## Abstract

We propose a novel approach to massively reduce the memory of the novel look-up table (N-LUT) for computer-generated holograms by employing one-dimensional (1-D) sub-principle fringe patterns (sub-PFPs). Two-dimensional (2-D) PFPs used in the conventional N-LUT method are decomposed into a pair of 1-D sub-PFPs through a trigonometric relation. Then, these 1-D sub-PFPs are pre-calculated and stored in the proposed method, which results in a remarkable reduction of the memory of the N-LUT. Experimental results reveal that the memory capacity of the LUT, N-LUT and proposed methods have been calculated to be 149.01 TB, 2.29 GB and 1.51 MB, respectively for the 3-D object having image points of 500 × 500 × 256, which means the memory of the proposed method could be reduced by 103 × 10^{6} fold and 1.55 × 10^{3} fold compared to those of the conventional LUT and N-LUT methods, respectively.

©2012 Optical Society of America

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### Equations (8)

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(1)
$$T(x,y;{z}_{p})\equiv \mathrm{cos}\left[\frac{k}{{z}_{p}}\left\{{\left(x-{x}_{p}\right)}^{2}+{\left(y-{y}_{p}\right)}^{2}+{z}_{p}^{2}\right\}\right]$$
(2)
$$I(x,y)={\displaystyle \sum _{p=1}^{N}{a}_{p}T\left(x-{x}_{p},y-{y}_{p};{z}_{p}\right)}$$
(3)
$$\begin{array}{l}T(x,y;{z}_{p})=\mathrm{cos}\left[\frac{k}{{z}_{p}}\left(\Delta {x}^{2}+\Delta {y}^{2}+{z}_{p}^{2}\right)\right]\\ \begin{array}{cccc}& & & =\end{array}\mathrm{cos}\left[k\left(\frac{\Delta {x}^{2}}{{z}_{p}}+\frac{\Delta {y}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}+\frac{{z}_{p}^{2}}{2}\right)\right]=\mathrm{cos}\left[k\left(\frac{\Delta {x}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)+k\left(\frac{\Delta {y}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)\right]\\ \begin{array}{cccc}& & & =\end{array}\mathrm{cos}\left[k\left(\frac{\Delta {x}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)\right]\mathrm{cos}\left[k\left(\frac{\Delta {y}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)\right]-\mathrm{sin}\left[k\left(\frac{\Delta {x}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)\right]\mathrm{sin}\left[k\left(\frac{\Delta {y}^{2}}{{z}_{p}}+\frac{{z}_{p}^{2}}{2}\right)\right]\end{array}$$
(4)
$$\begin{array}{l}\text{Horizontal}\text{resolution}\text{of}\text{the}\text{PFP}\text{:}\left[\left({x}_{rightmost}-{x}_{leftmost}\right)\times disc+{h}_{x}\right]\\ \text{Vertical}\text{resolution}\text{of}\text{the}\text{PFP}\text{:}\left[\left({y}_{top}-{y}_{bottom}\right)\times disc+{h}_{y}\right]\end{array}$$
(5)
$${t}_{\text{RT}}={\displaystyle \sum _{d=1}^{{d}_{\mathrm{max}}}\left\{{t}_{gen\_holo}\times {t}_{multi\_amp}\times {N}_{D}\right\}}$$
(6)
$${t}_{\text{LUT}}={\displaystyle \sum _{d=1}^{{d}_{\mathrm{max}}}\left\{\left({t}_{load\_EFP}+{t}_{multi\_amp}\right)\times {N}_{D}\right\}}$$
(7)
$${t}_{\text{N}-\text{LUT}}={\displaystyle \sum _{d=1}^{{d}_{\mathrm{max}}}\left\{{t}_{load\_PFP}+\left({t}_{multi\_amp}\times {N}_{D}\right)\right\}}$$
(8)
$${t}_{\text{Proposed}}={\displaystyle \sum _{d=1}^{{d}_{\mathrm{max}}}\left\{{t}_{load\_sub-PFP}+{t}_{restore\_PFP}+\left({t}_{multi\_amp}\times {N}_{D}\right)\right\}}$$