Two-point, parallel-beam focused laser differential interferometry with a Nomarski prism

Abstract

A Nomarski polarizing prism has been used in conjunction with a focused laser differential interferometer to measure the phase velocity of a density disturbance at sampling frequencies ≥ 10 M H z . Use of this prism enables the simultaneous measurement of density disturbances at two closely spaced points that can be arbitrarily oriented about the instrument’s optical axis. The orientation is prescribed by rotating the prism about this axis. Since all four beams (one beam pair at each measurement point) propagate parallel to one another within the test volume, any bias imparted by density fluctuations away from the measurement plane on the disturbance phase velocity is minimized. A laboratory measurement of a spark-generated shock wave and a wind tunnel measurement of a second-mode instability wave on a cone model in a Mach 6 flow are presented to demonstrate the performance of the instrument. High-speed schlieren imaging is used in both cases to verify the results obtained with the instrument.

A low-effort and inexpensive methodology to determine beam separation distance of multi-foci FLDI

“…Results agreed to hot-wire measurements and a velocity decay model if a certain distance from the jet exit was observed, although large uncertainties were reported. Bathel et al (2020) used a carefully adjusted D-FLDI with parallel optical axes to probe a laser-induced breakdown shock wave and a conical hypersonic boundary layer with second-mode instabilities. Measured shock wave convection velocity was in close agreement to the reference obtained from simultaneous high-speed schlieren, and with lower uncertainty.…”

“…Reasonable agreement was also verified for the velocity of the instability wavepackets, for which FLDI and high-speed schlieren were performed in different runs of the shock tunnel. Weisberger et al (2020) presented FLDI velocimetry using a novel type of arrangement, in which a multi-point line FLDI is obtained. Convection velocity of laser-induced breakdown shock waves were reported with close agreement to high-speed schlieren measurements.…”

“…The second parameter is how this distance is measured, as the quality of the obtained value is directly transferred to the velocity estimation. This was highlighted by Weisberger et al (2020) concerning their measurements using adjacent channels of a multi-point line FLDI array, which yielded uncertainties in the order of ±10% . In that same work measurements with ±0.9% uncertainty were reported when using channels from separate lines, the difference being only how the spacing between the FLDI probes was determined.…”

“…Three methods are currently established in the literature to obtain the separation distance between FLDI systems: directly imaging the beams with a beam profiler; gradually blocking the beams with a precision-controlled stopper (Weisberger et al 2020); or analyzing the system response to a lens with large focal length crossing the path of the beams (Ceruzzi and Cadou 2019).…”

“…These difficulties are minor if beam separation measurements are performed in the preparation phase of an experimental campaign, with flexible time and physical constraints. However, the FLDI has a number of flexible parameters (positioning, differentiation axis, sensitivity, beam convergence, to name a few) which may be tuned or changed in the course of the experiments, as exemplified in Weisberger et al (2020) andSiddiqui et al (2021). Such adjustments require choosing and manipulating optical components, which may change the separation distance of the FLDI systems.…”