1. 35. Diffraction and Image Formation
Where was modern optical imaging technology born?
Jena
Zeiss
Abbe
Schott

2. Geometrical Optics…
point sources
point images f f
…implies perfect resolution.

3. Physical Optics…
diffracting source
Imperfect image
Every lens is a diffracting aperture.

4. a b r
Multiple Slits

5. Central maximum
Principle maxima
secondary maxima

6. Diffraction Grating
A special corner of multi-slit-space: N ~ 104, a ~ l, b ~ l
b ~ l: central maximum is very large!
a ~ l: principle maxima are highly separated!
(most don’t exist)
N ~ 104: Principle maxima are very narrow! Secondary maxima are very low!
typical grating specs: 900 g/mm, 1 cm grating.
N = 9,000
a = 1.11 microns
b = 1.11 microns
l = microns!

7. m = 1
“first order”
grating
m = 0
monochromatic light
Maxima at:

8. Abbe Theory of Image Formation
grating
m = +1
m = 0
m = -1
focal plane
diffraction plane

9. Abbe Theory of Image Formation
grating
m = +1
Resulting interference pattern is the image
m = 0
m = -1
focal plane
diffraction plane

10. Image formation requires a lens large enough to capture the first order diffraction.
Grating Equation: a D
m = 0 f
To resolve a:
Resolution (diffraction limited):

11. Rectangular Apertures
P(X,Y,Z) R r
dA(x,y,z) a b
Rather than an aperture, consider an object:

12. Remember, the integral is over the aperture area:
Let’s rearrange that a little it (this is where the magic happens):
THAT’S A FOURIER TRANSFORM!!
EP(X,Y,Z) = F{EFeynman}
Where does diffraction put the spatial frequencies in EFeynman?