Phase-based velocity extraction method for photonic Doppler velocimetry with potential higher time resolution

We present an extension of the [Takeda et al., J. Opt. Soc. Am. 72, 156 (1982)] phase extraction method to heterodyne photonic Doppler velocimetry applications. The method yields results equivalent to those obtained by the short-time Fourier transform (STFT), while offering potential improvements in time resolution. Unlike STFT, which relies on window functions, such as the Hamming window, that emphasize central data points and diminish the influence of edges, the extended Takeda method utilizes all data uniformly. This uniform treatment allows for the derivation of empirical equations that directly relate velocity error to the actual time resolution rather than to the local analysis duration. The established equation provides a useful metric for both optimizing hardware configuration and guiding data analysis. Simulation and experimental results confirm that, for a given dataset, specifying a target time resolution yields consistent velocity errors for both methods. These findings underscore the Takeda method's advantages, particularly its potential higher time resolution and reduced computational burden, making it a valuable tool for high-throughput applications such as laser dynamic compression experiments.