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Published April 20, 2023 | public
Journal Article

Recovering density disturbance spectra from FLDI. Part 1


Focused laser differential interferometry (FLDI) measures the phase shift corresponding to localized fluctuations in the refractive index of a medium. The sensitivity, bandwidth, and spatial filtering properties of FLDI make it particularly suited to applications in high-speed gas flows. Such applications often require the quantitative measurement of density fluctuations, which are related to changes in the refractive index. In a two-part paper, a method is presented for the recovery of a spectral representation of density disturbances from the measured time-dependent phase shift for a particular class of flows able to be modeled using sinusoidal plane waves. The approach is based on the ray-tracing model of FLDI due to Schmidt and Shepherd [Appl. Opt. 54, 8459 (2015) [CrossRef https://opg.optica.org/ao/fulltext.cfm?uri=ao-54-28-8459&id=327392] ]. In this first part, the analytical results for FLDI response to single- and multiple-frequency plane waves are derived and validated against a numerical implementation of the instrument. A spectral inversion method is then developed and validated, including consideration for the frequency-shifting effects of any underlying convective flows. In the second part [Appl. Opt. 62, 3054 (2023) [CrossRef https://opg.optica.org/ao/fulltext.cfm?uri=ao-62-12-3054&id=529080] ], results from the present model are compared with previous exact solutions temporally averaged over a wave cycle and with an approximate method.

Additional Information

© 2023 Optica Publishing Group. The authors gratefully acknowledge and thank Prof. Joe Shepherd at Caltech for many very valuable discussions. The doctoral thesis of the lead author [23], of which this work formed a part, was partially supported by the ONR with Dr. Eric Marineau as program officer. Funding: Office of Naval Research (N00014-16-1-2503). Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. he authors have no conflicts of interest nor relevant commercial relationships to disclose.

Additional details

August 22, 2023
October 20, 2023