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Light Scattering predictions.Light Scattering predictions.
G. Grehan
L. Méès, S. Saengkaew, S. Meunier-Guttin-Cluzel
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Rainbow: Far field scatteringFluorescence : Internal field
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TheoriesTheories
• Airy theory (1838): A scalar solution. Could be applied only close of rainbow• Lorenz-Mie theory (1890-1908): rigorous solution of Maxwell equations. All the scattering effects are merged. Extension to multilayered spheres.• Debye theory (1909): post processing of Lorenz-Mie. The different scattering effects could be separated.• Nussenzveig theory (1969) : is “analytical integration” of Debye series, leading to a generalization of Airy. It is clean to have a larger domain of application than Airy
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One particle A cloud (section)
Rainbow
Fluorescence
Airy, Lorenz-Mie, Debye, Nussenzveig
Global
Lorenz-Mie, DebyeInternal field
Multiple scattering
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List of programList of programInternal field and homogeneous sphere: INTGLMT
Internal fields+near field : NEARINT
1or 2 beam(s) impinging on a sphere, internal field : 3D2F (3 dimensions)
2D2F (2dimensions)
DEBYE internal field : INTDEBYE
Far field and homogeneous sphere: DIFFGLMT
Far field and multilayered sphere : MCDIFF
DEBYE Far field : DIFFDEBYE
Far field for pulses : PULSEDIFF
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Rainbow far the rainbow angle Rainbow far the rainbow angle according with Nussenzveigaccording with Nussenzveig
Scattering angle
Geometrical optics angle
Impactparameter
Geometricalrainbow rayimpact parameter
III
IIIIV
V
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Comparison of Lorenz-Mie, Debye, Nussenzveig and Comparison of Lorenz-Mie, Debye, Nussenzveig and Airy predictions for one particleAiry predictions for one particle
Comparison of Lorenz-Mie, Debye, Nussenzveig and Comparison of Lorenz-Mie, Debye, Nussenzveig and Airy predictions for one particleAiry predictions for one particle
Fig 4. Scattering diagram around first rainbow simulated by Lorenz-Mie, Debye, Airy and Nussenzveig theories (d=95.5 µm, m=1.33-0.0i, =500)
Scattering angle
136 138 140 142 144 146 148 150
Nor
med
inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Mie
Fig 4. Scattering diagram around first rainbow simulated by Lorenz-Mie, Debye, Airy and Nussenzveig theories (d=95.5 µm, m=1.33-0.0i, =500)
Scattering angle
136 138 140 142 144 146 148 150
Nor
med
inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Mie Debye, p = 2
Fig 4. Scattering diagram around first rainbow simulated by Lorenz-Mie, Debye, Airy and Nussenzveig theories (d=95.5 µm, m=1.33-0.0i, =500)
Scattering angle
136 138 140 142 144 146 148 150
Nor
med
inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Mie Debye, p = 2NussenzveigAiry
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Rainbow far the rainbow angle Rainbow far the rainbow angle according with Nussenzveigaccording with Nussenzveig
Scattering angle
130 135 140 145 150 155 160
Nor
med
Int
ensi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Nussenzveig, Eqs (19) and (20)Debye, p = 2
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y = -0.2523x + 1.2807
y = -0.1642x + 1.1722
y = -0.0946x + 1.0982
y = -0.0593x + 1.0639
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-2 0 2 4 6 8 10
Z
Inte
nsit
y R
atio
Deb
ye/N
usse
nzve
ig) 10 micron
20 micron
50 micron
100 micron
Comparision scattering diagrame between Debye & Nussenzveig without and with coef160°For water (m=1.333)
Scattering Angle
125 130 135 140 145 150 155 160 165
No
rmal
ized
sca
tter
ing
Inte
nsi
ty
0.0
.2
.4
.6
.8
1.0
1.2
Debye 20 micronOriginal Nus20 micron
Comparision scattering diagrame between Debye & Nussenzveig without and with coef160°For water (m=1.333)
Scattering Angle
125 130 135 140 145 150 155 160 165
No
rmal
ized
sca
tter
ing
Inte
nsi
ty
0.0
.2
.4
.6
.8
1.0
1.2
Debye 20 micronNus160° 20 micronOriginal Nus20 micron
Comparision scattering diagrame between Debye & Nussenzveig without and with coef160°For water (m=1.333)
Scattering Angle
125 130 135 140 145 150 155 160 165
No
rmal
ized
sca
tter
ing
Inte
nsi
ty
0.0
.2
.4
.6
.8
1.0
1.2
Debye 10 micronDebye 20 micronDebye 50 micronCol 1 vs Debye_100 Nus160° 10 micronNus160° 20 micronNus160° 50 micronNus160° 100 micronOriginal_Nus 10 micronOriginal Nus20 micronOriginal_Nus50 micronOriginal_Nus100 micron
D<=15 Y= -0.2523Z+1.2807Y= -0.1642Z+1.1722Y= -0.0946Z+1.0982Y= -0.0593Z+1.0639
15>D<=35 35>D<=75 75>D<=150
mhRh
Z ,3/23/1
211
Z is the argument of Airy function
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Fig 6 Comparison scattering diagram between Lorenz-Mie, Debye (p=0+2) and Nussenzveig (p=0+2)
Scattering angle135 140 145 150 155 160
Nor
med
sca
tter
ed in
ten
sity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Nussenzveig, p = 0 and 2Debye p = 0 and 2 Lorenz-Mie
Comparison of Lorenz-Mie, Debye and Nussenzveig Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for one particle predictions for one particle
Comparison of Lorenz-Mie, Debye and Nussenzveig Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for one particle predictions for one particle
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Fig 7. Global rainbow distribution simulated by Lorenze-Mie, Nussenzveig Theory
(mean diameter = 50 micron, rms = 200)
Angle125 130 135 140 145 150 155 160 165
Nor
mal
ized
In
ten
sity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Lorenz-Mie Nussenzveig Original
Fig 7. Global rainbow distribution simulated by Lorenz-Mie, Nussenzveig Theory
(mean diameter = 50 micron, rms = 200)
Angle125 130 135 140 145 150 155 160 165
Nor
mal
ized
Int
ensi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Lorenz-Mie Nussenzveig by add coefficientNussenzveig Original
Comparison of Lorenz-Mie, Debye and Nussenzveig Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for cloud of particle predictions for cloud of particle
Comparison of Lorenz-Mie, Debye and Nussenzveig Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for cloud of particle predictions for cloud of particle
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Scattering angle
120 125 130 135 140 145 150
Nor
med
inte
nsit
y
0.0
0.2
0.4
0.6
0.8
1.0nk=0.0005 nk=0.001 nk=0.0025 nk=0.005
Effect of an imagining part of the refractive index
maximum Refractive index
nk=0.0005 139.60 1.330
nk=0.001 139.63 1.3299
nk=0.025 139.58 1.3298
nk=0.005 /////// ///////
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Refractive index at center is nc
Refractive index at surface is ns
The law is :
1
1)(
b
bx
csce
ennnn
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Behaviour of the radial raf ractive index
Normad radius
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Rea
l par
t of
ref
ract
ive
index
1.325
1.330
1.335
1.340
1.345
1.350
1.355
1.360
1.365
b = -2 b = 2 b = -6 b = 6
Global rainbow f or a particle with gradient. The ref racive index at centeris equal to 1.33 and at surf ace to 1.36.
Scattering angle
120 130 140 150 160N
orm
ed int
ensi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
b = -2 b = 2 b = -6 b = 6
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b=2 1.3259
b=-2 1.3459
b=6 1.3198
b=-6 1.3578
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2D model
Two steps:•Excitation by the laser•Collection in a given solid angle of the fluorescence
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2D model : Excitation map
Internal intensity (in log-scale) created by a beam with a beam waist diameter equal to 20 µm, and a wavelength equal to 0.6 µm. The particle is a water droplet with a diameter equal to 100 µm and a complex refractive index equal to 1.33 – 0.0 i. The parameter is the impact location of the beam: (a) = 50 µm (on the edge of the droplet), (b) = 30 µm and (c) = 0 µm (on the symmetry axis of the droplet).
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2D model : Detection map
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Map of fluorescence emission. The particle is a water droplet of 100 µm on which impinges a laser beam with a diameter equal to 20 µm, and for an impact location equal to 50 µm (Fig. 2a). The parameter is the location of the collecting lens: (a) 0°, (b) 90° and (c) 180°.
2D model : Answer
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2D model
Diagram of fluorescence for a water droplet of 100 µm. The parameter is the impact location which runs from 60 µm to –60 µm by steps of 10 µm. The left figure is in linear scale while rigth figure is in logarithm scale.
Logarithm scale
0 5 10 15 20
0
5
10
15
20
05101520
0
5
10
15
20
0
12
3
4
5
6
60 µm50 µm40 µm30 µm20 µm10 µm0 µm-10 µm-20 µm-30 µm-40 µm-50 µm-60 µm
Logarithm scale
0.01 0.1 1 10
0.01
0.1
1
10
0.010.1110
0.01
0.1
1
10
0
12
3
4
5
6
60 µm50 µm40 µm30 µm20 µm10 µm0 µm-10 µm-20 µm-30 µm-40 µm-50 µm-60 µm
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3D model : Excitation map
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