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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 π π π π ⎛ ⎞ = = ⋅ = ⎜ ⎟ ⎝ ⎠ ¡ ¡ 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 π ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 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 π π ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ¡ 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 π ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 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 π π π π π π π π π π π π π π π π = − − + − = ⋅ − − ⋅ + − = ⋅ ⋅ = ⋅ ⋅ ¡ Location Shape EMSE 312 – Diffraction Principles...
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Lecture08-FT-OD-cont - EMSE 312 – Diffraction Principles...

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