wk11a - Resolution (contd) IT 2.71/2.710 Optics 1/15/04...

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Unformatted text preview: Resolution (contd) IT 2.71/2.710 Optics 1/15/04 wk11-a-1 Coherent imaging as a linear, shift-invariant system IT 2.71/2.710 Optics 1/15/04 wk11-a-2 Thin transparency ( ) y x t , ( ) y x g , 1 ( ) ) , ( , ) , ( 1 2 y x t y x g y x g = = output amplitude impulse response ( ) ) , ( ) , ( , 2 3 y x h y x g y x g = = convolution illumi nation (field) Fourier transform Fourier transform transfer function ( plane wave spectrum) ) , ( ) , ( ) , ( 2 3 v u H v u G v u G = = ( ) v u G , 2 multiplication transfer function of coherent system H ( u , v ): aka amplitude transfer function Incoherent imaging as a linear, shift-invariant system IT 2.71/2.710 Optics 1/15/04 wk11-a-3 Thin transparency ( ) y x t , ( ) y x I , 1 ( ) 2 1 2 ) , ( , ) , ( y x t y x I y x I = = ( ) v u I , 2 incoherent impulse response ( ) 2 2 3 ) , ( ) , ( , y x h y x I y x I = = output intensity convolution illumi nation (intensity) Fourier transform Fourier transform transfer function ) , ( ~ ) , ( ) , ( 2 3 v u H v u I v u I = = multiplication ( ) v u H , ~ optical transfer function (OTF) transfer function of incoherent system: The Optical Transfer Function ( ) ( ) { } ( ) ( ) ( ) = v u v u H v u v v v u u H v u H y x h v u H d d , d d , , 1 to normalized , , ~ 2 * 2 IT 2.71/2.710 Optics 1/15/04 wk11-a-4 ( ) H ~ real 1 real( H ) 1 u max u max 2 u max 2 u max 1D amplitude transfer function 1D OTF Amplitude transfer function and MTF of circular aperture in a 4F system physical aperture (pupil function) IT 2.71/2.710 Optics 1/15/04 wk11-a-5 Amplitude transfer function and MTF of circular aperture in a 4F system pinhole, radius 1mm 1 f 1 f 1 f 1 f 1 f 1 f 1 f ( ) 1 mm u 1 f 1 f 1 f 1 f 1 f 1 f 1 f pinhole, radius 1mm ( ) 1 mm u ( ) 1 mm y s amplitude transfer function OTF/MTF IT 2.71/2.710 Optics 1/15/04 wk11-a-6 IT 2.71/2.710 Optics 1/15/04 wk11-a-7 x ( ) NA 22 . 1 = r Safe resolution in optical systems ( ) ( ) + + NA 61 . ~ NA 61 . ~ x h x h Diffractionlimited resolution (safe) Two point objects are just resolvable just resolvable (limited by diffraction only) if they are separated by: Twodimensional systems...
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This note was uploaded on 04/17/2011 for the course ME 525 taught by Professor Lucth during the Spring '11 term at Purdue University-West Lafayette.

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wk11a - Resolution (contd) IT 2.71/2.710 Optics 1/15/04...

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