Generation of Focal Patterns With Uniform Intensity Distribution From Speckle by Hadamard-Genetic Algorithm

When a coherent beam transmits through a scattering medium, a random intensity distribution known as speckle is generated. Generally, such speckles can be modulated by feedback-based wavefront shaping, as exemplified by the generation of a bright focal spot. However, it is more challenging to generate a specific focal pattern with uniform intensity distribution. In this study, the Hadamard–Genetic algorithm (HGA), namely a hybrid phase modulation scheme of Hadamard encoding algorithm (HEA) and genetic algorithm (GA), is proposed to face these challenges. This algorithm takes advantages of the high intensity of HEA and the high uniformity of GA and outperforms traditional optimization schemes, especially in suppressing intensity fluctuations of the focal pattern. This research is expected to be applied in the field of laser processing and particle manipulation.