

Existing synthesis methods suffer from coarse handling of exposure time:

  • Fixed Exposure: Many methods use a single exposure setting for all samples, resulting in uniform blur statistics that fail to reflect temporal variability in real imaging.
  • Binary Exposure: Some methods only distinguish between "Short Exposure" (SE) and "Long Exposure" (LE) modes using \(\text{MTF}_{\text{SE}}\) and \(\text{MTF}_{\text{LE}}\), ignoring the smooth transitions occurring at intermediate exposure times.
  • Physical Simulation: Devices like gas stoves are limited by short optical paths, and multi-step phase screen methods involve massive computational overhead.

These limitations lead to a significant domain gap between synthetic data and real turbulence, restricting the generalization of trained models.

Method

Overall Architecture

The paper models turbulence degradation as \(I(\mathbf{x}) = \mathcal{B}_\tau(\mathcal{T}(J(\mathbf{x})))\): first applying an exposure-time-independent geometric tilt operator \(\mathcal{T}\) to the clean image \(J\) to obtain a tilt image \(I_T\), then applying an exposure-time-dependent blur operator \(\mathcal{B}_\tau\). While tilt follows existing random displacement field modeling, the contribution focuses on making \(\mathcal{B}_\tau\) continuously vary with exposure time, vary with spatial position, and extend to video.

The blur synthesis pipeline consists of four core designs: ① Deriving the Exposure-Time dependent MTF (ET-MTF) from Azoulay’s finite exposure theory, connecting the discrete "SE/LE" states into a continuous knob; ② Blur width reparameterization of ET-MTF, replacing the Fried parameter \(r_0\) with local blur width \(\omega\) to introduce a pixel-wise spatial dimension; ③ Using a spatially varying blur width field \(\mathcal{W}(\mathbf{x},\tau)\), constrained by optical turbulence statistics, to assign local \(\omega\) and perform pixel-wise convolution; ④ Employing Taylor’s Frozen Flow for inter-frame correlation modeling to extend single frames into coherent videos. Finally, this pipeline generates the ET-Turb dataset.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Clean Image J(x) → Geometric Tilt<br/>Exposure-independent, yields tilt image I_T"]
    A --> C["ET-MTF<br/>MTF continuous in exposure time τ"]
    C --> D["Blur Width Reparameterization<br/>Replace r₀ with ω to add spatial dimension"]
    D --> E["Pure Blur PSF<br/>Inverse Fourier of ET-MTF (tilt-removed)"]
    F["Spatially Varying Blur Width Field W(x,τ)<br/>Physically-constrained random field, assigns ω pixel-wise"] --> E
    E --> G["Pixel-wise Convolution B_τ<br/>Yields single-frame degraded image"]
    G --> H["Inter-frame Correlation Modeling<br/>Translation by wind via Taylor's Frozen Flow"]
    H --> I["ET-Turb Video Dataset"]

Key Designs

1. Exposure-Time dependent MTF (ET-MTF): Turning the binary "SE vs LE" switch into a continuous knob

Existing methods only provide extremal states \(\text{MTF}_{\text{SE}}\) and \(\text{MTF}_{\text{LE}}\), leaving intermediate exposures without a physical model or relying on empirical interpolation. This work returns to Azoulay’s finite exposure MTF theory using the concept of effective coherence length \(\rho_p(\tau)\). In SE, turbulence is almost "frozen" within the aperture \(D\); in LE, the sensor accumulates multiple states, equivalent to an aperture "stretched" by wind to \(D + v_w \tau\). The MTF is:

\[\text{MTF}_{\text{ET}}(\boldsymbol{\xi}, \tau) = e^{-\left(\frac{\lambda \|\boldsymbol{\xi}\|}{\rho_p(\tau)}\right)^{5/3}}, \qquad \rho_p(\tau) = 1 + 0.35 \left(\frac{r_0}{D + v_w \tau}\right)^{1/3}\]

where \(r_0\) is the Fried parameter, \(v_w\) is wind speed, and \(\boldsymbol{\xi}\) is spatial frequency. As \(\tau\) increases, the effective aperture grows, \(\rho_p(\tau)\) smoothly decreases, and high-frequency attenuation accelerates—making the transition from weak to strong blur continuous and physically grounded.

2. Blur Width Reparameterization: Making the MTF vary spatially and temporally

Since \(\rho_p(\tau)\) only depends on \(\tau\), the entire image would have uniform blur intensity. Real turbulence blur is spatially non-uniform due to local refractive index fluctuations. To introduce the spatial dimension, the authors define local blur width \(\omega \approx \frac{0.49 \lambda f}{r_0}\) using PSF Full-Width at Half-Maximum (FWHM). Solving for \(r_0\) and substituting it back:

\[\rho_p(\omega, \tau) = 1 + 0.28 \left(\frac{\lambda f}{\omega(D + v_w \tau)}\right)^{1/3}\]

After reparameterization, ET-MTF is determined by both local blur width \(\omega\) (space) and exposure time \(\tau\) (time), making \(\omega\) a pixel-wise adjustable "blur knob."

3. Spatially Varying Blur Width Field: Upgrading scalar \(\omega\) to a physically-constrained random field

The blur width is modeled as a spatially correlated random field \(\mathcal{W}(\mathbf{x}, \tau)\), with mean and standard deviation constrained by optical turbulence theory:

\[\mathcal{W}(\mathbf{x}, \tau) = \max\!\big(\epsilon,\; \bar{\omega}(\tau) + \sigma_\omega(\tau)\, \mathcal{R}(\mathbf{x})\big)\]

where \(\bar{\omega}(\tau)\) and \(\sigma_\omega(\tau)\) are functions of \(\tau\), and \(\mathcal{R}(\mathbf{x})\) is a zero-mean, unit-variance Gaussian random field processed by a low-pass filter to ensure smooth transitions. The final spatially varying blur operation applies the local PSF to the tilt-corrected image:

\[\mathcal{B}_\tau(I_T(\mathbf{x})) = \text{PSF}_{\text{ET}}(\mathbf{x}, \mathcal{W}(\mathbf{x}, \tau), \tau) * I_T(\mathbf{x})\]

This enables the synthetic images to exhibit realistic "clear foreground, blurry background, and local fluctuations" characteristics within a single frame.

4. Inter-frame Correlation Modeling: Extending single frames to videos via Taylor's Frozen Flow

To ensure temporal consistency, Taylor’s Frozen Flow hypothesis assumes a quasi-static refractive index field translated by mean wind:

\[\mathcal{H}(J_t(\mathbf{x})) = \mathcal{H}\!\left(J_0\!\left(\mathbf{x} - \frac{f \mathbf{v}_w t}{L}\right)\right)\]

By sampling from a degradation field larger than the frame and translating the window according to wind direction, the method generates temporally correlated frames with consistent drifting effects.

Loss & Training

The core contribution is dataset construction. ET-Turb includes 12 configurations covering various optical and atmospheric conditions:

  • Parameter Space: Distance 30-1000m, focal length 0.1-1m, F-number 2.8-24, \(C_n^2\) from \(0.5 \times 10^{-14}\) to \(300 \times 10^{-14}\) m\(^{-2/3}\), wind speed 1-10 m/s, exposure time 0.5-40ms.
  • Scale: 5,083 videos, 2,005,835 frames (3,988 training / 1,095 testing).
  • Real Data: ET-Turb-Real contains 74 videos from 3 different imaging devices.

Key Experimental Results

Main Results

Evaluation of models trained on different synthetic datasets using real-world turbulence (no-reference metrics, lower is better):

Training Dataset TSR-WGAN NIQE↓ TSR-WGAN BRISQUE↓ TMT NIQE↓ TMT BRISQUE↓ DATUM NIQE↓ DATUM BRISQUE↓ MambaTM NIQE↓ MambaTM BRISQUE↓
TMT-dynamic 4.231 52.502 4.361 58.581 4.219 54.921 4.217 55.062
ATSyn-dynamic 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

ET-Turb achieved the best results in 7 out of 8 evaluations (4 models × 2 metrics).

Ablation Study

Comparison of exposure modeling strategies (using MambaTM):

Exposure Strategy NIQE↓ BRISQUE↓
Fixed Exposure τ=1ms 4.355 55.457
Binary MTF_SE/LE 4.297 55.123
Continuous ET-MTF 4.212 55.050

Key Findings

  1. Fixed exposure models struggle to restore strong blur as they lack exposure variation in training data.
  2. Binary MTF models show improvement but retain residual blur, indicating insufficient coverage of intermediate exposures.
  3. Continuous ET-MTF yields the most natural and visually consistent results, proving the necessity of continuous modeling.
  4. Models trained on ET-Turb avoid common artifacts like text distortion or utility pole warping seen with other datasets during zero-shot transfer to real data.

Highlights & Insights

  1. Physical Modeling Elegance: Naturally bridges SE/LE MTF via the intuitive "effective aperture = physical aperture + wind × exposure" concept.
  2. Reparameterization Trick: Swapping \(r_0\) for \(\omega\) elegantly introduces spatial variability.
  3. Dataset Design: Systematic sampling of 12 configurations × 7 physical parameters covers real-world diversity better than random sampling.
  4. Rational Evaluation: Testing on real data with no-reference metrics avoids the circular reasoning of testing synthetic data with synthetic models.

Limitations & Future Work

  1. Taylor’s Frozen Flow validity is limited to short exposure scales and might fail in extreme conditions.
  2. Only isotropic turbulence is considered; real near-ground atmospheres may be anisotropic.
  3. Synthetic data lacks other effects like scattering or chromatic dispersion.
  4. Exposure time is limited to 0.5-40ms; ultra-long exposures (e.g., astronomy) may require different modeling.
  5. Future work could integrate learnable exposure scheduling for end-to-end degradation-aware training.

Rating

⭐⭐⭐⭐ 4/5

Solid physical modeling contribution to the specialized field of turbulence synthesis. ET-MTF derivation is grounded in physics, and the dataset is well-designed with thorough validation (cross-validation across 4 SOTA models). The minor drawback is the focus on data/simulation rather than architectural innovation, with metric improvements (NIQE 4.297→4.212) being subtle despite clear visual gains.