# Review of Random Phase Encoding in Volume Holographic Storage

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{3}based on random phase multiplexed holographic memory has been reported by He et al. [12]. An effective analysis model for estimating diffraction selectivity of random phase multiplexing was first proposed by Sun et al. [14] in 2000.

## 2. Random Phase Multiplexing

#### 2.1. Shifting Selectivity

_{2}is the distance between the decoding ground glass and the hologram, which can be expressed as ${r}_{2}={\left\{{\left({x}_{3}-{x}_{2}\right)}^{2}+{\left({y}_{3}-{y}_{2}\right)}^{2}+{\left({z}_{3}-{z}_{2}\right)}^{2}\right\}}^{1/2}$; $\varphi \left({x}_{2},{y}_{2}\right)$ is the initial phase of each point source on the ground glass used for encoding the reading wave. Once the ground glass encoding the reading wave is not the same as that encoding the reference wave, the diffraction is suppressed, due to destructive interference. Therefore, no obvious diffraction light can be observed. Therefore, in the following analyses, the ground glass used for encoding the reference is the same as that used for the reading waves, but the position could be different. The effective diffraction is caused only by the self-reading of each point source. Then the conditions of $\varphi \left({x}_{2},{y}_{2}\right)-\varphi \left({x}_{1},{y}_{1}\right)=0$ must be satisfied in Equation (2). Supposed the ground glass is shifted at a distance of $\Delta =\sqrt{\Delta {x}^{2}+\Delta {y}^{2}+\Delta {z}^{2}}$, where Δx, Δy and Δz are the shifting in horizontal, vertical, and longitudinal directions, respectively. In the following, we discuss the cases when the ground glass is shifted in the lateral and longitudinal directions respectively.

#### 2.1.1. Lateral Shifting Selectivity

_{0}is the distance between the ground glass and the crystal. Equation (2) can be rewritten

#### 2.1.2. Longitudinal Shifting Selectivity

_{0}= 1 cm, $\ell =1\text{}cm$, and $\lambda =514.5\text{}nm$. The evaluation of the 3-D shifting tolerance is useful to random phase encoding for multi-layer storage. Assuming that the full shifting tolerance in three dimensions are $\Delta {x}_{s}$, $\Delta {y}_{s}$, and $\Delta {z}_{s}$, respectively, and the ground glass can be shifted in a range of ${L}_{x}\times {L}_{y}\times {L}_{z}$, then the multiplexing capacity is $\raisebox{1ex}{${L}_{x}$}\!\left/ \!\raisebox{-1ex}{$\Delta {x}_{s}$}\right.\times \raisebox{1ex}{${L}_{y}$}\!\left/ \!\raisebox{-1ex}{$\Delta {y}_{s}$}\right.\times \raisebox{1ex}{${L}_{z}$}\!\left/ \!\raisebox{-1ex}{$\Delta {z}_{s}$}\right.$. Based on VOHIL model, we have derived a general expression for the diffraction selectivity of the ground glass for random phase encoding. The mechanisms of 3-D selectivity are described theoretically, and the experimental results support those theoretical predictions [13,14]. From our analysis and corresponding experimental observation, a convenient method for increasing the shifting selectivity as well as the multiplexing capacity is to enlarge the illumination dimension on the ground glass and to shorten the distance between the ground glass and the volume hologram.

**Figure 3.**Theoretical shifting selectivity for random phase multiplexing in volume holographic storage.

#### 2.2. Rotational Selectivity

**Figure 4.**(

**a**) Schematic diagram of the rotational random phase encoding for volume holograms; (

**b**) Three different locations of the illumination area on the ground glass.

## 3. Image Encryption for Volume Holographic Storage

_{3}photorefractive crystal, with a reference plane wave. To store more frames of data, angular multiplexing can be employed. In the decryption process, the phase conjugate of the reference beam is used to read the stored encrypted data in the crystal. The data of ith stored image can be reconstructed when the readout beam is incident at a correct angle. The conjugate diffracted light will go back to the Fourier plane. If the decryption phase mask is the same as the original one, we can obtain a well-decrypted pattern. If a different decryption phase mask were to be used in the decryption process, the output image in the plane P4 would remain as white noise.

_{0}= 2 cm, 5 cm, and 10 cm is shown in Figure 7c. We find that the shifting tolerance is proportional to the distance between hologram and the phase mask. From theoretical analysis and experimentally investigated results, we can conclude that the lateral diffraction selectivity is determined by the convolution of the point-spread function induced by the crystal and the correlation function of the mask. The longitudinal diffraction selectivity depends on the longitudinal point-spread function. Therefore, enlarging the point-spread function is helpful to increase the shifting tolerance. From the analyses, there are two kinds of methods to enlarge the point-spread function. One is to increase the distance between the crystal and the phase mask and the other is to reduce the crystal size. The diffraction selectivity derived here offers important information for alignment and repositioning of the decrypted phase key in practical optical implementations.

## 4. All Optical Fiber Sensors

**Figure 9.**(

**a**–

**c**) are three selected diffraction images from the sensor system; (

**d**–

**f**) are the reference speckles corresponding (

**a**–

**c**), respectively.

## 5. Conclusions

## Acknowledgment

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**MDPI and ACS Style**

Su, W.-C.; Sun, C.-C.
Review of Random Phase Encoding in Volume Holographic Storage. *Materials* **2012**, *5*, 1635-1653.
https://doi.org/10.3390/ma5091635

**AMA Style**

Su W-C, Sun C-C.
Review of Random Phase Encoding in Volume Holographic Storage. *Materials*. 2012; 5(9):1635-1653.
https://doi.org/10.3390/ma5091635

**Chicago/Turabian Style**

Su, Wei-Chia, and Ching-Cherng Sun.
2012. "Review of Random Phase Encoding in Volume Holographic Storage" *Materials* 5, no. 9: 1635-1653.
https://doi.org/10.3390/ma5091635