1 tfj, simulation of electrical signal path, part 1 medt8807 scattering of sound point spread...
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TFJ, Simulation of electrical signal path, part 1 MEDT8807
Scattering of soundPoint spread function
Medt8007 2015
Tonni Franke Johansen
Hans Torp
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Outline
• Scattering of single sphere (Cobbold ch 5.1-5.3)• Scattering from a distribution of scatterers ch 5.9• Point spread function ch 5.7 + «Notes on psf»
(H.Torp) • Simple 2D k-space simulator• Anisotrophy in US imaging
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Scattering cross section
ss
sd
b d
W scattering cross-section
I
ddW 1, differential scattering cross-section
d I d
,0 back scattering cross-section
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Scattering by a sphere
pi
ps
p=pi+ps
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r a
m 2m m 1
m 0 mm
m 1 m
p0 giving
r
mn ka n kaj 2m 1 kaA p where K ka
m1 jK ka j ka j kaka
The rigid, heavy sphere.
7 From cobbold:
2s 2 a ,
when ka
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Let the sphere be compressible with density rv and speed of sound cv. The surrounding mediumhas density ro and speed of sound co.
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From Lars Hoff
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From Cobbold:
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Distribution of scatterers
• Common to use Rayleigh scatterers with distributed strength and/or posistion (blood, liver tissue)
• Distribution of scatterers presented in e.g.Angelsen ch.7.4-5 and Cobbold ch.5.9
• Stochastic models (gaussion distributions, correlation)
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Human blood cell distribution
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Pulse-echo response
Field II Pulse-Echo response
Rx transducer impulse response
Rx spatial impulse response
ExcitationTx transducer impulse response
Tx spatial impulse response
• The Pulse-echo response is the “true” sensitivity map of our beam, where the echos most likely are originating from.
Tore Bjåstad
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Point spread function 1
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Point spread function 2
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Point spread function 3
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PSF in k-space
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Examining septum from different angles makes the bright line shift sideways
Backscatter depends on fiber angleTorbjørn Hergum/Jonas Crosby
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Examining septum from different angles makes the bright line shift sideways
Backscatter depends on fiber angle
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Examining septum from different angles makes the bright line shift sideways
Backscatter depends on fiber angle
Backscatter void not just attenuation: no shadow
beneath