Light Scattering predictions.

Muscle, September 2004 1

Light Scattering predictions.Light Scattering predictions.

G. Grehan

L. Méès, S. Saengkaew, S. Meunier-Guttin-Cluzel


Rainbow: Far field scatteringFluorescence : Internal field


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


One particle A cloud (section)

Rainbow

Fluorescence

Airy, Lorenz-Mie, Debye, Nussenzveig

Global

Lorenz-Mie, DebyeInternal field

Multiple scattering


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


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


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


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


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


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


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


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


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


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


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


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 /////// ///////


Refractive index at center is nc

Refractive index at surface is ns

The law is :

1

1)(

b

bx

csce

ennnn


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


b=2 1.3259

b=-2 1.3459

b=6 1.3198

b=-6 1.3578


2D model

Two steps:•Excitation by the laser•Collection in a given solid angle of the fluorescence


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).


2D model : Detection map


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


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


3D model : Excitation map

Light Scattering predictions.

Documents

intdebyefar field

diffglmtfar field

diffdebyefar field

field scatteringfluorescence

dimensionsdebye internal

debye theory

rainbow angle

list of programinternal