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...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.展开更多
We propose a new algorithm for the error correction of scanning positions in ptychographic microscopy.Since the scanning positions are varied mechanically by moving the illuminating probes laterally,the scanning error...We propose a new algorithm for the error correction of scanning positions in ptychographic microscopy.Since the scanning positions are varied mechanically by moving the illuminating probes laterally,the scanning errors will accumulate at multiple positions,greatly reducing the reconstruction quality of a sample.To correct the scanning errors,we use the correlation analysis for the diffractive data combining with the additional constraint of dual wavelengths.This significantly improves the quality of ptychographic microscopy.Optical experiments verify the proposed algorithm for two samples including a resolution target and a fibroblast.展开更多
基金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)+4 种基金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)the Natural Science Foundation of Hebei Province,China(Grant No.F2018402285).
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No. 61575197the Fusion Foundation of Research and Education of CAS+2 种基金the Youth Innovation Promotion Association of CAS (2017489)the University of Chinese Academy of Sciencesthe Natural Science Foundation of Hebei Province of China (F2018402285)
文摘We propose a new algorithm for the error correction of scanning positions in ptychographic microscopy.Since the scanning positions are varied mechanically by moving the illuminating probes laterally,the scanning errors will accumulate at multiple positions,greatly reducing the reconstruction quality of a sample.To correct the scanning errors,we use the correlation analysis for the diffractive data combining with the additional constraint of dual wavelengths.This significantly improves the quality of ptychographic microscopy.Optical experiments verify the proposed algorithm for two samples including a resolution target and a fibroblast.
