Scattering and Diffraction Flashcards
What are we trying to image?
The scattering distribution
Which two properties of a wave scatter differently?
Sound speed and density heterogeneities
How does a point scatterer that is a sound speed heterogeneity scatter?
like a monopole source
How does a point scatterer that is a density heterogeneity scatter?
like a dipole source (with no scattering perpendicular to incident wave)
What is Class 0?
Molecular: absorption
What is Class 1?
Diffusive: λ»_space; scatter size so weak scattering (Rayleigh scattering)
spherical field produced by point scatterers
What is Class 2?
Diffractive: λ ≈ scatterer size (0.1-1mm)
Variable wavelength dependence
What is Class 3?
Specular: λ «_space;scatterer size
straightforward reflection
no wavelength dependence
What is Class 4?
Moving: Red blood cells
Which type of scattering obeys Snell’s law?
Specular
What happens to sound waves at boundaries?
They are partially reflected
What is a boundary to a sound wave?
A change in density or sound speed
A change in characteristic acoustic impedance
What is the impedance equation?
Z = λc_0
What are the boundary conditions?
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
What gives the amplitude of the reflected and transmitted waves?
Reflection coefficient
Transmission coefficient
What is the reflection coefficient equation?
R = p_r / p_i
What is the transmission coefficient equation?
T = p_t / p_i
What happens if the first impedance is smaller than second (Z_1 < Z_2) ?
R is positive
What happens if the second impedance is smaller than first (Z_1 > Z_2) ?
R is negative
What is the conservation of energy?
Fraction of reflected energy (Re) + fraction of transmitted energy (Te) = 1
What is the intensity equation for a plane wave?
I = pu = p^2 / Z
Why is coupling gel needed?
Large impedance mismatch between transducer/body and air which means no sound is transmitted
Gel is used to couple sound into the body
What is refraction?
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)
What does each spherical wave do in a medium?
It propagates at the local sound speed c and after time t, the radius is ct
What is Snell’s law?
The refraction for a plane wave incident on a flat boundary
What is the equation for Snell’s law?
sin θ_i / c_1 = sin θ_t / c_2
What happens when c_2 < c_1 ?
Direction of propagation moves towards the normal
(opposite for c_2 > c_1)
What happens to the pressure reflection and transmission coefficient?
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
What is equal to the critical angle?
θ_t = π/2
There is total reflection so R = 1
What is diffraction?
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
