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MIT2_71S09_ups8

# MIT2_71S09_ups8 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Spring ’09 Problem Set #8 Posted Wednesday, April 29, 2009 — Due Wednesday, May 6, 2009 1. In a diffraction–limited imaging system, the contrast is measured at spatial fre- quency 25mm - 1 and it is found to be 68.75%. 1.a) What is the contrast at spatial frequency 50mm - 1 ? 1.b) Is the spatial frequency 50mm - 1 “visible” through this imaging system under spatially coherent illumination consisting of a plane wave on–axis? 1.c) Does the answer to the previous question change if the on–axis constraint is relaxed, i.e. if we allow off–axis plane wave illumination? 2. The modulation transfer function (MTF) of an optical system is given in the figure below. The system is illuminated with quasi-monochromatic, spatially incoherent light. The intensity pattern at the input plane of the system is given by I ( x ) = 1 2 1 + 1 2 cos 2 π x 40 μ m + 1 2 cos 2 π 3 x 40 μ m -100 -50 0 50 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 u [cycles/mm] MTF

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2.a) What is the contrast of the intensity pattern at the input plane?
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MIT2_71S09_ups8 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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