Boiling flow estimation for aero-optic phase screen generation

TL;DR

This work addresses the need for scalable, realistic aero-optic phase-screen data by extending the computationally efficient boiling-flow model to aero-optics with anisotropy. It introduces a data-driven parameter-estimation pipeline to fit boiling-flow parameters $L_0$, $r_0$, and anisotropy $\gamma_0$, along with flow velocity $\mathbf{v}$ and flow-coefficient $\alpha$, to measured phase screens, enabling synthetic data generation of arbitrary length. The authors demonstrate isotropic estimation against simulated data, achieving TPS matches within roughly 12% and low structure-function errors, and show anisotropic estimation on measured data improves 2D structure-function fidelity by capturing elliptical spatial correlations, though TPS fidelity may lag. Overall, the approach provides a flexible, low-cost pathway to generate aero-optic phase screens that reproduce key temporal and spatial statistics, with tunable fidelity between temporal and spatial aspects, suitable for training and benchmarking disturbance-mitigation algorithms.

Abstract

Aero-optic effects due to turbulence can reduce the effectiveness of transmitting light waves to a distant target. Methods to compensate for turbulence typically rely on realistic turbulence data, which can be generated by i) experiment, ii) high-fidelity CFD, iii) low-fidelity CFD, and iv) autoregressive methods. However, each of these methods has significant drawbacks, including monetary and/or computational expense, limited quantity, inaccurate statistics, and overall complexity. In contrast, the boiling flow algorithm is a simple, computationally efficient model that can generate atmospheric phase screen data with only a handful of parameters. However, boiling flow has not been widely used in aero-optic applications, at least in part because some of these parameters, such as r0, are not clearly defined for aero-optic data. In this paper, we demonstrate a method to use the boiling flow algorithm to generate arbitrary length synthetic data to match the statistics of measured aero-optic data. Importantly, we modify the standard boiling flow method to generate anisotropic phase screens. While this model does not fully capture all statistics, it can be used to generate data that matches the temporal power spectrum or the anisotropic 2D structure function, with the ability to trade fidelity to one for fidelity to the other.

Figures (11)

• Figure 1: Outline of the boiling flow algorithm as used in this paper. Starting with a time series of measured phase screens $\phi_n$, our method estimates the boiling flow parameters and decomposes the data into the weighted sum of a boiling component and a flow component. The method then uses these components and the parameters to generate synthetic phase screens using boiling flow. We introduce the parameter $\gamma_0$ into the boiling model to produce spatially anisotropic correlations.
• Figure 2: Left: Estimation of the boiling parameters $(L_0, r_0)$. We set $\hat{L}_0$ to the aperture length in meters. We then do per-frequency scaling by $(r_0(\bm{f}))^{-5/3}$ of the unit-scale Von Kárman PSD to match the spatial PSD of the measured data. Then we average over frequencies to obtain $\hat{r}_0$. Right: Instead of regarding $r_0$ as a length scale, we interpret it as a scaling parameter for the spatial PSD of phase screens. Smaller $r_0$ corresponds to larger variance of the phase screens.
• Figure 3: Left: Estimation of the flow velocity $\bm{v}$. Given a time-lag $T$, we find $\bm{v}$ to maximize the correlation between $\phi_n$ and Flow$(\phi_{n-T}; T \bm{v})$, then average $\bm{v}(T)$ over $T$ between 1 and $T_{\max}$. Right: Uncertainty in the time-shift $T$. Small values of $T$ yield imprecise estimates of the flow velocity due to limited data and numerical ill-conditioning, while large $T$ yield inaccurate estimates due to the decorrelation induced by boiling.
• Figure 4: Estimation of the flow-coefficient $\alpha$. The expected inner product between boiling $B_n$ and flow $F_n$ is 0, so we estimate the flow-coefficient $\alpha$ by projecting the data onto the 1D span of $F_n$. In practice, we do this projection in Fourier space since $F_n$ is computed in Fourier space, and we make use of all times steps $n$.
• Figure 5: Top: Relative errors of the flow velocity estimates for various image sizes, ground-truth values of $\alpha$ (horizontal axis), and physical velocity (color). Note that the errors are generally smallest for (1) large ground-truth values of $\alpha$ (less boiling relative to flow), (2) large ground-truth flow speeds (larger pixel displacements per time step), and (3) large images. The errors are below 10% in the majority of cases. Bottom: Relative errors of the flow-coefficient estimates $\hat{\alpha}$ for various image sizes and ground-truth values of $\alpha$. Note that the errors are smallest for large ground-truth values of $\alpha$ (less boiling relative to flow) and are slightly lower for larger image sizes. Importantly, the errors remain below 4% in all cases.