Lecture08-FT-OD-cont

Lecture08-FT-OD-cont - EMSE 312 Diffraction Principles...

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Unformatted text preview: EMSE 312 Diffraction Principles Lecture 8 Fourier Transforms Optical Diffraction (cont.) EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 Diffraction Principles Fourier Transforms - Review The Fourier Transform of a single slit: ( ) ( ) ( ) ( ) 2 2 2 2 sin ka a I k f k a sin ka ka ka = = = a 0; x a / 2 f (x) 1; a / 2 x a / 2 x a / 2 < = < x 1 a 2 a 2 Transmission function x 1/ a 2/ a 3/ a 3/ a 2/ a 1/ a k ( ) I k 2 a 2 1 k Fraunhofer Pattern Inverse Relationship 1 k a EMSE 312 Diffraction Principles Fourier Transforms - Review The Fourier Transform of a single slit: ( ) ( ) 2 2 a I k sin ka ka = a x 1/a 1/a 1/ a 2/ a 3/ a 3/ a 2/ a 1/ a k ( ) I k 2 a 2 1 k k NOTE: Streak perpendicular to the slit EMSE 312 Diffraction Principles Fourier Transforms - Review The Fourier Transform of a Double slit: a x 1 a b b a a ( ) ( ) ( ) { } ( ) ( ) [ ] ( ) ( ) { } ( ) ( ) [ ] ( ) ( ) ( ) { } ( ) [ ] 1 f k exp ika exp ika exp ikb exp ikb 2 i k 2 1 1 exp ika exp ika exp ikb exp ikb k 2 i 2 2 a sin ka cos kb sin ka 2cos kb k ka = + = + = = Location Shape EMSE 312 Diffraction Principles...
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Lecture08-FT-OD-cont - EMSE 312 Diffraction Principles...

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