In order to calculate the lost phase from the intensity information effectively, a new method of phase retrieval which based on cosine grating modulation and transport of intensity equation is proposed. Firstly, the cosine grating is loaded on the spatial light modulator in the horizontal and vertical direction respectively, and the corresponding amplitude of the light field is modulated. Then the phase is calculated by its gradient which is extracted from different direction modulation light illumination. The capability of phase recovery of the proposed method in the presence of noise is tested by simulation experiments. And the results show that the proposed algorithm has a better resilience than the traditional Fourier transform algorithm at low frequency noise. Furthermore, the phase object of different scales can be retrieved using the proposed algorithm effectively by changing the frequency of cosine grating, which can control the imaging motion expediently.
In this paper, a novel phase retrieval algorithm is presented which combines the advantages of the Transport of Intensity Equation (TIE) method and the iteration method. TIE method is fast, but its precision is not high. Though the convergence rate of iteration method is slow, its result is more accurate. This algorithm consists of Iterative Angular Spectrum (IAS) method to utilize the physical constraints between the object and the spectral domain, and the relationship between the intensity and phase among the wave propagation. Firstly, the phase at the object plane is calculated from two intensity images by TIE. Then this result is treated as the initial phase of the IAS. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. During the iteration process, the feedback mechanism is imposed on it that improve the convergence rate and the precision of phase retrieval and the simulation results are given.
The phase carries details of the depth information about an optical wave field and is very important in many applications, such as optical field reconstruction and 3D display. However, optical waves oscillate too fast for detectors to record the intensity and phase directly and simultaneously. The phase retrieval technology or algorithm has been the focus of enormous research recently. Among the valuable algorithms transport-of-intensity equation (TIE) and angular-spectrum- iteration (ASI) are widely used in various fields such as electron microscopy and x-ray imaging. Unfortunately, the former one is originally derived for a coherent illumination and can not be directly applied to the phase retrieval of partially coherent light field when not been uniformly lit. While the ASI deducted from wave propagating with wave vector has itself shortcomings due to iterative uncertainty and slow convergence. In this paper, a novel hybrid phase retrieval algorithm extended TIE for partially coherent light illuminations is investigated in both case of uniformly and non-uniformly lit. This algorithm consists of multi-plane ASI to utilize the physical constraints between the object domain and the spectral domain, and the relationship between the intensity and phase among the wave propagation. The phase at the center image plane is calculated from three intensity images. Then this result is treated as the initial value of the multi-plane ASI. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. This hybrid algorithm expands the application of tradition TIE while improving the convergence rate of ASI method.
Phase is an inherent characteristic of any wave field. Statistics show that greater than 25% of the information is encoded in the amplitude term and 75% of the information is in the phase term. The technique of phase retrieval means acquire phase by computation using magnitude measurements and provides data information for holography display, 3D field reconstruction, X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Mathematically, solving phase retrieval problem is an inverse problem taking the physical and computation constraints. Some recent algorithms use the principle of compressive sensing, such as PhaseLift, PhaseCut and compressive phase retrieval etc. they formulate phase retrieval problems as one of finding the rank-one solution to a system of linear matrix equations and make the overall algorithm a convex program over n × n matrices. However, by "lifting" a vector problem to a matrix one, these methods lead to a much higher computational cost as a result. Furthermore, they only use intensity measurements but few physical constraints. In the paper, a new algorithm is proposed that combines above convex optimization methods with a well known iterative Fourier transform algorithm (IFTA). The IFTA iterates between the object domain and spectral domain to reinforce the physical information and reaches convergence quickly which has been proved in many applications such as compute-generated-hologram (CGH). Herein the output phase of the IFTA is treated as the initial guess of convex optimization methods, and then the reconstructed phase is numerically computed by using modified TFOCS. Simulation results show that the combined algorithm increases the likelihood of successful recovery as well as improves the precision of solution.
In classical compressive holography (CH), which based on the Gabor holography setup, two nonlinear terms are inherent in the intensity recorded by a 2D detector arrays, the DC term and the squared field term. The DC term (the term at the origin) can be eliminated by filtering the Fourier transform of the interference irradiance measurements using appropriate high-pass filter near the zero frequency. The nonlinearity caused by the squared field term can be neglected and modeled as a error term in the measurement. However, the above assumptions are significantly limited, which yields the degradation of reconstruction quality. In this paper, an novel scheme using phase-shifting method is presented. To accurately recover the complex optical field caused by the propagation of the object, without the influence of the DC term and the squared field term, a very effective method for removing these two terms is introduced. The complex optical field of the 3D object and the complex optical field at the detector plane can be precisely represented by a linear mapping model. The complex optical field at the recorder plane is obtained by phase-shifting interferometry with multiple shots. Then, the corresponded complex optical field at the detector plane can be successfully extracted from multiple captured holograms using conventional four phase-shifting interferometry. From such complex optical field at the record plane, including the amplitude and phase information, the complex optical field of the 3D object can be reconstructed via an optimization procedure. Numerical results demonstrate the effectiveness of our proposed method.
Depth information of the image is really necessary information to reconstruct a 3-dimensional object.
The classical methods of depth estimation are generally divided into two categories: active and passive
methods. The active methods requires the additional lighting equipment, passive methods also have a
series of problems .They require a plurality of images obtained by capturing a plurality of viewpoints ,
and determine the locating occlusion boundary , etc., and hence the depth estimation has been a
challenging problem in the research field of computer vision.1 Because of the depth information of the
image has a natural sparse features, this paper uses a passive approach, the signal of sparse priori based
on compressed sensing theory is used to estimate the depth of the image, without capturing multiple
images, using a single input image can obtain a high quality depth map. Experimental results show that
the depth map obtaining by our method, compared to the classical passive method, the contour
sharpness, the depth of detail information and the robustness of noise are more advantages. The method
also can be applied to re-focus the defocused images, and automatic scene segmentation and other
issues, ultimately may have broad application prospects in the reconstruction of true 3-dimensional
The goal of phase retrieval is to extract the phase of an optical wave field from intensity measurements. The transport-of-intensity equation (TIE)-based method is a popular deterministic solution and has been applied in various fields such as optical microscopy, electron microscopy, and x-ray imaging. For macro-imaging, a camera is often used to capture the images, and thus the phase modulation of the lens should be considered. A new formulation is proposed to extend TIE for phase retrieval in a lens-based wave propagation model. To obtain the defocus step, a data-collection-reading device is designed by equipping a camera with a micrometer caliper. Simulation and real experiments are conducted to test the proposed method.