Optical-Axis Spatial Sensitivity of a Simulated Focused Laser Differential Interferometer

Abstract

A focused laser differential interferometer (FLDI) simulation was used to study the sensitivity of the FLDI technique to a variety of factors. The model takes in a series of density fields and computes the FLDI beam phase difference in response to those fields. For pure sinusoidal signals of finite width, the frequency was found to have no effect on the computed FLDI response below the photodetector threshold. The signal wavelength, however, has a direct correlation with FLDI amplitude; peak amplitude was achieved with a wavelength of double the FLDI beam separation when measured at the focal points. The ability of the FLDI to suppress signals away from the foci of the beams was observed. Simulated narrow-nozzle jet results using a large-eddy simulation were compared to an experimental test with good agreement. The jet simulation was then used to study the effects of varying the beam separation and profile diameter on the FLDI sensitivity falloff, with smaller beam spacing and larger profiles away from the foci corresponding to shorter optical-axis sensitivity lengths.

Displacement of hypersonic boundary layer instability and turbulence through transpiration cooling

“…Several recent publications discussed the depth-of-field of FLDI in more detail with some particularly focusing on its ability to penetrate turbulent environments around an object of interest. 70,74,76,77 All those sources reveal dependencies of the depth-of-field on the frequency, wavelength, and amplitude of density disturbances within the probed flowfield. Therefore, additional post-processing steps need to added to investigate the performance of the Oxford FLDI system as it is not possible to simply compare the FWHM of the sensitivity at 300 kHz to the beam-wise width of the boundary layer.…”

“…4(a), as the FLDI's response depends on both parameters. 70,74,76,77 A 300 kHz frequency correspond to k % 1:1 mm sound wavelength at standard conditions, whereas the second mode wavelength is around 2.5 mm in the relevant tunnel flow, 42 rendering the FWHM from the Gaussian fit above imprecise. Ceruzzi and Cadou 74 present an overview of a transfer function for FLDI systems, by reproducing and combining work from Parziale et al 70,78 and Schmidt and Shepherd.…”

“…This value is typically between 3 and 10 lm for other FLDI setups in the literature. 74,77,79,80 Using this value, we calculate the transfer function and evaluate it at k ¼ 2:5 mm, which predicts the FLDI depth-of-field at the relevant second mode frequency. It is plotted as the green curve in Fig.…”

“…In contrast, the beam separation is considerably larger at 168 lm. Benitez et al 77 warn how fluctuations with k > 1 mm are "integrated across the length of the beam," 77 when analyzing another set of simulation cases. They however also report that a smaller beam separation reduces the depth-of-field, albeit at the cost of total responsiveness.…”

“…They however also report that a smaller beam separation reduces the depth-of-field, albeit at the cost of total responsiveness. 77 With respect to line integration, the Oxford FLDI should exhibit more favorable characteristics than the setup simulated by Benitez et al 76,77 Furthermore, the noise spectrum of HDT does contain significantly less signal power around 300 kHz. Should, however, high frequency content at millimeter scale wavelengths be present around the nozzle core-flow, it is likely recorded to some extent by our FLDI setup.…”