wk8b - The imaging problem object imaging optics (lenses,...

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Unformatted text preview: The imaging problem object imaging optics (lenses, etc.) image IT 2.71/2.710 Optics 0/27/04 wk8-b-1 The imaging problem IT 2.71/2.710 Optics 0/27/04 wk8-b-2 x y x illumination (coherent vs incoherent) y imaging optics (lenses, etc.) object g in ( x , y ) image g out ( x , y ) free space free space The imaging problem IT 2.71/2.710 Optics 0/27/04 wk8-b-3 x y x y object image g in ( x , y ) g out ( x , y ) illumination (coherent vs incoherent) LSI LSI (spatial) linear shift-invariant system The imaging problem IT 2.71/2.710 Optics 0/27/04 wk8-b-4 x y x LSI LSI y object g in ( x , y ) image g out ( x , y ) (spatial) linear shift-invariant system Our approach Today: linear shift invariant (LSI) systems in the space/spatial frequency domains mathematical properties of Fourier transforms Monday: free space propagation: Fresnel and Fraunhofer diffraction Wednesday: examples of Fraunhofer diffraction: amplitude and phase diffraction gratings wave description of light propagation through a lens Fourier transformation and imaging using lenses IT 2.71/2.710 Optics 0/27/04 wk8-b-5 Spatial filtering IT 2.71/2.710 Optics 0/27/04 wk8-b-6 Spatial frequency representation Fourier domain (aka spatial frequency domain) space domain 3 sinusoids IT 2.71/2.710 Optics 0/27/04 wk8-b-7 Spatial frequency removal Fourier domain (aka spatial frequency domain) space domain 2 sinusoids (1 removed) IT 2.71/2.710 Optics 0/27/04 wk8-b-8 From space to spatial frequency: 2D 2D Fourier analysis Can I express an arbitrary g ( x,y) as a superposition of sinusoids? IT 2.71/2.710 Optics 0/27/04 wk8-b-9 + + + + + + + + + + = = ... etc. ... Spatial frequency representation space domain ( ) y x g , Fourier domain (aka spatial frequency domain) ( ) ( ) { } y x g v u G , , = IT 2.71/2.710 Optics 0/27/04 wk8-b-10 Low-pass filtering...
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wk8b - The imaging problem object imaging optics (lenses,...

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