Aberration correction of a spatial light modulator with a genetic algorithm

Abstract

A reflective liquid crystal spatial light modulator is a versatile electrically addressed optical device that is used to change the structure of light fields reflected off of it. It works by modulating the phase of the light field at the level of individual pixels. The spatial light modulator is controlled by displaying a digital phase mask image on it, which then applies the given phase structure onto the reflected light field. The construction of liquid crystal spatial light modulators is imperfect, leading to aberrations in its surface. These aberrations decrease the quality of the light fields that can be formed with the device. The aberrations can be corrected by applying a corrective phase mask onto the spatial light modulator before use. These corrective phase masks can be formed with a linear combination of Zernike polynomials, which are an infinite set of polynomials used to describe optical aberrations. Finding the correct linear combination coefficients for the chosen Zernike polynomials manually is inefficient and time-consuming.

The goal of this bachelor’s thesis is to develop a method for correcting the inherent aberration of the spatial light modulator automatically with a simple optical measurement system. An optimization algorithm called a genetic algorithm, provided by MATLAB, is utilized to find the optimal coefficients for correcting the aberration. Laguerre-Gaussian spatial modes of light are employed as probe fields to help determine the corrective ability of a given set of coefficients. These spatial modes of light can be created by modulating a light beam with the spatial light modulator. They are used because their transverse intensity profile is very strongly affected by aberrations in the spatial light modulator. The main focus of this work is the development of the fitness function of the genetic algorithm, which assigns each tested set of parameters a fitness value that describes its quality. The fitness function dictates the end result that the genetic algorithm is converging towards.

The final measurement system consists of a monochromatic laser, the spatial light modulator which the laser beam is reflected off of, and a camera to measure the transverse intensity profile of the modulated beam. The final version of the fitness function calculates a number value to describe the circular symmetry of the measured intensity profiles of the Laguerre-Gaussian modes and uses this value as a part of the fitness value calculation. Testing the final version of the method showed that it was working as intended, with the algorithm converging to a set of corrective coefficients, which resulted in the spatial light modulator achieving higher modulation quality.