wk10b - Today • Review of spatial filtering with coherent...

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Unformatted text preview: Today • Review of spatial filtering with coherent coherent illumination • Derivation of the lens law using wave optics • Point-spread function of a system with incoherent incoherent illumination • The Modulation Transfer Function (MTF) and Optical Transfer Function (OTF) • Comparison of coherent and incoherent imaging • Resolution and image quality – The meaning of resolution – Rayleigh criterion and image quality IT 2.71/2.710 Optics 1/10/04 wk10-b-1 Coherent imaging as a linear, shift-invariant system IT 2.71/2.710 Optics 1/10/04 wk10-b-2 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 ( s x , s y ): aka pupil function 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 λ λ ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ − ′ − ∗ y f f x f f h g 2 1 2 1 1 , ( ) v u G , 1 θ x object plane Fourier plane: aperture-limited Image plane: blurred (i.e. low-pass filtered) IT 2.71/2.710 Optics 1/10/04 wk10-b-3 Single-lens imaging condition s s ’ lens object image f s s 1 1 1 = ′ + Imaging condition ( aka Lens Law) Derivation using wave optics ?!? s s m ′ − = lateral Magnification IT 2.71/2.710 Optics 1/10/04 wk10-b-4 Single-lens imaging system s s ’ lens object image spatial spatial “LSI” system “LSI” system g in ( x , y ) g out ( x ’ , y ’ ) IT 2.71/2.710 Optics 1/10/04 wk10-b-5 Single-lens imaging system Impulse response (PSF) spatial spatial “LSI” system “LSI” system g in ( x , y ) g out ( x ’ , y ’ ) ( ) ( ) ( ) my y mx x y x y x h − ′ − ′ = ′ ′ δ δ , ; , Ideal PSF: Diffraction--limited PSF: ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ′ ′ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ′ ′ = ′ ′ 2 2 jinc , ; , s y s y s x s x R y x y x h λ IT 2.71/2.710 Optics 1/10/04 wk10-b-6 Imaging with incoherent light IT 2.71/2.710 Optics 1/10/04 wk10-b-7 Two types of incoherence temporal temporal incoherence spatial spatial incoherence incoherence incoherence 1 r 2 r 1 r matched paths point source d 2 d 1 Michelson interferometer Young interferometer poly-chromatic light (=multi-color, broadband) mono-chromatic light (= single color, narrowband) IT 2.71/2.710 Optics 1/10/04 wk10-b-8 Two types of incoherence temporal temporal incoherence spatial spatial incoherence incoherence incoherence 1 r 2 r 1 r matched paths point source d 2 d 1 waves from unequal paths waves from unequal paths do not interfere waves with equal paths waves with equal paths but from different points but from different points on the wavefront on the wavefront do not interfere do not interfere do not interfere IT 2.71/2.710 Optics 1/10/04 wk10-b-9 Coherent vs incoherent beams...
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wk10b - Today • Review of spatial filtering with coherent...

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