A hybrid Gerchberg–Saxton-like algorithm for DOE and CGH calculation

•A new Gerchberg–Saxton-like algorithm is proposed for phase retrieval.•The introduction of gradient descent and weighting technique in the proposed algorithm guarantees better convergence in comparison to the Gerchberg–Saxton algorithm.•Both simulation and optical experiments of DOE and CGH for holographic display are carried out to demonstrate the algorithm.

The Gerchberg–Saxton (GS) algorithm is widely used in various disciplines of modern sciences and technologies where phase retrieval is required. However, this legendary algorithm most likely stagnates after a few iterations. Many efforts have been taken to improve this situation. Here we propose to introduce the strategy of gradient descent and weighting technique to the GS algorithm, and demonstrate it using two examples: design of a diffractive optical element (DOE) to achieve off-axis illumination in lithographic tools, and design of a computer generated hologram (CGH) for holographic display. Both numerical simulation and optical experiments are carried out for demonstration.