SYNOPSISFourier transforms are proving to be of increasing value in the solution of problems in many fields of physics; in X‐ray diffraction studies in particular they find many applications. Their use, however, is often regarded as the province of the mathematician rather than of the physicist.This paper is intended to show that many of the useful concepts can be taught and assimilated visually, without mathematics, using optical diffraction patterns (usually called optical transforms). After an introductory section giving the basic principles and a brief description of the necessary apparatus, applications in musical analysis, in the study of resolution and image defects in microscopes, and in X‐ray crystallography are discus