Gomputational 3D Reconstruction Based On Fresnel Diffraction Approximation

The reconstruction technology of 3D scene is the developing direction of the modern imaging technology with huge market for application.Traditional cameras can only record the amplitude(intensity)of light waves——it can only get 2D projection information about the scene.However,the holography which invented by Gabor can simultaneously record the amplitude and phase of the light field for scene,achieving a perfect reconstruction of 3D scene by using light modulation principle,it's the ultimate goal for 3D imaging technology in future.The principle of Gabor holographic imaging is based on the wave optics,it can be described by scalar field when propagation in free space,Fresnel propagation approximation can further be used to approaching a complex wave under paraxial approximation.The research on computational reconstruction for 3D scene,also known as Computer Generated Hologram(CGH),which combines flexible computations with optics to avoid the high requirements for environment?the complex operation and other defects in recording process of traditional optical holography.However,CGH also faces its own challenges:the Fresnel propagation is based on the diffraction principle,that is to say,it faces the challenge of huge computational burdens due to high space-bandwidth products.Also,spatial discretization and numerical quantification of diffraction field involve several digital signal processing problems,including light field representation?data compression?noise effects imaging quality,all of which make heavy requirements for the design of the algorithm.Exploring how to improve the computational efficiency of 3D diffraction light field and quality of reconstruction image are the currently hot topics in CGH.The research work in this paper mainly focuses on the following two aspects,the paper aims to provide a better and practical algorithm for CGH.Firstly,aiming at the traditional point-cloud method,some special properties of Fresnel diffraction field is investigated,the traditional N-LUT method is optimized and improved.Secondly,the method is given to improve computational efficiency by combing with Compressive Sensing(CS):the Fresnel hologram of 3D complex objects is calculated by chromatography which can release the heavy computation problem in point-cloud method where depth layers are relative less,but sample points in each layer are relative much;the compressive sampling in the frequency domain is performed.The main content and innovative work of the thesis are as follows:(1)A fast method based on N-LUT is given,the main idea are combining the propagation reversibility of the coherent Fresnel diffraction with the spatial symmetry of the Gabor zone plate.The sampling interval or physical dimension between the source plane and the hologram plane can be set independently by using propagation reversibility.As the consequence,the hologram calculation of large-size scene can be achieved when the sampling interval of the source scene is increased.Meanwhile,The calculation of Principle Fringe Patterns is accelerated by using spatial symmetry and the middle results at the virtual plane is stored by using Look up table method.Finally,the computational efficiency of N-LUT method can be effectively improved under the premise of ensuring the quality of 3D reconstruction.(2)Taking advantages of similarity and redundancy in CGH,the high consumption of energy in the process of sampling and transmission of diffraction field can be solved by combing the compressive sensing technology and improving the computational efficiency.A compressive reconstruction method based on 3D total variation sparse model is devised for 3D complex object in Fresnel hologram frequency domain.The method constructs a linear model framework of compressive sensing adaptable for Fresnel diffraction,and the frequency domain of Fresnel hologram is sub-sampled by using the incoherent variable density sampling pattern of frequency domain with probability density function obeying exponential distribution.Finally,the compressive representation for frequency domain of Fresnel hologram can be realized,the storage and transmission rate of holography data can be improved.The calculation of the given method can not only be light,also it can significantly improve the peak signal-to-noise ratio of the focused reconstruction image under the condition of low sampling rate in frequency domain of Fresnel hologram.