| Holographic recording is the process of compressing signal from three dimensional data to two dimensional data. Each pixel in the hologram contains the information of every single point in the three-dimensional object. Theoretically, it has a large amount of redundant information. Compressive sensing can restore the original signal from a small amount of measurement data accurately or with high-probability, and meanwhile realize data reconstruction from low dimension to high dimension. Thereby it can realize tomographic reconstruction of three-dimensional object from small amount of holographic data. Therefore, more attention is gradually paid to digital holographic tomography based on compressive sensing. In this dissertation, after analyzing the domestic and overseas research status and the existing problems of this technology, related theoretical analysis and experimental research for different holographic recording system are carried out, which focus on the method, the quality and the axial resolution of digital holographic tomographic reconstruction based on compressive sensing. The main work is as follows.(1) Key factors of digital holographic tomographic reconstruction based on compressive sensing are analyzed.In the beginning of this dissertation, the mathematical model and key factors of compressive sensing theory are described. Then the adaptability of compressive sensing in digital holography is analyzed emphatically. According to the internal relation between compressive sensing and digital holography, as well as the characteristic of holographic measurement matrix, we analyze how to choose the sparse representation basis and the optimized reconstruction algorithm during the digital holographic tomographic reconstruction based on compressive sensing. And we propose the hologram frequency downsampling method based on compressive sensing-variable density downsampling, (including ray, spiral and exponential distribution downsampling mode). After comparing the three methods, exponential distribution downsampling is employed due to its better reconstruction results.(2) The non-amplified holographic tomographic reconstruction based on compressive sensing is studied.In this dissertation, for two kinds of non-amplified holographic recording systems: non-amplified in-line and off-axis holographic recording systems, we theoretically analyze the non-amplified holographic recording system and the method of non-amplified holographic tomographic reconstruction based on compressive sensing. We verify the feasibility of this method through experiments, and analyze the impacts of sampling ratio, signal to noise ratio and axial distance between multi-layer slice planes on reconstruction quality. Experimental results show that for the non-amplified hologram with sampling ratio more than 20% and signal-to-noise ratio more than 15 dB, tomographic reconstruction with higher quality can be achieved by compressive sensing.(3) 4F-amplified in-line holographic tomographic reconstruction based on compressive sensing is carried out.In this dissertation, to improve the axial resolution of digital holographic tomographic reconstruction based on compressive sensing, the method of 4F-amplified in-line holographic tomographic reconstruction based on compressive sensing is proposed and related researchs are carried out. Firstly, we theoretically derive the mathematic relation between 3D object plane and image plane in the 4F amplified system, and analyze the transverse magnification and longitudinal magnification. We study the 4F-amplified in-line holographic recording system and tomographic reconstruction method based on compressive sensing, and analyze the axial resolution of this method theoretically. This method shortens the distance between image plane and recording plane, thereby enlarges the numerical aperture of holographic recording system. Finally it improves the axial resolution of holographic tomographic reconstruction. In this dissertation, related experimental are carried out by use of 3D simulation data and optical elements. Experimental results show that the reconstruction quality is improved and the axial resolution is increased with a certain degree compared with the non-amplified in-line holographic tomographic reconstruction method based on compressive sensing.(4) Point-source-amplified in-line holographic tomographic reconstruction based on compressive sensing is performedIn this dissertation, aiming at lateral magnification of microhologram, point-source-amplified in-line holographic tomographic reconstruction based on compressive sensing is performed to realize tomographic reconstruction of hologram with high quality. Firstly, we theoretically study hologram recording system and the reconstruction method of 3D object in the case of point-source amplification, and use variable density downsampling method to extract a small amount of information in frequency domain during the process of data measurement. Experimental results show that this method is valid, meanwhile it can achieve compressive sensing reconstruction of tiny object from a small amount of information in frequency domain. |
