中国物理B ›› 2021, Vol. 30 ›› Issue (9): 94201-094201.doi: 10.1088/1674-1056/abf348

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Possibility to break through limitation of measurement range in dual-wavelength digital holography

Tuo Li(李拓)1, Wen-Xiu Lei(雷文秀)1, Xin-Kai Sun(孙鑫凯)2, Jun Dong(董军)1, Ye Tao(陶冶)3, and Yi-Shi Shi(史祎诗)3,†   

  1. 1 School of Electronic Engineering, Xi'an University of Posts&Telecommunications, Xi'an 710121, China;
    2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    3 School of Opto-Electronics, University of Chinese Academy of Sciences, Beijing 100049, China
  • 收稿日期:2020-12-29 修回日期:2021-03-08 接受日期:2021-03-30 出版日期:2021-08-19 发布日期:2021-08-30
  • 通讯作者: Yi-Shi Shi E-mail:optsys@gmail.com
  • 基金资助:
    Project supported by the Foundation of Science and Technology Department of Shaanxi Province, China (Grant No. 2018JQ6009), the Foundation of Education Department of Shaanxi Province, China (Grant No. 17JK1165), the Beijing Natural Science Foundation, China (Grant No. Z190004), the National Natural Science Foundation of China (Grant No. 61575197), the Innovation Capability Improvement Plan, Hebei Province, China (Grant No. 20540302D), the Fundamental Research Funds for the Central Universities, China, the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2017489), and the Natural Science Foundation of Hebei Province, China (Grant No. F2018402285).

Possibility to break through limitation of measurement range in dual-wavelength digital holography

Tuo Li(李拓)1, Wen-Xiu Lei(雷文秀)1, Xin-Kai Sun(孙鑫凯)2, Jun Dong(董军)1, Ye Tao(陶冶)3, and Yi-Shi Shi(史祎诗)3,†   

  1. 1 School of Electronic Engineering, Xi'an University of Posts&Telecommunications, Xi'an 710121, China;
    2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    3 School of Opto-Electronics, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2020-12-29 Revised:2021-03-08 Accepted:2021-03-30 Online:2021-08-19 Published:2021-08-30
  • Contact: Yi-Shi Shi E-mail:optsys@gmail.com
  • Supported by:
    Project supported by the Foundation of Science and Technology Department of Shaanxi Province, China (Grant No. 2018JQ6009), the Foundation of Education Department of Shaanxi Province, China (Grant No. 17JK1165), the Beijing Natural Science Foundation, China (Grant No. Z190004), the National Natural Science Foundation of China (Grant No. 61575197), the Innovation Capability Improvement Plan, Hebei Province, China (Grant No. 20540302D), the Fundamental Research Funds for the Central Universities, China, the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2017489), and the Natural Science Foundation of Hebei Province, China (Grant No. F2018402285).

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摘要： By using the beat frequency technique, the dual-wavelength digital holography (DWDH) can greatly increase the measurement range of the system. However, the beat frequency technique has a limitation in measurement range. The measurement range is not larger than a synthetic wavelength. Here, to break through this limitation, we propose a novel DWDH method based on the constrained underdetermined equations, which consists of three parts: (i) prove that the constrained underdetermined equation has a unique integer solution, (ii) design an algorithm to search for the unique integer solution, (iii) introduce a third wavelength into the DWDH system, and design a corresponding algorithm to enhance the anti-noise performance of DWDH. As far as we know, it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations, and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range. A series of results is shown to test the theory and the corresponding algorithms. More importantly, since the principle of proposed DWDH is based on basic mathematical principles, it can be further extended to various fields, such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.

关键词: digital holography, dual-wavelength interferometry, holographic interferometry

Abstract: By using the beat frequency technique, the dual-wavelength digital holography (DWDH) can greatly increase the measurement range of the system. However, the beat frequency technique has a limitation in measurement range. The measurement range is not larger than a synthetic wavelength. Here, to break through this limitation, we propose a novel DWDH method based on the constrained underdetermined equations, which consists of three parts: (i) prove that the constrained underdetermined equation has a unique integer solution, (ii) design an algorithm to search for the unique integer solution, (iii) introduce a third wavelength into the DWDH system, and design a corresponding algorithm to enhance the anti-noise performance of DWDH. As far as we know, it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations, and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range. A series of results is shown to test the theory and the corresponding algorithms. More importantly, since the principle of proposed DWDH is based on basic mathematical principles, it can be further extended to various fields, such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.

Key words: digital holography, dual-wavelength interferometry, holographic interferometry

中图分类号:  (Image reconstruction; tomography)

  • 42.30.Wb
42.30.-d (Imaging and optical processing) 42.40.Kw (Holographic interferometry; other holographic techniques)