Research On Phase Recovery And Reconstruction In Digital Holographic Microtomography

Digital holography is an important method to obtain the three-dimensional structure of samples.The interference fringe pattern of the object to be measured at multiple observation angles is obtained by means of the interference method and the phase information of each angle is reproduced numerically.Using the phase information as the projection data of the tomographic reconstruction,the 3D refractive index distribution of the internal structure of the object can be obtained by using the corresponding reconstruction algorithm.In recent years,digital holography has been widely used in the measurement of biological samples such as cells,pollen and fiber structures.Based on the Mach-Zehnder holographic interferometer,an experimental device for digital holographic micro-tomography is set up in this paper and the phase information of the sample under different angles is obtained by rotating the sample.We add a phase shifter to the reference light wave of the experimental device,and change the phase of the reference light wave by means of a uniform motion of the phase shifter.At the same time,the CCD continuously records the phase shift interference fringe video of the sample at the same observation angle.This method reduces the influence of environmental vibration noise on the phase shift accuracy and shortens the experiment time of the phase shift method.The information of the three-dimensional refractive index distribution of the sample was converted into the light intensity distribution in the interference fringe pattern throughout the experiment.After obtaining the interference fringe pattern of the sample in the 360°angle range,the phase information needs to be recovered according to the interference fringe pattern.The phase information is used as the input data of the tomographic reconstruction algorithm.So the accuracy of the phase information directly affects the reconstruction results.Based on the method of collecting phase-shifted video in experiments,we proposed a batch automatic selection algorithm of phase-shift interference fringe patterns based on Hilbert transform.Numerical simulation and error analysis are performed on the algorithm.First,each interference fringe pattern is extracted from the phase-shifted video,and then four interference fringe patterns with the smallest phase shift errors are automatically selected from the multiple interference fringe patterns of the sample at a certain angle by this algorithm.Through cyclic calculation,the phase shift interference fringe pattern of the sample in the 360°angle range can be quickly and automatically selected.The results shown that the algorithm reduces the phase shift error and the adverse effects caused by external vibration,and improves the accuracy of the phase shift method.The result obtained by the phase shift method is the wrapped phase and the unwrapping algorithm needs to be used to eliminate the phase value jump.In order to meet the double requirements of unwrapping reliability and reduce computing time,we designed and implemented a multi-set phase unwrapping algorithm based on amplitude guidance.The algorithm is sorted in descending order according to the amplitude of the interference fringe diagram,which is used as the quality diagram in the process of unwrapping.During the unwrapping process,an unwrapped set of pixels is continuously created and merged until the entire image is unwrapped.The results shown that this algorithm is a fast and fully automatic phase unwrapping algorithm with strong anti-noise ability.Finally,this paper introduces and derives two theories of the reconstruction algorithm,the Fourier projection slice theorem and the Fourier diffraction theory,and analyzes the differences and connections between the two theories.According to two theories,two corresponding classical reconstruction algorithms,filtered back-projection algorithm and filtered back-propagation algorithm are deduced,respectively.And the differences between the writing and implementation of the two algorithms are given.Comparing the two algorithms,it is found that the filtering back-propagation algorithm takes into account the effect of sample diffraction in the experiment.So the reconstruction accuracy is higher,which is more suitable for the reconstruction of the sample.Based on the filtered back-propagation algorithm,optical fiber samples and biological cell samples were reconstructed.We obtained the internal structure of single-mode fiber and photonic crystal fiber,which are consistent with the actual physical parameters of the fiber.In addition,by processing and reconstructing plant pollen and animal fat cells,the results shown that we can clearly distinguish the nuclear structure and other areas inside the cell.This is of great significance for us to study the internal structure and characteristics of samples and will play an important role in materials science and life sciences.