The phase recovery algorithm based on the transport of intensity equation uses the fast Fourier solution to calculate the phase from the acquired intensity, but the solution accuracy is not high, and there will be instability caused by zero points and minimum points. Aiming at this problem, An improved fast Fourier solution based on the intensity transfer equation is proposed. By finding a suitable constant value to replace the focused intensity value in the traditional formula, the initial guess solution of the phase is solved; the initial phase and the focused intensity form a new complex amplitude, and then a new intensity differential is obtained in the form of angular spectrum propagation, and then the new The intensity differential of is substituted into the phase solution formula to obtain a new phase, so as to iteratively optimize the phase; when the iteration converges, the exact solution of the phase can be obtained. This solution can bypass the instability caused by the zero point and the minimum value point and has the advantage of high precision. Keywords: Transport of intensity equation, Intensity differential, Iterative optimization, Angular spectrum propagation, Fast Fourier solution, phase recovery.
Compared with monochromatic holographic displays, color holographic displays have rich depth and color information, which can give observers a more pleasant visual effect. Inspiring by the adaptive weighted GS method, we introduced an optimized iterative method based on exponential weighted constraint to calculate phase-only holograms of color images. After channel separation of the target image to obtain each component image, the input complex amplitude is formed with quadratic phase and iterated. During the iteration, subtract the amplitude of the reconstructed image from the amplitude of the target image to construct an exponential constraint. This exponential constraint is applied to the signal area of the image plane. After calculating the three-channel phase hologram, a color holographic reconstruction can be obtained using the time multiplexing method. Simulated and optical experiments verify the effectiveness of this method.
Fourier ptychographic microscopy technique combines the concept of phase retrieval algorithm and synthetic aperture, which can solve the problem that large field of view and high resolution cannot coexist. However, describing the linear transfer process of the imaging system by coherent transfer function in conventional calculations leads to ringing artifacts. Gaussian apodization coherent transfer function constraints is proposed and embedded into the software platform, and a high-resolution Fourier ptychographic microscopy imaging system is constructed together with the designed hardware. The proposed algorithm can reduce the ringing artifacts and ensure the accuracy and resolution of the reconstructed results by simulating experiments and acquiring real images.
Holographic stereogram, as a marriage of holography and multi-view display technique, benefits of these two 3D display technologies. Recent research about the dual-view holographic stereogram 3D display technology shows an attractive way to present the visual information. However, due to the utilization of the random phase to smooth the spatial frequency spectrum, the troublesome of the quality of reconstructed images from holographic stereograms are those images containing speckle noise. In this paper, inspiring by the works about the computer-generated holograms, we introduced an optimized phase for the generation of dual-view holographic stereogram based on integral imaging to get a better suppression effect of speckle noise. The key goal is to determine the complex amplitude employed to calculate the holographic stereogram. Firstly, the pickup process of multiple parallax images corresponding to the left-view field and right-view field are finished by the virtual cameras. Then, the optimized phase is generated by the full-support iterative process, whose phase range is limited in the first time. Next, instead of the random phase, it is combined with corresponding parallax image to yield the complex amplitude. Holographic stereogram plane is segmented into many element holograms and each of them is generated by the Fourier transforming of the above complex amplitude. The phase of each complex element holograms is retained to generate the phase-only holographic stereogram, which have higher diffraction efficiency and no conjugate image than amplitude type holographic stereogram. Finally, the two set of holograms are combined together to reconstruct the corresponding dual-view. The optimized phase as the initial phase is demonstrated by simulations, the comparison of the simulated reconstructions shows that the method of this paper could improve the reproduction quality of the dual-view holographic stereogram, that extended its applicability and practicality.
A multiple-image encryption method based on a computer-generated phase-only hologram (POH) algorithm and chaotic systems is proposed. In the proposed method, first, a modified Gerchberg–Saxton (GS) algorithm is applied to transform the multiple-image into corresponding sub-sampled POHs. Then, the multiple POHs are combined using spatial division multiplexing (SDM). The combined hologram is then mapped into a digital image, and each pixel of the digital image is transformed by a chaotic system to improve security and form the final ciphertext. The modified GS algorithm is employed to generate a sub-sampled POH, which is a prerequisite for SDM. The adoption of SDM eliminates issues such as information leakage due to inter-image crosstalk and ensures the quality of decrypted images. The transformation based on a chaotic system leads to nonlinearity and unpredictability in the encryption process, which further increases the complexity of the encryption system. Numerical simulation demonstrates the security and feasibility of the proposed multiple-image encryption method.
Metalenses have drawn a lot of interest for use in near-infrared (NIR) bioimaging due to their benefits, such as flexible design, light weight, and simple integration. However, chromatic aberration is inevitable in optical systems, which substantially reduces their imaging quality. A broadband achromatic metalens for linearly polarized light in the range 1200 to 1550 nm is constructed to address this challenge. The phase and dispersion of the incident light are modulated by altering the ratio between the long and short axes of the elliptical nanopillars. Through the application of the particle swarm optimization algorithm, appropriate compensating phases can be added to the phase profiles at various wavelengths to align the real phase with the target phase of the broadband achromatic metalens. The structure of the nanopillar at any position in the metalens can be found from a relative phase library. Our numerical experimental results demonstrate that the proposed metalens has relatively consistent focusing characteristics and robustness in the 1200 to 1550 nm band, with an average focusing efficiency of 83.14%. The proposed high-efficiency robust NIR achromatic metalens can increase the quality of NIR biological imaging and the efficiency of a detector.
A high-precision phase retrieval algorithm based on the transport of intensity equation for multi-wavelength illumination is proposed. First of all, the traditional transport of intensity equation method is used to obtain the phase of a single wavelength, and the initial phase of different wavelengths is calculated according to the corresponding phase relationship between different wavelengths. Secondly, through the wavelength phase synthesis module, the phase of the object under multiple wavelengths is obtained. For the noise amplification problem introduced in the phase synthesis step, the phase unwrapping module is used to eliminate the noise level in the initial phase result and gradually reduce it to the noise level of two synthetic short wavelengths. Finally, the high-precision phase retrieval result is obtained. The experimental results verify the correctness and effectiveness of the proposed method.
In view of the limitation that the transport of intensity equation method can only be used at a single wavelength, we propose a binocular phase retrieval algorithm based on multiwavelength illumination. First, we solve for the corresponding single-phase results at different wavelengths and then calculate the surface height of the object by combining the obtained synthetic wavelengths and synthetic phases, in order to reconstruct the initial phase results at different wavelengths. To solve the problem of amplification of traditional noise and surface profile noise in the phase diagram in the phase synthesis step, we introduce a step-by-step noise reduction method that can reduce the noise in the initial phase results to the level for a single wavelength and finally obtain the corresponding high-precision phase results at different wavelengths. The intensity images collected by the proposed dual-microscope system verify the correctness and effectiveness of the algorithm.
When cells are observed with a microscope, the phase information for the sample is usually obtained from the acquired intensity images using the transport of intensity equation (TIE). However, to solve the TIE, it is necessary to obtain an in-focus image. The accuracy and speed of focus positioning affect the accuracy and time of phase retrieval. We propose a fast phase retrieval method based on the TIE and the threshold duty ratio. We first perform pixel reduction on a series of acquired intensity images, and these images are segmented using the optimal threshold to calculate the threshold duty ratios. The original image corresponding to the minimum threshold duty ratio is the optimal focus image. Finally, the optimal in-focus image and related defocused images are used to solve for the phase of the sample using the TIE under the boundary conditions. The correlation coefficient for the results of the simulation experiment reached 0.9317. In a microlens array experiment, the relative error between the results from our algorithm and the actual value was only 7.1%, thus, proving the correctness and effectiveness of the proposed method.
In the dual-camera phase retrieval method, the phase is solved by positive- and negative- defocusing images obtained through a single exposure after dual cameras are installed on an inverted microscope. However, due to the installation error of the cameras, translation and rotation of images exist between the images, resulting inaccurate phase retrieval results. In this paper, we proposed a dual-camera phase retrieval method based on fast adaption image restoration and transport of intensity equation. Firstly, let the positive-defocusing image be the reference image. Then using the fast adaption image restoration algorithm to find the texture information in order to find best matching block quickly. According to the number of high frequency information of the block, the size of block can be defined in order to increase the precision and speed of the restoration. After that, priority can be change as the sum of two parts, which can avoid the situation of 0 priority. Then, burring the boundary point of restored image in order to reduce the block effect. Finally, the transport of intensity equation can be used in phase retrieval results. Comparing with the normal algorithm, this method can restore the image much better.
Recently, the 3D display of the double observation point based on the parallax barrier has attracted attention because of its dual-view points and 2D/3D display compatibility, especially for display applications for mobile screens. At present, onedimensional integral imaging 3D display based on parallax barrier still has some challenges, such as lower resolution and small viewing angles. In order to increase resolution and the viewing angle, in this paper we analyzes the effect of the parallax barrier and parallax aperture width on the 3D image display under the assumption that the parallax barrier pitch is constant. Firstly, according to the geometric optics, the calculation formula of the resolution and the relationship between the viewing angle of the single slit and the aperture width of the slit are derived, further derive the formula for calculating the viewing angle. We had made a one-dimensional integral imaging dual-view 3D display prototype and studied the viewing angle and crosstalk of 3D images under different parallax aperture parameters. Applying the ideal optimal aperture value that we calculated to the prototype, we can finally see the 3D images of the two virtual scenes without crosstalk in the left 5° to 25°and the right 5° to 25°. The experiment results showed that the resolution and the viewing angle of the one-dimensional integral imaging dual-view 3D display increase with the decrease of the aperture width of the parallax barrier.
Optical waves can be described by intensity and phase. However, optical waves oscillate too fast for detectors to measure anything but time-averaged intensities. This is unfortunate since the phase can reveal important information about the object. Therefore, it is necessary to apply the known intensity information to retrieve the phase information, which is called phase retrieval. As a classical phase retrieval algorithm, the Gerchberg-Saxton iteration method has the characteristics of continuous error reduction, but a large number of iterations are needed to obtain high-quality retrieval results. The field of neural network algorithm was initially inspired by the goal of modeling biological neural systems, but then parted ways and became an engineering problem with good results in the field of machine learning. This kind of network relies on the complexity of the system to process information by adjusting the interconnection among a large number of internal nodes. A new algorithm combined the neural network and the Gerchberg-Saxton iterative is proposed. Firstly, the initial phase is obtained by Gerchberg-Saxton iteration method, and then a good training model is obtained by using paired initial phase and precise phase training neural network. For the samples in the test set, the trained model is applied to the phase retrieval results of Gerchberg-Saxton iteration method to obtain more accurate phase results. Experiments proved that the better retrieval results with a few iterations can be acquired.
The phase obtained in the interferogram is generally not continuous real phase information. Therefore, a phase larger than 2π will have a phase jump called wrapped phase. The traditional phase unwrapping algorithm usually requires a large amount of computation, and in reality, phase unwrapping is often a complex and morbid inverse problem due to factors such as speckle noise, random perturbations, low modulation, and phase discontinuity, and the processes of unwrapping of some algorithms depend on the path chosen. Therefore, it is difficult to obtain an accurate absolute phase under actual conditions. To improve the accuracy of the absolute phase, a phase unwrapping algorithm based on the transport-of-intensity equation with two-wavelength illumination is proposed. The experimental results illustrate that the proposed method not only improves the accuracy of absolute phase but also holds a good antinoise performance.
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.
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.
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.
The goal of phase retrieval is to recover the phase information from intensity distribution which is an important topic in optics and image processing. The algorithm based on the transport of intensity equation only need to measure the spatial intensity of the center plane and adjacent light field plane, and reconstruct the phase object by solving second order differential equations. The algorithm is derived in the coherent light field. And the partially coherent light field is described more complex. The field at any point in the space experiences statistical fluctuations over time. Therefore, traditional TIE algorithms cannot be applied in calculating the phase of partially coherent light field. In this thesis, the phase retrieval algorithm is proposed for partially coherent light field. First, the description and propagation equation of partially coherent light field is established. Then, the phase is retrieved by TIE Fourier transform. Experimental results with simulated uniform and non-uniform illumination demonstrate the effectiveness of the proposed method in phase retrieval for partially coherent light field.
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
objects.
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.
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