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4500PF15

# 4500PF15 - Fraunhofer Diffraction by Inverted Triangular...

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Fraunhofer Diffraction by Inverted Triangular Function A spatial light modulator is adjusted so that the amplitude transmittance, t , is an inverted triangular transmittance function, f it , as shown in the figure. At the center ( x = 0), the slit amplitude transmittance is 0% ( t = 0). The amplitude transmittance increases to 50% ( t = 0 . 5) at x = ± a/ 2. The amplitude transmittance further increases to 100% ( t = 1 . 0) at x = ± 3 a/ 2. The amplitude transmittance then drops to 0% ( t = 0) at x = ± 5 a/ 2. The spatial light modulator is illuminated at normal incidence by a plane wave of freespace wavelength λ . Derive, showing all work, the amplitude of the far-field (Fraunhofer) diffraction pattern resulting from the diffraction of the plane wave by this inverted triangular am- plitude transmittance function, f it . Express your answer as A ( k x ) where A ( k x ) is a func- tion of a and k x only , where k x is the x -component of the diffracted wavevector. Derive, showing all work, the radiant intensity of the far-field (Fraunhofer) diffraction pattern resulting from the diffraction of the plane wave by this inverted triangular amplitude

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4500PF15 - Fraunhofer Diffraction by Inverted Triangular...

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