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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