I have a circular telescope pupil, a magnifying optic, and a detector. I am trying to calculate the point spread function as a function of wavelength. I am running into the issue that Python's 2D FFT or matrix DFT declare their own spatial frequencies. Is there an obvious way to set my own spatial frequencies.
My "working" prototype is simply write my own matrix DFT:
numPixels = 1024 pupilCenter = numPixels / 2 W, H = np.meshgrid(np.arange(0, numPixels), np.arange(0, numPixels)) pupilMask = np.sqrt((W - pupilCenter)**2 + (H - pupilCenter)**2) <= numPixels/2 def DFT_matrix(N, M): """Calculate dft matrix N : number of pixels M : magnification factor""" i, j = np.meshgrid(np.arange(N)-N/2, np.arange(N)-N/2) omega = np.exp( - 2 * np.pi * 1.J / N / M ) W = np.power( omega, i * j ) / np.sqrt(N) return W
and to calculate the PSF by
M=25 W = DFT_matrix(numPixel, M) dft_of_pupil = W.dot(pupilMask).dot(W)
Is this a solution or have I missed something?