Theoretical framework of PDV spectral modeling and direct inversion in high-speed particle diagnostics

Photon Doppler velocimetry (PDV) for high-speed particles has gained significant attention due to its non-contact real-time diagnostic advantage and wide range of applications. This study establishes a theoretical framework linking PDV spectra to optical thickness distributions in high-speed particle fields. Through powder impact experiments with known particle states and Monte Carlo light transport simulations, we demonstrate that PDV spectral distributions are governed by particle optical thickness. The proposed model incorporates multiple scattering effects, resolving spectral underestimation issues in prior Simple Diffusion Model. A direct inversion method enables optical thickness retrieval via spectral intensity integration, validated against Asay foil diagnostics with ±30% error for time-averaged spectra and -58% to +42% error for instantaneous spectra. Compared to conventional fitting strategies exhibiting higher uncertainty (-40% to +322% error) and failure on instantaneous spectra, the inversion method shows superior robustness. The framework advances real-time diagnostics for high-speed particle scenarios including impact damage, spray combustion, space debris monitoring, and extreme ultraviolet lithography.