Scattering and Diffraction

Question 1

What are we trying to image?

Answer 1

The scattering distribution

Question 2

Which two properties of a wave scatter differently?

Answer 2

Sound speed and density heterogeneities

Question 3

How does a point scatterer that is a sound speed heterogeneity scatter?

Answer 3

like a monopole source

Question 4

How does a point scatterer that is a density heterogeneity scatter?

Answer 4

like a dipole source (with no scattering perpendicular to incident wave)

Question 5

What is Class 0?

Answer 5

Molecular: absorption

Question 6

What is Class 1?

Answer 6

Diffusive: λ&raquo_space; scatter size so weak scattering (Rayleigh scattering)

spherical field produced by point scatterers

Question 7

What is Class 2?

Answer 7

Diffractive: λ ≈ scatterer size (0.1-1mm)

Variable wavelength dependence

Question 8

What is Class 3?

Answer 8

Specular: λ &laquo_space;scatterer size

straightforward reflection

no wavelength dependence

Question 9

What is Class 4?

Answer 9

Moving: Red blood cells

Question 10

Which type of scattering obeys Snell’s law?

Answer 10

Specular

Question 11

What happens to sound waves at boundaries?

Answer 11

They are partially reflected

Question 12

What is a boundary to a sound wave?

Answer 12

A change in density or sound speed

A change in characteristic acoustic impedance

Question 13

What is the impedance equation?

Answer 13

Z = λc_0

Question 14

What are the boundary conditions?

Answer 14

Continuity of pressure (infinite force not allowed)

p_i + p_r = p_t

Continuity of normal particle velocity (fluid must stay in contact)

u_i + u_r = u_t

Question 15

What gives the amplitude of the reflected and transmitted waves?

Answer 15

Reflection coefficient

Transmission coefficient

Question 16

What is the reflection coefficient equation?

Answer 16

R = p_r / p_i

Question 17

What is the transmission coefficient equation?

Answer 17

T = p_t / p_i

Question 18

What happens if the first impedance is smaller than second (Z_1 < Z_2) ?

Answer 18

R is positive

Question 19

What happens if the second impedance is smaller than first (Z_1 > Z_2) ?

Answer 19

R is negative

Question 20

What is the conservation of energy?

Answer 20

Fraction of reflected energy (Re) + fraction of transmitted energy (Te) = 1

Question 21

What is the intensity equation for a plane wave?

Answer 21

I = pu = p^2 / Z

Question 22

Why is coupling gel needed?

Answer 22

Large impedance mismatch between transducer/body and air which means no sound is transmitted

Gel is used to couple sound into the body

Question 23

What is refraction?

Answer 23

The change in direction of a wave direction when entering a medium with a different sound speed (a change in sound speed)

(understood using Huygen’s principle)

Question 24

What does each spherical wave do in a medium?

Answer 24

It propagates at the local sound speed c and after time t, the radius is ct

Question 25

What is Snell’s law?

Answer 25

The refraction for a plane wave incident on a flat boundary

Question 26

What is the equation for Snell’s law?

Answer 26

sin θ_i / c_1 = sin θ_t / c_2

Question 27

What happens when c_2 < c_1 ?

Answer 27

Direction of propagation moves towards the normal

(opposite for c_2 > c_1)

Question 28

What happens to the pressure reflection and transmission coefficient?

Answer 28

As it also depends on angle

The Z_1 parameters are multiplied by cos θ at the incident at the normal

The Z_2 parameters are multiplied by cos θ transmitted at the normal

Question 29

What is equal to the critical angle?

Answer 29

θ_t = π/2

There is total reflection so R = 1

Question 30

What is diffraction?

Answer 30

The leakage of sound into shadow zones

It occurs around objects and corners

If sound travelled in straightly lines only, no sound would propagate into the shadow zones