Realization of equivalent multi-level DOEs by the stack of two few-level DOEs using phase dividing

Multi-level DOEs are always desired for the wider application. However, they require more accurate fabrication and expensive production costs. This paper presents an improved stacked DOEs method. Based on the phase distribution of t-level DOEs, a phase dividing method is used to divide the phase of t-level DOEs into m and n-level DOEs (t = n × m), the equivalent t-level DOEs can be realized by the stack of m and n-level DOEs. A 16-level beam shaping DOE is taken as an example to explore the method. The 4 and 4-level (or 2 and 8-level) stacked DOEs show the CV of 3.69% and diffractive efficiency of 98.11%, which is similar to 3.58% and 98.11% of a 16-level DOE. In addition, the tolerance of the stack method is also analyzed in horizontal displacement, vertical displacement, and angular deviation of stacked DOEs. The proposed stacked DOEs method can eliminate the need to directly manufacture multi-level DOEs with more steps, thus providing the possibility of reducing cost and fabricating difficulty.