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Tissue Optics

Includes materials fromScott Prahl, Steve J acques

Oregon Laser Medical CenterNimmi Ramanujam,

Duke UniversityRebecca Richards-Kortum,

Rice University

VariousBeckman Laser Institute

Light and Bulk MatterTypes of Interactions

Reflection (Fresnels law)

Refraction (Snells law)

Scattering, Diffraction

Absorption => Variation in Transmission

(Beers law) Phase shifts

Emission

)sin(n)sin(n 1122 =

2

21

2

211)nn(

)nn(TR

+

==

za

eIzI)(

0)(

=

Light and Turbid Sample

Optical Properties of Turbid Sample Refractive index: n

Absorption: a

Scattering: s Scattering Anisotropy: g Reduced Scattering: s(1-g) Total Attenuation: t=s+a Albedo: s/t Transport: tr=s(1-g) +a Diffusion: 1/ (3 tr)

Refractive Index

In visible range:

nr water: 1.33

nr soft tissue: 1.37-1.40

nr tooth enamel: 1.62

Vo-Dinh Chapter 2, Table 2.1

cn

innn

ia

ir

2=

+=

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Mean Free Path

a ~10 cm-1

la= 1 mm

Most tissues absorption coefficientis between 0.1-1cm-1

a

al

1=

Absorption SpectroscopyBeer-Lambert

Concentration c, length l, if we pass beam of light with intensity I andwavelength lambda how much light emerges?

Amount of molecules in thin layer:

Change of Intensity due to thin layer: IdxcdI =

is the absorption coefficient depending on concentration

le

lc

I

IT a

===10

0

Integrating of a path length of l results:

dxc

lclTI

IA ao

303.2)log(log ====

Absorbance is based on log 10 =Optical Density

%T is Transmission measured

is the molar extinction coefficient

Absorption Spectroscopy Scattering

Pool

Pole

mental picture

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Scattering Anisotropy &

Phasefunction

Imagine that a photon isscattered by a particle so thatits trajectory is deflected by

an angle,

Then, component of a newtrajectory aligned forwarddirection is cos()

Anisotropy is a measure offorward direction retainedafter a single scatteringevent, < cos()>

Scatterer

hvIncidenet

Photon

Scattering

Angle ()

Scattering

event

cos ()

d

Photon

trajectory

S

scattered

photon

hv

S

Scattering Phase Function

Often the scattering phase function does not depend on input direction:p()

p() describes the probability of a photon scattering into a unit solidangle, relative to the original photon trajectory

p() has historically been called the scattering phase function

)s,s(d

d s Differential scattering cross section:

scattering in direction s from input direction s

+

=d

)ss(d)ss(p s

as

4

The angular dependence of scattering is

Scattering AnisotropyThe proper definition of anisotropy (g) is the expectation valuefor cos ():

( )

( ) 120

20

=

=

>=