a) Find the Fraunhofer diffraction (far field) intensity pattern I(0,0,) for two identical rectangular apertures (illuminated...

 

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a) Find the Fraunhofer diffraction (far field) intensity pattern I(0,0,) for two identical rectangular apertures (illuminated uniformly by light of wavelength 2) as shown at the right, of size a by 4a, whose centers are separated horizontally (x direction) by a distance b. Your answer should be real and normalized such that the maximum intensity has the arbitrary value I. b Possibly useful: E(0,0)=E(x, y', 0)e' aperture -00 -ik(0₂x'+0₂y') N E(0,0)= Σe n=1 dx' dy' (g*h)(u)= [g(u'h(u-u')du' _F{(g*h)(1)}=g(0)h(o) F{g(1)h(1)} = _ _ _ 8(w)*h(w) 2π -ik (0xxn + Oy.vn) * E one a (0,0₂) 4a b). Sketch or describe the 2-D Fraunhofer pattern you would expect from the two apertures, and how it changes with b. (Can be done with conceptual understanding, or you can use your analytic results from a.) a) Find the Fraunhofer diffraction (far field) intensity pattern I(0,0,) for two identical rectangular apertures (illuminated uniformly by light of wavelength 2) as shown at the right, of size a by 4a, whose centers are separated horizontally (x direction) by a distance b. Your answer should be real and normalized such that the maximum intensity has the arbitrary value I. b Possibly useful: E(0,0)=E(x, y', 0)e' aperture -00 -ik(0₂x'+0₂y') N E(0,0)= Σe n=1 dx' dy' (g*h)(u)= [g(u'h(u-u')du' _F{(g*h)(1)}=g(0)h(o) F{g(1)h(1)} = _ _ _ 8(w)*h(w) 2π -ik (0xxn + Oy.vn) * E one a (0,0₂) 4a b). Sketch or describe the 2-D Fraunhofer pattern you would expect from the two apertures, and how it changes with b. (Can be done with conceptual understanding, or you can use your analytic results from a.)

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Problem a The Fraunhofer diffraction intensity pattern for two identical rectangular apertures can be found using the following steps 1Calculate the complex amplitude transmission function for each ap... View the full answer