# Precision and Accuracy in PDV and VISAR

## Abstract

This is a technical report discussing our current level of understanding of a wide and varying distribution of uncertainties in velocity results from Photonic Doppler Velocimetry in its application to gas gun experiments. Using propagation of errors methods with statistical averaging of photon number fluctuation in the detected photocurrent and subsequent addition of electronic recording noise, we learn that the velocity uncertainty in VISAR can be written in closed form. For PDV, the non-linear frequency transform and peak fitting methods employed make propagation of errors estimates notoriously more difficult to write down in closed form expect in the limit of constant velocity and low time resolution (large analysis-window width). An alternative method of error propagation in PDV is to use Monte Carlo methods with a simulation of the time domain signal based on results from the spectral domain. A key problem for Monte Carlo estimation for an experiment is a correct estimate of that portion of the time-domain noise associated with the peak-fitting region-of-interesting in the spectral domain. Using short-time Fourier transformation spectral analysis and working with the phase dependent real and imaginary parts allows removal of amplitude-noise cross terms that invariably show up when working with correlation-based methods ormore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1389994

- Report Number(s):
- LLNL-TR-737609

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 47 OTHER INSTRUMENTATION; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
Ambrose, W. P.
```*Precision and Accuracy in PDV and VISAR*. United States: N. p., 2017.
Web. doi:10.2172/1389994.

```
Ambrose, W. P.
```*Precision and Accuracy in PDV and VISAR*. United States. doi:10.2172/1389994.

```
Ambrose, W. P. Tue .
"Precision and Accuracy in PDV and VISAR". United States. doi:10.2172/1389994. https://www.osti.gov/servlets/purl/1389994.
```

```
@article{osti_1389994,
```

title = {Precision and Accuracy in PDV and VISAR},

author = {Ambrose, W. P.},

abstractNote = {This is a technical report discussing our current level of understanding of a wide and varying distribution of uncertainties in velocity results from Photonic Doppler Velocimetry in its application to gas gun experiments. Using propagation of errors methods with statistical averaging of photon number fluctuation in the detected photocurrent and subsequent addition of electronic recording noise, we learn that the velocity uncertainty in VISAR can be written in closed form. For PDV, the non-linear frequency transform and peak fitting methods employed make propagation of errors estimates notoriously more difficult to write down in closed form expect in the limit of constant velocity and low time resolution (large analysis-window width). An alternative method of error propagation in PDV is to use Monte Carlo methods with a simulation of the time domain signal based on results from the spectral domain. A key problem for Monte Carlo estimation for an experiment is a correct estimate of that portion of the time-domain noise associated with the peak-fitting region-of-interesting in the spectral domain. Using short-time Fourier transformation spectral analysis and working with the phase dependent real and imaginary parts allows removal of amplitude-noise cross terms that invariably show up when working with correlation-based methods or FFT power spectra. Estimation of the noise associated with a given spectral region of interest is then possible. At this level of progress, we learn that Monte Carlo trials with random recording noise and initial (uncontrolled) phase yields velocity uncertainties that are not as large as those observed. In a search for additional noise sources, a speckleinterference modulation contribution with off axis rays was investigated, and was found to add a velocity variation beyond that from the recording noise (due to random interference between off axis rays), but in our experiments the speckle modulation precision was not as important as the recording noise precision. But from these investigations we do appreciate that the velocity-uncertainty itself has a wide distribution of values that varies with signal-amplitude modulation (is not a single value). To provide a rough rule of thumb for the velocity uncertainty, we computed the average of the relative standard deviation distributions from 60 recorded traces (with distributions of uncertainties roughly between 0.1 % to 1 % in each trace) and found a mean of the distribution of uncertainties for our experiments is not better than 0.4 % at an analysis window width of 5 ns (although for brief intervals it can be as good as 0.1 %). Further imagination and testing may be needed to reveal other possible hydrodynamics-related sources of velocity error in PDV.},

doi = {10.2172/1389994},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2017},

month = {8}

}