Fourier optics intro

Question 1

Relation between angular and transverse magnification

Answer 1

inverse proportional: Ma = 1/Mt

Question 2

Diffraction limit formula

Answer 2

d ~ λ/sin(α)

Question 3

How is spherical aberration influenced by the opening angle of a lens

Answer 3

rsph(inf) ~ α^3

Question 4

Astigmatism

Answer 4

different focus points between xz and yz planes resulting in a “circle of least confusion” and not an actual single focus point

Question 5

Coma

Answer 5

Rays further away from the lens centre are focused at a lower point on the z-axis.

Question 6

What is the formula for the size of a focus spot on an image. Derive it

Answer 6

r = λ/4sin(α)

see notes

its not 2 because alpha is the angle to the central axis. This means that rsinalpha is then the path difference between the wave from the top that gets to the min point and the one that goes towards the maximum point( the same wave but stoped at different times due the path distance). The wave from the bottom also has the same path difference and thus a 2 factor appears.

Question 7

Diffraction limit / Abbes criterion

Answer 7

d = λ/2nsin(α) = λ/2NA

Question 8

spatial frequency definition

Answer 8

q= 1/p = sin(theta)/lambda

whete p is the pitch of the wave
the distance between the fringes
theta is the angle the top of the lens makes with the height of the focus point v = Fsin(theta) (F is focal distance).
This is 1D definition this can also be in 2D with u the horizontal coordinates included as well. then q is a vector

Question 9

Name of the distribution describing a PSF

Answer 9

Airy distribution

Question 10

Where can we see J.B.? In his:
A. Magnitude inverse FT.
B. Phase inverse FT.
C. Both.
D. Neither.

Answer 10

B. Phase inverse FT.

Question 11

How do you model the image of a fluorescent object?

Answer 11

the shape of the object as a sum fluorophore positions/Dirac-Delta functions convolved with PSF.

Question 12

Name of PSF in Fourier domain

Answer 12

optical transfer function (OTF)

Question 13

Shape of OTF

Answer 13

A cone which drops to 0 at q>2NA/λ (abbes)

Question 14

Rayleighs criterion

Answer 14

0.61λ/nsin(α) = 0.61λ/NA
unlike Abbes which is about a point source this is about the lowest distance at which you can distinguish two point sources

The images of two point sources are just
resolved when the central maximum of one
Airy pattern coincides with the first dark ring
of the other Airy pattern