Enhancement of Cryo-EM maps by a multiscale tubular filter.

We present an approach to enhance cryo-electron microscopy (cryo-EM) postprocessed maps based on a multiscale tubular filter. The method determines a tubularness measure locally by the analysis of the eigenvalues of the Hessian matrix. This information is used to enhance elongated local structures and to attenuate blob-like and plate-like structures. The approach, thus, introduces a priori information in the reconstructions to improve their interpretability and analysis at high-resolution. The proposed method has been tested with simulated and real cryo-EM maps including recent reconstructions of the SARS-CoV-2. Our results show that our methods can improve obtained reconstructions.

Windowed phase unwrapping using a first-order dynamic system following iso-phase contours.

In this work, we show a windowed phase-unwrapping technique that uses a first-order dynamic system and scans the phase following its iso-phase contours. In previous works, we have shown that low-pass first-order dynamic systems are very robust and useful in phase-unwrapping problems. However, it is well known that all phase-unwrapping methods have a minimum signal-to-noise ratio that they tolerate. This paper shows that scanning the phase within local windows and using a path following strategy, the first-order unwrapping method increases its tolerance to noise. In this way, using the improved approach, we can unwrap phase maps where the basic dynamic phase-unwrapping system fails. Tests and results are given, as well as the source code in order to show the performance of the proposed method.

Multiplicative phase-shifting interferometry using optical flow.

Fringe patterns with a multiplicative phase shift among them appear in experimental techniques as photoelasticity and RGB shadow moiré, among others. These patterns cannot be processed using standard phase-shifting demodulation techniques. In this work, we propose to use a multiframe regularized optical flow algorithm to obtain the interesting modulating phase. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results.

Two-step demodulation based on the Gram-Schmidt orthonormalization method.

This Letter presents an efficient, fast, and straightforward two-step demodulating method based on a Gram-Schmidt (GS) orthonormalization approach. The phase-shift value has not to be known and can take any value inside the range (0,2π), excluding the singular case, where it corresponds to π. The proposed method is based on determining an orthonormalized interferogram basis from the two supplied interferograms using the GS method. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results. A complete MATLAB software package is provided at http://goo.gl/IZKF3.

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, 2π), 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].

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.

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.

Phase-shifting interferometry based on induced vibrations.

The presence of uncontrolled mechanical vibrations is typically the main precision-limiting factor of a phase-shifting interferometer. We present a method that instead of trying to insolate vibrations; it takes advantage of their presence to produce the different phase-steps. The method is based on spatial and time domain processing techniques to compute first the different unknown phase-steps and then reconstruct the phase from these tilt-shifted interferograms. In order to compensate the camera movement, it is needed to perform an affine registration process between the different interferograms. Simulated and experimental results demonstrate the effectiveness of the proposed technique without the use of any phase-shifter device.

Two-step self-tuning phase-shifting interferometry.

A two-step self-tuning phase-shifting method is presented. The phase-step between the two interferograms is not known when the experiment is performed. Our demodulating method finds, in a robust way, this unknown phase-step. Once the phase-step is estimated we proceed to phase demodulate the interferograms. Moreover our method only requires the fringe patterns to have a constant unknown phase-shift between them. As a consequence, this technique can be used to demodulate open and closed-fringed patterns without phase-sign ambiguity. The method may be regarded as a self-tuning quadrature filter, which determines the phase-shift between the two fringe patterns and finally estimates the demodulated phase map. The proposed technique has been tested with simulated and real interferograms obtaining satisfactory results.

Local fringe density determination by adaptive filtering.

We demonstrate a method to easily and quickly determine the local fringe density map of a fringe pattern. The method is based on an isotropic adaptive bandpass filter that is tuned at different frequencies. The modulation map after applying a specific bandpass frequencies filter presents a maximum response in the regions where the bandpass filter and fringe frequencies coincide. We show a set of simulations and experimental results that prove the effectiveness of the proposed method.

Direct demodulation of closed-fringe interferograms based on active contours.

We demonstrate a method to directly demodulate closed-fringe interferograms using a kind of active contour called a snake. This method can be used to demodulate a single closed-fringe interferogram when its background illumination and/or contrast terms have a spatial frequency similar to the spatial frequency of the equivalent normalized interferogram. Among other cases, this problematic usually appears in interferometry when spurious reflection appears in the interferogram. In these situations, typical Fourier-based methods are of no help. We show a set of simulations and experimental results that prove the effectiveness of the proposed method.

Calibration of a Shack-Hartmann wavefront sensor as an orthographic camera.

We demonstrate a method to calibrate a Shack-Hartmann sensor as an orthographic camera. This calibration method permits us to obtain the distance, the rotation matrix between the microlens array and CCD imaging planes, and the projection matrix, which models the projection of the incoming rays to the CCD imaging plane. The proposed calibration method introduces a very compact matrix notation and allows wavefront reconstruction without an explicit centroid search between the reference and distorted spot diagrams. We show a set of simulations in code V that prove the effectiveness of the proposed method.

Estimation of the orientation term of the general quadrature transform from a single n-dimensional fringe pattern.

The spatial orientation of the fringe has been demonstrated to be a key point in the reliable phase demodulation from a single n-dimensional fringe pattern regardless of the frequency spectrum of the signal. The recently introduced general n-dimensional quadrature transform (GQT) makes explicit the importance of the fringe orientation in the demodulation process. The GQT is a quadrature operator that transforms cos phi into -sin phi--where phi is the modulating phase--and it is composed of two terms: an orientation factor directly related to the fringe's spatial orientation and an isotropic n-dimensional generalization of the one-dimensional Hilbert transform. We present a method for the determination of the orientation factor in a general n-dimensional case and its application to the demodulation of a single fringe pattern by the GQT. We have tested the algorithm with simulated as well as real photoelastic fringe patterns with good results.