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Zeiss. Jena. Abbe. Schott. 35. Diffraction and Image Formation. Where was modern optical imaging technology born?. point sources. Geometrical Optics…. point images. f. f. …implies perfect resolution. Physical Optics…. diffracting source. Imperfect image.

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

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

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

  4. b a b a b r a b Multiple Slits

  5. Central maximum Principle maxima secondary maxima

  6. typical grating specs: 900 g/mm, 1 cm grating. N = 9,000 a = 1.11 microns l = 0.633 microns! b = 1.11 microns 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!

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

  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. m = +1 Grating Equation: a D m = 0 f To resolve a: Resolution (diffraction limited):

  11. r dA(x,y,z) R Rectangular Apertures P(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?

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