Accuracy Of Phase Retrieval Research Articles

Accurate two-step random phase retrieval approach without pre-filtering based on hyper ellipse fitting

In this work, we propose a hyper ellipse fitting-based high-precision random two-frame phase shifting algorithm to improve the accuracy of phase retrieval. This method includes a process of Gram-Schmidt orthonormalization, followed by a hyper ellipse fitting procedure. The Gram-Schmidt orthonormalization algorithm constructs a quadrature fringe pattern relative to the original fringe pattern. These two quadrature fringe patterns are then fed into the hyper ellipse fitting procedure, which reconstructs the phase map and refines the background light to produce the final accurate phase of interest. Due to the hyper ellipse fitting procedure, the demodulation results are significantly improved in many cases. This method allows us to design a two-shot phase reconstruction algorithm without the need for least squares iteration or pre-filtering, effectively mitigating residual background to the greatest extent. It combines the advantages of both the Gram-Schmidt orthonormalization method and the Lissajous ellipse fitting method, making our hyper ellipse fitting approach a simple, flexible, and accurate phase retrieval algorithm. Experiments show that by using the weighted least squares method and adjusting the weights, this method can prioritize data points with more significant information or higher reliability, ensuring more accurate estimation of the ellipse parameters.

Single-frame interferogram phase retrieval using a phase-shifting generative adversarial network with physics-based fine-tuning

Phase retrieval from a single-frame interferogram is a challenge in optical interferometry. This paper proposes an accurate physics-based deep learning method for one-shot phase retrieval. This approach involves both data-driven pre-training of a phase-shifting network and subsequent model-driven fine-tuning. The well-designed pre-training network is capable of simultaneously generating π/2, π, and 3π/2 phase-shifted versions of the input interferogram to facilitate phase extraction. Moreover, integrating the interferometric model into the testing dataset enables self-supervised fine-tuning, optimizing the use of both data and physics-based priors. Simulations and experiments demonstrate the effectiveness of the proposed method in overcoming the common generalization limitation of data-driven models and achieving accurate phase retrieval. The proposed method not only enhances the accuracy of phase retrieval but also improves the generalization capability, making it robust under experimental conditions for interferometric applications.

Photoemission Orbital Tomography Using a Robust Sparse PhaseLift.

Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) is a powerful technique that visualizes the shape of the molecular orbitals (MOs) of molecular films. For further utilization of POT, a simple and low-cost method of POT is highly required. Here, we propose a new POT method based on the PhaseLift algorithm (PhaseLift POT). This method utilizes a lifting procedure to convert the PMM, which is a second-order polynomial of MO coefficients, into a first-order polynomial of the lifted MO coefficients and further relaxes the equality constraint for a given PMM. We also established a method to improve the accuracy of phase retrieval from the noisy PMM data by using sparsity for MO coefficients (sparse PhaseLift POT). These methods make it possible to reconstruct the three-dimensional MOs, including phases of the wave function, directly from a single experimental PMM. This method can also precisely determine the adsorption-induced molecular deformations with an accuracy of 0.05 [Å]. Furthermore, the robust sparse PhaseLift POT is robust against unavoidable noise in the experimental PMMs due to the relaxation of the matching condition for a given PMM. Therefore, this will be an innovative tool for POT, especially for analyzing the dynamics of the molecules during the chemical reaction and excitation processes.

Optimization of single-beam multiple-intensity reconstruction technique: Select an appropriate diffraction distance

The multi-distance phase retrieval technique is widely used in phase imaging due to its high accuracy, simple implementation, and strong robustness. However, the artificial selection of the diffraction distance for capturing images has been a limitation. This limitation has sparked the desire to improve the accuracy of multi-distance phase retrieval by either capturing more images at different diffraction distances or iterating more times in the algorithm. Unfortunately, these approaches significantly reduce the efficiency of the technique. In this study, we implemented detailed simulations of the single-beam multiple-intensity reconstruction (SBMIR) technique to investigate the relationship between the diffraction distance and phase retrieval accuracy. We conducted experiments using an USAF-1951 sample generated by LCOS-SLM, a circular steps sample, and a biological sample. The results verified that SBMIR achieves higher phase retrieval accuracy and faster efficiency at an optimal diffraction distance. This research provides valuable support for selecting the appropriate diffraction distance in SBMIR, thereby enhancing its accuracy and efficiency.

Two-step differential phase-shifting phase retrieval using generative adversarial network

Phase-shifting interferometry (PSI) is a high-accuracy optical measurement technique which requires accurate phase-shift estimation or sufficient phase-shifting interferograms to ensure phase-retrieval accuracy. Therefore, obtaining the highest phase retrieval accuracy from fewer interferograms remains a challenge. Based on this, we propose a two-step differential phase-shifting phase retrieval method using generative adversarial network, which can achieve higher phase-retrieval accuracy from two arbitrary phase-shifting interferograms, compared to representative two-step arbitrary phase-shifting phase retrieval methods. A phase retrieval generative adversarial network (PR-GAN) which can be trained with artificial training data for phase retrieval from experimental interferograms is employed. Experimental results demonstrate that accurate phase results can be obtained, even when the phase shift is approximately π or the fringe number is relatively small.

Simulated wrapped phase optimizes phase retrieval in phase-shifting interferometry.

Phase retrieval is crucial in phase-shifting interferometry and other phase measurement techniques. However, in noisy wrapped phase maps with high steepness, discontinuities arise and cause phase unwrapping errors. To solve this problem, this Letter presents a phase retrieval method based on a simulated wrapped phase. By establishing the correspondence between the simulated and measured interferograms, the difference in wrapped phases between them can be obtained. The difference in wrapped phase map, which has sparse and wide interference fringes, has a higher reliability of phase unwrapping. The proposed method not only possesses high phase retrieval accuracy but it also simplifies the processing of interferograms. Furthermore, the layout of all interferometric systems, the parameters of optical components, and the model of the measured object are known, so the proposed method can be used as a reference for phase retrieval.

Single-shot high-precision 3D reconstruction with color fringe projection profilometry based BP neural network

In order to reduce the influence of nonlinear factors such as gamma nonlinearity and color crosstalk on the phase retrieval accuracy with color fringe projection profilometry (CFPP) in rapid measurement, a single-shot high-precision backpropagation (BP) neural network based CFPP is proposed. Firstly, neural networks are trained from samples through a training process. The neural network inputs are the RGB components of composite color fringe patterns. The numerator and denominator of the arctangent function are used as network outputs. The monochromatic fringe patterns are adopted. The numerator and denominator of the arctangent function are calculated by the 15-step phase-shift method, which serves as the network training target. Applying this neural network to the prediction of the standard phase can reduce the influence of nonlinear factors on the phase accuracy. Then, the absolute phase was unwrapped by using geometric constraints. Finally, the 3D reconstruction with high precision can be realized by using only a single-shot color fringe. The theoretical model of the proposed method and the process of neural network training are introduced. The results of 3D reconstruction are compared with other algorithms in the same condition. The experimental results demonstrate that the RMS of the proposed algorithm can reach 0.0107 mm, compared with 0.0121 mm of the traditional 3-step phase-shift method. The proposed method is applied to the online quality inspection of relay components, and the results verify the high accuracy and high efficiency of measurement.

Interferogram blind denoising using deep residual learning for phase-shifting interferometry

The interferogram containing the noises often affects the accuracy of phase retrieval, leading to the degradation of the phase imaging quality. To address this issue, a new interferogram blind denoising (IBD) method based on deep residual learning is proposed. In the presence of unknown noise levels, during the training, the deep residual convolutional neural networks (DRCNN) in the IBD approach is able to remove the latent clean interferogram implicitly, and then gradually establish the residual mapping relation in the pixel-level between the interferogram and the noises. With a well-trained DRCNN model, this algorithm can deal not only with the single-frame interferogram efficiently but also with the multi-frame phase-shifted interferograms collaboratively, while effectively retaining interferogram features related to phase retrieval. Simulation and experimental results demonstrate the feasibility and applicability of the proposed IBD method.

Method with high accuracy for phase retrieval in Fourier FPP based on the modified FCM and variational image decomposition

Phase retrieval with high accuracy remains one of the most challenging problems in Fourier fringe projection profilometry (FPP). The variational image decomposition TV-Hilbert- L 2 model has been proved to be a powerful tool for phase retrieval. In this paper, we first propose a modified fuzzy c-means (FCM) clustering algorithm to remove background from fringe projection patterns. In order to further improve the accuracy, we combine the modified FCM and the variational image decomposition TV-Hilbert- L 2 model and propose a new method to get the fringe part from the single frame fringe projection pattern. We evaluate the performance of this method via application to two simulated and one experimental fringe projection patterns and comparison with the Fourier transform, morphological operation-based bi-dimensional empirical mode decomposition, and variational image decomposition TV-Hilbert- L 2 model. The experiment results show that our method improves the accuracy of phase retrieval for TV-Hilbert- L 2 model and can achieve similar accuracy to the phase-shifting method.

Improving phase retrieval accuracy of optical parallel plate by adjusting exposure time of CCD

A new phase retrieval method is investigated to reconstruct wavefronts of optical parallel plates with the use of a group of diffraction patterns. More specifically, the improved phase retrieval algorithm is realized by converting the measuring plane wave into a spherical wave and by using single or double discrete Fourier transforms to calculate both far- and near-field diffraction propagations, and the accuracy is improved by adjusting the exposure time of the charge-coupled device according to the distance between the focal plane and diffraction plane. Both the theoretical and experimental results are consistent with the results obtained using conventional wavelength-modulated phase-shifting interferometry. The new method opens new doors for realizing wavefront measurement of optical parallel plates with high accuracy, especially for large-aperture parallel plates in inertial confinement fusion laser systems.

Performance analysis of phase retrieval using transport of intensity with digital holography [Invited

The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.

CERES MODIS Cloud Product Retrievals for Edition 4—Part I: Algorithm Changes

The Edition 2 (Ed2) cloud property retrieval algorithm system was upgraded and applied to the MODerate-resolution Imaging Spectroradiometer (MODIS) data for the Clouds and the Earth's Radiant Energy System (CERES) Edition 4 (Ed4) products. New calibrations for solar channels and the use of the 1.24-μm channel for cloud optical depth (COD) over snow improve the daytime consistency between Terra and Aqua MODIS retrievals. Use of additional spectral channels and revised logic enhanced the cloud-top phase retrieval accuracy. A new ice crystal reflectance model and a CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -channel algorithm retrieved higher ice clouds, while a new regional lapse rate technique produced more accurate water cloud heights than in Ed2. Ice cloud base heights are more accurate due to a new cloud thickness parameterization. Overall, CODs increased, especially over the polar (PO) regions. The mean particle sizes increased slightly for water clouds, but more so for ice clouds in the PO areas. New experimental parameters introduced in Ed4 are limited in utility, but will be revised for the next CERES edition. As part of the Ed4 retrieval evaluation, the average properties are compared with those from other algorithms and the differences between individual reference data and matched Ed4 retrievals are explored. Part II of this article provides a comprehensive, objective evaluation of selected parameters. More accurate interpretation of the CERES radiation measurements has resulted from the use of the Ed4 cloud properties.

Exact phase recovery applying only phase modulations in an isolated region

In this paper, we propose an analytical phase retrieval approach applying only phase modulations in the region isolated from the object to be measured. This approach employs a series of intensity-only measurements and can accurately and conveniently achieve phase recovery in the range of [0, 2π) once a reference phase is calibrated in advance. To improve the robustness of the algorithm, this paper yields an over-determined method (OM) by extending the phase modulation procedure from 3 steps into n steps. The algorithm's exact phase retrieval ability, the influence of key parameters’ disturbance on solving precision, and the theory of robustness improvement are all verified through numerical simulations. It is noteworthy mentioning that the robustness enhancement method performs well–improving the phase retrieval accuracy efficiently. Also, an experiment is undertaken and the results are satisfactory, demonstrating the core of our approach and showing the capability of OM.

Robust composite sine-trapezoidal phase-shifting algorithm for nonlinear intensity

Phase-shifting profilometry (PSP) is an efficient three-dimensional (3D) measurement technique. The accuracy of the PSP based 3D measurement system is generally affected by the nonlinear intensity response of the projector. In general, nonlinear errors can be reduced by projecting more fringe patterns, but this approach significantly increases the measuring time. To improve the measurement accuracy and speed, a new composite sine-trapezoidal phase-shifting profilometry technique that suppresses nonlinear error is proposed in this study. The main idea of the proposed method is projecting a set of sinusoidal fringe patterns and two sets of composite sine-trapezoidal fringe patterns with different intensity ranges in sequence. Among these patterns, the sinusoidal fringe is used to encode the pixel position, and the order of the wrapping phase is determined by the region code of the composite fringe. The flat intensity parts of the composite fringe are used to encode the nonlinear intensity response of the measurement system. Through system identification, the response parameters of the pixels can be obtained, and the gray value of the pixels can be corrected to gain a better phase distribution. Compared to the straight edges of the trapezoidal fringe, the sinusoidal edges of the composite fringe are more robust to the projector defocus, which improves the accuracy of the identification of the system intensity response model. Simulation results show that the proposed method can achieve a higher phase retrieval accuracy than the trapezoidal PSP and the sine PSP. The experiment results indicate that the proposed method has a better measurement accuracy than those of the standard 3-step and 4-step sine PSP methods.

冲击噪声对多普勒差分干涉仪相位反演精度影响分析及校正方法

冲击噪声对多普勒差分干涉仪相位反演精度影响分析及校正方法

冲击噪声对多普勒差分干涉仪相位反演精度影响分析及校正方法

冲击噪声对多普勒差分干涉仪相位反演精度影响分析及校正方法

Investigation on the Dependency of Phase Retrieval Accuracy Versus Edge Enhancement to the Noise Ratio of X-ray Propagation-Based Phase-Contrast Imaging.

Phase retrieval is necessary for propagation-based phase-contrast imaging (PB-PCI). Arhatari established a model for predicting the impact of the sample-to-detector distance and the system noise on the phase retrieval performance. We have extended Arhatari's model to account for the parameters of excessive source size, finite detector resolution, and geometrical magnification for more practical cases. However, there exist interaction effects among these parameters resulting in difficulty of predicting the phase retrieval performance. In this study, we found that optimizing the trade-off among these parameters for phase retrieval is consistent with the improvement of edge enhancement to noise ratio (EE/N) in the "forward problem" of the PB-PCI. Hence, we engaged in establishing a relationship between EE/N and phase retrieval performance in terms of the "forward problem" and "inverse problem" of the PB-PCI, respectively. Our results showed that, at fixed detector resolution, phase retrieval from the phase-contrast projections at the same EE/N level resulted in the consistent phase retrieval performance. Therefore, the performance of phase retrieval can be predicted based on the EE/N level and be quantitatively optimized by increasing EE/N.

A simplified method of interferograms matching in the dual-channel phase-shifting interferometry

The dual-channel phase-shifting interferometry (DC-PSI) has been focused widely in the dynamic measurement field because of its outstanding advantages. The interferograms matching between two channels is a key factor to the high precision phase retrieval. Suffered from the relative poses of different channel cameras in six-degree of freedom (S-DOF), the interferograms matching between two channels, including translation, rotation and scaling, is always a difficult problem in the DC-PSI. Aiming at the only translation mismatching is here considered and the iterations are needed to get the translation parameters in the translation method, a simplified matching method based on the transformation matrix is proposed, minding all kinds of interferograms mismatching. In the proposed method, only one shot to the calibration plate is needed to obtain the adjustment parameters and the interferograms is matched quickly and precisely. Both the simulation and experimental results demonstrate that the proposed method can improve the phase retrieval accuracy and interferograms matching efficiency.

Higher Order Transport of Intensity Equation Methods: Comparisons and Their Hybrid Application for Noise Adaptive Phase Imaging

As a non-interferometric method, the transport of intensity equation (TIE) method suits for quantitative phase imaging with the commercial microscope platform, especially those higher order TIE approaches which can realize precise phase retrieval by eliminating undesired higher order derivatives are widely used. However, these approaches are mostly adopted separately without considering their phase retrieval precision in various noise levels. In this paper, we first compared these classical higher order TIE approaches through theoretical analysis, numerical simulations and experiments. Then, based on the quantitative comparisons mainly focusing on their phase retrieval accuracy and noise suppression capability, we determine the application scope corresponding to different noise levels of each higher order TIE approach. Finally, in order to deal with different noisy cases, we design the hybrid higher order TIE application, in which the specific higher order TIE approach is selected for phase retrieval according to the precise noise estimation, and the performance of the hybrid higher order TIE application is tested by both the numerical simulations and the experiments, proving it can perform high-quality phase imaging by balancing the trade-off between the phase retrieval accuracy and the noise influence. The paper not only provides a systematic reference for analysis and comparisons on different higher order TIE approaches, but also proposes the hybrid application for noise adaptive phase imaging, which can be a potential tool in biological observations and medical diagnostics.

Quantitative Phase Imaging Camera With a Weak Diffuser

We introduce the quantitative phase imaging camera with a weak diffuser (QPICWD) as a practical realization of quantitative phase imaging (QPI) on standard microscope platforms. The QPICWD is a compact stand-alone camera which measures sample induced phase delay under low-coherence quasi-monochromatic illumination by examining the deformation of the speckle intensity pattern. By interpreting the speckle deformation with an ensemble average of the geometric flow, we can obtain the high-resolution distortion field by solving the transport of intensity equation (TIE). Since the phase measured by TIE is the generalized phase of the partially coherent image, instead of the phase of the measured object, we analyze the effect of illumination coherence and imaging numerical aperture (NA) on the accuracy of phase retrieval, revealing that the phase of the object can be reliably retrieved when the coherence parameter (the ratio of illumination NA to objective NA) of the Kohler illumination is between 0.3 and 0.5. We present several applications for the new design including nondestructive optical testing of microlens array with nanometric thickness and imaging of fixed and live HeLa cells. Since the designed QPI camera does not require any modification of the widely available bright-field microscope or additional accessories for its use, it is expected to be adopted by the broader biology and medical community.