# Optimal Design of Segmented Planar Imaging System Based on Rotation and CLEAN Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

#### 2.1. Parity Baseline Selection

#### 2.2. Signal Transmission Model

_{1}and P

_{2}on the detection surface after passing through the z distance, and the cross-correlation strength J of P

_{1}and P

_{2}can be given by

_{1}(t) and U

_{2}(t) are the complex amplitude of light at P

_{1}and P

_{2}, and I (ξ, η) is the light intensity of the measured object. χ(θ

_{1}) and χ(θ

_{2}) are the inclining factors of the two lights. The long distance between the measured object and the detector meets the condition of the near axis, so χ(θ

_{1}) = χ(θ

_{2}) ≈ 1, $\frac{1}{{r}_{1}{r}_{2}}\approx \frac{1}{{z}^{2}}$ and

#### 2.3. Rotational Imaging

## 3. Results and Discussion

#### 3.1. Parameter Effects

#### 3.2. Rotational Imaging

#### 3.3. MP-CLEAN Algorithm

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Koekemoer, A.M.; Aussel, H.; Calzetti, D.; Capak, P.; Giavalisco, M.; Kneib, J.P.; Leauthaud, A.; Le Fèvre, O.; McCracken, H.J.; Massey, R.; et al. The cosmos survey: Hubble space telescope advanced camera for surveys observations and data processing. Astrophys. J. Suppl. Ser.
**2007**, 172, 196. [Google Scholar] [CrossRef] [Green Version] - Gehrels, N.; Fichtel, C.E.; Fishman, G.J.; Kurfess, J.D.; Schönfelder, V. The Compton Gamma Ray Observatory. Sci. Am.
**1993**, 269, 68–77. [Google Scholar] [CrossRef] - Weisskopf, M.C.; Tananbaum, H.D.; Van Speybroeck, L.P.; O’Dell, S.L. Chandra X-ray Observatory (CXO): Overview. In Proceedings of the Astronomical Telescopes and Instrumentation, Munich, Germany, 27 March–1 April 2000. [Google Scholar]
- Borucki, W.J. KEPLER Mission: Development and overview. Rep. Prog. Phys.
**2016**, 79, 036901. [Google Scholar] [CrossRef] [PubMed] - Pilbratt, G.L.; Riedinger, J.R.; Passvogel, T.; Crone, G.; Doyle, D.; Gageur, U.; Heras, A.M.; Jewell, C.; Metcalfe, L.; Ott, S.; et al. Herschel Space Observatory-An ESA facility for far-infrared and submillimetre astronomy. Astron. Astrophys.
**2010**, 518, L1. [Google Scholar] [CrossRef] [Green Version] - Yoo, S.J. Low-Mass Planar Photonic Imaging Sensor; No. HQ-E-DAA-TN56002; NASA: Washington, DC, USA, 2014.
- Duncan, A.; Kendrick, R.; Thurman, S.; Wuchenich, D.; Scott, R.P.; Yoo, S.J.B.; Su, T.; Yu, R.; Ogden, C.; Proiett, R. Spider: Next Generation Chip Scale Imaging Sensor. In Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, HI, USA, 15–18 September 2015. [Google Scholar]
- Kendrick, R.L.; Duncan, A.; Ogden, C.; Wilm, J.; Thurman, S.T. Segmented Planar Imaging Detector for EO Reconnaissance. In Proceedings of the Computational Optical Sensing and Imaging, Arlington, VA, USA, 23–27 June 2013. [Google Scholar]
- Badham, K.; Kendrick, R.L.; Wuchenich, D.; Ogden, C.; Chriqui, G.; Duncan, A.; Thurman, S.T.; Yoo, S.J.B.; Su, T.; Lai, W.; et al. Photonic Integrated Circuit-Based Imaging System for SPIDER. In Proceedings of the 2017 Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR). IEEE, Sands Expo and Convention Centre, Singapore, 31 July–4 August 2017; pp. 1–5. [Google Scholar]
- Scott, R.P.; Su, T.; Ogden, C.; Thurman, S.T.; Kendrick, R.L.; Duncan, A.; Yu, R.; Yoo, S.J.B. Demonstration of a Photonic Integrated Circuit for Multi-Baseline Interferometric Imaging. In Proceedings of the 2014 IEEE Photonics Conference, Hyatt Regency, La Jolla, San Diego, CA, USA, 12–16 October 2014. [Google Scholar]
- Sacher, W.D.; Huang, Y.; Lo, G.Q.; Poon, J.K.S. Multilayer silicon nitride-on-silicon integrated photonic platforms and devices. J. Light. Technol.
**2015**, 33, 901–910. [Google Scholar] [CrossRef] - Guo-Mian, L.; Qi, L.; Yue-Ting, C.; Hua-Jun, F.; Zhi-Hai, X.; Jingjing, M. An improved scheme and numerical simulation of segmented planar imaging detector for electro-optical reconnaissance. Opt. Rev.
**2019**, 26, 664–675. [Google Scholar] [CrossRef] - Chu, Q.; Shen, Y.; Yuan, M.; Gong, M. Numerical simulation and optimal design of segmented planar imaging detector for electro-optical reconnaissance. Opt. Commun.
**2017**, 405, 288–296. [Google Scholar] [CrossRef] - Gao, W.P.; Wang, X.R.; Ma, L.; Yuan, Y.; Guo, D.F. Quantitative analysis of segmented planar imaging quality based on hierarchical multistage sampling lens array. Opt. Express
**2019**, 27, 7955–7967. [Google Scholar] [CrossRef] [PubMed] - Gao, W.; Yuan, Y.; Wang, X.; Ma, L.; Zhao, Z.; Yuan, H. Quantitative analysis and optimization design of the segmented planar integrated optical imaging system based on an inhomogeneous multistage sampling lens array. Opt. Express
**2021**, 29, 11869–11884. [Google Scholar] [CrossRef] - Clark, B.G. An efficient implementation of the algorithm ‘CLEAN’. Astron. Astrophys.
**1980**, 89, 377. [Google Scholar]

**Figure 1.**Differences in structure and frequency between traditional SPIDER and the parity-baseline segmented planar imaging system. (

**a**) Structure of the conventional SPIDER; (

**b**) Method of parity baseline selection; (

**c**) Structure of the parity-baseline segmented planar imaging system; (

**d**) The u-v frequency components of the conventional SPIDER; (

**e**) The u-v frequency components of the parity-baseline segmented planar imaging system.

**Figure 3.**Imaging result with different parameters. (

**a**) Original image; (

**b**) Imaging result with the parameters in Table 1; (

**c**) The number of PICs and lenslets versus the mean square error (MSE).

**Figure 4.**(

**a**–

**d**) Rotational imaging result of the conventional SPIDER with the number of spins of 1, 5, 10, 15. (

**e**–

**h**) Rotational imaging result of the parity-baseline segmented planar imaging system with the number of spins of 1, 5, 10, 15.

**Figure 5.**(

**a**) Original image for MP-CLEAN simulation. (

**b**) Imaging result without MP-CLEAN. (

**c**) Imaging result with MP-CLEAN. (

**d**) Rendering of MP-CLEAN algorithm with iterations.

**Figure 6.**(

**a**) The imaging process of segmented planar imaging system based on rotation and MP-CLEAN. (

**b**) Imaging result of the conventional SPIDER before rotation without MP-CLEAN. (

**c**) Imaging result of the conventional SPIDER after rotation without MP-CLEAN. (

**d**) Imaging result of the parity-baseline segmented planar imaging system before rotation with MP-CLEAN. (

**e**) Imaging result of the parity-baseline segmented planar imaging system after rotation with MP-CLEAN.

Parameter | Symbol | Value |
---|---|---|

Number of PICs | M | 37 |

Number of lenslets per PIC | N | 51 |

Lenslet diameter | d | 2 mm |

Length of the longest baseline | B_{max} | 100 mm |

Wavelength | λ | 800~1600 nm |

Channel number | q | 10 |

Object distance | z | 100 km |

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## Share and Cite

**MDPI and ACS Style**

Ming, Z.; Liu, Y.; Li, S.; Zhou, M.; Du, H.; Zhang, X.; Zuo, Y.; Qiu, J.; Wu, J.; Gao, L.;
et al. Optimal Design of Segmented Planar Imaging System Based on Rotation and CLEAN Algorithm. *Photonics* **2023**, *10*, 46.
https://doi.org/10.3390/photonics10010046

**AMA Style**

Ming Z, Liu Y, Li S, Zhou M, Du H, Zhang X, Zuo Y, Qiu J, Wu J, Gao L,
et al. Optimal Design of Segmented Planar Imaging System Based on Rotation and CLEAN Algorithm. *Photonics*. 2023; 10(1):46.
https://doi.org/10.3390/photonics10010046

**Chicago/Turabian Style**

Ming, Zhizi, Yang Liu, Shanchuang Li, Mengchen Zhou, Haoran Du, Xiaochun Zhang, Yong Zuo, Jifang Qiu, Jian Wu, Lu Gao,
and et al. 2023. "Optimal Design of Segmented Planar Imaging System Based on Rotation and CLEAN Algorithm" *Photonics* 10, no. 1: 46.
https://doi.org/10.3390/photonics10010046