The theory, design, and use of a focusing laser differential interferometer (FLDI) instrument are described. The FLDI is a relatively simple, nonimaging, common-path polarization interferometer for measuring refractive signals generated by turbulence, as well as small-amplitude acoustics and boundary-layer instabilities. It has in principle a unique ability to look through wind-tunnel windows, ignore sidewall boundary-layers and vibration, and concentrate only on the refractive signal near a pair of sharp beam foci in the core flow. The instrument's low cost and ease of implementation make it a promising alternative to traditional hot-wire anemometry (HWA) and particle-based methods for turbulence characterization. A matrix equation is written for the overall optical behavior of the FLDI, and transfer functions are developed to account for spatial filtering, f/number of the field lenses, various turbulence profiles, etc. Benchtop experiments using a turbulent sonic airjet demonstrate the focusing ability of the FLDI, its frequency response, and unwanted signal rejection. The instrument is also used to optically interrogate the flow in the Penn State Supersonic Wind Tunnel and in USAF AEDC Hypervelocity Tunnel 9, where it made preliminary measurements of freestream disturbance levels and power spectra. A central feature of the FLDI used here is the replacement of traditional fixed Wollaston birefringent prisms with variable Sanderson prisms for separation and recombination of the helium–neon laser beams, and for the accurate setting of micrometer-range beam separation distances required for successful turbulence measurements. The instrument also features phase compensation of the output, where perpendicularly polarized light signals are separately sensed by the twin photodetectors. This provides a unique ability to measure the coherence of turbulent spectra and thus to reject low-coherence noise.
On the Use of Hot-Wire Anemometers for Turbulence Measurements in Clouds