# Low-Bit-Depth Detection for Phase Retrieval with Higher Efficiency in Holographic Data Storage

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## Abstract

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## 1. Introduction

## 2. Theory and Methods

_{n}, n = 1,2,3,…, with the subscript varying according to the number of iterations. As the information is phase-only encoded, we assume the amplitude to be 1. The expression for the complex amplitude distribution can be formulated as shown in Equation (1).

_{max}signifies the maximum values of the intensity distribution.

^{1/2}. The resulting expression is depicted in Equation (4).

_{n+}

_{1}to 1 and employing the embedded data to rectify the phase, the updated distribution is illustrated in Equation (5).

_{n+}

_{1}represents a new estimate of the phase pattern of the signal beam, and F

^{−1}{} denotes the inverse Fourier transform.

## 3. Simulation and Experiment

_{error}indicates the number of errors in a data page, and N

_{data}indicates the total amount of data in a data page.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the phase-modulated holographic storage system, where Sig. is the signal beam, Ref. is the reference beam, and Rec. is the reconstructed beam.

**Figure 2.**The impact of the bit depth on the intensity distribution. (

**a**–

**d**) The intensity distribution with the color corresponding to different bit depths (8 bit, 7 bit, 6 bit, and 5 bit).

**Figure 5.**The optical setup of the holographic data storage system, where BE is the beam expander, HWP is the half-wave plate, BS is the beam splitter, SLM is the spatial light modulator, and CMOS is the complementary metal oxide semiconductor.

**Figure 6.**(

**a**) Original phase data. (

**b**) Simulated Fourier spectrum intensity distribution. (

**c**) Spectrum intensity distribution obtained by experimental shooting.

Phase Level | Amount of Data | Oversampling | PER | ||||
---|---|---|---|---|---|---|---|

8-bit | 7-bit | 6-bit | 5-bit | 4-bit | |||

3 phase level | 16 × 16 | 3 × 3 | 0.004 | 0 | 0 | 0.004 | 0.019 |

4 × 4 | 0 | 0 | 0 | 0 | 0.008 | ||

5 × 5 | 0 | 0 | 0 | 0 | 0 | ||

32 × 32 | 3 × 3 | 0.019 | 0.018 | 0.005 | 0.022 | 0.077 | |

4 × 4 | 0.017 | 0.017 | 0.012 | 0.024 | 0.063 | ||

5 × 5 | 0.087 | 0.084 | 0.069 | 0.077 | 0.127 | ||

48 × 48 | 3 × 3 | 0.087 | 0.084 | 0.068 | 0.065 | 0.095 | |

4 × 4 | 0.195 | 0.192 | 0.180 | 0.178 | 0.185 | ||

5 × 5 | 0.265 | 0.263 | 0.264 | 0.262 | 0.265 | ||

4 phase level | 16 × 16 | 3 × 3 | 0.027 | 0.019 | 0.011 | 0.07 | 0.152 |

4 × 4 | 0.012 | 0.012 | 0.004 | 0.016 | 0.089 | ||

5 × 5 | 0.012 | 0.008 | 0.008 | 0.019 | 0.070 | ||

32 × 32 | 3 × 3 | 0.052 | 0.047 | 0.017 | 0.057 | 0.115 | |

4 × 4 | 0.07 | 0.069 | 0.041 | 0.055 | 0.099 | ||

5 × 5 | 0.109 | 0.107 | 0.084 | 0.113 | 0.167 | ||

48 × 48 | 3 × 3 | 0.153 | 0.146 | 0.125 | 0.134 | 0.182 | |

4 × 4 | 0.250 | 0.250 | 0.238 | 0.235 | 0.248 | ||

5 × 5 | 0.321 | 0.319 | 0.321 | 0.317 | 0.326 | ||

5 phase level | 16 × 16 | 3 × 3 | 0.167 | 0.160 | 0.078 | 0.086 | 0.141 |

4 × 4 | 0.113 | 0.113 | 0.066 | 0.074 | 0.105 | ||

5 × 5 | 0.047 | 0.043 | 0.058 | 0.082 | 0.141 | ||

32 × 32 | 3 × 3 | 0.154 | 0.151 | 0.126 | 0.171 | 0.254 | |

4 × 4 | 0.165 | 0.159 | 0.146 | 0.191 | 0.281 | ||

5 × 5 | 0.198 | 0.200 | 0.208 | 0.226 | 0.297 | ||

48 × 48 | 3 × 3 | 0.227 | 0.228 | 0.208 | 0.213 | 0.239 | |

4 × 4 | 0.313 | 0.313 | 0.299 | 0.291 | 0.315 | ||

5 × 5 | 0.359 | 0.363 | 0.354 | 0.350 | 0.354 |

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## Share and Cite

**MDPI and ACS Style**

Liu, H.; Zheng, S.; Lin, Y.; Song, H.; Xu, X.; Li, X.; Zheng, J.; Cao, Q.; Lin, X.; Tan, X.
Low-Bit-Depth Detection for Phase Retrieval with Higher Efficiency in Holographic Data Storage. *Photonics* **2024**, *11*, 680.
https://doi.org/10.3390/photonics11070680

**AMA Style**

Liu H, Zheng S, Lin Y, Song H, Xu X, Li X, Zheng J, Cao Q, Lin X, Tan X.
Low-Bit-Depth Detection for Phase Retrieval with Higher Efficiency in Holographic Data Storage. *Photonics*. 2024; 11(7):680.
https://doi.org/10.3390/photonics11070680

**Chicago/Turabian Style**

Liu, Hongjie, Shujun Zheng, Yongkun Lin, Haiyang Song, Xianmiao Xu, Xiong Li, Jihong Zheng, Qiang Cao, Xiao Lin, and Xiaodi Tan.
2024. "Low-Bit-Depth Detection for Phase Retrieval with Higher Efficiency in Holographic Data Storage" *Photonics* 11, no. 7: 680.
https://doi.org/10.3390/photonics11070680