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

Karl J. Weisenburger, Gregery T. Buzzard, Charles A. Bouman, Matthew R. Kemnetz

Abstract

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.

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

Abstract

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.
Paper Structure (21 sections, 14 equations, 15 figures, 1 table)

This paper contains 21 sections, 14 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodologies
  3. Physical Model
  4. Reconstruction Algorithm
  5. Using Non-Ideal Tip-tilt Removed Optical Path Difference
  6. Simulation and Validation Procedure
  7. Atmospheric phase volume generation
  8. Simulating OPL and tip-tilt removed OPD measurements
  9. Resolution reduction and conventions for error analysis
  10. Zernike expansion
  11. Results
  12. Comparison to Scale-Corrected FBP
  13. Reconstruction Error Analysis
  14. Error as a function of viewing geometry
  15. Zernike expansion error analysis
  16. ...and 6 more sections

Figures (15)

  • Figure 1: Notional depiction of a wind tunnel wavefront tomography set up.
  • Figure 2: Overhead view of (a) the geometry with the fewest views and narrowest angular extent and (b) the geometry with the most views and widest angular extent.
  • Figure 3: Schematic showing the depth axis relative to the location of the windows. The red shaded region designates range of possible view angles.
  • Figure 4: Example depiction of the integration process for reducing the resolution along the depth axis to 3 OPL planes. The windows in Fig. \ref{['Fig: Depth axis']} correspond to the left and right ends of this volume. The red cylinder represents our chosen reconstruction ROI, i.e., the path of the central beam.
  • Figure 5: The first 45 Zernike modes ordered by radial degree.
  • ...and 10 more figures