wk14b - Today Defocus Deconvolution inverse filters MIT...

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Today • Defocus • Deconvolution / inverse filters MIT 2.71/2.710 Optics 12/08/04 wk14-b-1
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Defocus MIT 2.71/2.710 Optics 12/08/04 wk14-b-2
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Focus in classical imaging Images removed due to copyright concerns in in - - focus focus defocus defocus MIT 2.71/2.710 Optics 12/08/04 wk14-b-3
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Focus in classical imaging Images removed due to copyright concerns in in - - focus focus defocus defocus MIT 2.71/2.710 Optics 12/08/04 wk14-b-4
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Intensity distribution near the focus of an ideal lens (rotationally symmetric wrt z axis) ( ) NA λ × = x z 61 . 0 λ z = ( NA 2 ) 2 MIT 2.71/2.710 Optics 12/08/04 wk14-b-5
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Back to the basics: 4F system 2 f 2 f x x x 1 f 1 f z object object Fourier Fourier image image plane plane plane plane plane MIT 2.71/2.710 Optics 12/08/04 wk14-b-6
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Back to the basics: 4F system 2 f 2 f x x x 1 f 1 f z max x a (NA) 1 (NA) 2 object object Fourier Fourier image image plane plane plane plane plane max ( NA ) = x ( NA ) = max x f 1 1 2 f 2 MIT 2.71/2.710 Optics 12/08/04 wk14-b-7
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Back to the basics: 4F system 2 f 2 f x x x 1 f 1 f z object object Fourier Fourier image image plane plane plane plane plane x x g ( ) G g f 1 x λ f 1 f 2 MIT 2.71/2.710 Optics 12/08/04 wk14-b-8
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4F system with defocused input 2 f 2 f x x x 1 f 1 f z ( ) x g object object Fourier Fourier image image plane plane plane plane plane MIT 2.71/2.710 Optics 12/08/04 wk14-b-9
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4F system with defocused input 2 f 2 f x x x 1 f 1 f z object object Fourier Fourier image image plane plane plane plane plane exp i π x 2 + y 2 ( ) x g z λ MIT 2.71/2.710 Optics 12/08/04 wk14-b-10
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4F system with defocused input 2 f 2 f x x x 1 f 1 f z ) 2 x exp i π object object Fourier Fourier image image plane plane plane plane plane 2 x x ( ) x g λ f 1 ( exp i λ π z λ f 1 G λ z MIT 2.71/2.710 Optics 12/08/04 wk14-b-11
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4F system with defocused input 2 f 2 f x x x 1 f 1 f z object object Fourier Fourier image image plane plane plane plane plane x 2 x g ( ) exp i π x 2 G x ( ) ( ) exp i π z λ z λ f 1 λ f 1 2 MIT 2.71/2.710 Optics 12/08/04 wk14-b-12
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Effect of defocus on the Fourier plane mild defocus 1 f x λ ( ) ( ) 2 1 2 cos f x z λ π ( ) z λ 2 1 1 0 MIT 2.71/2.710 Optics 12/08/04 wk14-b-13
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