Focused Laser Differential Interferometry

Abstract

The focused laser differential interferometer (FLDI) is a non-imaging optical diagnostic that is sensitive to density disturbances. A distinguishing feature is reduced sensitivity away from the focal plane of its beams. The spatial resolution is sub-mm, and the temporal resolution is restricted only by photodetector bandwidth, typically > 10 MHz. These traits make FLDI particularly suited to measurements in hypervelocity ground-testing facilities, where the low densities, short time-scales, and harsh environments preclude the use of intrusive diagnostics. Line of sight integration issues associated with other optical techniques are therefore minimized, a distinct advantage for measurements in impulse facilities, where the core flow of interest is often surrounded by highly-turbulent shear layers.

The systematic design principles for single and double FLDI systems are discussed, based on ray transfer matrix analysis combined with Gaussian optics. A detailed guide is presented for the practicalities of aligning, calibrating, and operating an FLDI.

A modular numerical implementation of Schmidt and Shepherd’s FLDI ray-tracing model is developed, capable of accepting arbitrary flow-fields defined via analytical expressions, simulation coupling, or experimental datasets. This numerical implementation is used to perform the first comprehensive experimental validation of the model, using known static and dynamic phase objects. Quantitatively-accurate predictions of the response of real FLDI systems are obtained. Importantly, the spatial sensitivity of the instrument is found to be dependent on disturbance wavelength, with scaling matching that predicted analytically from the model. Propagating shock waves are used as another highly-dynamic test phase object, and it is shown that FLDI maintains its theoretical performance at sub-µs time-scales.

The validated ray-tracing model is used to develop analytical expressions for the response of FLDI to propagating plane waves, extending on the results of Schmidt and Shepherd, and Settles and Fulghum. For the first time, the inverse problem is solved for this class of flow-field, allowing the density fluctuation spectrum to be recovered quantitatively from FLDI phase shift data. This approach is validated using synthetic flow-fields with the numerical ray-tracing scheme, and is also compared with the approximate approach introduced by Parziale et al.

FLDI is used to make freestream density fluctuation measurements on two facilities: a conventional blowdown tunnel, and an expansion tube. On the conventional tunnel, a comparison is made between pitot-probe and FLDI measurements after converting both to freestream pressure fluctuation spectra. A modification of Stainback and Wagner’s theory, incorporating recent numerical results from Chaudhry et al., is used to interpret the pitot data, while the new inversion algorithm is applied to the FLDI data. Close agreement is found between the two sets of spectra, showing that accurate quantitative data can be obtained with FLDI, and used to extend spectra beyond the pitot bandwidth.

On the expansion tube, the theory of Paull and Stalker for freestream noise originating in the driver gas is investigated. Their proposed relationship between freestream density fluctuations and the primary interface sound speed ratio is not observed. Spectral banding is also absent, however this is expected due to the relatively low secondary expansion strengths.