Lecture 3

Question 1

numerical aperture (formula)

Answer 1

= nsinθ = (D/2)/(object distance)

Question 2

grating transmission

Answer 2

T(x) = 1/2(1+cos(kx))

period d = 2π/k

Question 3

Diffracted order at:

Answer 3

x = 0 ± zλ/d

Question 4

frequency content

Answer 4

object can be decomposed into its component Fourier components

these are not transmitted perfectly to the image

high spatial frequencies are filtered out at the system’s aperture

leads to loss of resolution and contrast in the image

Question 5

spatial frequency in image (formula)

Answer 5

fXi = 1/di = s/ziλ

diffracted orders at

x = 0, ± zoλ/do

Question 6

spatial period in image

Answer 6

di = ziλ/(zoλ/do) = zi/(zo/do) = Mdo

Question 7

spatial frequency only resolved

Answer 7

if diffraction orders corresponding to that frequency pass through the aperture of the system

otherwise information about that frequency is lost

Question 8

Image amplitude

Answer 8

Ui(X,Y) = h(X,Y)*Ug(X,Y)

Question 9

Image intensity

Answer 9

Ii(X,Y) = |h(X,Y)|^2 * Ig(X,Y)

Question 10

Convolution theorem

Answer 10

Fourier transform of convolution is the product of the Fourier transforms

Question 11

to obtain the frequency content of an image take

Answer 11

the fourier transform

Question 12

Fourier transform of intensity (formula)

Answer 12

Ii = H . Ig

where H is the optical transfer function (OTF)

Question 13

what is attributed to the Optical Transfer Function

Answer 13

filtering and degradation of the system attributed to the OTF

it transmits low spatial frequencies and attenuates high spatial frequencies

Question 14

Optical Transfer Function describes

Answer 14

how optical system filters or modifies spatial frequencies that would otherwise contribute to the image

Question 15

the magnitude of OTF, |H|, corresponding

Answer 15

to contrast

Question 16

phase of OTF , arg(H) corresponds to

Answer 16

Distortion

Question 17

Modulation (formula)

Answer 17

M = Imax -Imin / Imax + Imin

Question 18

Modulation of the image (formula)

Answer 18

Mobj = b1/b0

Question 19

Similarly, modulation of the image (formula)

Answer 19

Mim = c1/c0

Question 20

Modulation transfer function (formula)

Answer 20

|H| - Mim/Mobj ≤ 1

Question 21

MTF is a measure of the loss of contrast in the optical system - values that describe the MTF are

Answer 21

|H| = 1 good contrast
|H| < 1 reduced contrast
|H| = 0 no contrast

Question 22

Radius of airy disc (formula)

Answer 22

r = 1.22Fλ/D

Question 23

cut off frequency (formula)

Answer 23

fc = D/λF

Question 24

atmospheric turbulence

Answer 24

pockets of air with different temperatures, densities and refractive indices

corrugated wavefronts

dominant cause of aberrations for large-scale telescopes

Question 25

Atmospheric Turbulence: Telescope

Answer 25

Single-values

well-defined

static

analytical

Question 26

Atmospheric Turbulence: Atmosphere

Answer 26

Random

Stochastic

Changing

Statistical

Question 27

how to include effects of atmospheric turbulence within a description of the optical system

Answer 27

auto-correlation

Question 28

the power spectrum is equal to

Answer 28

the Fourier transform of autocorrelation

Question 29

the fourier transform of power is equal to the

Answer 29

autocorrelation of frequency

Question 30

Amplitude Transfer Function (ATF)

Answer 30

H(fx,fy) = Ƒ {h}

{h} point spread aperture

Question 31

Autocorrelation of Pupil

Answer 31

H(fx,fy) = area of overlap / total area

Question 32

The Optical Transfer Function can also be understood to be

Answer 32

the autocorrelation of the pupil function