A comparison of iterative algorithms and a mixed approach for in-line X-ray phase retrieval

Previous studies have shown that iterative in-line X-ray phase retrieval algorithms may have higher precision than direct retrieval algorithms. This communication compares three iterative phase retrieval algorithms in terms of accuracy and efficiency using computer simulations. We found the Fourier transformation based algorithm (FT) is of the fastest convergence, while the Poisson-solver based algorithm (PS) has higher precision. The traditional Gerchberg-Saxton algorithm (GS) is very slow and sometimes does not converge in our tests. Then a mixed FT-PS algorithm is presented to achieve both high efficiency and high accuracy. The mixed algorithm is tested using simulated images with different noise level and experimentally obtained images of a piece of chicken breast muscle.     

Phase iteration and spacing iteration algorithms for speckle fringe pattern processing

Speckle fringe pattern is characterized by speckle noise because the speckle is the information carrier. Phase iteration and Spacing iteration are algorithms that are able to extract the information as well as suppress noise. Phase iteration is a loop of smoothing, phase calculation, and pattern reconstruction. Spacing Iteration is a repetition of correlation, phase calculation, and least-squares fit. The two algorithms are reviewed and compared in this paper. The modern computer provides the capability to explore all sorts of convergent methods by simply ‘do it again’. Phase iteration and Spacing iteration are two of the convergent methods in processing optical metrology fringe pattern.     

A spatial filtering technique for improved holographic character recognition

Conventional holographic pattern recognition systems suffer from the disadvantage that, in dealing with highly ordered patterns such as Arabic numerals or the letters of the Roman alphabet it is sometimes impossible to distinguish between patterns with a high degree of similarity (eg the capital letters ‘E’ and ‘F’ or ‘B’ and ‘P’).The present paper analyzes a simple case and shows how the insertion of a suitable spatial filter in the Fourier transform plane can reduce the unwanted cross-correlation signal between dissimilar patterns to zero, without removing the desired auto-correlation signal between similar patterns. Although no attempt is made to generalize the analysis, it seems probable that in cases involving the recognition of a small number of patterns with a strong ‘family resemblance’ a compromise filtering arrangement could be developed which would lead to a substantially improved performance.     

Interferometric testing of optical aspherical surfaces

This paper explains theoretically the principle of the Talbot interferometer using two ‘Fourier images’. The experimental results show that video techniques are more useful for superimposing two ‘Fourier images’ than photographic techniques.     

‘Best-case’ noise performance of feedback interferometers, potential for micromachine applications

We present a theoretical analysis of the noise performance of phase measuring feedback interferometers. We first analyse the operation of this kind of instrument and note that under certain circumstances bistability can occur. The bistable region should be avoided if possible when using feedback interferometry for high-accuracy measurement with low-input powers, as it can give rise to very high-noise levels. We then go on to investigate the effects of shot noise (on the interferometer output signal) and thermal noise (in the feedback loop), and relate these to the phase measurement accuracy of the interferometer. A ‘best-case’ calculation indicates that phase noise of about 0.005λ is possible at input powers in the nanowatt region. In practice, we expect that noise levels will be higher than predicted (particularly at high-input powers) due to the effects of vibration and air turbulence.     

A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: The POCS example

The projection-onto-convex-sets (POCS) algorithm is a powerful tool for reconstructing high-resolution images from undersampled k-space data. It is a nonlinear iterative method that attempts to estimate values for missing data. The convergence of the algorithm and its other deterministic properties are well established, but relatively little is known about how noise in the source data influences noise in the final reconstructed image. In this paper, we present an experimental treatment of the statistical properties in POCS and investigate 12 stochastic models for its noise distribution beside its nonlinear point spread functions. Statistical results show that as the ratio of the missing k-space data increases, the noise distribution in POCS images is no longer Rayleigh as with conventional linear Fourier reconstruction. Instead, the probability density function for the noise is well approximated by a lognormal distribution. For small missing data ratios, however, the noise remains Rayleigh distributed. Preliminary results show that in the presence of noise, POCS images are often dominated by POCS-enhanced noise rather than POCS-induced artifacts. Implicit in this work is the presentation of a general statistical method that can be used to assess the noise properties in other nonlinear reconstruction algorithms.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB environment

In the process of measurements such as optical interferometry and fringe projection, an important stage is fringe pattern analysis. Many advanced fringe analysis algorithms have been proposed including regularized phase tracking (RPT), partial differential equation based methods, wavelet transform, Wigner–Ville distribution, and windowed Fourier transform. However, most of those algorithms are computationally expensive. MATLAB^® is a general algorithm development environment with powerful image processing and other supporting toolboxes. It is also commonly used in photomechanical data analysis. With rapid development of multicore CPU technique, using multicore computer and MATLAB^® is an intuitive and simple way to speed up the algorithms for fringe pattern analysis. The paper introduces two acceleration approaches for fringe pattern processing. The first approach is task parallelism using multicore computer and MATLAB^® parallel computing toolbox. Since some algorithms are embarrassing problems, our first approach makes use of this characteristic to parallelize these algorithms. For this approach, parallelized windowed Fourier filtering (WFF) algorithm serves as an example to show how parallel computing toolbox accelerates the algorithm. Second, data parallelism using multicore computer and MATLAB^® parallel computing toolbox is proposed. A high level parallel wrapping structure is designed, which can be used for speeding up any local processing algorithms. WFF, windowed Fourier ridges (WFR), and median filter are used as examples to illustrate the speedup. At last, the results show that the parallel versions of former sequential algorithm with simple modifications achieve the speedup up to 6.6 times.     

Experimental Study and Comparison of Imbalance Ensemble Classifiers with Dynamic Selection Strategy

Imbalance ensemble classification is one of the most essential and practical strategies for improving decision performance in data analysis. There is a growing body of literature about ensemble techniques for imbalance learning in recent years, the various extensions of imbalanced classification methods were established from different points of view. The present study is initiated in an attempt to review the state-of-the-art ensemble classification algorithms for dealing with imbalanced datasets, offering a comprehensive analysis for incorporating the dynamic selection of base classifiers in classification. By conducting 14 existing ensemble algorithms incorporating a dynamic selection on 56 datasets, the experimental results reveal that the classical algorithm with a dynamic selection strategy deliver a practical way to improve the classification performance for both a binary class and multi-class imbalanced datasets. In addition, by combining patch learning with a dynamic selection ensemble classification, a patch-ensemble classification method is designed, which utilizes the misclassified samples to train patch classifiers for increasing the diversity of base classifiers. The experiments’ results indicate that the designed method has a certain potential for the performance of multi-class imbalanced classification.     

Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform

A novel two-dimensional (2D) Gabor continuous wavelet transform (CWT) for phase retrieval and fringe filtering of speckle fringe patterns with spatial carriers is proposed. Theoretical analysis of 2D Gabor CWT is presented and results are compared with advanced fan 2D CWT using both the computer simulated and experimental speckle fringe patterns. It is shown that noise reduction by 2D Gabor CWT demonstrates better results than that of the advanced fan 2D CWT. Two-dimensional Gabor CWT is also compared with 2D Fourier transform and results show that 2D Gabor CWT algorithm has better noise immunity.     

New Developments in the Eight Vertex Model II. Chains of Odd Length

We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity pointsη=mK/L with m odd the transfer matrix is known to satisfy the famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(υ) matrix is qualitatively different from the case of evenN and in particular they satisfy a previously unknown equation which is more general than what is often called ‘‘Bethe’s equation.’’ For the case of even m where no Q(υ) matrix is known we demonstrate that there are many states which are not obtained from the formalism of the SOS model but which do satisfy the TQ equation. The ground state for the particular case of η=2K/3 and N odd is investigated in detail.     

Hard X ray holographic diffraction imaging

We determine the absolute electron density of a lithographically grown nanostructure with 25 nm resolution by combining hard x-ray Fourier transform holography with iterative phase retrieval methods. While holography immediately reveals an unambiguous image of the object, we deploy in addition iterative phase retrieval algorithms for pushing the resolution close to the diffraction limit. The use of hard (8 keV) x rays eliminates practically all constraints on sample environment and enables a destruction-free investigation of relatively thick or buried samples, making holographic diffraction imaging a very attractive tool for materials science. We note that the technique is ideally suited for subpicosecond imaging that will become possible with the emerging hard x-ray free-electron lasers.     

Holographic digital data storage using phase-modulated pixels

We propose and demonstrate the use of phase images for holographic data storage. Use of phase images as input leads to uniform diffraction efficiency of multiplexed data pages. Use of binary phase-based data pages with 0 and π phase changes produces uniform spectral distribution at the Fourier plane. This in turn facilitates better recording of higher spatial frequencies. We experimentally demonstrate a phase-based holographic data storage system using shift multiplexing in a Fe:LiNbO₃ crystal, and use it for associative retrieval. Preliminary studies indicate high discrimination capabilities of phase-based holographic data storage system over the amplitude-based system in a content-addressable memory.     

A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise

Various levels of random noise have been added to simulated digital images of a spherical dome illuminated by fringes projected from an offset angle. The noisy images have then been analysed using Fourier transform profilometry, phase shifting profilometry and spatial phase detection. The theoretical dome was subtracted from the domes reconstructed using these methods to form error maps. The maximum and RMS errors for each error map were calculated and plotted against the added noise level. At low levels of added noise the phase shifting method produced the lower errors, but above around 10% noise the Fourier transform method was better. Only at very high levels of added noise did the spatial phase detection method achieve the lowest errors.     

红外背景抑制与弱小目标的检测算法

强噪声背景下红外图像中弱小目标的检测一直是研究的重点和难点。根据弱小目标、背景干扰和噪声在红外图像中的差异,研究了三种低信噪比条件下红外图像中弱小目标的检测算法:小波变换、数学形态学、Top—hat算子,分别给出了处理的图像和相应的数据。仿真实验表明:这三种检测算法能十分有效地提高信噪比、增强目标、抑制背景杂波和去除噪声干扰,对信噪比约为2的弱小目标检测能得到很好的结果。三种算法所得结果一致,而且处理速度快,适合于实时图像处理和目标探测。     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Evaluation of a metaphase chromosome finder: Potential application to chromosome-based radiation dosimetry

An automated metaphase chromosome finder is described which combines a microscope, state-of-the-art computer technology and a simple decision-making algorithm. A microscope slide is systematically scanned under computer control and the location of each positive ‘signal’ placed into memory for later recall and review by a human operator. The software identifies two events, positives (the presence of a ‘signal’) and negatives (the absence of a ‘signal’). The performance of the metaphase finder was evaluated using receiver operating characteristic curve analysis. At the optimum decision threshold, the detection rates for true positives (metaphase spreads) was about 74%, false positives (type I error) about 6%, and false negatives (type II error) about 26%. The overall accuracy, which accounts for differences in the sensitivity of the detector to positive and negative events, was 89.4% (±0.01%; standard error of the mean, n = 8). Potential applications to radiation dosimetry are discussed.