Fig. 1. Basic schematic of photonic Doppler velocimetry (PDV).

Fig. 2. (a) Simulated raw PDV signal with Gaussian noise of 10% of the beats amplitude (black), and normalized PDV signal (blue). The signal represents a starting frequency of −10 GHz with a sudden change to 3 GHz at 1.5 ns, followed by a slow decrease in frequency and an exponential decrease in target signal intensity. (b) Simulated intensity data with Gaussian noise (magenta), and smoothed intensity data (dark yellow). (c) Short-time Fourier transform (STFT) of simulated signal loses most of the intensity by 2.5 ns (within ∼1 ns of the change), and the frequency profile obtained from finding the maximum intensity at each time-point fluctuates. (d) STFT of normalized signal shows that most of the intensity is kept up to 3.5 ns (an additional 1 ns compared to the raw signal) and that the obtained frequency profile does not fluctuate significantly.

Fig. 3. Schematic of PDV.

Fig. 4. Target alignment setup.

Fig. 5. Shot EOS3-S09. (a) Raw PDV signal collected from a 40-µm Au foil (black), and normalized PDV signal (blue, shifted). The reference channel was set to start with beats of 1.16 GHz. (b) Measured intensity data (magenta) and smoothed intensity data (dark yellow). Note that a different detector was used for the intensity measurement and hence the difference in voltage scales (c) STFT of raw PDV signal (using a Hann window of 1 ns and 1500 bins) loses almost all of the intensity by 1 ns, and the frequency profile (red) obtained from finding the maximum intensity at each time-point fluctuates. Dark red represents values above the set upper limit. (d) STFT of normalized signal shows that enough intensity is kept up to ∼2 ns (an additional 1 ns compared to the raw signal) and that the obtained frequency profile does not fluctuate significantly. Note that the beats of the initial frequency of 1.16 GHz are spaced apart at intervals very close to the 1 ns of the FFT window, resulting in slightly different contributing frequencies at different window positions, which leads to fluctuations in the frequency with the most significant contribution, even following normalization. The reported initial frequency value was obtained using a fit to a duration of several nanoseconds. It is possible to use a wavelet transform instead of an STFT to prevent fluctuations in low-frequency contributions.

Fig. 6. Shot EOS3-S15. (a) Raw PDV signal collected from a 20-µm Au foil (black), and normalized PDV signal (blue, shifted). The reference channel was set to start with beats of −1.02 GHz. (b) Measured intensity data (magenta) and smoothed intensity data (dark yellow). Note that a different detector was used for the intensity measurement and hence the difference in voltage scales (c) STFT of raw PDV signal (Hann window of 1 ns, with 1500 bins) loses almost all of the intensity by ∼0.55 ns, and the frequency profile (red) obtained from finding the maximum intensity at each time-point fluctuates. Dark red represents values above the set upper limit. (d) STFT of normalized signal has better intensity up to ∼0.75 ns (an additional 0.2 ns compared to the raw data), and the signal fluctuates significantly less. Note that the beats of the initial frequency of 1.02 GHz are spaced apart at intervals very close to the 1 ns of the FFT window, resulting in slightly different contributing frequencies at different window positions, which leads to fluctuations in the frequency with the most significant contribution, even following normalization. Without normalization, we observe a frequency above 2 GHz, which is an artifact of the FFT window [other frequencies can also be seen in panel (c)].

Fig. 7. STFT of EOS3-S09 using a sliding window of 512 data points (4 ns) following (a) normalization by a smoothed intensity measurement, (b) normalization by the raw intensity measurement, and (c) no normalization. White represents values above the set maximum value. Red lines are the maximum contribution to the frequency at each time and represent the frequency profile.

Fig. 8. STFT of EOS3-S15 using a sliding window of 512 data points (4 ns) following (a) normalization by a smoothed intensity measurement, (b) no normalization, and (c) removal of the DC component. White represents values above the set maximum value. Red lines are the maximum contribution to the frequency at each time and represent the frequency profile.

Fig. 9. Frequency profile obtained for EOS3-S15 using a sliding window of 512 data points (4 ns) following normalization (black) compared to following removal of the DC signal (blue).