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.50                   2. Signal Processing with Optics

       2.6 Given an input-output linear spatially invariant optical system under
            strictly incoherent illumination,
            (a) Derive the incoherent transfer function in terms of the spatial impulse
               response of the system.
            (b) State some basic properties of the incoherent transfer function.
            (c) What are the cutoff frequencies of the system under coherent and
               incoherent illuminations?
       2.7 Consider an optical imaging system that is capable of combining two
            Fraunhofer diffractions resulting from input objects /,(.x, y) and /" 2(.x, y),
            as shown in Fig. 2.60.
            (a) Compute the output irradiances under the mutual coherent and the
               mutual incoherent illuminations, respectively.
            (b) Comment on the results of part (a).
                            y













                                     Fig. 2.60.


       2.8. Assume that a coherent light distribution on the (a, /?) spatial coordinate
           system is shown in Fig. 2.61. Use it to evaluate the complex light field at
           the (x, y) plane.



                                                                   g(a.P)

       f(x,y)
                              direction of wave
                              propagation









                                     Fig. 2.61.
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