WindDensity-MBIR: Model-Based Iterative Reconstruction for Wind Tunnel 3D Density Estimation

Experimentalists often use wind tunnels to study aerodynamic turbulence, but most wind tunnel imaging techniques are limited in their ability to take non-invasive 3D density measurements of turbulence. Wavefront tomography is a technique that uses multiple wavefront measurements from various viewing angles to non-invasively measure the 3D density field of a turbulent medium. Existing methods make strong assumptions, such as a spline basis representation, to address the ill-conditioned nature of this problem. We formulate this problem as a Bayesian, sparse-view tomographic reconstruction problem and develop a model-based iterative reconstruction algorithm for measuring the volumetric 3D density field inside a wind tunnel. We call this method WindDensity-MBIR and apply it using simulated data to difficult reconstruction scenarios with sparse data, small projection field of view, and limited angular extent. WindDensity-MBIR can recover high-order features in these scenarios within 10% to 25% error even when the tip, tilt, and piston are removed from the wavefront measurements.

Boiling flow parameter estimation from boundary layer data

Atmospheric turbulence and aero-optic effects cause phase aberrations in propagating light waves, thereby reducing effectiveness in transmitting and receiving coherent light from an aircraft. Existing optical sensors can measure the resulting phase aberrations, but the physical experiments required to induce these aberrations are expensive and time-intensive. Simulation methods could provide a less expensive alternative. For example, an existing simulation algorithm called boiling flow, which generalizes the Taylor frozen-flow method, can generate synthetic phase aberration data (i.e., phase screens) induced by atmospheric turbulence. However, boiling flow depends on physical parameters, such as the Fried coherence length r0, which are not well-defined for aero-optic effects. In this paper, we introduce a method to estimate the parameters of boiling flow from measured aero-optic phase aberration data. Our algorithm estimates these parameters to fit the spatial and temporal statistics of the measured data. This method is computationally efficient and our experiments show that the temporal power spectral density of the slopes of the synthetic phase screens reasonably matches that of the measured phase aberrations from two turbulent boundary layer data sets, with errors between 8-9%. However, the Kolmogorov spatial structure function of the phase screens does not match that of the measured phase aberrations, with errors above 28%. This suggests that, while the parameters of boiling flow can reasonably fit the temporal statistics of highly convective data, they cannot fit the complex spatial statistics of aero-optic phase aberrations.

Boiling flow estimation for aero-optic phase screen generation

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.