wk12b - Today Resolution Wavefront modulation IT 2.71/2.710...

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Unformatted text preview: Today Resolution Wavefront modulation IT 2.71/2.710 Optics 1/24/04 wk12-b-1 Resolution IT 2.71/2.710 Optics 1/24/04 wk12-b-2 Coherent imaging as a linear, shift-invariant system IT 2.71/2.710 Optics 1/24/04 wk12-b-3 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 1/24/04 wk12-b-4 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: Transfer Functions of Clear Aperture IT 2.71/2.710 Optics 1/24/04 wk12-b-5 ( ) ( ) { } ( ) ( ) ( ) = 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 u max u max 1 2 u max 2 u max real( H ) ( ) H ~ real 1 1D amplitude transfer function (ATF) 1D optical transfer function (OTF) ( ) ( ) { } y x h v u H , , Coherent Coherent Incoherent Incoherent PSF Connection between PSF and NA IT 2.71/2.710 Optics 1/24/04 wk12-b-6 ( ) ( ) ( ) y x y x g = , in ( ) r f R r f R 1 1 1 2 2 J 2 .,. jinc object plane impulse Fourier plane circ-aperture image plane observed field (PSF) 1 f 1 f ( ) = R r y x H circ , monochromatic coherent on-axis illumination Fourier transform x x x 1 f 1 f radial coordinate @ Fourier plane 2 2 y x r + = 2 2 y x r + = radial coordinate @ image plane 2 R (unit magnification) Connection between PSF and NA IT 2.71/2.710 Optics 1/24/04 wk12-b-7 Fourier plane circ-aperture image plane 1 f 1 f monochromatic coherent on-axis illumination x x x 1 f 1 f ( ) ( ) r r r f R r f R y f R x f R = NA 2 NA 2 J 2 2 2 J 2 2 , 2 jinc 1 1 1 1 1 1 ( ) 1 NA f R Numerical Aperture (NA) by definition: NA: angle of acceptance for onaxis point object 2 R Numerical Aperture and Speed (or FNumber) medium of refr. index n : half-angle subtended by the imaging system from an axial object Numerical Aperture (NA) = n sin...
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wk12b - Today Resolution Wavefront modulation IT 2.71/2.710...

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