Radial Fringes Research Articles

Comparative analysis of circular and linear fringe projection profilometry: from calibration to 3D reconstruction

This study compares the accuracy of circular and linear fringe projection profilometry in the aspects of system calibration and 3D reconstruction. We introduce, what we believe to be, a novel calibration method and 3D reconstruction technique using circular and radial fringe patterns. Our approach is compared with the traditional linear phase-shifting method through several 2 × 2 experimental setups. Results indicate that our 3D reconstruction method surpasses the linear phase-shifting approach in performance, although calibration efficiency does not present a superior performance. Further analysis reveals that sensitivity and estimated phase error contribute to the relative underperformance in calibration. This paper offers insights into the potentials and limitations of circular fringe projection profilometry.

Scanning gate microscopy mapping of edge current and branched electron flow in a transition metal dichalcogenide nanoribbon and quantum point contact

We study scanning gate microscopy conductance mapping of a zigzag ribbon exploiting tight-binding and continuum models. We show that, even though the edge modes of a pristine nanoribbon are robust to backscattering on the potential induced by the tip, the conductance mapping reveals presence of both the edge modes and the quantized spin- and valley-current carrying modes. By inspecting the electron flow from a split gate quantum point contact (QPC) we find that the mapped current flow allows to determine the nature of the quantization in the QPC as spin–orbit coupling strength affects the number of branches in which the current exits the constriction. The radial conductance oscillation fringes found in the conductance mapping reveal the presence of two possible wavevectors for the charge carriers that correspond to spin and valley opposite modes. Finally, we show that disorder induced valley mixing leads to a beating pattern in the radial fringes.

Rotation and Position Encoder from a Mark of Radial Fringe in Color-RGB by using Phase Shifting

espanolEn este trabajo, se presenta un metodo que pretende localizar una marca radial a color adherida al objeto, usando la alta sensibilidad de la fase para determinar con resolucion subpixel la posicion espacial y angular debida al movimiento de un objeto en una escena 2D. El patron de referencia esta constituido por una distribucion regular con simetria radial de franjas a color. La reconstruccion de la fase absoluta asociada a las franjas permite la localizacion precisa del centro de la mira, que conlleva a la determinacion de la posicion del objeto con resolucion subpixel. La reconstruccion de la fase absoluta asociado a las franjas se calcula utilizando la tecnica phase shifting a tres imagenes y un algoritmo de desenvolvimiento de la fase. Posteriormente se realiza una transformacion de coordenadas y un ajuste por minimos cuadrados, obteniendo una funcion, que permite extraer el centro del patron de referencia. Se presentan resultados experimentales de medidas de posicion, desplazamiento y orientacion con resolucion subpixel, asi como, la descripcion del procedimiento para la optimizacion del sistema. EnglishIn this work, a method which seeks to locate a radial-color mark attached to the object using the high sensitivity of the phase to determine the position spatial and angular with subpixel resolution due to movement of an object in a 2D scene is presented. The reference pattern is formed by a regular distribution with radially symmetrical of color-RGB fringes. The reconstruction of the absolute phase associated to the fringes allows the location the precise center of the mark and it finds position of the object with sub-pixel resolution. The reconstruction of absolute phase associated with the fringes using the phase shifting technique at three-frame and a development phase algorithm is calculated. A transformation of coordinates and a least squares adjustment is realized giving a function for to extract the center of the reference pattern. Experimental results of measurements of position, displacement and orientation with subpixel resolution is presented, as well as the description of the process for system optimization.

Neural bandwidth of veridical perception across the visual field.

Neural undersampling of the retinal image limits the range of spatial frequencies that can be represented veridically by the array of retinal ganglion cells conveying visual information from eye to brain. Our goal was to demarcate the neural bandwidth and local anisotropy of veridical perception, unencumbered by optical imperfections of the eye, and to test competing hypotheses that might account for the results. Using monochromatic interference fringes to stimulate the retina with high-contrast sinusoidal gratings, we measured sampling-limited visual resolution along eight meridians from 0° to 50° of eccentricity. The resulting isoacuity contour maps revealed all of the expected features of the human array of retinal ganglion cells. Contours in the radial fringe maps are elongated horizontally, revealing the functional equivalent of the anatomical visual streak, and are extended into nasal retina and superior retina, indicating higher resolution along those meridians. Contours are larger in diameter for radial gratings compared to tangential or oblique gratings, indicating local anisotropy with highest bandwidth for radially oriented gratings. Comparison of these results to anatomical predictions indicates acuity is proportional to the sampling density of retinal ganglion cells everywhere in the retina. These results support the long-standing hypothesis that “pixel density” of the discrete neural image carried by the human optic nerve limits the spatial bandwidth of veridical perception at all retinal locations.

Microstructure and growth of the lenses of schizochroal trilobite eyes

AbstractLenses within the schizochroal eyes of phacopine trilobites are made principally of calcite, and characterization of them using light microscopy and high‐resolution electron imaging and diffraction has revealed an array of microstructural arrangements that suggest a common original pattern across the suborder. The low convexity lenses of Odontochile hausmanni and Dalmanites sp. contain calcite fibres termed trabeculae. The c axis of trabecular calcite lies parallel to the lens axis, and adjacent trabeculae are distinguished by small differences in their a axis orientations. Despite the common alignment, the boundaries between trabeculae cross‐cut the c axis as they fan out towards the lens base. Trabeculae are absent from the lens immediately beneath the visual surface, and instead, a radial fringe is present and is composed of micrometre‐thick sheets of calcite whose c axes are oriented at a low angle to the visual surface. High convexity lenses are more common than those of lower convexity among the species studied, and they have a much thicker radial fringe. Beneath this fringe, all of the lens calcite is oriented with its c axis parallel to the lens axis and it lacks trabeculae. We propose that both the high and low convexity lenses formed by rapid growth of calcite from a surface that migrated inwards from the cornea, and they may have had an amorphous calcium carbonate precursor. The trabeculae and radial fringes are unlikely to have had any beneficial effect on the transmission or focusing of light, but rather are the outcomes of an elegant solution to the problem of how to construct a biconvex lens from a crystalline solid.

Transverse relativistic effects in paraxial wave interference

We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay analogous to the relativistic time delay. We illustrate these observations by the interference between a vortex wave beam and a plane wave, which exhibits a pronounced deformation of the radial fringes into a fork-like pattern (relativistic Hall effect). Furthermore, we describe an additional relativistic motion of the interference fringes (a counter-rotation in the vortex case), which becomes noticeable at the same non-relativistic velocities.

Scanning gate microscopy simulations for quantum rings: Effective potential of the tip and conductance maps

We simulate electron flow through a semiconductor quantum ring perturbed by a charged tip of a scanning microscope. We describe the interaction of the tip with the electron gas solving the density functional theory equations for up to several hundred electrons forming the background potential for the current flow at the Fermi level. The screening of the repulsive tip potential involves an appearance of the Friedel oscillations of the electron density. The effective potential of the tip turns out to be anisotropic and close to a Lorentzian along the channel. The Lorentzian width along the channel is comparable to the distance between the tip and the electron gas. The width is insensitive to the charge of the tip and the electron density. We discuss the conductance maps as calculated in the Landauer approach including the case when the tip is outside the ring. We discuss both the case of weak perturbation introduced by the tip in the context of extraction of the local density of states as well as the case of strong tip-electron-gas interaction, which modifies the potential landscape within the structure. For strong perturbation we find that the repulsive tip introduces radial fringes of conductance within the ring and concentric ones outside the ring. The radial ones correspond to interrupted current circulation around the ring and are insensitive to the external magnetic field while the external concentric fringes evolve in external magnetic field due to an interplay of the electrostatic and magnetic Aharonov-Bohm effects.

Scanning gate microscopy of quantum rings: effects of an external magnetic field and ofcharged defects

We study scanning gate microscopy (SGM) in open quantum rings obtained from buriedsemiconductor InGaAs/InAlAs heterostructures. By performing a theoretical analysisbased on the Keldysh–Green function approach we interpret the radial fringes observed inexperiments as the effect of randomly distributed charged defects. We associate SGMconductance images with the local density of states (LDOS) of the system. We show thatsuch an association cannot be made with the current density distribution. By varying anexternal magnetic field we are able to reproduce recursive quasi-classical orbits in LDOSand conductance images, which bear the same periodicity as the Aharonov–Bohmeffect.

Displacement and Strain Measurement by Circular and Radial Gratings Moiré Method

Direct digital moire method of circular and radial gratings with its phase shifting technique is proposed and applied in a mixed-mode fracture problem of large deformation materials. Circular and radial curves are used as both reference and specimen gratings in this digital moire method for deformation measurement. And phase shifting technique is automatically implemented directly on circular and radial fringes, which facilitates obtaining displacement fields in polar coordinate system, radial ur and circumferential uθ, and strain fields er, eθ, erθ are calculated subsequently. Application of the direct digital moire method of circular and radial gratings in a mixed-mode fracture problem with large deformation illustrates the process of this method, and also demonstrates its feasibility and validity for large deformation materials.

Direct Sedimentation Analysis of Interference Optical Data in Analytical Ultracentrifugation

Sedimentation data acquired with the interference optical scanning system of the Optima XL-I analytical ultracentrifuge can exhibit time-invariant noise components, as well as small radial-invariant baseline offsets, both superimposed onto the radial fringe shift data resulting from the macromolecular solute distribution. A well-established method for the interpretation of such ultracentrifugation data is based on the analysis of time-differences of the measured fringe profiles, such as employed in the g(s*) method. We demonstrate how the technique of separation of linear and nonlinear parameters can be used in the modeling of interference data by unraveling the time-invariant and radial-invariant noise components. This allows the direct application of the recently developed approximate analytical and numerical solutions of the Lamm equation to the analysis of interference optical fringe profiles. The presented method is statistically advantageous since it does not require the differentiation of the data and the model functions. The method is demonstrated on experimental data and compared with the results of a g(s*) analysis. It is also demonstrated that the calculation of time-invariant noise components can be useful in the analysis of absorbance optical data. They can be extracted from data acquired during the approach to equilibrium, and can be used to increase the reliability of the results obtained from a sedimentation equilibrium analysis.

Circular grating moirè deflectometry analysis by zeroth and first radial fringe order angle measurement

The previous method of counting integer fringe orders in circular grating moirè deflectometry yields inaccurate measurements. One way to improve the measurement accuracy with this method is by lowering the grating pitch. The attendant higher cost and possible encroachment of the diffraction limit, however, restricts the practicality of this approach. An alternative analysis method, which measures the angle between the zeroth and first radial fringe order, is presented in this paper to overcome this problem.

Lorentz Force Calibrator for Magnetogasdynamic Interaction Coils

A device is described which measures the Lorentz force of any magnet coil with radial fringe component due to the axial motion of a metallic slug. The first method uses the effect of this force on the logarithmic decrement of a mass-spring system; in the second a feedback circuit effects self-excited oscillations, the Lorentz force being measured by its effect on the loop gain necessary to maintain a given oscillation amplitude.

Cylindrical Mode of Oscillation in a Ruby Optical Maser

A particular type of mode in optical maser oscillation was obtained with a ruby rod having parallel-plate resonator with a central hole in one of the reflector coatings. The oscillation has occurred in a region of cylindrical pipe distributed coaxially with the ruby rod. Around the periphery of the active region of annular-shape on the end-surface of the rod, a standing wave of the azimuthal mode number of about 225±10 has been formed with a good spatial coherence. The far-field pattern of annular-shape accompanied by fine radial fringes was observed, and it was well interpreted on the basis of Fraunhofer diffraction theory. The reason for the occurrence of particular azimuthal mode number was attributed to the slightly concave nature of the reflectors. The experimental results on the associated relaxation oscillation of a particular type are briefly described.