# Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Working Flow of Reconstruction Phase Distribution

#### 3.2. Analysis of Resolution

#### 3.3. Static Phase Measurement for Thin Object

#### 3.4. Dynamic Phase Measurement of a Standard Object

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, Z.; Millet, L.; Mir, M.; Ding, H.; Unarunotai, S.; Rogers, J.; Gillette, M.U.; Popescu, G. Spatial light interference microscopy (SLIM). Opt. Express
**2011**, 19, 1016–1026. [Google Scholar] [CrossRef] [PubMed] - Belashov, A.; Zhikhoreva, A.; Belyaeva, T.; Nikolsky, N.; Semenova, I.; Kornilova, E.; Vasyutinskii, O. Quantitative assessment of changes in cellular morphology at photodynamic treatment in vitro by means of digital holographic microscopy. Biomed. Opt. Express
**2019**, 10, 4975–4986. [Google Scholar] [CrossRef] [PubMed] - O’Connor, T.; Anand, A.; Andemariam, B.; Javidi, B. Deep learning-based cell identification and disease diagnosis using spatio-temporal cellular dynamics in compact digital holographic microscopy. Biomed. Opt. Express
**2020**, 11, 4491–4508. [Google Scholar] [CrossRef] [PubMed] - Pirone, D.; Sirico, D.; Miccio, L.; Bianco, V.; Mugnano, M.; Ferraro, P.; Memmolo, P. Speeding up reconstruction of 3D tomograms in holographic flow cytometry via deep learning. Lab A Chip
**2022**, 22, 793–804. [Google Scholar] [CrossRef] - Xia, P.; Ri, S.; Wang, Q.; Tsuda, H. Nanometer-order thermal deformation measurement by a calibrated phase-shifting digital holography system. Opt. Express
**2018**, 26, 12594–12604. [Google Scholar] [CrossRef] - Thomas, B.P.; Pillai, S.A.; Narayanamurthy, C. Computed time average digital holographic fringe pattern under random excitation. Appl. Opt.
**2021**, 60, A188–A194. [Google Scholar] [CrossRef] - Tahara, T.; Quan, X.; Otani, R.; Takaki, Y.; Matoba, O. Digital holography and its multidimensional imaging applications: A review. Microscopy
**2018**, 67, 55–67. [Google Scholar] [CrossRef] - Xia, P.; Wang, Q.; Ri, S.; Tsuda, H. Calibrated phase-shifting digital holography based on space-division multiplexing. Opt. Lasers Eng.
**2019**, 123, 8–13. [Google Scholar] [CrossRef] - Wang, H.; Li, K.; Jiang, X.; Wang, J.; Zhang, X.; Liu, X. Zero-order term suppression in off-axis holography based on deep learning method. Opt. Commun.
**2023**, 537, 129264. [Google Scholar] [CrossRef] - Lim, J.; Choi, H.; Park, N.-C. Phase-shift digital holography using multilayer ceramic capacitor actuators. Opt. Lasers Eng.
**2022**, 156, 107080. [Google Scholar] [CrossRef] - Xia, P.; Ri, S.; Inoue, T.; Awatsuji, Y.; Matoba, O. Dynamic phase measurement of a transparent object by parallel phase-shifting digital holography with dual polarization imaging cameras. Opt. Lasers Eng.
**2021**, 141, 106583. [Google Scholar] [CrossRef] - Meng, X.; Cai, L.; Xu, X.; Yang, X.; Shen, X.; Dong, G.; Wang, Y. Two-step phase-shifting interferometry and its application in image encryption. Opt. Lett.
**2006**, 31, 1414–1416. [Google Scholar] [CrossRef] - Shaked, N.T.; Newpher, T.M.; Ehlers, M.D.; Wax, A. Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics. Appl. Opt.
**2010**, 49, 2872–2878. [Google Scholar] [CrossRef] - Smythe, R.; Moore, R. Instantaneous phase measuring interferometry. Opt. Eng.
**1984**, 23, 361–364. [Google Scholar] [CrossRef] - Koliopoulos, C.L. Simultaneous phase-shift interferometer. In Proceedings of the Advanced Optical Manufacturing and Testing II, San Diego, CA, USA, 22–23 July 1991; pp. 119–127. [Google Scholar]
- Sivakumar, N.; Hui, W.; Venkatakrishnan, K.; Ngoi, B. Large surface profile measurement with instantaneous phase-shifting interferometry. Opt. Eng.
**2003**, 42, 367–372. [Google Scholar] [CrossRef] - Wang, Y.; Meng, H.; Liu, X.; Liu, J.; Cui, X. Pixel Resolution Imaging in Parallel Phase-Shifting Digital Holography. Appl. Sci.
**2022**, 12, 5812. [Google Scholar] [CrossRef] - Lokesh Reddy, B.; Nelleri, A. Single-pixel compressive digital holographic encryption system based on circular harmonic key and parallel phase shifting digital holography. Int. J. Opt.
**2022**, 2022, 6298010. [Google Scholar] [CrossRef] - Liu, H.; RV, V.; Ren, H.; Du, X.; Chen, Z.; Pu, J. Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging. Photonics
**2022**, 9, 126. [Google Scholar] [CrossRef] - Safrani, A.; Abdulhalim, I. Real-time phase shift interference microscopy. Opt. Lett.
**2014**, 39, 5220–5223. [Google Scholar] [CrossRef] - Zhang, J.; Ye, Y.; Xie, Y.; Liu, J.; Luo, Y. Synchronous Multi-Channel Phase-Shifting Digital Holographic Technology. Acta Opt. Sin.
**2013**, 33, 1009002–1009037. [Google Scholar] [CrossRef] - Muñoz, V.F.; Arellano, N.-I.T.; García, D.S.; García, A.M.; Zurita, G.R.; Lechuga, L.G. Measurement of mean thickness of transparent samples using simultaneous phase shifting interferometry with four interferograms. Appl. Opt.
**2016**, 55, 4047–4051. [Google Scholar] [CrossRef] [PubMed] - Zhu, Y.; Tian, A.; Liu Sr, B.; Wang Sr, H.; Wang, K.; Wang, S. Common-path and synchronous phase shifting of lateral shearing interferometry based on micro-polarizer array. In Proceedings of the Eighth Symposium on Novel Photoelectronic Detection Technology and Applications, Kunming, China, 7–9 December 2021; pp. 1050–1056. [Google Scholar]
- Majeed, H.; Sridharan, S.; Mir, M.; Ma, L.; Min, E.; Jung, W.; Popescu, G. Quantitative phase imaging for medical diagnosis. J. Biophotonics
**2017**, 10, 177–205. [Google Scholar] [CrossRef] [PubMed] - Muthukumaran, D.; Sivakumar, M. Medical image registration: A Matlab based approach. Int. J. Sci. Res. Comput. Sci. Eng. Inf. Technol.
**2017**, 2, 29–34. [Google Scholar] - Abbe, E. Die Lehre von der Bildentstehung im Mikroskop; Vieweg, F., Ed.; University of Michigan Library: Ann Arbor, MI, USA, 1910. [Google Scholar]
- Gissibl, T.; Thiele, S.; Herkommer, A.; Giessen, H. Two-photon direct laser writing of ultracompact multi-lens objectives. Nat. Photonics
**2016**, 10, 554–560. [Google Scholar] [CrossRef] - Ghiglia, D.C.; Romero, L.A.J.J.A. Minimum Lp-norm two-dimensional phase unwrapping. J. Opt. Soc. Am. A
**1996**, 13, 1999–2013. [Google Scholar] [CrossRef] - Muñoz, V.F.; Toto-Arellano, N.; López-Ortiz, B.; García, A.M.; Rodríguez-Zurita, G. Measurement of red blood cell characteristic using parallel phase shifting interferometry. Optik
**2015**, 126, 5307–5309. [Google Scholar] [CrossRef] - Pérez, A.M.; Rodríguez-Zurita, G.; Flores-Muñoz, V.; Parra-Escamilla, G.; Serrano-García, D.; Martínez-García, A.; Islas-Islas, J.; Ortega-Mendoza, J.; Lechuga, L.G.; Toto-Arellano, N.-I. Dynamic Mach–Zehnder interferometer based on a Michelson configuration and a cube beam splitter system. Opt. Rev.
**2019**, 26, 231–240. [Google Scholar] [CrossRef]

**Figure 1.**The designed PSDH system. (

**a**) The schematic of the designed PSDH system; (

**b**) The physical diagram of the designed system. P: linear polarization; BS: non-polarizing beamsplitter cube; QWP: quarter-wave plate; PBS: polarizing beamsplitter cube; MO: microscope objective.

**Figure 2.**The workflow of reconstructing phase using the proposed system. The first column displays four phase-shifted images (including the holograms of the sample and the calibration holograms). The second column are the reconstructed phases. The last column illustrates compensated phase distribution of the resolution chart.

**Figure 3.**Evaluation of the resolution. (

**a**) The reconstructed phase of the resolution chart; (

**b**) The enlargement of the red square; (

**c**) The phase heights across the designated lines in (

**b**).

**Figure 4.**Phase reconstruction of a static phase object. (

**a**) Reconstructed phase of 200 nm; (

**b**) Reconstructed phase of 300 nm; (

**c**) Reconstructed phase of 350 nm; (

**d**) The 3D map of (

**a**); (

**e**) The 3D map of (

**b**); (

**f**) The 3D map of (

**c**).

**Figure 6.**Dynamic phase measurement of the PMMA pellets. (

**a**–

**f**) are the phase maps reconstructed at 0.5 s intervals over a 3-s period. (

**g**) The phase heights across the red line in (

**a**) and blue line in (

**f**).

**Figure 7.**Dynamic phase image of the new PMMA pellets. (

**a**–

**f**) are the phase maps reconstructed of the new PMMA pellets.

Expected Thickness | Actual Manufactured Thickness | The Proposed Method |
---|---|---|

200 nm | 213.8 nm | 216.9 nm |

300 nm | 321.5 nm | 318.9 nm |

350 nm | 385.5 nm | 389.5 nm |

**Table 2.**Measurement results of the new PMMA pellets in Figure 7.

Number | Diameter (µm) | Phase Height (rad) | Thickness (µm) |
---|---|---|---|

1 | 9.85 | 2.36 | 9.98 |

2 | 10.24 | 2.43 | 10.30 |

3 | 9.72 | 2.33 | 9.88 |

4 | 10.40 | 2.41 | 10.22 |

5 | 10.38 | 2.39 | 10.12 |

6 | 10.41 | 2.44 | 10.34 |

Average | 10.17 | 2.39 | 10.14 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, J.; Liu, L.; Wang, T.; Wang, X.; Du, X.; Hao, R.; Liu, J.; Zhang, J.
Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics. *Sensors* **2023**, *23*, 4339.
https://doi.org/10.3390/s23094339

**AMA Style**

Zhao J, Liu L, Wang T, Wang X, Du X, Hao R, Liu J, Zhang J.
Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics. *Sensors*. 2023; 23(9):4339.
https://doi.org/10.3390/s23094339

**Chicago/Turabian Style**

Zhao, Jiaxi, Lin Liu, Tianhe Wang, Xiangzhou Wang, Xiaohui Du, Ruqian Hao, Juanxiu Liu, and Jing Zhang.
2023. "Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics" *Sensors* 23, no. 9: 4339.
https://doi.org/10.3390/s23094339