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

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)

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)!

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

Fraunhofer angular form

Rectangular slit

Square aperture plots Square aperture Zooming in…

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

Fraunhofer diffraction of a very tall slit, uniformly illuminated

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

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

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

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

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?

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

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

Other 2D apertures semicircle equilateral triangle hexagon

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

Complicated mixture of diffraction and refraction: For a discussion of “glory” physics see http://www.scientificamerican.com/article.cfm?id=the-science-of-the-glory&page=1

Camera diffraction http://chemaguerra.com/category/optics/