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

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.