1. Atmospheric “corona” caused by diffraction around uniform droplets or ice particles

4. Review of Fresnel approximation
Approximation made: z > aperture size, interference pattern size
For I on screen at z, we can ignore the factors in front
(We only need the factors in front if we interfere
the diffracted light with another source)

5. Next approx as z gets bigger
(or aperture smaller)
Which goes to zero faster as z gets big (and why)?
A. B.
Fraunhofer approximation:
Rough boundary between Fresnel and Fraunhofer diffraction:
Or: for big z, the aperture-screen length differences between any 2 points on the aperture becomes less than l/2… (the center can’t become dark)!

6. Diffraction for increasing screen distance
Looks like the aperture with fringes! (Fresnel)
Aperture
200x100 l/2p
z screen
20 l/2p
z screen
100 l/2p
“Far field” looks like |FT|2 of aperture!
(Fraunhoffer diffraction)
z screen
500 l/2p
z screen
2500 l/2p

7. Fraunhofer angular form

8. Rectangular slit

9. Square aperture plots
Square aperture
Zooming in…

10. The square diffraction pattern is shown on the left
The square diffraction pattern is shown on the left. Which pattern on the right belongs to the rectangular aperture shown?
A) top B) bottom

11. Fraunhofer diffraction of a very tall slit, uniformly illuminated

13. Single slit Fraunhoffer diffraction
In reality just need to illuminate slit by beam >> slit width to ignore diffraction in the y direction

14. Angular scale of diffraction
How big should we expect the pattern to be on the screen
without doing integrals?
Or, what is the average change of angle of a photon? a
What should it depend on?
Can use photon momentum uncertainty

15. Two interference views of Fraunhoffer diffraction
Huygen’s wavelets in the aperture weighted by Eaperture[x’,y’]
interfere to give Escreen[x,y]
2. Reverse time: Plane waves coming from screen at angle qx,qy weighted by Escreen[qx,qy] interfere to give Eaperture[x’,y’] by Fourier theory! a

16. Can laser beams propagate without spreading?
Use angular scale of diffraction

17. Diffraction of a “Gaussian aperture”
A laser beam has a Gaussian profile of 2mm width, and a constant phase across the beam. How wide will it be after propagating 100m?

18. Fresnel vs Fraunhofer
Figures in order were made by increasing something. Which could it be? a l z

19. Review of approximations, regimes
z > aperture size > l
z > aperture size, z > interference pattern size:
z > (aperture size)2 / l :

20. Other 2D apertures
semicircle equilateral triangle hexagon

21. Atmospheric (pilot’s) “Glory”
Light scattered back from droplets

22. Complicated mixture of diffraction and refraction: For a discussion of “glory” physics see

23. Camera diffraction