Abstract

The phases and amplitudes of all the elements of the scattering matrix for radiation scattered by microparticles are shown to be measurable by a technique which was inspired by the phase differential scattering method developed by Johnston et al. of the Experimental Pathology Group at the Los Alamos National Laboratory. The present method synthesizes a laser beam from a superposition of two coherent beams in which a small frequency offset between perpendicular polarization components has been acoustooptically introduced. The heterodyne signal in the scattered radiation is used to detect the polarimetric null obtained by a variable phase compensator and linear polarizer placed in front of the scattered intensity detector. The reciprocity theorem is used to obtain a complementary set of data to completely determine all the elements of the matrix.

© 1990 Optical Society of America

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References

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  1. R. G. Johnston, S. B. Singham, G. C. Salzman, “Phase Differential Scattering from Microspheres,” Appl. Opt. 25, 3566–3572 (1986).
    [Crossref] [PubMed]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 34.
  3. Ref. 2, p. 48.
  4. J.-P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543–546 (1985).
    [Crossref]
  5. See, for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1976), p. 306.

1986 (1)

1985 (1)

J.-P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543–546 (1985).
[Crossref]

Johnston, R. G.

Monchalin, J.-P.

J.-P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543–546 (1985).
[Crossref]

Salzman, G. C.

Singham, S. B.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 34.

Yariv, A.

See, for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1976), p. 306.

Appl. Opt. (1)

Rev. Sci. Instrum. (1)

J.-P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543–546 (1985).
[Crossref]

Other (3)

See, for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1976), p. 306.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 34.

Ref. 2, p. 48.

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Figures (1)

Fig. 1
Fig. 1

Synthesis of a dual-frequency laser beam in which orthogonal polarization components have rf offset in frequency with respect to each other: L, Ar+ laser; BC, Bragg cell; P1, P2, and P3, linear polarizers; M1 and M2, plane mirrors; BS, beam splitter; PC, phase compensator; PM, photomultiplier; T, individual isolated target microparticle.

Equations (21)

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( E ρ s E τ s ) = exp [ i k ( r - z ) ] - i k r ( S 2 S 3 S 4 S 1 ) ( E ρ i o exp ( - i ω 1 t ) E τ i o exp [ - i ( ω 2 t + δ ) ] ) .
( cos 2 α cos α sin α cos α sin α sin 2 α ) ( 1 0 0 exp ( i ψ ) ) ( E ρ s E τ s ) .
I d = ½ [ cos α E ρ s + sin α exp ( i ψ ) E τ s ] 2 .
I d = 1 / 2 E ρ i o [ cos α S 2 + sin α exp ( i ψ ) S 4 ] exp ( - i ω 1 t ) + E τ i o [ cos α S 3 + sin α exp ( i ψ ) S 1 ] exp [ - i ( ω 2 t + δ ) ] 2 .
[ cos α S 2 + sin α S 4 exp ( i ψ ) ] = A 24 exp ( - i Φ 24 ) , [ cos α S 3 + sin α S 1 exp ( i ψ ) ] = A 31 exp ( - i Φ 31 ) ,
I d = 1 / 2 E ρ i o A 24 exp [ - i ( ω 1 t + Φ 24 ) ] + E τ i o A 31 exp [ - i ( ω 2 t + Φ 31 + δ ) ] 2 ,
I d = ½ E ρ i o 2 A 24 2 + ½ E τ i o 2 A 31 2 + E ρ i o E τ i o A 24 A 31 cos [ ( ω 2 - ω 1 ) t + Φ 31 - Φ 24 + δ ]
cos α S 2 + sin α S 4 exp ( i ψ ) = 0 ,
cos α S 3 + sin α S 1 exp ( i ψ ) = 0.
S i = A i exp ( i ϕ i ) ,
ψ 1 = ϕ 2 - ϕ 4 ± π , ( A 24 = 0 ) , tan α 1 = A 2 / A 4 , ψ 2 = ϕ 3 - ϕ 1 ± π , ( A 31 = 0 ) . tan α 2 = A 3 / A 1 ,
( S 2 S 3 S 4 S 1 ) ( S 2 - S 4 - S 3 S 1 ) .
ψ 3 = ϕ 2 - ϕ 3 , tan α 3 = A 2 / A 3 , ψ 4 = ϕ 4 - ϕ 1 , tan α 4 = A 4 / A 1 .
I d / I i = cos 2 α 1 A 4 2 S 3 S 4 - S 2 S 1 2             ( A 24 = 0 ) , I d / I i = cos 2 α 2 A 1 2 S 3 S 4 - S 2 S 1 2             ( A 13 = 0 ) .
I d / I i = cos 2 α 2 A 4 2 tan α 1 exp ( i ψ 1 ) - tan α 2 exp ( i ψ 2 ) 2 .
tan 2 θ 24 = 2 A 2 / A 4 ( A 2 / A 4 ) 2 - 1 cos ( ϕ 2 - ϕ 4 ) , tan 2 θ 31 = 2 A 3 / A 1 ( A 3 / A 1 ) 2 - 1 cos ( ϕ 3 - ϕ 1 ) .
( S 2 S 3 S 4 S 1 ) ( cos ɛ - 1 sin ɛ - sin ɛ cos ɛ - 1 ) ( - ɛ S 3 ɛ S 2 - ɛ S 1 ɛ S 4 ) .
( S 2 S 3 S 4 S 1 ) = ( S 2 - S 3 - S 4 S 1 ) ,
( δ S ) = ( + ɛ S 3 - ɛ S 2 + ɛ S 1 - ɛ S 4 ) = ( - ɛ S 3 - ɛ S 2 + ɛ S 1 + ɛ S 4 ) .
( a exp ( i ψ / 2 ) i β ( a + b ) sin ( ψ / 2 ) i β ( a + b ) sin ( ψ / 2 ) b exp ( - i ψ / 2 ) ) ,
δ ψ = β ( a + b ) ( tan α a - cot α b ) sin ψ .

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