An undergraduate experiment to illustrate spatial transfer function concepts in Fourier optics

Fourier analysis is a key tool in physics and engineering in the broadest sense and is particularly used in the field of optics to design and study the properties of advanced imaging systems. Fourier optics as a distinct topic is usually taught in final-year undergraduate or first-year postgraduate studies, and a wide range of teaching approaches have been used to describe and explain its key concepts. Concerning practical work to accompany classroom lectures, the simplest laboratory experiments are based on studying how the properties of some diffracting aperture (pupil) are related to the corresponding Fraunhofer diffraction pattern, but this approach usually does not consider in detail the concepts of the optical transfer function and spatial frequencies. We here describe a simple experimental setup that fills this particular gap and that illustrates the spatial frequency-domain response of a simple optical system using incoherent light. The Modulation Transfer Function is directly measured for several different pupil geometries and shows very good agreement with theoretical calculations. This experiment clearly demonstrates spatial transfer function concepts in Fourier optics, complementing and extending other studies of Fourier transforms in physics that may consider similar ideas in a time and frequency signal-processing context.