Finite-aperture effects for Fourier transform systems with convergent illumination. Part II: 3-D system analysis

One of the most important optical signal processing operations is the optical Fourier transform (OFT). Of the arrangements for implementation of the OFT, perhaps the most flexible is that for the scaled optical Fourier transform (SOFT), as it allows control over the scale of the output Fourier transform distribution. By means of an analysis in cylindrical coordinates, we examine some of the practical limits introduced by the use of a thin lens of finite aperture in the implementation of the SOFT. Using simple rules of thumb that are based on an examination of the phase and magnitude deviations from the ideal (infinite-lens) diameter case, we define a volume inside the geometric shadow, which we refer to as a sub-geometric shadow. We then show that inside this sub-geometric shadow errors introduced by diffraction can be quantified.