Abstract

A method is proposed and verified by experiments to suppress disturbing reflections in laser Doppler anemometer (LDA) measurements. Disturbing reflections occur in a variety of practical applications of LDA, such as backscatter measurements near walls or in two-phase fluid or particle velocity measurements. The method uses circularly polarized light that changes the handedness when reflected and is quenched by a suitably oriented polarization analyzer. Scattered light, however, is partially transmitted by the analyzer to give undisturbed seeding particle signals. Verification experiments have been performed to demonstrate the method; systems for practical applications are proposed.

© 1981 Optical Society of America

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  1. H. Mischina, N. S. Vlachos, J. H. Whitelaw, Appl. Opt. 18, 2480 (1979).
    [CrossRef]
  2. F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).
  3. J. A. C. Humphrey, A. Melling, J. H. Whitelaw, “Laser-Doppler-Anemometry for the Verification of Turbulence Models,” in Proceedings, Conference on Engineering Uses of Coherent Optics, Strathclyde UniversityK. J. Habell, Ed. (Cambridge U.P., London, 1975).
  4. W. Hösel, W. Rodi, “Errors occurring in LDA-Measurements with Counter Type Signal Processing,” in Proceedings, 1975 LDA Symposium, Copenhagen, P. Buchhave et al., Eds., (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).
  5. D. C. Look, T. J. Love, Investigation of the Effects of Surface Roughness Upon Reflectance, AIAA Paper 70-820 (1970).
  6. D. C. Look, AIAA J. 12, 656 (1974).
    [CrossRef]
  7. T. F. Smith, R. L. Suiter, “Bidirectional Reflectance Measurements for One-Dimensional Randomly Rough Surfaces,” at AIAA Fourteenth Thermophysics Conference1979, Orlando, Fla., AIAA Paper 70-1036.
  8. F. A. Jenkins, H. E. White, Fundamentals of Optics, Student Edition (McGraw–HillKogakusha, Tokyo, 1976).
  9. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  10. I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).
  11. J. Gardavský, J. Bok, Scattering of Circularly Polarized Light in Laser-Doppler-Anemometry, Applied Optics1981 (to be published).
  12. F. Durst, M. Zaré, “Laser Doppler Measurements in Two-Phase Flows,” in Proceedings, 1975 LDA Symposium Copenhagen, P. Buchhave et al., Eds. (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).
  13. F. Durst, “Studies of Particle Motion by Laser Doppler Techniques,” in Proceedings, 1978 Dynamic Flow Conference, Marseille and Baltimore, L. S. G. Kovashay et al., Eds. (Dynamic Flow Conference, P.O. Box 121, DK-2740 Skovlunde, Denmark).

1979 (1)

1974 (2)

D. C. Look, AIAA J. 12, 656 (1974).
[CrossRef]

I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bok, J.

J. Gardavský, J. Bok, Scattering of Circularly Polarized Light in Laser-Doppler-Anemometry, Applied Optics1981 (to be published).

Durst, F.

F. Durst, M. Zaré, “Laser Doppler Measurements in Two-Phase Flows,” in Proceedings, 1975 LDA Symposium Copenhagen, P. Buchhave et al., Eds. (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

F. Durst, “Studies of Particle Motion by Laser Doppler Techniques,” in Proceedings, 1978 Dynamic Flow Conference, Marseille and Baltimore, L. S. G. Kovashay et al., Eds. (Dynamic Flow Conference, P.O. Box 121, DK-2740 Skovlunde, Denmark).

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

Gardavský, J.

J. Gardavský, J. Bok, Scattering of Circularly Polarized Light in Laser-Doppler-Anemometry, Applied Optics1981 (to be published).

Hösel, W.

W. Hösel, W. Rodi, “Errors occurring in LDA-Measurements with Counter Type Signal Processing,” in Proceedings, 1975 LDA Symposium, Copenhagen, P. Buchhave et al., Eds., (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

Humphrey, J. A. C.

J. A. C. Humphrey, A. Melling, J. H. Whitelaw, “Laser-Doppler-Anemometry for the Verification of Turbulence Models,” in Proceedings, Conference on Engineering Uses of Coherent Optics, Strathclyde UniversityK. J. Habell, Ed. (Cambridge U.P., London, 1975).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics, Student Edition (McGraw–HillKogakusha, Tokyo, 1976).

Look, D. C.

D. C. Look, AIAA J. 12, 656 (1974).
[CrossRef]

D. C. Look, T. J. Love, Investigation of the Effects of Surface Roughness Upon Reflectance, AIAA Paper 70-820 (1970).

Love, T. J.

D. C. Look, T. J. Love, Investigation of the Effects of Surface Roughness Upon Reflectance, AIAA Paper 70-820 (1970).

Lukes, F.

I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).

Melling, A.

J. A. C. Humphrey, A. Melling, J. H. Whitelaw, “Laser-Doppler-Anemometry for the Verification of Turbulence Models,” in Proceedings, Conference on Engineering Uses of Coherent Optics, Strathclyde UniversityK. J. Habell, Ed. (Cambridge U.P., London, 1975).

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

Mischina, H.

Navrátil, K.

I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).

Ohlídal, I.

I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).

Rodi, W.

W. Hösel, W. Rodi, “Errors occurring in LDA-Measurements with Counter Type Signal Processing,” in Proceedings, 1975 LDA Symposium, Copenhagen, P. Buchhave et al., Eds., (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

Smith, T. F.

T. F. Smith, R. L. Suiter, “Bidirectional Reflectance Measurements for One-Dimensional Randomly Rough Surfaces,” at AIAA Fourteenth Thermophysics Conference1979, Orlando, Fla., AIAA Paper 70-1036.

Suiter, R. L.

T. F. Smith, R. L. Suiter, “Bidirectional Reflectance Measurements for One-Dimensional Randomly Rough Surfaces,” at AIAA Fourteenth Thermophysics Conference1979, Orlando, Fla., AIAA Paper 70-1036.

Vlachos, N. S.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics, Student Edition (McGraw–HillKogakusha, Tokyo, 1976).

Whitelaw, J. H.

H. Mischina, N. S. Vlachos, J. H. Whitelaw, Appl. Opt. 18, 2480 (1979).
[CrossRef]

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

J. A. C. Humphrey, A. Melling, J. H. Whitelaw, “Laser-Doppler-Anemometry for the Verification of Turbulence Models,” in Proceedings, Conference on Engineering Uses of Coherent Optics, Strathclyde UniversityK. J. Habell, Ed. (Cambridge U.P., London, 1975).

Zaré, M.

F. Durst, M. Zaré, “Laser Doppler Measurements in Two-Phase Flows,” in Proceedings, 1975 LDA Symposium Copenhagen, P. Buchhave et al., Eds. (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

AIAA J. (1)

D. C. Look, AIAA J. 12, 656 (1974).
[CrossRef]

Appl. Opt. (1)

Physics N.Y. (1)

I. Ohlídal, K. Navrátil, F. Lukeŝ, Physics N.Y. 16, 1 (1974).

Other (10)

J. Gardavský, J. Bok, Scattering of Circularly Polarized Light in Laser-Doppler-Anemometry, Applied Optics1981 (to be published).

F. Durst, M. Zaré, “Laser Doppler Measurements in Two-Phase Flows,” in Proceedings, 1975 LDA Symposium Copenhagen, P. Buchhave et al., Eds. (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

F. Durst, “Studies of Particle Motion by Laser Doppler Techniques,” in Proceedings, 1978 Dynamic Flow Conference, Marseille and Baltimore, L. S. G. Kovashay et al., Eds. (Dynamic Flow Conference, P.O. Box 121, DK-2740 Skovlunde, Denmark).

T. F. Smith, R. L. Suiter, “Bidirectional Reflectance Measurements for One-Dimensional Randomly Rough Surfaces,” at AIAA Fourteenth Thermophysics Conference1979, Orlando, Fla., AIAA Paper 70-1036.

F. A. Jenkins, H. E. White, Fundamentals of Optics, Student Edition (McGraw–HillKogakusha, Tokyo, 1976).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1976).

J. A. C. Humphrey, A. Melling, J. H. Whitelaw, “Laser-Doppler-Anemometry for the Verification of Turbulence Models,” in Proceedings, Conference on Engineering Uses of Coherent Optics, Strathclyde UniversityK. J. Habell, Ed. (Cambridge U.P., London, 1975).

W. Hösel, W. Rodi, “Errors occurring in LDA-Measurements with Counter Type Signal Processing,” in Proceedings, 1975 LDA Symposium, Copenhagen, P. Buchhave et al., Eds., (LDA Symposium Copenhagen 1975, P.O. Box 70, DK-2740 Skovlunde, Denmark).

D. C. Look, T. J. Love, Investigation of the Effects of Surface Roughness Upon Reflectance, AIAA Paper 70-820 (1970).

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Figures (23)

Fig. 1
Fig. 1

Modular LDA system for backscatter measurements.

Fig. 2
Fig. 2

Doppler signal of a single particle at far (a) distance from the wall and (b) small distance and (c) starting saturation at still smaller distance.

Fig. 3
Fig. 3

Counting errors for an LDA period-timing system dependent on the SNR.3

Fig. 4
Fig. 4

(a) Backscatter measurements near a window, at left. (b) Backscatter measurements near an opaque wall, at right.

Fig. 5
Fig. 5

Intensity distributions of reflected light from a wall dependent on the reflection angle β vs the incident light for varying angles of incidence ϕ (see Ref. 7). From left to right: σr = 125 μm, 400 μm, and 1250 μm: λ = 0.55 μm, sandblast brass.

Fig. 6
Fig. 6

Quenching of right-handed circularly polarized light after reflection on a flat surface (normal incidence at left, grazing incidence at right) by analyzers A, A consisting of a λ/4-retardation plate, and a linear polarizer with the indicated operations. I, I denote the transmitted light due to scattering, passing the analyzers after blocking the left- and right-handed polarized light components, respectively.

Fig. 7
Fig. 7

Ellipsometric angle ψ = tan−1(Rp/Rs)1/2 and Δ = δrpδrs as functions of the angle of incidence ϕ (degrees) (a) above: for reflection at an air–glass interface; λ = 0.5461 μm, mglass = 1.50 (b) below: for reflection at an air–gold interface; λ = 0.5461 μm, mgold = 0.35 − j2.45.

Fig. 8
Fig. 8

Dependence of the angular difference δγ = γpolγλ/4 between the settings of the linear polarizer and the λ/4-retardation plate on the angle of incidence for various surfaces.

Fig. 9
Fig. 9

Typical scattering diagram showing the polarization separated backscattering I (full curve), polarization-separated forwardscattering I (dotted curve), and scattering of linearly polarized light I (dashed curve).

Fig. 10
Fig. 10

Experimental setup for the visualization of the backscattering characteristics of the particles.

Fig. 11
Fig. 11

Scattering patterns from 1-μm silicon-oil droplets at (above) the backscattering RS-mode and (below) backscattering RT-mode.

Fig. 12
Fig. 12

Model wind tunnel with test surface at back.

Fig. 13
Fig. 13

Experimental setup for measuring the backscattered signal characteristics near a reflecting surface.

Fig. 14
Fig. 14

Typical backscattering LDA signals (at right) and the corresponding frequency spectra (at left) for the polarization reflection suppression (RS) mode.

Fig. 15
Fig. 15

SNR of backscattering signals plotted in dependence of the wall distance for reflection suppression and transmission mode and for Plexiglas and stainless steel.

Fig. 16
Fig. 16

Direct current-component of backscattering signals in dependence of the wall distance for reflection suppression and reflection transmission modes and for Plexiglas and steel.

Fig. 17
Fig. 17

Mie-scattering diagrams for one beam of linearly (I) and circularly polarized light (I) incident on a particle with m = 2.42 and increasing Mie parameter q.

Fig. 18
Fig. 18

Superimposed Mie-scattering diagrams for two beams incident on a particle with q = 11.14 and m = 2.42 for (a) linearly polarized light I and (b)–(c) circularly polarized light at increasing intersection angle 2ϕ.

Fig. 19
Fig. 19

Modular backscatter LDA systems with extension modules for polarization-separated reflectance suppression: PR = polarization rotation; BS = beam splitter; BR = double-bragg cell module; PM = photomultiplier; and LM = lens module.

Fig. 20
Fig. 20

Reflections on spherical particles: (a) spatial fringes in backscattering; (b) total reflection on a bubble; and (c) shadow region and source and sink of the fringes in forward direction for an opaque sphere.

Fig. 21
Fig. 21

Amplitude-separated Doppler signals generated by a reflecting sphere (B) swinging across an air jet with Mie particles (A).

Fig. 22
Fig. 22

Influence of reflectance from bubbles in the RT-mode (above) and the RS-mode (below). A laser beam with circular polarization is traveling from right to left through a liquid containing small bubbles.

Fig. 23
Fig. 23

Optical systems for two-phase flow signal separation by polarization-separating reflectance suppression: (a) above: for backscatter measurements, (b) below: for forwardscatter measurements.

Tables (1)

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Table I Comparison of Measured and Theoretical Increase of SNR

Equations (27)

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( 1 + y min / F ) σ 0 = y min tan ϕ - σ Z .
σ Z σ 0 = s Z s 0 = F + z F [ 1 + δ 4 A 2 B ( cos ϕ F + z - 1 F + 1 B δ ) 2 1 + δ 4 A 2 B ( cos ϕ F - 1 F + 1 B δ ) 2 ] ,
σ Z σ 0 F + z F = 1 + z F 1 + y F ,
y min 2 F F σ 0 tan ϕ - 1 cos ϕ - 1 .
y min 2 σ 0 tan ϕ .
y min l ,
I s ( t ) = I 0 exp [ - 1 2 ( u t σ 0 ) 2 ] [ 1 + η cos 2 π ( u t Δ x ) ] ,
I 0 = ( 4 P L / π σ 2 ) ( C s c / h · ν ) · η Q ,
i k 2 = 2 e I s Δ f .
SNR s = I s i k 2 = I s 2 e Δ f .
I ( t ) = I r + I s ( t ) ,
SNR r = SNR s ( 1 + I r I s ) - 1 / 2 .
[ exp ( j Δ ) tan ψ , 0 0 , 1 ] [ E x E y ] = [ E x E y ] ,
[ 1 ± j ] [ 1 j ]             at ϕ = 0 ° ,
[ 1 ± j ] [ 0 ± 1 ] at ϕ = ϕ B [ 1 ± j ] [ 1 ± 1 ] at ϕ ϕ P .
[ 1 ± j ] [ 1 ± j ]             at ϕ = 90 ° .
δ γ = γ pol - γ λ / 4 = ½ arcsin { - 2 cos Δ tan ψ + cotan ψ }
δ γ = 45 °             at ϕ = 0 °
δ γ = 180 °             at ϕ = ϕ B for dielectrics , and
δ γ = 0 °             at ϕ ϕ P for metals .
δ γ = 135 °             at ϕ = 90 °
R supp = ρ supp ρ λ = I min ( γ pol , γ λ / 4 ) I max ( γ pol + 90 , γ λ / 4 ) ,
I = I sc ( γ pol , γ λ / 4 ) ~ ( S 1 - S 2 ) 2 ,
I = I sc ( γ pol + 90 , γ λ / 4 ) ~ ( S 1 + S 2 ) 2 ,
Δ SNR = 20 log SNR RS SNR RT = 10 log ( I s + I r , RT I s + I r , RS ) ,
S = Ω 2 I 1 I 2 I 1 + I 2 sin ( 2 q sin ϕ ) 2 q sin ϕ d Ω ,
f D = 2 sin ϕ λ ( u cos β ± u sin β ) ,

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