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Differential interferometry for studying hypersonic flows


The purpose of this article is to describe an optical technique based on differential interferometry with strongly phase-shifted beams using a white light source and a Wollaston prism. This technique is recommonded particularly for measuring very small index variations. It has been used for analyzing hypersonic flows around slender axisymmetrical bodies. The radial gas density distributions obtained in the shock layers were compared with the analytical solutions developed by Merlen and Andriamanalina (1992) and with Jones' tabulated computations (1969).

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m :

exponent of the obstacle's power law

R, R′ :

radii of the shock and of the obstacle, respectively

R c :

radius of curvature of the spherical mirror

r :

radial coordinate

L :

obstacle length

L m :

distance from model to spherical mirror

x, y :

cartesian coordinates with origin at obstacle nose


geometric angle of incidence

ɛ :

birefringence angle of the Wollaston prism, ɛ=ɛ(λ)

λ :


τ :

relative thickness of the obstacle

θ c :

cone apex semi-angle

Y :

distance between the two partial beams at the level of the test section

n :

refractive index of the medium

E :

optical thickness

e :

test section width

σ y :

light deviation along the y axis

h :

length of the path traveled by one of the two beams through the shock layer

ϱ :

gas density

ϱ s :

gas density under standard conditions

ϱ :

freestream gas density

δ min :

minimum detectable phase difference


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Correspondence to J. M. Desse.

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Desse, J.M., Fabre, E. Differential interferometry for studying hypersonic flows. Experiments in Fluids 20, 273–278 (1996).

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  • Light Source
  • Density Distribution
  • Index Variation
  • White Light
  • Optical Technique