6 tissue optics
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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
=
=
>=
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