# Improvement in Signal Phase Detection Using Deep Learning with Parallel Fully Connected Layers

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Principle of Phase Detection Using Interpixel Crosstalk

#### 2.2. Acquisition of Experimental Training Data

#### 2.3. Structure of the Neural Network

## 3. Results and Discussions

_{10}PxER increases to −3.4 at 64 pixels. This is due to the reduction in the number of training data extracted from one detected image, but it is not a critical defect of our method. If the number of training data can be made large enough, PxER can maintain a small value even at 64 pixels. Therefore, we confirm that PxER in our proposed method can be significantly reduced compared with that in the conventional minimum-finding algorithm. Simultaneously, the phase-output time can be suppressed to almost the same level by employing parallel fully connected layers.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Arrangement of the known phase-reference pixel in a four-level phase signal. ϕ

_{s}represents the signal phase.

**Figure 2.**Preparation of the training data from the intensity image detected by the imager. The image with 3 × 3 pixels that surround the target signal pixel is extracted and added with the label of the corresponding signal phase.

**Figure 5.**Experimental results of the phase determination with deep learning. “Conventional” in the figure represents the minimum-finding algorithm mentioned in Section 2.1.

**Figure 6.**Phase-output time using a network with parallel fully connected layers. The horizontal axis represents the number of signal pixels that are simultaneously output. The vertical axis is the phase-output time normalized by the output time of the minimum-finding algorithm. The dashed line represents the fitted curve.

Number of Fully Connected Layers | Input Image Size |
---|---|

1 | 3 × 3 data pixels |

2 | 4 × 4 data pixels |

4 | 4 × 6 data pixels |

8 | 6 × 6 data pixels |

16 | 6 × 10 data pixels |

32 | 10 × 10 data pixels |

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**MDPI and ACS Style**

Tokoro, M.; Fujimura, R.
Improvement in Signal Phase Detection Using Deep Learning with Parallel Fully Connected Layers. *Photonics* **2023**, *10*, 1006.
https://doi.org/10.3390/photonics10091006

**AMA Style**

Tokoro M, Fujimura R.
Improvement in Signal Phase Detection Using Deep Learning with Parallel Fully Connected Layers. *Photonics*. 2023; 10(9):1006.
https://doi.org/10.3390/photonics10091006

**Chicago/Turabian Style**

Tokoro, Michito, and Ryushi Fujimura.
2023. "Improvement in Signal Phase Detection Using Deep Learning with Parallel Fully Connected Layers" *Photonics* 10, no. 9: 1006.
https://doi.org/10.3390/photonics10091006