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Three-dimensional (3D) reconstruction of high-dynamic-range (HDR) surfaces plays an important role in the fields of computer vision and image processing. Traditional 3D measurement methods often face the risk of information loss when dealing with surfaces that have HDR characteristics. To address this issue, this paper proposes a simple 3D reconstruction method, which combines the features of non-overexposed regions in polarized and unpolarized images to improve the reconstruction quality of HDR surface objects. The optimum fringe regions are extracted from images with different polarization angles, and the non-overexposed regions in normally captured unpolarized images typically contain complete fringe information and are less affected by specular highlights. The optimal fringe information from different polarized image groups is gradually used to replace the incorrect fringe information in the unpolarized image, resulting in a complete set of fringe data. Experimental results show that the proposed method requires only 24~36 images and simple phase fusion to achieve successful 3D reconstruction. It can effectively mitigate the negative impact of overexposed regions on absolute phase calculation and 3D reconstruction when reconstructing objects with strongly reflective surfaces. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) reconstruction of high-dynamic-range (HDR) surfaces plays an important role in the fields of computer vision and image processing. Traditional 3D measurement methods often face the risk of information loss when dealing with surfaces that have HDR characteristics. To address this issue, this paper proposes a simple 3D reconstruction method, which combines the features of non-overexposed regions in polarized and unpolarized images to improve the reconstruction quality of HDR surface objects. The optimum fringe regions are extracted from images with different polarization angles, and the non-overexposed regions in normally captured unpolarized images typically contain complete fringe information and are less affected by specular highlights. The optimal fringe information from different polarized image groups is gradually used to replace the incorrect fringe information in the unpolarized image, resulting in a complete set of fringe data. Experimental results show that the proposed method requires only 24~36 images and simple phase fusion to achieve successful 3D reconstruction. It can effectively mitigate the negative impact of overexposed regions on absolute phase calculation and 3D reconstruction when reconstructing objects with strongly reflective surfaces.

Using numerical simulation methods, we study the features of the light field dynamics during filamentation under conditions of anomalous group velocity dispersion of mid-IR femtosecond pulses focused by an axicon into lithium and calcium fluoride crystals. The emergence of singularities with a wavefront discontinuity, which do not appear in a beam focused by a parabolic lens, is found. Wavefront discontinuities form near minima of the light field intensity. A strictly periodic change in spatial and energy parameters is demonstrated—the "breathing" of a light bullet formed in an axicon-focused beam as it propagates in a medium with material dispersion. A change in the oscillation period of the light bullet core with a change in the carrier wavelength is independent of the radiation focusing method and coincides with the results of analytical estimates that are calculated for a Gaussian wave packet focused by a parabolic lens with an undistorted harmonic carrier. [ABSTRACT FROM AUTHOR]

Phase measurement profilometry (PMP) is widely used to reconstruct three-dimensional (3D) shape of objects. However, errors are introduced during standard phase unwrapping process, which considerably brings down measurement accuracy and lowers method reliability. This paper proposes a novel method to identify the errors, and subsequently correct these errors through erecting adaptive local windows. Under proposal, two robust algorithms are developed to correct these errors in initial rudimentary correction as well as in subsequent refined error removal. The adaptive local window is designed as such that the fringe order corresponding to each period of the wrapping phase is independent of each other. Therefore, it avoids the error transmission in the correction process. Experiments are carried out on absolute phase error correction and 3D point cloud reconstruction. Experimental results verified the developed method in terms of reducing the stratification of 3D point cloud and improving the quality of 3D measurement. [ABSTRACT FROM AUTHOR]

The phase obtained in the interferogram is generally not continuous real phase information. Therefore, a phase larger than 2π will have a phase jump called wrapped phase. The traditional phase unwrapping algorithm usually requires a large amount of computation, and in reality, phase unwrapping is often a complex and morbid inverse problem due to factors such as speckle noise, random perturbations, low modulation, and phase discontinuity, and the processes of unwrapping of some algorithms depend on the path chosen. Therefore, it is difficult to obtain an accurate absolute phase under actual conditions. To improve the accuracy of the absolute phase, a phase unwrapping algorithm based on the transport-of-intensity equation with twowavelength illumination is proposed. The experimental results illustrate that the proposed method not only improves the accuracy of absolute phase but also holds a good antinoise performance. [ABSTRACT FROM AUTHOR]

This paper provides a review for absolute phase recovery methods that are applicable for digital fringe projection (DFP) systems. Specifically, we present two conventional absolute phase unwrapping methods: multi-frequency or -wavelength phase-shifting methods, and hybrid binary coding and phase-shifting methods; and also introduce some non-conventional methods that are specific for DFP systems: multiview geometry methods with additional camera(s) or projector(s), DFP system geometric constraint-based phase unwrapping method, and pre-knowledge (e.g., computer-aided-design, CAD, model) based phase unwrapping method. This paper also briefly overviews hybrid methods including phase coding, composite, and pre-defined markers based absolute phase unwrapping methods. This paper explains the principle behind each individual absolute phase unwrapping method; and finally offers some practical tips to handle common phase unwrapping artifact issues. [ABSTRACT FROM AUTHOR]

Automatic detection of horizons and other geological structures of interest is often employed as a preliminary step in seismic interpretation. Although necessary, the identification and extraction of horizons can be a laborious and time-consuming step for the interpreter. Therefore, we present a semi-automatic horizon extraction algorithm based on the absolute phase of seismic data obtained through phase unwrapping techniques. We assess the algorithm accuracy and robustness in several examples, including noisy data sets. In addition, we present comparative results between two phase unwrapping methods, showing their robustness when associated with seismic horizon extraction. We compare the results obtained by our methods with the results obtained by seismic horizon extraction algorithms available in the literature. • Seismic horizon extraction tool using absolute seismic phase. • Comparison of our method with other algorithms for seismic horizon extraction. • Robustness evaluation of two classes of phase unwrapping algorithms in seismic data. [ABSTRACT FROM AUTHOR]

Phase-measuring deflectometry (PMD)-based methods have been widely used in the measurement of the three-dimensional (3D) shape of specular objects, and the existing PMD methods utilize visible light. However, specular surfaces are sensitive to ambient light. As a result, the reconstructed 3D shape is affected by the external environment in actual measurements. To overcome this problem, an infrared PMD (IR-PMD) method is proposed to measure specular objects by directly establishing the relationship between absolute phase and depth data for the first time. Moreover, the proposed method can measure discontinuous surfaces. In addition, a new geometric calibration method is proposed by combining fringe projection and fringe reflection. The proposed IR-PMD method uses a projector to project IR sinusoidal fringe patterns onto a ground glass, which can be regarded as an IR digital screen. The IR fringe patterns are reflected by the measured specular surfaces, and the deformed fringe patterns are captured by an IR camera. A multiple-step phase-shifting algorithm and the optimum three-fringe number selection method are applied to the deformed fringe patterns to obtain wrapped and unwrapped phase data, respectively. Then, 3D shape data can be directly calculated by the unwrapped phase data on the screen located in two positions. The results here presented validate the effectiveness and accuracy of the proposed method. It can be used to measure specular components in the application fields of advanced manufacturing, automobile industry, and aerospace industry.

A conservative difference scheme is constructed for the system of equations that describe, in the semi-classical approximation, resonance and nonresonance interaction of an electromagnetic pulse with matter. The conservativity of the scheme is proved. A cascade mechanism for the excitation of high energy levels in the medium under the impact of a narrow-spectrum electromagnetic pulse is demonstrated. In the cascade mechanism, if the spectrum does not contain a pulse of sufficiently high frequencies to trigger direct transitions from the ground state to high excited states, the molecules of the medium may still reach the high states through a series of successive transitions between nearer lying energy levels. This may lead to the appearance in the transmitted pulse of higher frequencies than those observed in the incident pulse. For a medium whose length is comparable with the spatial extent of the pulse, distortion of the transmitted pulse spectrum is observed. The absolute phase of the small-period pulse substantially affects the transformation of the pulse spectrum during the transmission through the matter. If the matter contains several close energy levels, the corresponding transition rates will depend on the absolute phase of the field. We demonstrate and explain the generation of the third harmonic during the interaction of the electromagnetic pulse with the medium due to the nonstationary and nonlinear character of the response. [ABSTRACT FROM AUTHOR]

This paper presents a method that can recover absolute phase pixel by pixel without embedding markers on three phase-shifted fringe patterns, acquiring additional images, or introducing additional hardware component(s). The proposed three-dimensional (3D) absolute shape measurement technique includes the following major steps: (1) segment the measured object into different regions using rough priori knowledge of surface geometry; (2) artificially create phase maps at different z planes using geometric constraints of structured light system; (3) unwrap the phase pixel by pixel for each region by properly referring to the artificially created phase map; and (4) merge unwrapped phases from all regions into a complete absolute phase map for 3D reconstruction. We demonstrate that conventional three-step phase-shifted fringe patterns can be used to create absolute phase map pixel by pixel even for large depth range objects. We have successfully implemented our proposed computational framework to achieve absolute 3D shape measurement at 40 Hz. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for estimating the absolute phase offset in interferometric synthetic aperture radar (SAR) measurements for digital elevation model (DEM) generation. The method is based on “phase-offset functions (POF),” relating phase offset to topographic height, and are computed for two different overlapping interferometric data acquisitions performed with considerably different incidence angles over the same area of interest. For the purpose of extended mapping, opposite viewing directions are preferred. The two “phase-offset functions” are then linearly combined, yielding a “combined phase-offset function (CPOF)”. The intersection point of several straight lines (CPOFs), corresponding to different points in the overlap area allows for solving the phase offset for both acquisitions. Aiming at increasing performance and stability, this intersection point is found by means of averaging many points and applying principal component analysis. The method is validated against traditional phase offset estimation with corner reflectors (CR) using real OrbiSAR-1 data in X- and P-band.

As technologies evolve, diverse 3D measurement techniques using cameras and pattern projectors have been developed continuously. In 3D measurement, high accuracy, fast speed, and easy implementation are very important factors. Recently, 3D measurement using multi-frequency fringe patterns for absolute phase computation has been widely used in the fringe projection profilometry. This paper proposes an improved method to compute the object's absolute phase using the reference plane’s absolute phase and phase difference between the object and the reference plane. This method finds the object's absolute phase by adding the difference between the reference plane's wrapped phase and the object's wrapped phase to the reference plane's absolute phase already obtained in the calibration stage. Through this method, there is no need to obtain multi-frequency fringe patterns about new object for the absolute phase computation. Instead, we only need the object's phase difference relative to the reference planes's phase in the measurement stage. [ABSTRACT FROM AUTHOR]

An improved composite Fourier transform profilometry is proposed in this study to quickly measure the three-dimensional (3D) contour of an object. Three groups of fringe patterns with different frequencies are combined in this method. Compared with the other composite profilometry, it solves the problem of phase error propagation in phase unwrapping. The absolute phase of the object is accurately calculated and the measuring accuracy is improved greatly by filtering out the background direct current noise. Both simulation and experiment results show that the 3D contour of the measured object can be reconstructed quickly and accurately by this method. It has great application potential in the field of real-time 3D measurement. [ABSTRACT FROM AUTHOR]

We describe and analyze the effects of transients within radio-frequency (RF) pulses on multiple-pulse NMR measurements such as the well-known Carr–Purcell–Meiboom–Gill (CPMG) sequence. These transients are functions of the absolute RF phases at the beginning and end of the pulse, and are thus affected by the timing of the pulse sequence with respect to the period of the RF waveform. Changes in transients between refocusing pulses in CPMG-type sequences can result in signal decay, persistent oscillations, changes in echo shape, and other effects. We have explored such effects by performing experiments in two different low-frequency NMR systems. The first uses a conventional tuned-and-matched probe circuit, while the second uses an ultra-broadband un-tuned or non-resonant probe circuit. We show that there are distinct differences between the absolute phase effects in these two systems, and present simple models that explain these differences. [ABSTRACT FROM AUTHOR]

The article examines the interaction of a few-cycle optical pulse with an optically thin transparent and/or absorbing layer. The reflection of light energy is shown to be nonmonotone depending on layer thickness. The interaction of a few-cycle light pulse with the layer may produce total transparency of the layer for pulses of a certain carrier frequency. Absorption in the layer also has a nonmonotone effect on both reflected and transmitted light energy. The energy absorbed in the layer may decrease with increasing layer absorption coefficient due to the increase of energy reflection from the layer. The layer thickness when the reflected energy is maximized depends on the electrical conductivity of the medium. Under certain conditions, the interaction of the light pulse with the optically thin plate may essentially alter the spectrum of the reflected pulse and, in particular, its absolute phase, which depends on plate thickness. This property can be exploited in applications to generate few-cycle pulses with the required absolute phase. [ABSTRACT FROM AUTHOR]

An alignment method of a 2CCD camera to build pixel-to-pixel correspondence between the infrared (IR) CCD sensor and the visible CCD sensor by using the absolute phase data is presented. Vertical and horizontal sinusoidal fringe patterns are generated by software and displayed on a liquid crystal display screen. The displayed fringe patterns are captured simultaneously by the IR sensor and the visible sensor of the 2CCD camera. The absolute phase values of each pixel at IR and visible channels are calculated from the captured fringe pattern images by using Fourier transform and the optimum three-fringe number selection method. The accurate pixel corresponding relationship between the two sensors can be determined along the vertical and the horizontal directions by comparing the obtained absolute phase data in IR and visible channels. Experimental results show the high accuracy, effectiveness, and validity of the proposed 2CCD alignment method. By using the continuous absolute phase information, this method can determine the pixel-to-pixel correspondence with high resolution. [ABSTRACT FROM AUTHOR]

Based on the characteristics of speech signal, this paper develops a new digital information hiding algorithm. The basic idea: according to the characteristics of human ear's insensitiveness to speech signal absolute phases, the paper makes full use of the short-time energy of speech signal to find the silence sections of the signal, then makes the absolute silence sections, and takes advantage of the absolute silence sections to create a number of ?independent sections?. By changing the absolute phases of the ?independent sections?, all sampling points of the ?independent sections? are inverted, the positive proportion of sampling points of these sections are changed accordingly, and thus those secret digital pieces of information are carried. The experiments show that the proposed algorithm has excellent properties in robustness and invisibility. [ABSTRACT FROM AUTHOR]

Abstract: Because of the intrinsic drawbacks of existing 3D measurement methods, which are based on structured light projection, they often need precise linear z stage or other precise devices involvement, and the projector''s parameter or relative position between projector and camera needs to be calibrated; therefore, the system costs very high and the processing time is very long. In this paper, we present a 3D shape measurement method based on structured light projection applying polynomial interpolation technique. We have deduced that phase and depth coordinates meet a polynomial relation, and the relation is used to calibrate relative position between camera and projector. The proposed approach can realize 3D shape measurement without projector calibration, without system calibration, and without precise linear z stage to be used. The relative position between camera and projector can be arbitrary, and the only involved device is a plane board. Experiment results validated that the accuracy of the proposed approach is not lower than that of many previous methods, but our approach costs lower and can be set up more easily. [Copyright &y& Elsevier]

Abstract: This paper presents a method to recover absolute phase by using only four images: three phase-shifted patterns and one stair pattern. The stair pattern is designed in such a way that the stair changes are perfectly aligned with the phase jumps, and thus absolute phase can be recovered by referring to the stair pattern. Due to system noises and camera and/or projector blurring, a computational framework is also proposed. Because this technique only requires four fringe images for absolute phase recovery, it has the merit of measurement speed. And since the absolute phase is obtained, this technique is suitable for measuring step-height objects. We have developed a digital fringe projection system to verify the performance of the proposed technique. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to develop a four-step pattern encoding strategy through the combination of a triangle waveform, a step waveform, and two square waveforms. The proposed pattern encoding strategy makes the range of unique phase distribution up to , which is 5 times as large as of conventional four-step phase shifting encoding approach. Therefore, the proposed encoding strategy enables the structured light-based measurement system to measure complicated objects without ambiguity, which is the common limitation of the phase shifting algorithms. Furthermore, the proposed strategy is a pixel-level method, leading to a high-density 3D reconstruction. The decoding approach is a pixel independent computation, which can eliminate the error propagation and enhance the reliability. The phase errors between the phase shifting and the proposed encoding strategy are compared by the numerical simulation and they are very close. Experiments with different objects are carried out to validate the robustness and accuracy for the proposed encoding strategy. The results show that it is efficient for the 3D reconstruction of complicated objects. [Copyright &y& Elsevier]

The Rabi oscillation of the thin bulk semiconductor GaAs, which takes into account the effect of the local-field correction induced by the interacting excitons, is investigated by numerically solving the semiconductor Bloch equations. It is found, for a 2π few-cycle pulse excitation, that two incomplete Rabi-floppings emerge due to the competition between the Rabi frequency of the incident pulse and the internal-field matrices. Furthermore, for a sub-cycle 2π pulse excitation a complete Rabi-flopping can occur because of the absolute phase effect. We ascribe these characteristics of the Rabi oscillation to the renormalized Rabi frequency. [ABSTRACT FROM AUTHOR]

A method for measuring the tide height near the coast from L-band synthetic aperture radar (SAR) data is presented. Twenty-one coherent interferograms have been successfully constructed from Japanese Eearth Resources Satellite 1 (JERS-1) SAR data obtained over oyster sea-farming structures. A coherence analysis of the 21 interferometric pairs showed that a perpendicular baseline of less than 3 km, with a temporal baseline within 500 days, are required to obtain a coherent pair, with a coherence higher than 0.25, in the study area. The coherent phases preserved in the interferograms showed a close relation with the sea level. The problem of phase unwrapping to restore an absolute tide height was overcome by introducing normalized image intensities. The radar measurements estimated by the proposed method were verified using tide gauge data, and comparison of the two datasets yielded a correlation coefficient R² of 0.91, with a root mean square error of 5.76 cm. The results demonstrate that radar interferometry can be applied for a tide height measurement near the coast given sufficient structures that return off-nadir radar pulses to the antenna. The multipolarized L-band SAR system will provide better results, using only double-bounced signals, in the future. [ABSTRACT FROM AUTHOR]

A new method for accurately determining the transmission response of frequency-translating devices (FTDs) is presented. The absolute amplitude and phase of the FTD under test is obtained using a vector network analyzer (VNA) and two test FTDs, where one FTD must have reciprocal frequency response characteristics. The characterization of single-sideband (SSB) FTDs is obtained in a straightforward manner by combining data from three VNA two-port swept measurements. The characterization of double-sideband (DSB) FTDs can be performed in the same manner as for SSB FTDs, or, more accurately, by combining data from six two-port swept baseband measurements. A complete analysis of the characterization method using low-pass equivalent (LPE) signals and systems is presented, along with the development of the appropriate data reduction procedures needed to arrive at the de-embedded LPE FTD transmission responses. The validation and accuracy of the method is demonstrated with results for both SSB and DSB FTDs operating at 20 GHz. [ABSTRACT FROM AUTHOR]

A phase-sensitive scanning optical microscope is described which can measure surface height changes of less than 3 ångströms. The system is based on a heterodyne version of the Michelson interferometer, and has been designed to reject phase noise caused by vibration in the optics and the sample. A specially constructed objective lens is used to direct two laser beams on to the object surface. The first beam forms a tightly focused spot to probe the sample structure, and the second remains collimated, acting as a large-area on-sample reference beam.The configuration allows the relative areas illuminated by the two beams to be varied both arbitrarily and independently, thus guaranteeing an accurate absolute phase measurement. This is an important advantage over existing techniques, in which the range of suitable samples is restricted by the limited size of the on-sample reference beam. The two beams reflected from the sample are interfered with a third, frequency-shifted, beam, so forming two heterodyne Michelson interferometers in parallel. The phase from each interferometer is then compared to provide the object-surface phase structure. Path-length fluctuations due to microphonics are common to both interferometers and are cancelled by this comparison.Results from a bench-top version of the system are presented which demonstrate the principle of the technique, and the factors limiting the sensitivity are discussed. [ABSTRACT FROM PUBLISHER]

• To the best of our knowledge, two patterns is current state-of-the-art method for obtaining high-slope absolute phase of complex objects in the FPP system. • The designed ALCNN network has the excellent functions of segmentation and recognition, which can be used to solve the fringe order from only one code pattern. • The proposed MCDL method has high accuracy since the measurement error of a standard ball is 0.0189 mm in FOV of 250 mm × 200 mm. Benefiting from the merits of low cost, high accuracy and high resolution, fringe projection profilometry has been developing rapidly over the past decades. However, recovering the absolute phase with high accuracy and robustness effectively has always been significant challenge in fringe projection profilometry. In this paper, an intelligent Multi-code Deep Learning (MCDL) technique is developed to solve the high-slope absolute phase from only two patterns with high accuracy and robustness. Two sub-networks are designed for obtaining the wrapped phase and the fringe order. Specially, the proposed MCDL method can solve the high-level fringe orders by only a special multi-code pattern itself through a cooperative multi-connected convolutional neural network. By training the deep network with numerous datasets, the principle of unwrapping phase can be learned by the MCDL approach. Experiments demonstrate that the proposed method has the abilities of high robustness, efficiency and accuracy (measurement error: 0.0189mm, FOV: 250 mm × 200 mm), indicating potential applications for high-speed and high-accuracy three dimensional optical measurement. [ABSTRACT FROM AUTHOR]

Fringe Projection Profilometry is one of the important techniques in three-dimensional vision. However, traditional Fringe Projection Profilometry employing a lot of patterns has significant challenges for efficiently recovering the absolute phase. In this paper, a multi-purpose neural network combining with code-based patterns is proposed to recover the absolute phase firstly, which can greatly decrease the number of patterns with high accuracy. Different from the traditional approach of trigonometric calculation, the well-trained multi-purpose network can learn the principle of extracting absolute phase from few patterns. Experiments demonstrate that the proposed method can acquire high accuracy for complex texture objects, indicating potential application in precision engineering with high speed. [ABSTRACT FROM AUTHOR]

Phase-measuring deflectometry (PMD)-based methods have been widely used in the measurement of the three-dimensional (3D) shape of specular objects, and the existing PMD methods utilize visible light. However, specular surfaces are sensitive to ambient light. As a result, the reconstructed 3D shape is affected by the external environment in actual measurements. To overcome this problem, an infrared PMD (IR-PMD) method is proposed to measure specular objects by directly establishing the relationship between absolute phase and depth data for the first time. Moreover, the proposed method can measure discontinuous surfaces. In addition, a new geometric calibration method is proposed by combining fringe projection and fringe reflection. The proposed IR-PMD method uses a projector to project IR sinusoidal fringe patterns onto a ground glass, which can be regarded as an IR digital screen. The IR fringe patterns are reflected by the measured specular surfaces, and the deformed fringe patterns are captured by an IR camera. A multiple-step phase-shifting algorithm and the optimum three-fringe number selection method are applied to the deformed fringe patterns to obtain wrapped and unwrapped phase data, respectively. Then, 3D shape data can be directly calculated by the unwrapped phase data on the screen located in two positions. The results here presented validate the effectiveness and accuracy of the proposed method. It can be used to measure specular components in the application fields of advanced manufacturing, automobile industry, and aerospace industry. [ABSTRACT FROM AUTHOR]

We report on a grating Bonse-Hart interferometer for phase-contrast imaging with hard X-rays. The method overcomes limitations in the level of sensitivity that can be achieved with the well-known Talbot grating interferometer, and without the stringent spectral filtering at any given incident angle imposed by the classic Bonse-Hart interferometer. The device operates in the far-field regime, where an incident beam is split by a diffraction grating into two widely separated beams, which are redirected by a second diffraction grating to merge at a third grating, where they coherently interfere. The wide separation of the interfering beams results in large phase contrast, and in some cases absolute phase images are obtained. Imaging experiments were performed using diffraction gratings of 200 nm period, at 22.5 keV and 1.5% spectral bandwidth on a bending-magnetic beamline. Novel design and fabrication process were used to achieve the small grating period. Using a slitted incident beam, we acquired absolute and differential phase images of lightly absorbing samples. An advantage of this method is that it uses only phase modulating gratings, which are easier to fabricate than absorption gratings of the same periods. [ABSTRACT FROM AUTHOR]

A Rice factor (K) estimator is described which uses simple operations on the phase of the well-defined Rice channel. Multiple receive channels, such as used in MIMO communications, enable spatial sampling which enhances the accuracy. For an example configuration of four uncorrelated receive antennas with a ten wavelength linear trajectory in isotropic scattering, the estimator works well for small to medium K (i.e., K \lesssim7). Limitations of the estimator include an assumption of isotropic scattering and that the angle-of-arrival of the dominant component is fixed and cannot be perpendicular to the mobile trajectory. [ABSTRACT FROM PUBLISHER]