Radial Gerchberg-Saxton algorithm for phase retrieval and spatial flat-top beam shaping of azimuthally symmetric laser beams

Abstract

The Gerchberg Saxton(GS) algorithm is a powerful phase retrieval process that can be used for both phase retrieval and phase mask design. Over the last 50 years, different versions of the GS algorithm have been developed that expand upon the original process and increase solution accuracy. A radial and multi-plane GS algorithm is developed for phase retrieval of azimuthally symmetric optics. This algorithm is shown to accurately retrieve the phase of an f=300mm lens and is used to characterize a commercially available flat-top beam shaping solution, the AdlOptica Focal Pi-Shaper. A single-optic phase mask is designed with a 2-plane version of this algorithm. The mask is designed to generate a spatial flat-top in a beam near focus. Shaping towards a flat-top beam profile is useful for many experiments and industrial processes. The new phase shaper will be used in highly non-linear experiments where imperfections are exaggerated. A design is presented for shaping that produces a flat top with sharper edges and a smoother flat-top than can be obtained with commercially available shapers.