Fast recurrence relation for computer-generated-hologram

In this paper, we derive a fast recurrence relation for a computer-generated-hologram (CGH). The recurrence relation based on Taylor expansion reduces the number of cosine computations as compared with conventional CGH formula. The recurrence relation calculates a CGH 7 or 8 times faster than the conventional CGH formula on a CPU and graphics processing unit (GPU). In addition, there is almost no difference between a CGH generated by the recurrence relation and that generated by the conventional type.

► We derive a fast recurrence relation for a computer-generated-hologram (CGH).
► The proposed method reduces the number of cosine computations.
► The proposed method calculates a CGH eight times faster than typical formula.
► There is no difference between a CGHs made by the proposed method and typical type.