New transform to project axisymmetric deflection fields along arbitrary rays

Abstract

Axisymmetric tomography is used to extract quantitative information from line-of-sight measurements of gas flow and combustion fields. For instance, background oriented schlieren (BOS) measurements are typically inverted by tomographic reconstruction to estimate the density field of a high-speed or high-temperature flow. Conventional reconstruction algorithms are based on the inverse Abel transform, which assumes that rays are parallel throughout the target object. However, camera rays are not parallel, and this discrepancy can result in significant errors in many practical imaging scenarios. We present a generalization of the Abel transform for use in tomographic reconstruction of light-ray deflections through an axisymmetric target. The new transform models the exact path of camera rays instead of assuming parallel paths, thereby improving the accuracy of estimates. We demonstrate our approach with a simulated BOS scenario in which we reconstruct noisy synthetic deflection data across a range of camera positions. Results are compared to state-of-the-art Abel-based algorithms. Reconstructions computed using the new transform are consistently more stable and accurate than conventional reconstructions.

Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS

“…For axisymmetric flows, we employ a Sipkens deflectometry operator [40], which is specified in Appendix A. For planar fields, we directly approximate Eq.…”

“…Neither axial gradients in the flow nor axial deflections are considered in the inversion. Therefore, inverting a high-fidelity 2D forward model like the unified BOS matrix is more robust [25,40].…”

“…By way of context, well-instrumented cones support up to 16 taps [74], and a typical field-ready design has no taps at all. Since real schlieren data is LoS-integrated and camera rays may diverge in the measurement volume [40,75], particularly when access windows are required for imaging, we restrict our tests to plausible synthetic data and real experimental images.…”

“…Typically, these functions are uniform, linear, or quadratic in BOS tomography. Following Sipkens et al [40], we utilize a uniform discretization scheme in the axial direction and a linear scheme in the radial direction.…”

“…Both techniques yield a kernel, K, that relates δ y to a radial density field, ρ. Separately, the Sipkens kernel, derived in [40], is a discrete forward operator that relaxes the assumption of parallel rays. Sipkens et al [40] developed the transform for a variety of bases; we utilize the linear-uniform basis introduced above.…”