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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 14 — Jul. 7, 2008
  • pp: 10372–10383
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Partial polarization of light induced by random defects at surfaces or bulks

Claude Amra, Myriam Zerrad, Laure Siozade, Gaelle Georges, and Carole Deumié  »View Author Affiliations


Optics Express, Vol. 16, Issue 14, pp. 10372-10383 (2008)
http://dx.doi.org/10.1364/OE.16.010372


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Abstract

Partial polarization may be the result of a scattering process from a fully polarized incident beam. It is shown how the “loss of polarization” is connected with the nature of scatterers (surface roughness, bulk heterogeneity) and on the receiver solid angle. These effects are theoretically predicted and confirmed via multiscale polarization measurements in the speckle pattern of rough surfaces. “Full” polarization can be recovered when reducing the receiver aperture.

© 2008 Optical Society of America

1. Introduction

Polarization is a classical property of light that has led to numerous principles, components and systems in the optics community. In most situations, one can attribute a polarization behaviour to any deterministic micro-object, which describes how the incident polarization state is modified by the interaction of light and matter. However this is mainly true for specular and diffracted waves, while it remains a great range of applications where the random nature of scatterers is responsible for a “loss of polarization” [1

1. J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics”, J. Biomed.Opt. 7, 307 (2002). [CrossRef] [PubMed]

], most often called partial polarization or depolarization. Though these phenomena were extensively studied, they still constitute a key limitation to numerous optical techniques involving ellipsometry [2

2. D. J. L. Graham, A. S. Parkins, and L. R. Watkins, “Ellipsometry with polarisation-entangled photons,” Opt. Express 14, 7037–7045 (2006). [CrossRef] [PubMed]

], optical microscopy [3

3. M. J. R. Previte and C. D. Geddes, “Fluorescence microscopy in a microwave cavity,” Opt. Express 15, 11640–11649 (2007). [CrossRef] [PubMed]

] and imaging in random media [4

4. J. Moreau, V. Loriette, and A. -C. Boccara, “Full-Field Birefringence Imaging by Thermal-Light Polarization-Sensitive Optical Coherence Tomography. I. Theory,” Appl. Opt. 42, 3800–3810 (2003). [CrossRef] [PubMed]

]…

In two recent papers [5

5. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

, 6

6. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

] the polarization properties of the scattered light were used to build a far field procedure for the selective cancellation of scattering sources. The technique was shown to be successful when considering low-level scattering from polished surfaces or slightly heterogeneous bulks, but a key limitation appeared for arbitrary rough or inhomogeneous samples that scatter the total incident light. Such limitation is the result of partial polarization connected with the presence of microscopic irregularities at the samples under study. Therefore the aim of this work is to:

  • specify which kind of irregularities is responsible for the polarization loss
  • derive a relationship able to quantify partial polarization versus the random nature of roughness or bulk
  • bring solutions to generalize the cancellation procedure to arbitrary scattering samples

2. Basic principles

2-1 Polarization of a plane wave

Within the framework of classical electromagnetism, polarization is basically defined in the case of a parallel and monochromatic light beam. Let us denote by E(ρ) the complex electric field associated with a plane wave (Fig. 1):

E(ρ)=A(σ)exp[jk(σ).ρ]
(1)

with A the vector complex amplitude, ρ=(r,z) =(x,y,z) the space coordinates, k the wave vector and σ the spatial pulsation:

k=[σ,α(σ)]σ=(σx,σy)
(2-a)
α(σ)=(k2σ2)0.5k=2πnλ
(2-b)

In Eq. (2), λ and n designate the illumination wavelength and the refractive index of the propagation medium, and σ the modulus of spatial pulsation (σ=|σ|). The propagation angles (Fig. 1) are derived in the far field (σ<k) from the spatial pulsation as:

σ=σ(cosϕ,sinϕ)σ=ksinθα=kcosθ
(3)

with θ and ϕ the normal and polar angles, respectively.

Fig. 1. Propagation angles (θ,ϕ) of a retrograde plane wave in the far field, with the associated wave vector k and spatial pulsation σ

Because the vector amplitude A lies in a plane perpendicular to the wave vector (Fig. 2), it can be splitted into two polarization vector components:

A=AS+AP
(4-a)

whose tangential projections are given in the (u,v) plane as:

AS=ASv(σ)
(4-b)
AP,tg=AP,tgu(σ)
(4-c)
with:u(σ)=σσandv(σ)=(1σ)dσdϕ
(5)
and:AS=ASexp(jδS)andAP=APexp(jδP)
(6)

where S and P designate the transverse electric (TE) and magnetic (TM) modes.

Fig. 2. Transverse electric (S) and magnetic (P) polarization modes with respect to the wave vector k and normal z. The tangential P mode is also drawn.

At this step the real (physical) electric field is given by:

E(ρ,t)=Re[E(ρ)exp(jωt)]=
[AScos(ωtk.ρδS),APcos(ωtk.ρδP)]
(7)

with ω the temporal pulsation and t the time parameter. Therefore at a given location ρ the field direction is constant when δSP, in which case polarization is said to be linear. In other situations (δ=δSP≠0), rotation of the field occurs in the plane perpendicular to the wave vector, and polarization is said to be elliptic. The case of non polarized (natural) light is traditionally addressed with δ as a random variable within the interval (0,2π).

2-2 Measurements procedure

Consider now an ellipsometric procedure to measure the polarization state of a polarized plane wave. The basic idea consists in aligning the S and P modes in order to reach an algebric or interferential sum of the two polarizations. Such projection A’ is obtained when the beam passes through an analyzer at angular position ψ from the S direction:

A=AScosψ+APsinψ
(8)

with ψ≠0 or π/2, so that the resulting measurable intensity will be proportional to:

I(ψ)=AS2cos2ψ+AP2sin2ψ+2sinψcosψASAPcosδ
(9)

Now a rotating analyzer allows to record the whole I’(ψ) curve whose analysis provides the key polarization parameters that are δ and |AP/AS|. In the case |AS|=|AP|, the contrast of the curve is given by 2cosδ, which constitutes a signature of the polarized interference (Fig. 3). Other techniques allow accurate analysis of polarization, in particular those involving specific devices to modulate the incident polarization. Most often with these techniques Eq. (9) is unchanged but a time function η(t) is added to the polarimetric phase term δ, which creates several harmonics in the resulting field.

Fig. 3. Resulting intensity versus rotation angle of the analyzer (see text)

2-3 Procedure limits

However such procedure does not a priori allow to detect partial polarization of light, since any reduction of the measured contrast (2cosδ) will be attributed to a lower δ’ value of the polarimetric phase. In the case where δ is a random variable, Eq. (9) provides an apparent phase term given by cosδ’=<cosδ>, with cosδ’=0 in the extreme case of natural light (no variation of I’ versus ψ angle if |AS|=|AP|). Mueller matrices [7

7. T. Novikova, A. De Martino, P. Bulkin, Q. Nguyen, B. Drévillon, V. Popov, and A. Chumakov, “Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction,” Opt. Express 15, 2033–2046 (2007). [CrossRef] [PubMed]

] have been used to solve this point, but here we limit ourselves to a deterministic approach. One should also notice a key property of polarized light that consists in the possibility to cancel it via destructive interferences. Such extinction can be reached thanks to a retardation plate introduced on the beam, which turns Eq. (8) and (9) into:

A=ASexp(jηS)cosψ+APexp(jηP)sinψ
(10)
I(ψ)=AS2cos2ψ+AP2sin2ψ+2sinψcosψASAPcos(δ+η)
(11)

3. Polarization of a wave packet

Let us consider the case of a monochromatic spatial wave packet E(ρ) in the far field (Fig. 4):

E(ρ)=σA(σ)exp[jk(σ).ρ]dσ=σÊ(σ,z)exp[jσ.r]dσ
(12)

Eq. (12) is a general expression for the harmonic field in a homogeneous medium; it is based on the assumption of the existence of a transverse (r=> σ) Fourier Transform Ê(σ,z) of the field, which is valid for waves of finite spatial extension. Therefore the field given in Eq. (12) can be the far field result of a diffraction or scattering process. Since Maxwell equations offer rigorous solutions to these optical interactions, each elementary component Ê(σ,z) under the integral (12) is a “fully” polarized plane wave provided that the original (incident) field is fully polarized. Therefore all polarization parameters δ(σ) and r(σ)=|AP/AS|(σ) can be theoretically derived from the knowledge of the sample under illumination. Strictly speaking, the phase difference δ(σ) will be characteristic of the elliptic or linear polarization of the Fourier component Ê(σ,z) at infinity in the far field.

Fig. 4. Retrograde wave packet and sensor

3.1 Measurements procedure

Here we analyze the measurement procedure to investigate the polarization state of the wave packet E. Measurements at a finite distance involve a solid angle ΔΩ in which the polarization parameters δ(σ) and r(σ) should not vary in order to be able to define a polarization state in a classical way. If it is not the case, the angular frequency or angular variations create an averaging process within the receiver solid angle ΔΩ, resulting in an apparent “loss” of polarization. To investigate and quantify this effect, we first write the wave packet after passing through the analyzer, as an algebric sum on the analyzer axis:

E*(ρ)=σA*(σ)exp[jk(σ).ρ]dσ
(13-a)
A*(σ)=AS(σ)cosψ+AP(σ)sinψ
(13-b)

In Eq. (13) we have neglected the influence of incidence (θ,ϕ) on the analyzer plate, which limits us to slight solid angles (less than a few degrees) that are currently used in experiment.

In a second step we calculate the Poynting flux F of the packet E* which is carried within the receiver. For this purpose we limit the frequency support Δσ of integral (13) to spatial frequencies that give rise to scattering angles collected in the far field within the receiver solid angle. After direct analytical calculation, this flux can be expressed as:

F=(4π22ωμ)Δσα(σ)A*(σ)2dσ
(14-a)
α(σ)=Real[α(σ)]
(14-b)

Such formula recalls the zero contribution of the evanescent waves (high frequencies: σ>k⇔α’=0) in the energy balance within a non absorbing medium, in opposition to plane waves that carry energy in the far field (low frequencies: σ<k⇔α’≠0). Coming back to Eq. (13-b), we obtain:

F=(4π22ωμ)[cos2ψΔσα(σ)AS(σ)2dσ
+sin2ψΔσα(σ)AP(σ)2dσ+X]
(15)

with X the interferential term given as:

X=2sinψcosψΔσα(σ)AS(σ)AP(σ)cos[δ(σ)]dσ
(16)

In a last step we use a similarity with Eq. (9) given for a plane wave by the introduction of parameter β, so that:

F(ψ)=cos2ψFS+sin2ψFP+2βsinψcosψ(FSFP)0.5
(17)
FS=(4π22ωμ)Δσα(σ)AS(σ)2dσ
(18-a)
FP=(4π22ωμ)Δσα(σ)AP(σ)2dσ
(18-b)
β=(4π22ωμ)[1(FSFP)0.5]Δσα(σ)AS(σ)AP(σ)cos[δ(σ)]dσ
(19)

Eq. (17) allows to determine the polarization parameters β and FS/FP of the wave packet in a way similar to that of plane waves.)

3-2 Equivalent or apparent polarization

Eq. (17) is specific of the interference between the polarization states of the wave packet. It permits to analyze the polarization measurement of the packet within a given receiver solid angle. In regard to the case of a plane wave (see Eq. (9)), the difference in the variation of the resulting F(ψ) curve lies in the presence of the β parameter that replaces the cosδ term of the plane wave. However we notice, thanks to the Schwartz inequality, that:

β1=>β=cosδ*
(20)

so that measurements will provide an equivalent phase term δ*. In case of low variations of parameters within integrals (18–19), we obtain δ*=δ specific of a plane wave. But in the general case, depending on solid angle and the random nature of scatterers further discussed in the text, the equivalent phase δ*≠δ will be the result of an averaging process.

One point to discuss now concerns the existence or not of an equivalent polarization for the wave packet, with δ* as a specific signature. In section 2–3 we have seen that a key property of polarized light lies in the possibility to cancel it via destructive interferences of its polarization modes, what was performed with a retardation plate in relation (10–11) relative to a plane wave. Such property is crucial to offer selective cancellation of scattering in random media [5

5. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

,6

6. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

]. Hence consider that the wave packet has also passed a retardation plate similar to that of section 2. As for the analyzer, we neglect the influence of incidence on this plate, so that the unique term modified in Eq. (17–19) is the interferential term X proportional to parameter β, that must be rewritten as:

β=(4π22ωμ)[1(FSFP)0.5]Δσα(σ)AS(σ)AP(σ)cos[δ(σ)+η]dσ
(21)

By comparison with Eq. (19), the phase term δ(σ) has been replaced by δ(σ)+η, with η the tunable phase delay. When the angular variations can be neglected in the integral (21), we obtain a relationship similar to that of a plane wave (see section 4–1), and zero values of intensity can again be obtained provided that the condition δ+η=(2n+1)π is fulfilled. In all other situations, extinction of the field cannot be reached, due to the constant η value in opposition to the variable phase term δ(σ). In other words, the extreme values ±1 cannot be reached by parameter β in the general case of a wave packet with high angular polarization variations. The result is that the ellipsometric zeros of the intensity curve F(ψ,η) will be replaced by minima. Therefore equivalent polarization cannot here be introduced, and the equivalent phase δ* will be said to be characteristic of partial polarization.

Such major difference (zeros replaced by minima) with polarized light constitutes the limit of our cancellation technique based on destructive interferences between polarization modes [5

5. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

]. However a solution can be found in the reduction of solid angle to values ΔΩ0 that allow to neglect the variations of parameters δ(σ) and r(σ) within the integrals, so that “full” polarization can be recovered. The correlation length of scatterers will be responsible for the minimum value ΔΩ0.

4- Defect-induced partial polarization

In this section we show that low-scattering levels cannot create partial polarization, in opposition to high scattering levels.

4-1 The case of low-scattering levels

Low scattering levels can be predicted with perturbative theories. These theories are valid for samples that are slightly inhomogeneous at their surfaces or in their bulk. This is currently the case of polished surfaces that scatter an amount of the incident light much lower than specular reflection. Several works [8–10

8. J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–19 (1983). [CrossRef] [PubMed]

] have been devoted to first-order electromagnetic theories and predict the scattered field Ed to be proportional to the Fourier Transform ĝ(σ) of defects, with g(r) the surface topography (case of surface scattering) or the relative variations in the bulk permittivity (case of volume scattering). These theories have shown successful results when the ratio of roughness to wavelength, or the root mean square of bulk heterogeneity, is much less than unity [9

9. C. Amra, C. Grezes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–503 (1993). [CrossRef] [PubMed]

].

Due to this proportionality relationship (Ed~ĝ(σ)), it is immediate to show that the polarimetric phase term δ(σ) does not depend on the microstructure of the scattering sample:

EdS(σ)=CS(σ)ĝ(σ),EdP(σ)=CP(σ)ĝ(σ)
=>δ(σ)=Arg(EdSEdP)=Arg[CS(σ)CP(σ)]
(22)

This result has been used to cancel first-order scattering without any knowledge of the sample microstructure [6

6. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

], thanks to the fact that the CSorP optical coefficients are connected with polarization, refractive index, wavelength and incidence…, but not on microstructure. Moreover, these coefficients exhibit low variations versus scattering angle in the whole range (0°, 90°) [5

5. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

], which can therefore be neglected within the receiver solid angle. As a consequence, Eq. (17–19) can be rewritten with a retardation plate as:

FS=(4π22ωμ)αCS2Δσĝ(σ)2dσ
(23-a)
FP=(4π22ωμ)αCP2Δσĝ(σ)2dσ
(23-b)
β=(4π22ωμ)[1(FSFP)0.5]αCSCPcosδΔσĝ(σ)2dσ
(23-c)

with γ(σ)=(4π2/S)|ĝ(σ)|2 the roughness or permittivity spectrum of defects, and S the illuminated area on the sample.

As a consequence, the resulting flux F is now given by:

{(4π22ωμ)α[Δσĝ(σ)2dσ]}1F=
cos2ψCS2+sin2ψCP2+2sinψcosψcos(δ+η)CSCP
(24)

This last relation shows that cancellation of the flux can still be reached, with a polarimetric behaviour similar to that of a plane wave (see Eq. (9)). Hence the polarization can here be clearly and classically defined, for which reason we conclude that low-level scattering cannot be responsible for partial polarization.

4.2 Arbitrary scattering levels

4.3 Comparison with Stokes formalism

S0=<AS2+AP2>,S1=<AS2AP2>
(25-a)
S2=2<ASAPcosδ>,S3=2j<ASAPsinδ>
(25-b)

With these Stokes components introduced, Eq. (9) can be rewritten as:

2<I(ψ)>=S0+S1cos2ψ+S2sin2ψ
(26)

One can also define the linear polarization degree as:

ρL=(1S0)[S12+S22]0.51
(27)

d=(1+ρL)(1ρL)
(28)

Finally, the parameter β of Eq. (19) can also be expressed with the Stokes parameters as:

β=S2[S02S12]0.51
(29)

This dimensionless parameter tends to unity when the light is totally polarized.

5- Experimental data on rough surfaces

For each sample we recorded the far field scattering speckle versus the rotation angles of analyzer (angle ψ) and quarterwave plates (τ angle). Hence the procedure allowed us to extract maxima Fmax and minima Fmin for each pixel or collection of pixels of the sensor. For the sake of simplicity, we will be focused on the dynamic d=Fmax/Fmin of the data rather that on the phase term δ that can be derived from the whole F(ψ,τ) curve.

5-1 Case of a polished surface

The first sample was a polished black glass that scatters light at its front surface. Its level of total scattering (a few 10-4) is specific of first-order scattering. The scattering speckle is given in figure 5, for a 2080×2600 µm2 field view. Since the measurement distance is 50cm from the sample, the angular aperture Δθ is 0.30° for the whole sensor field.

The left figure was recorded when the analyzer and quarterwave plates are matched to reach a maximum average signal (over all pixels) with a grey level of 160. The right figure is approximately recorded for the minimum signal (here in the noise) whose grey level is taken to the value 10. Therefore the dynamic (d) of the measurements, defined as the ratio of maximum to minimum, is greater than 16 (d>16). This contrast value of the F(ψ,τ) curve is characteristic of polarized light, as predicted in section 4-1 for slightly inhomogeneous samples. However the investigation is here limited by the performances of the sensor; strictly speaking we should be able to reach the dynamic value that is currently measured with crossed analyzer and polarizer on a specular beam (d≈200). Actually we have at disposal 256 grey levels and a noise level of 10, so that the dynamic is limited to 25 in the best case. Varying the integration time did not allow to improve this point.

One key point in Fig. 5 is that all pixels are simultaneously cancelled, for which reason we did not investigate additional average effects. This is in accordance with relation (24) specific of first-order scattering, which predicts the same reduction for all pixels when the two plates are rotated. Such result recalls why selective imaging can be performed in a large solid angle with a unique matching [6

6. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

] of the analyzer and quarterwave plates.

Fig. 5. Maximum (left) and minimum (right) average signals measured for the speckle of a polished black glass (see text). The field view is 2080×2600µm2

5-2 Case of an arbitrary rough surface: multiscale polarization data

The second sample scatters all the incident light with an angular lambertian distribution. It is a metallic (Au) etalon used for calibration, whose scattering originates from roughness [12

12. O. Gilbert, C. Deumié, and C. Amra, “Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks,” Opt. Express 13, 2403–2418 (2005). [CrossRef] [PubMed]

]. The speckle pattern was again measured at 50 cm and is given in figure 6, with a field view of 2500×2020 µm2.

Fig. 6. Speckle pattern of a metallic lambertian sample (see text) measured for an arbitrary position of analyzer and quarterwave plates. The field view is 2500×2020 µm. The circled zone is studied in figure 7.

  • The first zone (1) is circled in red in Fig. 6 and can be seen on the left of Fig. 7. The field view is 780×1155 µm2, which corresponds to an angular aperture (Δθ) of 0.13°.
  • The second zone (2) is included in zone (1), and appears at the middle of Fig. 7. The field view is 165×300 µm2, which corresponds to an angular aperture (Δθ) of 0.034°.
  • The third zone (3) is included in zone (2), and appears at the right of Fig. 7. It is related to one pixel (5×5µm2), which corresponds to an angular aperture (Δθ) of 5.7 10-4°.

Such procedure permits to address a multiscale study of polarization, that is, polarization versus solid angle.

Fig. 7. Multiscale measurements of the speckle pattern of figure 6 (see text). 3 zones are investigated and are fitted into each other

For each zone (1, 2 and 3) we have measured the average signal variations I(ψ,τ) versus the rotation angles of analyzer (Δψ=2°) and quarterwave plates (Δτ=2°). The results are given in figure 8.

Fig. 8. Variations for each zone (1–3) of the average polarimetric signal versus rotation angles of quarterwave (horizontal unit) and analyzer (vertical units) plates. Left figure is for zone 1, middle figure is for zone 2 and right figure is for zone 3 (see text).

Table 1:. Angular aperture and dynamic for each zone (see text)

table-icon
View This Table

In Fig. 9 (a, b, c) we give the pictures recorded for each zone at the minima and the maxima average signals. The left, middle and right figures are respectively for zones 1, 2 and 3. For each zone the top picture is for the maximum signal, and the bottom picture is for the minimum signal. We observe as predicted that the pictures obtained for the minima are different for each zone.

Fig. 9. Pictures recorded for each zone at minima and maxima values of the average signal (see text).

6- Conclusion

Recent results [5

5. C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

, 6

6. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

] allowed us to address the field of imaging in random media via a selective cancellation procedure of scattering sources. The procedure was derived from what could be called an advanced ellipsometric imaging in the scattering pattern. However though the technique revealed successful performances for slightly inhomogeneous media, key limitations were emphasized in the case of arbitrary scattering samples, due to partial or total depolarization.

In this paper we showed that scattering processes of a polarized incident beam do not create partial polarization in the classical sense. What we observe is an average process of polarization states over the receiver solid angle, that can be quantified versus solid angle and correlation length of scatterers. An analytical formula was given to investigate these effects that were shown not to lead to an equivalent polarization, but that can be interpreted as partial polarization.

References and links

1.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics”, J. Biomed.Opt. 7, 307 (2002). [CrossRef] [PubMed]

2.

D. J. L. Graham, A. S. Parkins, and L. R. Watkins, “Ellipsometry with polarisation-entangled photons,” Opt. Express 14, 7037–7045 (2006). [CrossRef] [PubMed]

3.

M. J. R. Previte and C. D. Geddes, “Fluorescence microscopy in a microwave cavity,” Opt. Express 15, 11640–11649 (2007). [CrossRef] [PubMed]

4.

J. Moreau, V. Loriette, and A. -C. Boccara, “Full-Field Birefringence Imaging by Thermal-Light Polarization-Sensitive Optical Coherence Tomography. I. Theory,” Appl. Opt. 42, 3800–3810 (2003). [CrossRef] [PubMed]

5.

C. Amra, C. Deumié, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005). [CrossRef] [PubMed]

6.

G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007). [CrossRef] [PubMed]

7.

T. Novikova, A. De Martino, P. Bulkin, Q. Nguyen, B. Drévillon, V. Popov, and A. Chumakov, “Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction,” Opt. Express 15, 2033–2046 (2007). [CrossRef] [PubMed]

8.

J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–19 (1983). [CrossRef] [PubMed]

9.

C. Amra, C. Grezes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–503 (1993). [CrossRef] [PubMed]

10.

S. Kassam, A. Duparre, K. Hehl, P. Bussemer, and J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–13 (1992). [CrossRef] [PubMed]

11.

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: Theoretical analysis”, Optics Communications , Volume 281, Issue 6, 15 March 2008, Pages1739–1744. [CrossRef]

12.

O. Gilbert, C. Deumié, and C. Amra, “Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks,” Opt. Express 13, 2403–2418 (2005). [CrossRef] [PubMed]

OCIS Codes
(120.6150) Instrumentation, measurement, and metrology : Speckle imaging
(240.5770) Optics at surfaces : Roughness
(260.2110) Physical optics : Electromagnetic optics
(260.2130) Physical optics : Ellipsometry and polarimetry
(290.5820) Scattering : Scattering measurements
(290.5825) Scattering : Scattering theory

ToC Category:
Scattering

History
Original Manuscript: January 2, 2008
Revised Manuscript: March 7, 2008
Manuscript Accepted: March 21, 2008
Published: June 27, 2008

Citation
Claude Amra, Myriam Zerrad, Laure Siozade, Gaelle Georges, and Carole Deumié, "Partial polarization of light induced by random defects at surfaces or bulks," Opt. Express 16, 10372-10383 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-14-10372


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References

  1. J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002). [CrossRef] [PubMed]
  2. D. J. L. Graham, A. S. Parkins, and L. R. Watkins, "Ellipsometry with polarisation-entangled photons," Opt. Express 14, 7037-7045 (2006). [CrossRef] [PubMed]
  3. M. J. R. Previte and C. D. Geddes, "Fluorescence microscopy in a microwave cavity," Opt. Express 15, 11640-11649 (2007). [CrossRef] [PubMed]
  4. J. Moreau, V. Loriette, and A. -C. Boccara, "Full-Field Birefringence Imaging by Thermal-Light Polarization-Sensitive Optical Coherence Tomography. I. Theory," Appl. Opt. 42, 3800-3810 (2003). [CrossRef] [PubMed]
  5. C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express 13,10854-10864 (2005). [CrossRef] [PubMed]
  6. G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007). [CrossRef] [PubMed]
  7. T. Novikova, A. De Martino, P. Bulkin, Q. Nguyen, B. Drévillon, V. Popov, and A. Chumakov, "Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction," Opt. Express 15, 2033-2046 (2007). [CrossRef] [PubMed]
  8. J. M. Elson, J. P. Rahn, and J. M. Bennett, "Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties," Appl. Opt. 22, 3207-19 (1983). [CrossRef] [PubMed]
  9. C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32, 5492-503 (1993). [CrossRef] [PubMed]
  10. S. Kassam, A. Duparre, K. Hehl, P. Bussemer, and J. Neubert, "Light scattering from the volume of optical thin films: theory and experiment," Appl. Opt. 31, 1304-13 (1992). [CrossRef] [PubMed]
  11. L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: Theoretical analysis," Opt. Commun. 281, 1739-1744 (2008). [CrossRef]
  12. O. Gilbert, C. Deumié, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005). [CrossRef] [PubMed]

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