A novel Bayesian approach to PDV analysis

Photon Doppler Velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the classical approach to PDV analysis, a short-time Fourier transform is used to generate a spectrogram from which the velocity history of the target is inferred. Issues with this method include choices made by the user (such as the window function), which are prone to human biases, and difficulty in quantifying uncertainties. We present a novel Bayesian method to infer the velocity, with uncertainty, directly from the PDV oscilloscope trace, negating the need to use a spectrogram for analysis. We forward-model the velocity history using a parametrized time-series, from which a synthetic PDV signal is then generated. The noise is modelled using a covariance matrix, where the standard deviation and correlations are estimated from Monte-Carlo simulations of bandpass filtered Gaussian noise. Due to the inherently periodic nature of the data this is clearly a difficult inference problem, but we find that with carefully chosen prior distributions for the model parameters we can accurately recover an injected velocity history. We validate this method using PDV data from the STAR two-stage light gas gun (Skidmore et al., submitted to PRL), recovering shock-front velocity histories in quartz that are consistent with those inferred using the classical approach, and importantly, are interpolated at early times and across regions of missing or noisy data.