In order to perform holographic microwave imaging, an antenna performs measurements over a 30 cm x 30 cm aperture with steps of 1 cm along both x and y directions and at 20 frequencies at each position to reconstruct images over 4 planes. The Fourier variables corresponding to r and y are named kr and ky which change with 100 steps from 2k to 2k, where k is the wavenumber in the medium. Assuming the system of equations at each (kr,ky) pair is constructed as E"(kx,ky)Esc.00(kx,ky)F(kt,ky), where Es is a vector including Fourier transforms of the measured responses, Exc.ce is the coefficient matrix including the Fourier transforms of the point-spread functions, and F is the vector containing the Fourier transform of the object's contrasts (unknowns). • How many samples are collected (at all spatial positions and all frequencies). • What is the length of vector E*? • What is the length of vector F? • What are the dimensions of matrix of coefficients Esc.co for each system of equations? How many systems of equations need to be solved in this problem? • Comment on the conditions (in terms of size and contrast) for the objects to guarantee the best outcome using this imaging method?