\\ . , J"\\'l- I 1. Consider the imaging system shown in Fig. 1. The aperture stop on the lens is a circular aperture of diameter D with a circular obstruction of diameter A centered on the optical axis (see Fig. 2 on next page). Mathematically, the aperture or the pupil function can be written as: P($,y) = circ (, %) circ (i, %) where, circ($_$n 990): 1 (iv3:0) -(y yn)2D/2 Aperture Lens Object Figure 1: Imaging system layout. Consider the imaging system with D 2 2mm A 2 0.561%, A 2 1pm, d3- 2 do = 1m and f = 0.5m. (a) Calculate and sketch the coherent transfer function (CTF) of the imaging system. (b) Calculate the lower and higher radial cut-off spatial frequencies of the CTF. (c) Calculate and plot the coherent point spread function of the imaging system using MATLAB. (d) Consider a sinusoidal object field Hall's, yo) = (203(27T501ro) + cos(2srnoyo) where 50 = 500 cycles/m and 17,, = 5000 cycles/m. Compute the eld Ui($i,y) in the image plane of the imaging system using the coherent transfer function and cutoff frequencies in (a) and (b). [60 points]