Legacies of the Gerchberg–Saxton algorithm

To celebrate W. Owen Saxtonʹs 65th birthday, this paper presents some of the impact that the Gerchberg–Saxton algorithm has had over the last 40 years. We explore some of the fundamental concepts underlying the success of the Gerchberg–Saxton algorithm, in the context of how it stimulated many related methods for estimating fields and deepening the understanding of the relationships between complex objects, images and their Fourier transforms.