Compensation for refractive-index variations in laser Doppler anemometry

Anthony B. Kehoe; Prateen V. Desai

doi:10.1364/AO.26.002582

Applied Optics
Vol. 26,
Issue 13,
pp. 2582-2591
(1987)
•https://doi.org/10.1364/AO.26.002582

Compensation for refractive-index variations in laser Doppler anemometry

Anthony B. Kehoe and Prateen V. Desai

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Anthony B. Kehoe and Prateen V. Desai, "Compensation for refractive-index variations in laser Doppler anemometry," Appl. Opt. 26, 2582-2591 (1987)

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Abstract

Techniques to compensate for index of refraction variations in the application of a laser Doppler anemometer are examined. For discontinuous plane-layered media a method of discrete elements is employed. An alternative set of equations is derived for continuous cylindrically layered media and simplified to make comparisons with available results for a single cylinder. Results of velocity measurements in a Plexiglas model of a cylindrically layered nuclear fuel assembly are presented to establish a positioning accuracy of the method to within 0.025 cm.

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Equations (27)

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x	=x coordinate of probe volume.
y	=y coordinate of probe volume.
R_p	=radius of probe volume.
R_i_,_j	=radius of a particular cylinder. i indicates the cylinder (from center outward). j indicates which radius (1 means inner radius, 2 means outer radius).
α_i_,_j_,_k	=angle that the laser beam makes with respect to the normal at the Plexiglas–water interface. i indicates the cylinder (from center outward). j indicates inner or outer radius (1 means radius, 2 means outer radius). k indicates the angle (1 means inner angle, 2 means outer angle).
ALPHW	=direction angle for the laser beam in the fluid between the outer cylinder and the Plexiglas box.
ALPHP	=direction angle for the laser beam in the Plexiglas box.
ALPH4G	=direction angle of the laser beam in the at the probe volume.
ALPHGH	=half-angle of the LDA in air.
Y1	=y coordinate of the point at which the laser beam exits the Plexiglas box.
D	=distance between the origin and the inside of the Plexiglas wall.
t	=thickness of the Plexiglas box.
ANGLE	=angle between the line from the origin through the point where the laser beam exits the outermost cylinder and the horizontal.
i	=number of cylinders.

x	=x coordinate of probe volume.
y	=y coordinate of probe volume.
R_p	=radius of probe volume.
R_i_,_j	=radius of a particular cylinder. i indicates the cylinder (from center outward). j indicates which radius (1 means inner radius, 2 means outer radius).
α_i_,_j_,_k	=angle that the laser beam makes with respect to the normal at the Plexiglas–water interface. i indicates the cylinder (from center outward). j indicates inner or outer radius (1 means radius, 2 means outer radius). k indicates the angle (1 means inner angle, 2 means outer angle).
ALPHW	=direction angle for the laser beam in the fluid between the outer cylinder and the Plexiglas box.
ALPHP	=direction angle for the laser beam in the Plexiglas box.
ALPH4G	=direction angle of the laser beam in the at the probe volume.
ALPHGH	=half-angle of the LDA in air.
Y1	=y coordinate of the point at which the laser beam exits the Plexiglas box.
D	=distance between the origin and the inside of the Plexiglas wall.
t	=thickness of the Plexiglas box.
ANGLE	=angle between the line from the origin through the point where the laser beam exits the outermost cylinder and the horizontal.
i	=number of cylinders.

Abstract

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Equations (27)

Applied Optics