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Goodman’s solutions work because they move from "ray tracing" to "Fourier transforming." When you design a spectrometer or a telescope, ask: What is the Optical Transfer Function (OTF) of this system?
pupil = np.where(R <= pupil_diameter/2, 1, 0) introduction to fourier optics goodman solutions work
A hidden gem in Goodman’s problems is the SBP. It tells you the information capacity of your system. A solution that ignores the SBP is physically unrealizable. If your solution yields infinite resolution, you made a mistake (diffraction limits you). Goodman’s solutions work because they move from "ray
Goodman assumes continuous functions. The moment you digitize a Fourier transform (FFT), you must respect the Nyquist limit. Fix: Ensure your aperture width ( \Delta x ) and wavelength ( \lambda ) satisfy ( \Delta x < \lambda z / (N \Delta x) ) in Fresnel simulations. A solution that ignores the SBP is physically unrealizable