wave propagation II

Question 1

For the Fresnel approximation z is small but still

Answer 1

z&raquo_space; (x0-u)+(y0-v)

Question 2

Fraunhofer Propagation known as

Answer 2

Also known as ‘Far field’ approximation

Question 3

replace which wavefronts to what

Answer 3

Replace spherical wavefronts of Huygens principle or parabolic wavefronts of Fresnel propagation with planar wavefronts

Question 4

fraunhofer model holds if

Answer 4

F = a*a/(lambda * z) &laquo_space;1
ie. z is large

fixed a: is the resolution you want to archive
fixed lambda: is the wavelength you use
variable z: is the distance of detector to sample

Question 5

Rayleigh resolution criterion

Answer 5

Just resolved if maximum of first Airy disk falls on
first zero of second Airy disk

Question 6

Sparrow resolution criterion

Answer 6

Just resolved if there is a vanishing derivative
in the center of the sum of the first and second Airy disk

Question 7

The atmosphere is a major problem for

Answer 7

ground-based telescopes because of atmospheric turbulence (changing refractive index)

Question 8

Fraunhofer propagation implies a Fourier transform relationship between the

Answer 8

complex field at the aperture and focal plane

Question 9

fraunhofer: Measured intensity is absolute value of

Answer 9

complex field squared

Question 10

x ray:
+ at higher energies …… absorption (……. dose)
+ and …… cross section ~1000 times bigger (better …….

Answer 10

+ at higher energies less absorption (lower dose)
+ and phase shift cross section ~1000 times bigger (better contrast

Question 11

Fresnel Regime to small z
typically at least two unknowns:

Answer 11

attenuation and phase

Question 12

Two propagation distances – a direct solution
The result is called

Answer 12

Transport of Intensity Equation” (TIE)

Question 13

one propagation distance steps

Answer 13

1. Take the Intensity at distance z=d
2. Divide by the incident intensity (normalize)
3. Take the Fourier transform
4. Multiply by a filter term in Fourier space ( )
5. Take the inverse Fourier transform
6. Scale the answer to make it quantitative

filter term:
Inverse proportional to distance from origin (ie. low-pass filter)
* Tuned to sample material (d,µ) and propagation distance (d)
* Acting more strongly when phase (d) is large compared to attenuation
(µ), or when the propagation distance (z=d) is large.

Question 14

Fraunhofer (far field) propagation
Intensity is squared Fourier transform of the wave at

Answer 14

the aperture

Question 15

Propagation based Phase Contrast:;

Measured intensities > Equation
Two unknowns <–>
Paganin‘s one distance method with…… filter

Answer 15

Measured intensities > Transport of Intensity Equation
Two unknowns <–> two distances
Paganin‘s one distance method with d/µ filter

Question 16

True or false?
The propagation-based phase-contrast imaging is a far-field imaging method.

Answer 16

False

Question 17

T or F?
phase contrast uses the phase shift due to vphase > cvacuum inside the object as contrast mechanism

Answer 17

True

Question 18

What is the additional assumption for the single distance method?

Answer 18

It is assumed that for homogeneous samples the ratio delta/mu is constant.

no coherence/no isolation assumption