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Abbe

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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