Abstract
Noncontact optical methods (e.g., shadowgraphy, schlieren, and interferometry) allow visualization of propagating shock waves, avoid sensor-field interaction, and retain the potential for very high bandwidth. The heterodyne Mach-Zehnder interferometer produces quantifiable noncontact samples of the accumulated phase shifts induced by a shock wave, as viewed through its beam projection. This instrument is commercially available as a Laser Doppler Vibrometer (LDV). For shocked wave fields in air obeying spherical symmetry, point values for density and overpressure can be inferred. An important shortcoming for inference quality is the finite spatial dependence of the probe beam cross section, the profile shape itself serving to limit both the spatial resolution and the measurement bandwidth. We propose to model both of these effects of spatial averaging by constructing a model waveform and a model beam profile, convolving them, and comparing the result to synthesized LDV output. Mismatch between the convolved result and spatially averaged measurement can be quantified by a cost function, which is minimized via gradient descent.
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