Lecture 3: Optical Transfer Function

Question 1

period

Answer 1

d_0 = 1/f_0

Question 2

width D where D/d_0

Answer 2

> > 1

Question 3

diffracted amplitude

Answer 3

fourier transform of A(x)

Question 4

diffracted order at

Answer 4

x=0 +/- Z_0 λ/d

where z_0 is the object distance

Question 5

objects can be decomposed into

Answer 5

its fourier components
these are not transmitted perfectly to the image

Question 6

high spatial frequencies are filtered out (removed) at

Answer 6

the system’s aperture

leads to loss of resolution and contrast in the image

Question 7

another perspective

Answer 7

Two small patches separated by s
Interference of two sources (c.f. Young’s slits)
point sources centred on +/- s/2

Question 8

aperture function for point sources centred on +/- s/2

Answer 8

A(x)=δ(x-s/2)+δ(x+s/2)

Question 9

spatial frequency in image

Answer 9

fi=s/zi lambda

zi=image distance

Question 10

what if spacing corresponds to diffraction orders and let zi=z0=z

Answer 10

spatial frequency in image fi=f0

also di=d0

Question 11

For a particular spatial frequency to be present in the image, the aperture must

Answer 11

be large enough to accommodate the spacing between the 0th and 1st diffracted orders, s=lambda z f0, of the corresponding spatial frequency in the object.

Question 12

Spatial frequency only resolved if

Answer 12

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

otherwise info about frequency is lsot

Question 13

minimum requirement for spatial frequency to be resolved

Answer 13

at least two orders to be supported
by the system

Question 14

Structure of object resolved if

Answer 14

first diffraction order
propagates through the optical system

Question 15

Fidelity of the image increases with

Answer 15

the number of diffraction orders propagating through the optical system

Question 16

Object can be considered to be made up of

Answer 16

many point sources
image of each is spread out

Question 17

Image is convolution of

Answer 17

the geometrical image with
the Point Spread Intensity

Question 18

Actual image is the convolution of

Answer 18

the ideal image predicted by
geometrical optics with the Point Spread Intensity

Question 19

Start with Image Amplitude and Image Intensity as functions of spatial coordinates. Image amplitude:

Answer 19

Convolution of Point Spread Amplitude with Geometrical Amplitude,

Question 20

Start with Image Amplitude and Image Intensity as functions of spatial coordinates. Image intensity

Answer 20

Convolution of Point Spread Intensity with Geometrical Intensity

Question 21

Fourier transform of convolution is

Answer 21

the product of the Fourier transforms

Question 22

fourier transform of product is

Answer 22

convolution of the fourier transforms

Question 23

spatial angular frequency

Answer 23

kx=2pifx

in radians per metre

Question 24

Image intensity is the convolution of

Answer 24

the geometric image intensity with the Point Spread
Intensity

Question 25

get frequency content of image

Answer 25

take fourier transform

Question 26

fourier transform of intensity

Answer 26

frequency spectrum of image = optical transfer function x frequency spectrum of geometrical image

Question 27

filtering/degradation of system attributed to

Answer 27

H(kx,ky)

Question 28

H(kx,ky) transmits

Answer 28

low spatial frequencies

Question 29

H(kx,ky) attenuates

Answer 29

high spatial frequencies

Question 30

H (optical transfer function) describes how

Answer 30

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

Question 31

magnitude of OTF |H| corresponds to

Answer 31

contrast modulation transfer function (MTF)

Question 32

Phase of OTF, arg(H) corresponds to

Answer 32

distortion ie a shift in position phase transfer function (PTF)

Question 33

atmospheric turbulence

Answer 33

* Pockets of air with different temperatures, densities and refractive indices * Corrugated wavefronts * Dominant cause of aberrations for large-scale telescopes

Question 34

atmospheric turbulence: airy

Answer 34

small aperture short exposure

Question 35

atmospheric turbulence: speckle

Answer 35

large aperture short exposure

Question 36

atmospheric turbulence: time average

Answer 36

large aperture long exposure

Question 37

atmospheric turbulence: telescope

Answer 37

well-defined static analytical

Question 38

atmospheric turbulence: atmosphere

Answer 38

random changing statistical

Question 39

convolution

Answer 39

(f⊗g)(z)

Question 40

cross-correlation

Answer 40

(f★g)(z)

Question 41

auto-correlation

Answer 41

(f★f)(z)

Question 42

power spectrum=

Answer 42

fourier transform of autocorrelation

Question 43

fourier transform of power=

Answer 43

autocorrelation of amplitude spectrum

Question 44

amplitude transfer function (ATF)

Answer 44

H(fx,fy)= F{h}

Question 45

optical transfer function

Answer 45

H(fx,fy) = F{|h|^2} / normalisation

Question 46

aurtocorrelation of ATF, what are p and q?

Answer 46

spatial frequency variables

Question 47

H(fx,fy)≡

Answer 47

scaled version of aperture / pupil function

Question 48

autocorrelation of pupil, H(f'x,f'y)=

Answer 48

area of overlap / total overlap

Question 49

With Fourier Optics we can understand

Answer 49

how an optical system filters frequencies present within the object

Question 50

the optical transfer function expresses

Answer 50

how that frequency content in filtered at the aperture of the optical system

Question 51

atmospheric turbulence requires a

Answer 51

statistical description

Question 52

the optical transfer function can also be understood to be the

Answer 52

autocorrelation of the pupil function