Sign Ambiguity Research Articles

De-embedding method for a sensing area characterization of planar microstrip sensors without evaluating error networks

A de-embedding method for determining all scattering (S-) parameters (e.g., characterization) of a sensing area of planar microstrip sensors (two-port network or line) is proposed using measurements of S-parameters with no calibration. The method requires only (partially known) non-reflecting line and reflecting line standards to accomplish such a characterization. It utilizes uncalibrated S-parameter measurements of a reflecting line, direct and reversed configurations of a non-reflecting line, and direct and reversed configurations of the sensing area. As different from previous similar studies, it performs such a characterization without any sign ambiguity. The method is first validated by extracting the S-parameters of a bianisotropic metamaterial slab, as for a two-port network (line), constructed by split-ring-resonators (SRRs) from waveguide measurements. Then, it is applied for determining the S-parameters of a sensing area of a microstrip sensor involving double SRRs next to a microstrip line. The root-mean-square-error (RMSE) analysis was utilized to analyze the accuracy of our method in comparison with other techniques in the literature. It has been observed from such an analysis that our proposed de-embedding technique has the lowest RMSE values for the extracted S-parameters of the sensing area of the designed sensor in comparison with those of the compared other de-embedding techniques in the literature, and have similar RMSE values in reference to those of the thru-reflect-line calibration technique. For example, while RMSE values of real and imaginary parts of the forward reflection S-parameter of this sensing area are, respectively, around 0.0271 and 0.0279 for our de-embedding method, those of one of the compared de-embedding techniques approach as high as 0.0318 and 0.0324.

Kinematic modeling and simultaneous calibration for acupuncture robot

Acupuncture robot is a new-era product combining traditional acupuncture and cutting-edge technology. The calibration of the vision system and the acupuncture mechanism is a crucial prerequisite for humanoid acupuncture control, which has not yet been explored. In this paper, a simultaneous offline calibration method is proposed for acupuncture robots. Analysis reveals that its calibration problem is defined with three closed kinematic chains, while the typical problems cover only a single chain. Decoupling them, a Kronecker product-based method is deduced to access the closed-form rotation component. As opposed to quaternion-based methods, it only experiences linear complexity in sign ambiguity, which can produce a more precise solution in finite time. Further, a simultaneous optimization model that encompasses all components is established, which can be solved with stochastic gradient descent-based methods. It is free of truncation errors and thus has higher calibration accuracy and convergence speed. Besides, the impairment in error propagation between different closed kinematic chains is mitigated compared to step-by-step methods. Finally, simulations and experiments are carried out. Notably, the proposed method can be easily extended to other robot calibration problems with multiple closed kinematic chains.

On the periodicity of singular vectors and the holomorphic block-circulant SVD on the unit circumference

We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output channel. Our analysis is based on the Puiseux series expansion of the eigenvalue decomposition of analytic para-Hermitian matrices on the complex unit circumference. We study the case in which the rectangular matrix does not admit a full analytic singular value factorization, either due to partly multiplexed systems or to sign ambiguity. We show how to find an SVD factorization in the ring of Puiseux series where each singular value and the associated singular vectors present the same period and multiplexing structure, and we prove that it is always possible to find an analytic pseudo-circulant factorization, meaning that any arbitrary arrangements of multiplexed systems can be converted into a parallel form. In particular, one can show that the sign ambiguity can be overcome by allowing non-real holomorphic singular values.

A High Precison Phase Extraction Algorithm from a Single Shot Interferogram

Abstract. Phase shifting interferometry is an optical metrology with a high precision, but it usually requires the expensive high precision phase shifter. Therefore, low cost methods of extracting phase from a single shot interferogram were very valuable, but available algorithms are usually effective only in a limited conditions. To solve these problems, a novel method is presented in this work. Based on this method, the interference fringe is retrieved to a wrapped phase and divided into different regions and the index of the pixel is calculated. The pixels in the same region have the same parity and the PSF’s gravity center of part wavefront so as to solve the sign ambiguity. The theoretical simulation results indicate that the PV of wavefront error is 0.00054λ and the rms is 0.000125λ,which is much better than the results from the Fast Fourier Transformation method. The experimentally measured interferogram is also used to validate the method. It has the advantages of simplicity, high precision and effective for both open and closed interferometer fringes.

A bound on the cosmic opacity of unparticles from the CMB temperature

Unparticle cosmology gives an unconventional outlook on the dark sector of cosmology, increasingly challenging ΛCDM by H0-tension. This model derives from a finite temperature broken conformal symmetry of radiation, described by a non-radiative correction with unknown sign in energy density. This symmetry breaking has a sign ambiguity, in which corrections about the IR fixed point are normal or tachyonic. While the first has been ruled out in a recent study, the latter possesses a late-time temperature Tc≃4TCMB associated with ΩU≃1 (ΩU≃104ΩCMB), where TCMB denotes the temperature of the Cosmic Microwave Background (CMB). Thus exposed to the enormous heat bath of unparticles, TCMB is constrained by the astronomical age of the Universe Tu,0. The relative temperature shift ΔT/T in any heat exchange to the CMB is hereby limited to the uncertainty of a few percent in Tu,GC. This bounds the effective cross-section of unparticles interactions with CMB photons to σγU≲10−40m2=10−3nb. Assuming a standard cross-section across the broadband mass and energy spectrum of unparticles, a more stringent bound σγU≲10−3pb derives from COBE-FIRAS constraints on spectral distortions. The first is midway of photon-neutrino σγν and photon–photon cross-sections σγγ, the second is on par with σγν. These constraints put late-time unparticle cosmology, if present, at the edge of the standard model.

Deep learning estimation of modified Zernike coefficients and recovery of point spread functions in turbulence.

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to predict a modified set of Zernike polynomial coefficients corresponding to wavefront aberrations in the pupil due to turbulence. The modified set assigns an absolute value to coefficients of even radial orders due to a sign ambiguity associated with this problem and is shown to be sufficient for specifying the intensity point spread function. Simulated image data of a point object and simple extended objects over a range of turbulence and detection noise levels are created for the learning model. The MSE results for the learning model show that the best prediction is found when observing a point object, but it is possible to recover a useful set of modified Zernike coefficients from an extended object image that is subject to detection noise and turbulence.

Anchor-Aided Channel Estimation for RIS-Assisted Multiuser Broadband Communications

Due to the passive nature of reconfigurable intelligent surface (RIS) and a large number of users, it is very challenging to estimate the cascaded base station (BS)-RIS-user channel directly, especially for multiuser broadband communication systems. In this letter, we propose a novel two-phase method to estimate multiuser broadband cascaded channels with the assistance of two anchor nodes. Specifically, in the first phase, the cascaded channel from the two anchors to the BS and that between two anchors are estimated to acquire the BS-RIS channel state information (CSI) with sign ambiguities. It is accomplished based on cyclic-prefixed single-carrier transmission and phase configuration at the RIS, which creates multiple cyclic delayed versions of transmitted signals for isolating all broadband channel taps. In the second phase, the RIS-user channel and subsequently the cascaded BS-RIS-user channel are estimated in the frequency domain using the knowledge of the partial BS-RIS CSI. Simulation results verify the superiority of the proposed scheme over the state-of-the-art methods in terms of estimation overhead, normalized mean-squared error and bit error rate.

A deep learning approach for focal-plane wavefront sensing using vortex phase diversity

Context. The performance of high-contrast imaging instruments is limited by wavefront errors, in particular by non-common path aberrations (NCPAs). Focal-plane wavefront sensing (FPWFS) is appropriate to handle NCPAs because it measures the aberration where it matters the most, that is to say at the science focal plane. Phase retrieval from focal-plane images results, nonetheless, in a sign ambiguity for even modes of the pupil-plane phase. Aims. The phase diversity methods currently used to solve the sign ambiguity tend to reduce the science duty cycle, that is, the fraction of observing time dedicated to science. In this work, we explore how we can combine the phase diversity provided by a vortex coronagraph with modern deep learning techniques to perform efficient FPWFS without losing observing time. Methods. We applied the state-of-the-art convolutional neural network EfficientNet-B4 to infer phase aberrations from simulated focal-plane images. The two cases of scalar and vector vortex coronagraphs (SVC and VVC) were considered using a single post-coronagraphic point spread function (PSF) or two PSFs obtained by splitting the circular polarization states, respectively. Results. The sign ambiguity has been properly lifted in both cases even at low signal-to-noise ratios (S/Ns). Using either the SVC or the VVC, we have reached a very similar performance compared to using phase diversity with a defocused PSF, except for high levels of aberrations where the SVC slightly underperforms compared to the other approaches. The models finally show great robustness when trained on data with a wide range of wavefront errors and noise levels. Conclusions. The proposed FPWFS technique provides a 100% science duty cycle for instruments using a vortex coronagraph and does not require any additional hardware in the case of the SVC.

Flexible and simple telecentric camera calibration method.

The measurement accuracy of telecentric imaging technique straightforwardly depends on the calibration of the telecentric camera. We present a flexible and simple calibration method based on a telecentric imaging model and orthogonality of rotation matrix. First, we use the orthogonality of rotation matrix to solve the magnification. Second, the external parameters are solved by the imaging model, and the ambiguity of sign is solved. Finally, we use the LM nonlinear optimization method to solve the distortion parameters. Experimental results show that the reprojection error is 0.7 pixels, which represents the actual dimension of 6.37µm. In addition, the standard measuring block and real objects are measured, and the results verify the measurement accuracy and robustness of the proposed method.

Sign determination to measure non-monotonous displacements in temporal speckle pattern interferometry without a temporal carrier

In this paper, we present a generalized function to automatically detect the correct sign of non-monotonous displacements in temporal speckle pattern interferometry without the introduction of a temporal carrier in the optical setup. This approach can be used with any phase retrieval technique. Here, when the phase change is evaluated, the sign ambiguity is resolved due to a function that determines the correct sign of the displacement between two consecutive speckle interferograms. The errors introduced by the proposed function are determined using computer-simulated speckle interferograms, and its performance is analyzed using three phase recovery techniques and different phase distributions and average speckle sizes. A relation between the sliding window used to compute the correct sign and the speckle sizes is also presented. Finally, the presentation is illustrated with an experimental application of the proposed method to detect the correct sign of the out-of-plane displacement field of a metal plate.

Multidimensional directional derivatives and AM-FM dual-band image demodulation by higher order Teager-Kaiser operators

In this work we tackle the problem of demodulation of multidimensional AM-FM signals by multidirectional higher order Teager-Kaiser operators. This new class of operators extends those reported in the literature, which are restricted to partial derivatives. We illustrate this class of operators on signals made up of two components (bi-band signals). We show that this mixture of bi-band multidimensional AM-FM signals extends a solution of the fourth-order generating differential equation (GDE). This result generalizes the findings reported in [1] to multidimensional case. Coefficients of GDE expressed in terms of Teager-Kaiser energy operators of higher orders, yield estimates for the instantaneous amplitude and frequency of each component of the multidimensional signal in any direction. To resolve the sign ambiguity problem of the estimated frequency components of the frequency vector, a relative signs estimation strategy is presented. Three frequency estimation algorithms are developed. To show the effectiveness of the introduced new class of operators and the interest of directional derivatives, demodulation results on synthetic and real images are presented and analyzed. We compare our results to methods of the literature. Capability of the methods to track signal demodulation is measured by the norm of demodulation error and also by the well known structural similarity index measure. Even the aim of this paper is focused on bi-band multidimensional AM-FM signals, we report promising preliminary results on tri-band signals showing that the present work can be extended to more than two components.

Angular Velocity Estimation and Error-Covariance Analysis from Accelerometers Using Least Squares

In this work angular velocity solutions are presented from accelerometers. Two main formulations are presented. The first is based on using multiple vector sets of accelerometers, and the second is based on using multiple single-axis accelerometers. Linear least-squares approaches are derived for both, along with error-covariance expressions for the angular velocity estimates. Nonlinear least-squares approaches are also derived for both, which also provide the Cramér–Rao lower bound as a byproduct. All approaches have a sign ambiguity in the angular velocity solutions, which is resolved using a simple linear Kalman filter. Simulation results are shown to compare the formulations, along with the linear and nonlinear least-squares solutions.

Measurement of the hyperfine coupling constants and absolute energies of the 12s 2S1/2, 13s 2S1/2 , and 11d 2DJ levels in atomic cesium

We report measurements of the absolute energies of the hyperfine components of the $12s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $13s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ levels of atomic cesium, $^{133}\mathrm{Cs}$. Using the frequency difference between these components, we determine the hyperfine coupling constants for these states, and report these values with a relative uncertainty of $\ensuremath{\sim}0.06$%. We also examine the hyperfine structure of the $11d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{J}$ ($J=3/2,5/2$) states, and resolve the sign ambiguity of the hyperfine coupling constants from previous measurements of these states. We also derive new, high precision values for the state energies of the $12s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}, 13s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$, and $11d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{J}$ states of cesium.

Determination of error-corrected full scattering parameters of a two-port device from uncalibrated measurements

A methodology relying on relating terms of a two-port error network to the scattering (S-) parameters of a two-port network or device is applied to extract its full S-parameters. The new methodology has only one sign ambiguity problem (two solutions) in evaluation of S11 (and thus S22) while the similar methodology in the literature has two sign ambiguity problems (4 solutions). This ambiguity problem of our method is shown to be eliminated by applying an approach based on continuity of the argument of S11 in the frequency domain. On the other hand, our methodology, as compared with the thru-reflect-line calibration technique, does not necessitate usage of any reflection standard in determining full S-parameters of a two-port network or device. Finally, it gives information about error networks. For its validation, S-parameters of a microwave phase shifter and a polyethylene sample flushed with the left/bottom terminal of the coaxial cell were extracted.

Polarization Pipeline for Fast Radio Bursts Detected by CHIME/FRB

Abstract Polarimetric observations of fast radio bursts (FRBs) are a powerful resource for better understanding these mysterious sources by directly probing the emission mechanism of the source and the magneto-ionic properties of its environment. We present a pipeline for analyzing the polarized signal of FRBs captured by the triggered baseband recording system operating on the FRB survey of The Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). Using a combination of simulated and real FRB events, we summarize the main features of the pipeline and highlight the dominant systematics affecting the polarized signal. We compare parametric (QU-fitting) and non-parametric (rotation measure synthesis) methods for determining the Faraday rotation measure (RM) and find the latter method susceptible to systematic errors from known instrumental effects of CHIME/FRB observations. These errors include a leakage artifact that appears as polarized signal near RM ∼ 0 rad m−2 and an RM sign ambiguity introduced by path length differences in the system’s electronics. We apply the pipeline to a bright burst previously reported (FRB 20191219F), detecting an RM of +6.074 ± 0.006 ± 0.050 rad m−2 with a significant linear polarized fraction (≳0.87) and strong evidence for a non-negligible circularly polarized component. Finally, we introduce an RM search method that employs a phase-coherent de-rotation algorithm to correct for intra-channel depolarization in data that retain electric field phase information and successfully apply it to an unpublished FRB, FRB 20200917A, measuring an RM of −1294.47 ± 0.10 ± 0.05 rad m−2 (the second largest unambiguous RM detection from any FRB source observed to date).

CW Direct Detection Lidar with a Large Dynamic Range of Wind Speed Sensing in a Remote and Spatially Confined Volume

A novel continuous-wave (CW) direct detection lidar (DDL) is demonstrated to be capable of wind speed measurement 40 m away with an update rate of 4 Hz using a fiber-based scanning Fabry–Perot interferometer as an optical frequency discriminator. The proposed CW DDL has a large dynamic wind speed range with no sign ambiguity and its sensitivity is assessed by comparing its performance with that of a CW coherent detection lidar (CDL) in a side-by-side wind measurement. A theoretical model of the spatial weighting function of the fiber-based CW DDL is also presented and validated experimentally. This work shows that the CW DDL has a spatially confined measurement volume with a Lorentzian axial profile similar to that of a CW CDL. The proposed DDL has potential use in various applications in which requirements such as high-speed wind sensing and directional discrimination are not met by state-of-the-art Doppler wind lidar systems.

Theoretical analysis of Fresnel reflection and transmission in the presence of gain media

When a monochromatic electromagnetic plane-wave arrives at the flat interface between its transparent host (i.e., the incidence medium) and an amplifying (or gainy) second medium, the incident beam splits into a reflected wave and a transmitted wave. In general, there is a sign ambiguity in connection with the k-vector of the transmitted beam, which requires at the outset that one decide whether the transmitted beam should grow or decay as it recedes from the interface. The question has been posed and addressed most prominently in the context of incidence at large angles from a dielectric medium of high refractive index onto a gain medium of lower refractive index. Here, the relevant sign of the transmitted k-vector determines whether the evanescent-like waves within the gain medium exponentially grow or decay away from the interface. We examine this and related problems in a more general setting, where the incident beam is taken to be a finite-duration wavepacket whose footprint in the interfacial plane has a finite width. Cases of reflection from and transmission through a gainy slab of finite-thickness as well as those associated with a semi-infinite gain medium will be considered. The broadness of the spatiotemporal spectrum of our incident wavepacket demands that we develop a general strategy for deciding the signs of all the k-vectors that enter the gain medium. Such a strategy emerges from a consideration of the causality constraint that is naturally imposed on both the reflected and transmitted wavepackets.

An Investigation of the Communicative Purposes of Road Signs: How Signs Do Things

This study explores the important communicative roles carried out by road signs both directly and indirectly. The qualitative analysis is based on a corpus of 150 road signs collected from signage on state and local highways and roadways in seven U.S. states. Road signs were identified as either full, grammatical sentences or as block language. They were further analyzed as speech acts and their performativity was briefly explored in three areas: agency, lexis, and emplacement. Road sign ambiguity in regard to punctuation and syntactic ambiguity was also identified. The findings pointed to several areas for future research including drivers’ behavioral reactions, road safety and wayfinding potential.

Tribimaximal mixing in the SU(5)×T13 texture

We extend the recently proposed $SU(5) \times \mathcal{T}_{13}$ model for the asymmetric texture to the up-type quark and seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vectorlike messengers. The complex-tribimaximal (TBM) seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with $m_{\nu_1} = 27.6\ \mathrm{meV}$, $m_{\nu_2} = 28.9\ \mathrm{meV}$ and $m_{\nu_3} = 57.8\ \mathrm{meV}$. Their sum almost saturates Planck's cosmological upper bound ($120$ $\text{meV}$). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the $\require{cancel}\cancel{CP}$ Jarlskog-Greenberg invariant to be $|\mathcal{J}| = 0.028$, consistent with the current PDG estimate, and Majorana invariants $|\mathcal{I}_1| = 0.106$ and $|\mathcal{I}_2| = 0.011$. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter $|m_{\beta \beta}|$: $13.02$ or $25.21$ $\text{meV}$, both within an order of magnitude of the most rigorous experimental upper limit ($61$--$165$ $\text{meV}$).

AUTOMATIC EXTRACTION AND SIGN DETERMINATION OF RESPIRATORY SIGNAL IN REAL-TIME CARDIAC MAGNETIC RESONANCE IMAGING.

In real-time (RT) cardiac cine imaging, a stack of 2D slices is collected sequentially under free-breathing conditions. A complete heartbeat from each slice is then used for cardiac function quantification. The inter-slice respiratory mismatch can compromise accurate quantification of cardiac function. Methods based on principal components analysis (PCA) have been proposed to extract the respiratory signal from RT cardiac cine, but these methods cannot resolve the inter-slice sign ambiguity of the respiratory signal. In this work, we propose a fully automatic sign correction procedure based on the similarity of neighboring slices and correlation to the center-of-mass curve. The proposed method is evaluated in eleven volunteers, with ten slices per volunteer. The motion in a manually selected region-of-interest (ROI) is used as a reference. The results show that the extracted respiratory signal has a high, positive correlation with the reference in all cases. The qualitative assessment of images also shows that the proposed approach can accurately identify heartbeats, one from each slice, belonging to the same respiratory phase. This approach can improve cardiac function quantification for RT cine without manual intervention.