wk10a - Today Imaging with coherent light Coherent image...

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Unformatted text preview: Today Imaging with coherent light Coherent image formation space domain description: impulse response spatial frequency domain description: coherent transfer function IT 2.71/2.710 Optics 1/08/04 wk10-a-1 The 4F system 1 f 1 f 2 f 2 f Fourier transform relationship Fourier transform relationship IT 2.71/2.710 Optics 1/08/04 wk10-a-2 The 4F system 1 f 1 f 2 f 2 f ( ) { } { } ( ) y x g y x g = , , Theorem: IT 2.71/2.710 Optics 1/08/04 wk10-a-3 The 4F system 1 f 1 f 2 f 2 f ( ) y x g , 1 1 1 1 , f y f x G y f f x f f g 2 1 2 1 1 , object plane Image plane Fourier plane IT 2.71/2.710 Optics 1/08/04 wk10-a-4 The 4F system 1 f 1 f 2 f 2 f ( ) y x g , 1 1 1 1 , f y f x G y f f x f f g 2 1 2 1 1 , ( ) y x s s G , 1 x y y x x s s sin sin = = object plane Image plane Fourier plane IT 2.71/2.710 Optics 1/08/04 wk10-a-5 The 4F system with FP aperture 1 f 1 f 2 f 2 f ( ) y x g , 1 R r f y f x G circ , 1 1 1 ( ) y f f x f f h g 2 1 2 1 1 , ( ) v u G , 1 x object plane Fourier plane: aperture-limited Image plane: blurred (i.e. low-pass filtered) IT 2.71/2.710 Optics 1/08/04 wk10-a-6 Impulse response & transfer function A point source at the input plane ... ... results not in a point image but in a diffraction pattern h ( x , y ) Point source at the origin delta function ( x , y ) h ( x , y ) is the inpulse response of the system More commonly, h ( x , y ) is called the Coherent Point Spread Function (Coherent PSF) IT 2.71/2.710 Optics 1/08/04 wk10-a-7 Coherent imaging as a linear, shift-invariant system IT 2.71/2.710 Optics 1/08/04 wk10-a-8 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 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 H ( u , v ): aka pupil function Transfer function & impulse response of circular aperture R f 2 22 . 1 2 R Transfer function: circular aperture Impulse response: Airy function 2 jinc f R r R r circ IT 2.71/2.710 Optics 1/08/04 wk10-a-9 Coherent imaging...
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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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wk10a - Today Imaging with coherent light Coherent image...

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