Legacies of the Gerchberg-Saxton algorithm

To celebrate W. Owen Saxton's 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.