Optoelectronic Systems Theory Assignment

1. For a cylindrical diffraction-limited optical system, on which a plane monochromatic wave with length \lambda and amplitude A=1 falls, find:

   1. A coherent transfer function \tilde{h}(\nu_x) and plot its graph
   2. An optical transfer function \tilde{H}_N^{OS}(\nu_x) and plot its graph

2. Find a polychromatic transfer function \tilde{H}^{PC}(\nu_x) for the radiation of a corresponding blackbody with temperature T, if the image is formed in the rear focal plane, and the spectral sensitivity of the radiation receiver is approximated by a Gaussian distribution with a mathematical expectation of 600 nm and a standard deviation of 100 nm.

3. Find the time-frequency spectrum of the radiation flux \tilde{\Phi}_t(\nu_t) and the magnitude of the radiation flux \Phi_t(t) in the image analysis plane of the optical system at the output of the modulator of the image analyzer during its linear scanning and plot their graphs. The optical system is a lens with a normalized scattering function H_N^{OS}(x', y')=\delta(x', y'), the source of radiation is an object in the form of a rectangle with a constant energy brightness L_0, the study of which obeys Lambert's law. The modulator of the image analyzer is a lattice with a cosine distribution of the transmission coefficient along the x axis.