Complex Fringe Research Articles

Quantification analysis of mural defects in digital holography with fundamental voice excitation based on local phase field separation

Previous collaborative studies have shown that fringe patterns by optical interference way are used as a direct diagnostic tool for qualitative analysis of defects in Culture Heritage. Nevertheless, the complexity of the fringe patterns prevents the accurate quantification of defects. In this study, a phase separation method based on the weighted least-squares algorithm is proposed to conveniently isolate the local phase distribution from the whole, complex fringe pattern. This method is examined to accurately quantify the deformation and strain distribution of visible and invisible defects. In experimental work, the Non-destructive Acoustic excitation and Digital Holography (NDA-DH) detection is employed for the superficial and subsurface defects in the Ruting murals of the Forbidden City, Beijing. Under the impact of fundamental human voice, the frequency range of the acoustic excitation was considered from 100–800 Hz. All results show that the suggested phase separation method allows direct observation of defects as well as quantified surface deformation providing a precious documentation to the conservators.

Interferogram analysis of X-pinch plasmas with a synthetic dark-field Schlieren image

The Mach-Zehnder interferometer and dark-field Schlieren imaging systems are developed to diagnose high electron densities of the X-pinch plasmas. Interferogram analysis can be challenging due to stiff electron density gradients of the X-pinch plasmas. This stiff gradient results in complex fringe patterns which may lead to miscounted indices of the fringes, and even refraction losses. To address these challenges, the geometrical acceptance angle of the imaging system is increased to reduce the refraction losses caused by the X-pinch plasmas. This is achieved by using physically larger optics. Results show that the imaging systems can detect higher line-integrated electron densities. Additionally, to verify the reliability of interferogram analysis results, a synthetic dark-field Schlieren image generated based on the interferogram is qualitatively compared to the measured dark-field Schlieren image which is simultaneously taken with the interferogram. Practicality of the synthetic Schlieren images is examined by comparing them with the measured Schlieren images.

A comparative evaluation of 2-D Hilbert transforms and 2-D continuous wavelet transforms for robust phase extraction in complex fringe patterns

A comparative evaluation of 2-D Hilbert transforms and 2-D continuous wavelet transforms for robust phase extraction in complex fringe patterns

Harmonics elimination in phase-shifting fringe projection profilometry by use of a non-filtering algorithm in frequency domain.

In phase-shifting fringe projection profilometry, fringe harmonics caused by device nonlinearities as well as other factors may badly ruin the measurement results. Generally, the used phase-shifting algorithm enables restraint of effects of harmonics below a certain order depending on the number of phase shifts. When reducing the number of phase shifts for efficiency, high order harmonics will affect the phase-measuring results because of aliasing caused by insufficient sampling rate. To overcome this issue, this paper suggests a non-filtering technique operating in frequency domain, that enables improvement of measurement accuracy by eliminating effects of high order harmonics. With this technique, the phase-shifting algorithm is restated as a process of retrieving the fundamental complex fringes from the phase-shifted fringe patterns. Implementing a Fourier transform to this calculated complex fringe pattern, the actual fundamental signals and the aliased harmonics have their own lobes with separated peaks in the frequency domain. We reconstruct each order of the aliased harmonics by exploiting their relations with the fundamental signals and then estimate their magnitudes by using the spectral peaks. Instead of directly filtering the fringe spectrum, we subtract spectra of the harmonics from Fourier transform of the just calculated complex fringes, so that the Fourier spectrum of the fundamental fringes without harmonics is recovered through an iterative operation. Further, the phase map is measured accurately. Simulation and experimental results confirm that this proposed method can significantly suppress effects of fringe harmonics. Meanwhile, by taking advantage of non-filtering, it effectively preserves the edges and details of the measured surfaces from being blurred.

Interferometric beam combination with a triangular tricoupler photonic chip

Beam combiners are important components of an optical/infrared astrophysical interferometer, with many variants as to how to optimally combine two or more beams of light to fringe-track and obtain the complex fringe visibility. One such method is the use of an integrated optics chip that can instantaneously provide the measurement of visibility without temporal or spatial modulation of the optical path. Current asymmetric planar designs are complex, resulting in a throughput penalty, and so here, we present developments into a three-dimensional triangular tricoupler that can provide the required interferometric information with a simple design and only three outputs. Such a beam combiner is planned to be integrated into the upcoming Pyxis interferometer, where it can serve as a high-throughput beam combiner with a low size footprint. Results into the characterization of such a coupler are presented, highlighting a throughput of 85 ± 7 % and a flux splitting ratio between 33:33:33 and 52:31:17 over a 20% bandpass. We also show the response of the chip to changes in the optical path, obtaining an instantaneous complex visibility and group delay estimate at each input delay.

PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image.

Quantifying the stress field induced into a piece when it is loaded is important for engineering areas since it allows the possibility to characterize mechanical behaviors and fails caused by stress. For this task, digital photoelasticity has been highlighted by its visual capability of representing the stress information through images with isochromatic fringe patterns. Unfortunately, demodulating such fringes remains a complicated process that, in some cases, depends on several acquisitions, e.g., pixel-by-pixel comparisons, dynamic conditions of load applications, inconsistence corrections, dependence of users, fringe unwrapping processes, etc. Under these drawbacks and taking advantage of the power results reported on deep learning, such as the fringe unwrapping process, this paper develops a deep convolutional neural network for recovering the stress field wrapped into color fringe patterns acquired through digital photoelasticity studies. Our model relies on an untrained convolutional neural network to accurately demodulate the stress maps by inputting only one single photoelasticity image. We demonstrate that the proposed method faithfully recovers the stress field of complex fringe distributions on simulated images with an averaged performance of 92.41% according to the SSIM metric. With this, experimental cases of a disk and ring under compression were evaluated, achieving an averaged performance of 85% in the SSIM metric. These results, on the one hand, are in concordance with new tendencies in the optic community to deal with complicated problems through machine-learning strategies; on the other hand, it creates a new perspective in digital photoelasticity toward demodulating the stress field for a wider quantity of fringe distributions by requiring one single acquisition.

Optimization of the photoelastic conoscopic fringe pattern processing for the stress measurement on uniaxial PWO crystal cut parallel to the a-c plane and with variable thickness.

This paper presents a case study in which conoscopic, non-invasive, photoelastic techniques and the associated model are applied for the first time to investigate the internal stress state of the PbWO4 (PWO) uniaxial crystal, cut normal to the crystallographic a-c plane and with non-uniform thickness. As a matter of facts indeed, in the mass production of crystals it is rather probable to have specimen of non-constant thickness. In addition, the crystal cut, normal to the a-c plane, lead to a complex fringes structure and modeling. This can affect the fringe patterns interpretation, and in turn the interpretation of the stress state within the sample. In this paper we analyze the dependence of some model parameters on the thickness, and the relative interpretation of the fringe pattern in order to obtain a reliable measure of the stress for observations normal to the a-c plane. This procedure can speed up the crystal analysis whatever the thickness of the crystal is.

The Origin and 3D Architecture of a Km-Scale Deep-Water Scour-Fill: Example From the Skoorsteenberg Fm, Karoo Basin, South Africa

Scours, and scour fields, are common features on the modern seafloor of deep-marine systems, particularly downstream of submarine channels, and in channel-lobe-transition-zones. High-resolution images of the seafloor have improved the documentation of the large scale, coalescence, and distribution of these scours in deep-marine systems. However, their scale and high aspect ratio mean they can be challenging to identify in outcrop. Here, we document a large-scale, composite erosion surface from the exhumed deep-marine stratigraphy of Unit 5 from the Permian Karoo Basin succession in South Africa, which is interpreted to be present at the end of a submarine channel. This study utilizes 24 sedimentary logs, 2 cored boreholes, and extensive palaeocurrent and thickness data across a 126 km2 study area. Sedimentary facies analysis, thickness variations and correlation panels allowed identification of a lower heterolithic-dominated part (up to 70 m thick) and an upper sandstone-dominated part (10–40 m thick) separated by an extensive erosion surface. The lower part comprises heterolithics with abundant current and sinusoidal ripples, which due to palaeocurrents, thickness trends and adjacent depositional environments is interpreted as the aggradational lobe complex fringes. The base of the upper part comprises 2-3 medium-bedded sandstone beds interpreted as precursor lobes cut by a 3–4 km wide, 1–2 km long, and up to 28 m deep, high aspect ratio (1:100) composite scour surface. The abrupt change from heterolithics to thick-bedded sandstones marks the establishment of a new sediment delivery system, which may have been triggered by an updip channel avulsion. The composite scour and subsequent sandstone fill support a change from erosion- and bypass-dominated flows to depositional flows, which might reflect increasingly sand-rich flows as a new sediment route matured. This study provides a unique outcrop example with 3D stratigraphic control of the record of a new sediment conduit, and development and fill of a large-scale composite scour surface at a channel mouth transition zone, providing a rare insight into how scours imaged on seafloor data can be filled and preserved in the rock record.

Non-invasive deformation metrology using subspace analysis in digital holographic interferometry

For non-invasive precision measurement of deformation using digital holographic interferometry (DHI), reliable estimation of interference phase from complex fringe signal is required. This article introduces a method for estimation of interference phase in DHI. The proposed method is based on computing roots of a frequency estimation function obtained from noise subspace of the fringe signal. The main advantage of the proposed method is robustness against severe noise. In addition, the method also offers the capability of direct phase derivative estimation. The performance of the proposed method is validated using numerical simulations. Our simulation results show that even for signal to noise ratio as low as −5 dB, the proposed method offers root mean square errors of less than 1 radian for phase retrieval. The practical utility of the method for non-invasive deformation analysis is demonstrated using experimental results in DHI.

Deep-learning-based hologram generation using a generative model.

We propose a new learning and inferring model that generates digital holograms using deep neural networks (DNNs). This DNN uses a generative adversarial network, trained to infer a complex two-dimensional fringe pattern from a single object point. The intensity and fringe patterns inferred for each object point were multiplied, and all the fringe patterns were accumulated to generate a perfect hologram. This method can achieve generality by recording holograms for two spaces (16 Space and 32 Space). The reconstruction results of both spaces proved to be almost the same as numerical computer-generated holograms by showing the performance at 44.56 and 35.11 dB, respectively. Through displaying the generated hologram in the optical equipment, we proved that the holograms generated by the proposed DNN can be optically reconstructed.

Variable mesh optimization applied to fringe pattern demodulation using a Bézier surface

We present a parametric method to carry out a demodulation process in complex fringe pattern images with either open or closed fringes; this method is based on the parallel demodulation algorithm and introduces a novel way, to the best of our knowledge, to approximate the phase map using the Bezier surface control points. For this study, a recently developed population meta-heuristic called Variable Mesh Optimization is introduced to implement the optimization process. The results of the proposed method improve the phase error and the run time scores in comparison with other global optimization algorithms, which address this type of problem.

Framing the Open (Urban) Project: Insights from Landscape and Ecology

In the 80’s and 90’s, architects grew interested in experimenting with change over time, flexibility, indeterminacy, multiple layers and programs – what Manuel Gausa defined as an emerging open logic in architecture. At the same time, landscape and ecology were seen by many as the most appropriate medium to operate in the context of complex urban infrastructure and fringe areas. Currently, the threat posed by climate change and the increasing investment from cities on creating and repurposing open spaces and infrastructure, is feeding a renovated interest in landscape design. However, it is also leading to an increasing objectification of landscape. This paper will look at five recent projects of landscape architecture to reflect on the value and limits of 'open-ness' in urban design.

On the Response of Polarimetric GNSS-Reflectometry to Sea Surface Roughness

Reflectometry of Global Navigation Satellite Systems (GNSS) signals from the ocean surface has provided a new source of observations to study the ocean-atmosphere interaction. We investigate the sensitivity and performance of GNSS-Reflectometry (GNSS-R) data to retrieve sea surface roughness (SSR) as an indicator of sea state. A data set of one-year observations in 2016 is acquired from a coastal GNSS-R experiment in Onsala, Sweden. The experiment exploits two sea-looking antennas with right- and left-hand circular polarizations (RHCP and LHCP). The interference of the direct and reflected signals captured by the antennas is used by a GNSS-R receiver to generate complex interferometric fringes. We process the interferometric observations to estimate the contributions of direct signals and reflections to the total power. The power estimates are inverted to the SSR using the state-of-the-art model. The roughness measurements from the RHCP and LHCP links are evaluated against match-up wind measurements obtained from the nearest meteorological station. The results report on successful roughness retrieval with overall correlations of 0.76 for both links. However, the roughness effect in LHCP observations is more pronounced. The influence of surrounding complex coastlines and the wind direction dependence are discussed. The analysis reveals that the winds blowing from land have minimal impact on the roughness due to limited fetch. A clear improvement of roughness estimates with an overall correlation of 0.82 is observed for combined polarimetric observations from the RHCP and LHCP links. The combined observations can also improve the sensitivity of GNSS-R measurements to the change of sea state.

Stable complex conjugate artifact removal in OCT using circularly polarized light as reference

In Fourier domain optical coherence tomography (FDOCT), the depth profile is mirrored about the zero delay between the sample and reference optical paths, limiting the imaging depth to half of the entire ranging space and undermining the optimal sensitivity window. We present a new method, to the best of our knowledge, to remove the complex conjugate artifact by using circularly polarized light as reference. Quadrature detection of the complex fringe is achieved by utilizing the intrinsic λ/4 delay between two polarization channels. We use passive broadband polarization optics to control the polarization state of the light in the reference and sample arms and a balanced polarization diversity detection unit to simultaneously detect phase-shifted fringes. We demonstrate a 40 dB artifact suppression ratio with a swept-source optical coherence tomography system. Our proposed method is immune to sample motion and laser phase noise, and imposes no restrictions to the source bandwidth, imaging speed, or computational power. In vivo images of the human finger, as well as the cornea and retina of a non-human primate, were demonstrated.

Parallel phase shifting radial shear interferometry with complex fringes and unknown phase shift.

We present an interferometric method to analyze transparent samples using complex fringes generated by a parallel phase shifting radial shear interferometer using two coupled interferometers. Parallel interferograms are generated using two interferometers: the first one generates the polarized base pattern, and the second system is used to generate parallel interferograms allowing the adjustment of the x-y positions of the parallel interferograms. To obtain the optical phase map, parallel phase shift is generated by collocating polarizing filters at the output of the system; the polarizers are placed at arbitrary angles since they do not require adjustment because of the phase-recovery algorithm. The optical phase was processed using a two-step algorithm based on a modified Gram-Schmidt orthogonalization method. Such an algorithm has the advantage of not being iterative and is robust to amplitude modulation. The proposed method reduces the number of captures needed in phase-shifting interferometry. We applied the developed system to examine static and dynamics phase objects.

Accurate phase retrieval algorithm based on normalized vector of three interferograms

A phase retrieval method from three interferograms based on normalized vector is proposed to achieve high accuracy and less time computation. It needn’t pre-filtering for the interferograms, which reduces its complexity and shortens the processing time. The difference maps are used to filter out the background intensity after compensating the fluctuation. Then, the normalized vector is used to obtain tested phase distribution with high precision. It is suitable for simple and complex fringes. Moreover, the phase can be correctly extracted when the fluctuation of background intensity and modulation amplitude is existed. The reliability of the algorithm is verified with simulated and experimental data.

Rapid and precise phase retrieval from two-frame tilt-shift based on Lissajous ellipse fitting and ellipse standardization.

A rapid and precise phase-retrieval method based on Lissajous ellipse fitting and ellipse standardization is demonstrated. It only requires two interferograms without pre-filtering, which reduces its complexity and shortens the processing time. The elliptic coefficients obtained by ellipse fitting are used for ellipse standardization. After compensating phase-shift errors by ellipse standardization, the phase distribution is extracted with high precision. It is suitable for fluctuation, noise, tilt-shift, simple and complex fringes. This method is effective for the number of fringes less than 1. The reliability of the method is verified by simulations and experiments, indicating high accuracy and less time consumption.

Fringe Pattern Denoising using U-Net based neural network

Fringe visibility and noise removal, are key success factors in interferometric techniques, where novel deep learning techniques can be applied. We test the use U-Net deep convolutional network applied to the obtained interference images, trained with an ad-hoc generated image dataset with complex fringe patterns, computed using high order Zernike polynomials.

Random phase retrieval approach using Euclidean matrix norm of sum and difference map and fast least-squares algorithm

In order to meet the requirements of the in-situ optical measurement, a random phase retrieval approach using the Euclidean matrix norm of sum and difference map and fast least-squares algorithm (EMNSD&FLSA) is proposed. It can obtain the high accuracy as the iterative algorithm and cost less computational time as the non-iterative algorithm simultaneously. No pre-filtering, iteration and relatively accurate initial phase lead to the high accuracy, fast iterative method and only two phase shifted interferograms lead to the high speed. It can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect. Moreover, it is suitable for different levels of noises. If the high accuracy is required, it would be best to suppress the noise before using EMNSD&FLSA, and the phase shift would be best to far away from 0 rad and π rad, furthermore, the numbers of patterns are best to be more than 2. Last but not least, it is robust for the circular, straight or complex fringes. The simulations and experiments verify the correctness and feasibility of EMNSD&FLSA.

How voters form associative issue ownership perceptions. An analysis of specific issues

To achieve high measurement accuracy with less computational time in phase shifting interferometry, a random phase retrieval approach based on difference map normalization and fast iterative algorithm (DN&FIA) is proposed, it doesn't need pre-filtering, and has the advantage of the iterative algorithms-high accuracy, moreover, it also has the advantage of non-iterative algorithms-timesaving, it only needs three randomly phase shifted interferograms, and the initial phase shifts of the iteration can be random, last but not least, it is effective for the circular, straight or complex fringes. The simulations and experiments verify the correctness and feasibility of DN&FIA.