Phase-shifting interferometry based on principal component analysis

An asynchronous phase-shifting method based on principal component analysis (PCA) is presented. No restrictions about the background, modulation, and phase shifts are necessary. The presented method is very fast and needs very low computational requirements, so it can be used with very large images and/or very large image sets. The method is based on obtaining two quadrature signals by the PCA algorithm. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results

Analysis of the principal component algorithm in phase-shifting interferometry

We recently presented a new asynchronous demodulation method for phase-sampling interferometry. The method is based in the principal component analysis (PCA) technique. In the former work, the PCA method was derived heuristically. In this work, we present an in-depth analysis of the PCA demodulation method

Non-uniformly polarized beams across their transverse profiles: an introductory study for undergraduate optics courses

We provide a simple theoretical study of beams non-uniformly polarized across their transverse sections which can be introduced in undergraduate optics courses. In order to generate such beams we propose to use a slightly convergent (or divergent) linearly and uniformly polarized beam impinging on an anisotropic uniaxial material with the beam propagation direction along the optic axis. Analytical expressions for the Jones vector, Stokes parameters, ellipticity and azimuth at each point of the transverse section, perpendicular to the propagation direction, are obtained at the output of this system. By means of these parameters a detailed description of the state of polarization across the transverse profile is given

Hierarchical autoclassification of cryo-EM samples and macromolecular energy landscape determination

Background and objective: Cryo-electron microscopy using single particle analysis is a powerful technique for obtaining 3D reconstructions of macromolecules in near native conditions. One of its major advances is its capacity to reveal conformations of dynamic molecular complexes. Most popular and successful current approaches to analyzing heterogeneous complexes are founded on Bayesian inference. However, these 3D classification methods require the tuning of specific parameters by the user and the use of complicated 3D re-classification procedures for samples affected by extensive heterogeneity. Thus, the success of these approaches highly depends on the user experience. We introduce a robust approach to identify many different conformations presented in a cryo-EM dataset based on Bayesian inference through Relion classification methods that does not require tuning of parameters and reclassification strategies. Methods: The algorithm allows both 2D and 3D classification and is based on a hierarchical clustering approach that runs automatically without requiring typical inputs, such as the number of conformations present in the dataset or the required classification iterations. This approach is applied to robustly determine the energy landscapes of macromolecules. Results: We tested the performance of the methods proposed here using four different datasets, comprising structurally homogeneous and highly heterogeneous cases. In all cases, the approach provided excellent results. The routines are publicly available as part of the CryoMethods plugin included in the Scipion package. Conclusions: Our results show that the proposed method can be used to align and classify homogeneous and heterogeneous datasets without requiring previous alignment information or any prior knowledge about the number of co-existing conformations. The approach can be used for both 2D and 3D autoclassification and only requires an initial volume. In addition, the approach is robust to the "attractor" problem providing many different conformations/views for samples affected by extensive heterogeneity. The obtained 3D classes can render high resolution 3D structures, while the obtained energy landscapes can be used to determine structural trajectories

Optical inspection of liquid crystal variable retarder inhomogeneities

Liquid crystal variable retarders (LCVRs) are starting to be widely used in optical systems because of their capacity to provide a controlled variable optical retardance between two orthogonal components of incident polarized light or to introduce a known phase shifting (PS) between coherent waves, both by means of an applied voltage. Typically, the retardance or PS introduced by an LCVR is not homogeneous across the aperture. On the one hand, the LCVR glass substrates present a global bend that causes an overall variation of the retardance or PS. On the other hand, in the manufacturing process of an LCVR, there sometimes appears a set of micro-air bubbles that causes local retardance or PS inhomogeneities. In this work, we present an interferometric technique based on a Mach-Zehnder interferometer that is insensitive to vibrations and capable of inspecting and characterizing the LCVR's retardance or PS inhomogeneities. The feasibility of the proposed method is demonstrated in the experimental results, where the LCVR retardance is measured with an error of about 0:2 rad. The thickness of possible micro-air bubbles is obtained with a resolution of about 50 nm

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open-and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2 π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7]

Incremental PCA algorithm for fringe pattern demodulation

This work proposes a new algorithm for demodulating fringe patterns using principal component analysis (PCA). The algorithm is based on the incremental implantation of the singular value decomposition (SVD) technique for computing the principal values associated with a set of fringe patterns. Instead of processing an entire set of interferograms, the proposed algorithm proceeds in an incremental way, processing sequentially one (as minimum) interferogram at a given time. The advantages of this procedure are twofold. Firstly, it is not necessary to store the whole set of images in memory, and, secondly, by computing a phase quality parameter, it is possible to determine the minimum number of images necessary to accurately demodulate a given set of interferograms. The proposed algorithm has been tested for synthetic and experimental in ter ferograms showing a good performance. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreemen

Image processing tools for the validation of CryoEM maps

The number of maps deposited in public databases (Electron Microscopy Data Bank, EMDB) determined by cryo-electron microscopy has quickly grown in recent years. With this rapid growth, it is critical to guarantee their quality. So far, map validation has primarily focused on the agreement between maps and models. From the image processing perspective, the validation has been mostly restricted to using two half-maps and the measurement of their internal consistency. In this article, we suggest that map validation can be taken much further from the point of view of image processing if 2D classes, particles, angles, coordinates, defoci, and micrographs are also provided. We present a progressive validation scheme that qualifies a result validation status from 0 to 5 and offers three optional qualifiers (A, W, and O) that can be added. The simplest validation state is 0, while the most complete would be 5AWO. This scheme has been implemented in a website https://biocomp.cnb.csic.es/EMValidationService/ to which reconstructed maps and their ESI can be uploaded

Advances in Xmipp for cryo-electron microscopy: from Xmipp to Scipion

Xmipp is an open-source software package consisting of multiple programs for processing data originating from electron microscopy and electron tomography, designed and managed by the Biocomputing Unit of the Spanish National Center for Biotechnology, although with contributions from many other developers over the world. During its 25 years of existence, Xmipp underwent multiple changes and updates. While there were many publications related to new programs and functionality added to Xmipp, there is no single publication on the Xmipp as a package since 2013. In this article, we give an overview of the changes and new work since 2013, describe technologies and techniques used during the development, and take a peek at the future of the package

Nuevos métodos de medida 3D mediante triangulación activa

Los métodos ópticos basados en triangulación activa han experimentado un gran avance en la pasada década y están comenzando a sustituir a los sensores tridimensionales basados en contacto en las diversas aplicaciones industriales de estos dispositivos. Estos métodos ópticos tienen propiedades que los hacen muy interesantes, como su gran velocidad, su capacidad de medida sin contacto y a campo completo y su bajo coste. No obstante, estos métodos presentan limitaciones prácticas cuando se está interesado en medir objetos extensos con gran precisión. En primer lugar los métodos de calibración para estos sistemas con los que se obtiene los resultados más precisos son muy difíciles de utilizar cuando se está interesado en calibrar un volumen de gran tamaño. Por otra parte, los sistemas de medida 3D basados en triangulación activa están caracterizados por tener una relación fija entre el área escaneada y la resolución en profundidad obtenida. Si se desea inspeccionar un área extensa se debe esperar obtener una resolución en profundidad pobre. Para obtener una medida 3D de un área extensa con alta resolución en profundidad es necesario realizar una medida en multiresolución. Finalmente, los métodos de triangulación activa estándares no son aplicables en el caso de que se desee inspeccionar una superficie no-cooperativa con una gran resolución espacial. Las superficies no-cooperativas se caracterizan por presentar una gran variación espacial de la reflectividad, de forma que existen regiones muy brillantes y muy oscuras. En la presenta memoria de tesis se presentan nuevos métodos de medida 3D mediante triangulación activa para resolver los problemas anteriormente mencionados. Por una parte, se introduce un nuevo método de calibración mixto para un sistema de triangulación activa que permite calibrar con gran precisión volúmenes de gran tamaño. Adicionalmente, se presentan dos nuevos métodos para la medida en multiresolución, uno local y otro global y finalmente se presenta un método para la medida 3D de superficies no-cooperativas