Lecture 2

Question 1

angular resolution (formula)

Answer 1

α = 1.22 λ/D

Question 2

resolution improves with

Answer 2

scale

Question 3

Fraunhofer diffraction

Answer 3

plane-parallel waves incident upon aperture

viewed in far field L&raquo_space; D^2/λ

Question 4

2D Fourier transform of aperture

Answer 4

Up ∝ ∫ ( ∫ A )A(x,y) exp(-i(xkx+yky)dxdy

Question 5

A single-slit is modelled mathematically as

Answer 5

a step function

A(x) = { 1 , -a < x < a
{ 0 , elsewhere

Question 6

Intensity in a single slit is proportional to

Answer 6

|Up|^2

the modulus of the fourier aperture function squared

Question 7

Bessel functions

Answer 7

Up = Uo [ 2J1(kα) / kα ]

first zeros for kα = 1.22 π

Question 8

Geometrical optics

Answer 8

Image formed of object at point of convergence rays.

Consider object to be made up of many individual point sources.

One-to-one mapping

Spacing in the image plane governed by the magnification of the system

Question 9

Image formation

Answer 9

When imaging an object at infinity, the image plane is simply the focal plane

Mapping between incident angle and position on focal plane

Question 10

Point Spread Function (formula)

Answer 10

I(α) = Ig * I(PSF)

I(α) = image intensity

Ig = geometrical image intensity

I(PSF) = point spread function intensity

Question 11

Point spread function (formula in words)

Answer 11

actual image is the convolution of the ideal image predicted by geometrical optics with the point spread function intensity

Question 12

U(PSF) =

Answer 12

Uo [ 2J1(πDα/λ) / (πDα/λ) ]

Question 13

I(PSF) =

Answer 13

Io [ 2J1(πDα/λ) / (πDα/λ) ]^2

Question 14

diffraction limit

Answer 14

effects of aberrations are negligible, said to be diffraction limited

Question 15

Resolution - Strehl Ratio (formula)

Answer 15

S = I(PSF)(0) / I(airy)(0)

Question 16

encircled energy

Answer 16

integrate PSF intensity within a circle of a given radius and compare to that of ideal PSF

Question 17

Strehl Ratio (definition)

Answer 17

is the ratio of intensity at the centre of the PSF peak with that expected in the ideal case (Airy disc)

Question 18

aberrations reduce

Answer 18

peak intensity of PSF

Question 19

Point spread function tells us

Answer 19

how the light from a source spreads out in an image

Question 20

for an ideal telescope the PSF is simply the

Answer 20

airy pattern

Question 21

use the expression for the point spread function to obtain the Rayleigh
criterion expression.

Answer 21

kα = 1.22π

(2π/λ D/2) sinα = 1.22π

angular separation of first zero:

sinα ≈ α = 1.22λ /D