Lecture_6 - Holography and Faraday Rotation Fourier Optics...

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Holography and Faraday Rotation Fourier Optics Make up lab - this Thursday Lab reports : due Thursday or Get to Tas’ mail boxes on Friday Make up lab – next Thursday (Nov. 17 th )
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Fourier Analysis Fourier series for periodic functions: Hecht, Pg 304 Fourier’s Theorem: a function f(x), having a spatial period λ , can be synthesized by a sum of harmonic functions whose wavelengths are integral of submultiples of λ . 0 00 ( ) cos( ) sin( ) 2 mm A f x A mkx B mkx ∞∞ = + ∑∑ 0 2 ( )cos( ) m A f x mkx dx λ = 0 2 ( )sin( ) m B f x mkx dx = k=2 π / λ Determine A and B through Fourier analysis.
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Holograms: Fourier Optics Hecht pg 626, fig. 13.45 Recording amplitude and phase of light field. Gives 3D picture. Key Idea – record interference pattern between object beam and reference beam 1960, Leith & Upatnieks @ U. Michigan Making holograms Reconstruct wavefront mirror Coherent reference wave Scattered light Photo plate Virtual image What does standard photograph do? Dennis Gabor
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Hecht pg 628, fig. 13.48 Reference wave Object wave H A B C A B λ θ sin AB λ θ = A Simple View of Hollogram x () 2 xx AB φ π = ( ) 2 sin( ) / sin( ) kx θλ = = If intensity is correct, a cosine (sine) grating
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Lecture_6 - Holography and Faraday Rotation Fourier Optics...

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