Transcription of 30. Diffraction and the Fourier Transform
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30. Diffraction and the Fourier Transform
30. Diffraction and the Fourier Transform Diffraction examples Diffraction by an edge Arago spot The far-field Fraunhofer Diffraction Some examples Simeon Poisson Francois Arago (1781 - 1840) (1786 - 1853). Reminder: Fresnel-Kirchoff Diffraction aperture (x0, y0). Coordinates: (x1, y1). the plane of the aperture: x1, y1 r01 z 2 x0 x1 y0 y1 . 2 2. the plane of observation: x0, y0. z (a distance z downstream). observation region x12 2 x0 x1 y12 2 y0 y1 . E x0 , y0 . exp jk . 2 z . 2 z Aperture x1 , y1 E x1 , y1 dx1dy1.. Quadratics in the exponent: a messy integral A plane wave incident on a sharp edge Fresnel Diffraction integral, in one dimension: .. 1 x x 2 . E ( x0 ) exp jkz exp jk 0 1 dx1. j z 2 z . x1 0. geometrical exact Diffraction result shadow Intensity The irradiance exactly at the edge is 25% of the value far from the edge.
If D = 10 microns, then: 2 10 2 630 microns 0.5 D z Example #2: microwaves ( = 3 cm) If D = 10 centimeters, then: 2 10 2 1 meter 3 D z If D = 1 millimeter, then: 2 1 2 0.1 millimeters 30 D z But notice that z >> 1 mm is required in this case for the paraxial
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