# High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation

## TL;DR

This paper presents a novel method for precise control of both phase and amplitude in holograms using conjugate gradient minimisation on a phase-only SLM, achieving high fidelity and efficiency.

## Contribution

The authors introduce a conjugate gradient minimisation technique for phase-only holograms that enables simultaneous phase and amplitude control with high fidelity.

## Key findings

- Achieved a fidelity of 0.999997 for a target pattern.
- Demonstrated a light-usage efficiency of 41.5%.
- Experimental results showed a fidelity of 0.97 with 7.8% efficiency.

## Abstract

We demonstrate simultaneous control of both the phase and amplitude of light using a conjugate gradient minimisation-based hologram calculation technique and a single phase-only spatial light modulator (SLM). A cost function which incorporates the inner product of the light field with a chosen target field within a defined measure region is efficiently minimised to create high fidelity patterns in the Fourier plane of the SLM. A fidelity of $F=0.999997$ is achieved for a pattern resembling an $LG^{0}_{1}$ mode with a calculated light-usage efficiency of $41.5\%$. Possible applications of our method in optical trapping and ultracold atoms are presented and we show uncorrected experimental realisation of our patterns with $F = 0.97$ and $7.8\%$ light efficiency.