Redistribution of output weighting coefficients for complex multiplexed phase-diffractive elements

Hua Liu,Zhenwu Lu,Fengyou Li

doi:10.1364/opex.12.004347

Abstract

The formation of multiplexed phase-only holograms with more weighted phase functions creates spurious cross terms and nonlinear scaling. We extend previously reported work [Appl. Opt. 25, 3767 (1986)] by proposing a normal method to analyze multiplexed holograms mathematically. We show that the output of holograms with any number weighted phase function can be written as a new linear combination for the original phase function with new weights. The relationship between the original weights and the new weights is developed for real-time optimization of hologram performance. We focus on the analysis of two and three multiplexed holograms to demonstrate the effectiveness of this approach.

Highlights

There are several applications including optical pattern recognition [1], optical interconnections [2,3], three-dimensional display, and an absolute interferometric test of aspherics [4,5], in which several phase functions with different weights are multiplexed into a single phase-only or a binary phase-only hologram
No previous research mathematically deduced the relationship between the encoded weights and the output weights with a normal method that is suitable for holograms with N-weighted phase functions
We show that the output can be written as a new linear combination for the original phase functions with new weights

Summary

Introduction

There are several applications including optical pattern recognition [1], optical interconnections [2,3], three-dimensional display, and an absolute interferometric test of aspherics [4,5], in which several phase functions with different weights are multiplexed into a single phase-only or a binary phase-only hologram. Research has shown that spurious cross terms are formed and the weights of the output have a nonlinear relation with the weights of the encoded linear combination [6], which is a fundamentally different result compared with the desired output. This problem forces one to use a variety of complicated numerical techniques to compensate for the nonlinearities [7,8,9]. We extend previously reported results [8] by proposing a normal method to analyze mathematically multiplexed holograms with N-weighted phase functions. It is believed that holograms with less than N phase functions can be used without the need for analysis when we analyze a hologram with N-weighted phase functions

Theory

Validation

Simulation

Conclusion