Considering the effect of diffraction on the scaled optical Fourier transform

Analogue Optical Signal Processing is a very important area in optics and central to it, is the implementation of the Optical Fourier Transform (OFT). There are many bulk optical arrangements for implementing the OFT however one which is particularly popular is the Scaled Optical Fourier Transform (SOFT) because it offers the user to the ability to change the size or scale of the output Fourier distribution. In this paper we examine the some of the practical limits introduced by the use of a cylindrical lens of finite aperture. We examine the phase and intensity deviations and provide simple rules of thumb, which allows the cautious user to, not only avoid, but also to quantify the worst case errors arising due to diffraction.