Unwrapping phase fluctuations in one dimension

Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are applied to lattice field theory in order to map compact random phases to noncompact random variables that can be numerically sampled without sign or signal-to-noise problems. A cumulant expansion can be used to reconstruct average correlation functions from moments of unwrapped phases, but points where the field magnitude fluctuates close to zero lead to ambiguities in the definition of the unwrapped phase and significant noise at higher orders in the cumulant expansion. Phase unwrapping algorithms that average fluctuations over physical length scales improve, but do not completely resolve, these issues in one dimension. Similar issues are seen in other applications of phase unwrapping, where they are found to be more tractable in higher dimensions.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with arXiv:1806.0183

Phase Unwrapping and One-Dimensional Sign Problems

Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time series are integrated to construct non-compact unwrapped phase differences. By combining phase unwrapping with a cumulant expansion, path integrals with sign problems arising from phase fluctuations can be systematically approximated as linear combinations of path integrals without sign problems. This work explores phase unwrapping in zero-plus-one-dimensional complex scalar field theory. Results with improved signal-to-noise ratios for the spectrum of scalar field theory can be obtained from unwrapped phases, but the size of cumulant expansion truncation errors is found to be undesirably sensitive to the parameters of the phase unwrapping algorithm employed. It is argued that this numerical sensitivity arises from discretization artifacts that become large when phases fluctuate close to singularities of a complex logarithm in the definition of the unwrapped phase.Comment: 42 pages, 16 figures. Journal versio

Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

Blind deconvolution of medical ultrasound images: parametric inverse filtering approach

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.910179The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used

Image inversion analysis of the HST OTA (Hubble Space Telescope Optical Telescope Assembly), phase A

Technical work during September-December 1990 consisted of: (1) analyzing HST point source images obtained from JPL; (2) retrieving phase information from the images by a direct (noniterative) technique; and (3) characterizing the wavefront aberration due to the errors in the Hubble Space Telescope (HST) mirrors, in a preliminary manner. This work was in support of JPL design of compensating optics for the next generation wide-field planetary camera on HST. This digital technique for phase retrieval from pairs of defocused images, is based on the energy transport equation between these image planes. In addition, an end-to-end wave optics routine, based on the JPL Code 5 prescription of the unaberrated HST and WFPC, was derived for output of the reference phase front when mirror error is absent. Also, the Roddier routine unwrapped the retrieved phase by inserting the required jumps of +/- 2(pi) radians for the sake of smoothness. A least-squares fitting routine, insensitive to phase unwrapping, but nonlinear, was used to obtain estimates of the Zernike polynomial coefficients that describe the aberration. The phase results were close to, but higher than, the expected error in conic constant of the primary mirror suggested by the fossil evidence. The analysis of aberration contributed by the camera itself could be responsible for the small discrepancy, but was not verified by analysis

Reducing of phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

In order to measure the radial displacements of facets on surface of a growing spherical Cu_{2-\delta}Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to non-integer number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces the error in the case of small fringe density.Comment: 24 pages, 5 figures, submitted to JOSA

Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking (RPT) algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n + 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results