Presence Of Tilt Research Articles

Artificial neural network for tilt compensation in yaw estimation

Low-cost inertial measurement units (IMUs) are commonly used to determine the orientation of objects, such as unmanned aerial vehicles (UAVs) and smartphones. They calculate yaw by measuring Earth’s magnetic field’s horizontal components. However, in the presence of tilt (pitch or roll), a tilt-compensation operation is necessary. This is usually done by projecting measurements onto a horizontal plane. This method has limitations, particularly for large tilt angles and when the IMU is pointing toward the east or west directions. In this paper, we expose the shortcomings of this conventional approach and propose a novel machine learning–based solution employing an artificial neural network (ANN). This method eliminates the need to determine tilt angles and uses accelerometer and magnetometer measurements as its inputs. The dataset for training and testing the ANN was collected based on a 3D nonmagnetic scaled platform, using a low-cost IMU and a Raspberry Pi platform. On one hand, our method outperforms the conventional tilt-compensation technique and other complementary filters (Madgwick and Mahony) in terms of accuracy, as evidenced by the root mean square error (RMSE = 1.95°). However, this superiority comes at the expense of a more complex system that consumes more processing time.

Theoretical Study of Refraction Effects of Plano Ophthalmic Prisms

Nominally plano prisms can have appreciable refractive errors that exceed the usual prescribing step of 0.25 D, particularly when an eye rotates to view off-axis objects. The purpose of this study was to determine theoretically the refractive power effects of nominally plano-refracting power prisms. Plano prisms with zero refraction were designed for the as-worn condition. A basic method was developed to determine refractive effects in the presence of pantoscopic tilt. A refined method was developed that considers the eye rotating behind the lens, and this and the basic method were compared with accurate raytracing. Plano prisms of 4 and 8 Δ were designed with astigmatic back surfaces to compensate for oblique incidence, and tangential and sagittal image vergence errors were investigated for base-up (BU) and base-down (BD) directions, 0 and -3.33 D object vergences, and pantoscopic tilts up to 10°. Basic and refined results did not differ from accurate results by more than 0.04 and 0.08 D, respectively. Errors for 8 Δ prisms were approximately twice those for 4 Δ prisms. Errors were approximately proportional to tilt. With 10° tilt, the errors ranged between -0.65 D/-0.23 D (8 Δ BD, -3.33 D object vergence) and +0.36 D/+0.15 D (8 Δ BU, 0 D object vergence). Sagittal errors were generally about one third of corresponding tangential errors. In the presence of tilt, BU prisms had positive errors, and BD prisms had similar, but negative, errors for distance objects. At -3.33 D object vergence with tilt, negative errors for BD were greater than positive errors for BU. When the eye rotates to look at objects at different positions, errors can increase beyond those occurring on-axis. When designed for nontilted conditions, but then subjected to tilt or to viewing off-axis objects, plano prisms can have errors exceeding the usual prescribing step of 0.25 D.

Study of annular recess hydrostatic tilted thrust pad bearing under the influence of couple stress lubricant behaviour

This paper concerns with the theoretical investigation to predict the combined influence of couple stress lubricant and tilt between bearing pad surfaces, on the performance of externally pressurised annular recess thrust pad bearing. Stokes micro-continuum theory is used to derive modified Reynolds equation accounting for the presence of couple stress additives in lubricant. A MATLAB code has been developed to solve the governing equation using FEM technique. Influence of annular recess location and tilt between pad surfaces are investigated on the performance of hydrostatic thrust pad bearing. It has been observed that the use of couple stress lubricant significantly improves the performance of annular recessed hydrostatic thrust pad bearing. Presence of tilt between bearing surfaces proved to be beneficial in terms of dynamic characteristics of bearing system.

Optical Characterization Method for Tilted or Decentered Intraocular Lenses.

To test and validate a method for measuring the optical quality and optical power of monofocal intraocular lenses (IOLs) in the presence of a tilt or a decentration as well as its optical power. The experimental system consists of an artificial eye (wet-cell) and a commercial aberrometer with a Shack-Hartmann sensor. Optical image quality parameters such as point spread function (PSF), modulation transfer function (MTF), and the simulations of the retinal image of an extended object are computed from the in vitro wavefront data of an IOL. Repeatability and reproducibility of the system are tested. Mathematical and ray-tracing simulations are used to ascertain the precision and accuracy of the method. Comparison with a standard single-pass method of measurement is also made. Optical properties of four commercial monofocal IOLs are measured under tilts of 0°, 2°, and 4°, and vertical decentrations of 0, 0.2, and 0.4 mm; the results of such measurements are compared with a ray-tracing simulation. Precision and accuracy of the system are in good agreement with theoretical calculations. Reproducibility and repeatability are within standard ISO norms. MTFs obtained with this method and with the standard method are very similar. The precision of the estimation of the IOL's optical power is higher than 98.6%. Commercially tested IOLs show a decrease of optical quality in the presence of decentrations and tilts, and their susceptibility to tilts and decentrations depends on the asphericity. These results are in concordance with the results obtained by ray-tracing simulation. A simple wavefront-based method for in vitro measurements of the wavefront aberrations and power of an IOL is proposed and tested showing accurate and precise results.

Reflected waves in finely layered tilted orthorhombic media

Upscaling in seismics is a homogenization of finely layered media in the zero-frequency limit. An upscaling technique for arbitrary anisotropic layers has been developed by Schoenberg and Muir. Applying this technique to a stack of layers of orthorhombic (ORT) symmetry whose vertical symmetry planes are aligned, results in an effective homogeneous layer with orthorhombic symmetry. If the symmetry planes in a horizontal orthorhombic layer are rotated with respect to vertical, the medium is referred to as tilted orthorhombic (TOR) medium, and the stack composed of TOR layers in zero-frequency limit will produce an effective medium of a lower symmetry than orthorhombic. We consider a P-wave that propagates through a stack of thin TOR layers, then it is reflected (preserving the mode) at some interface below the stack, and then propagates back through the same stack. We propose to use a special modified medium for the upscaling in case of this sequential down- and up-propagation: each TOR layer in the stack is replaced by two identical TOR layers whose tilt angles have the opposite algebraic sign. In this modified medium, one-way propagation of a seismic wave (any wave mode) is equivalent to propagation of a pure-mode reflection in the original medium. We apply this idea to study the contribution from an individual layer from the stack and show how the approach can be applied to a stack of TOR layers. To demonstrate the applicability of the model, we use well log data for the upscaling. The model we propose for the upscaling can be used in well-seismic ties to correct the effective parameters obtained from well log data for the presence of tilt, if latter is confirmed by additional measurements (for example, borehole imaging).

Wavefront aberration function in terms of R. V. Shack's vector product and Zernike polynomial vectors.

Previous papers have shown how, for rotationally symmetric optical imaging systems, nodes in the field dependence of the wavefront aberration function develop when a rotationally symmetric optical surface within an imaging optical system is decentered and/or tilted. In this paper, we show how Shack's vector product (SVP) can be used to express the wavefront aberration function and to define vectors in terms of the Zernike polynomials. The wavefront aberration function is then expressed in terms of the Zernike vectors. It is further shown that SVP fits within the framework of two-dimensional geometric algebra (GA). Within the GA framework, an equation for the third-order node locations for the binodal astigmatism term that emerge in the presence of tilts and decenters is then demonstrated. A computer model of a three-mirror telescope system is used to demonstrate the validity of the mathematical development.

First approach to characterize tilts through multiple pistons in the classical Ronchi test.

In this work, it is shown how a tilt can be introduced into a segmented surface through several piston terms, by using the classical Ronchi test. We have developed tilt error simulations by adding multiple constant terms to each point on the sagitta surface of a segment using ray tracing. Thereby a comparison between simulated Ronchigrams for piston and tilt has been performed for two adjacent segments, so that it is possible to appreciate the tilt and piston effects on the shape of the patterns. As a result, we show the behavior of the central maximum of the fringes in the presence of tilt and/or piston. Additionally we present evidence of introducing tilting without changing the surface shape by adding multiple pistons, and a description of how to characterize both piston and tilt using the Ronchi test.

Research on the Influence of Different Surface Machining States on the Inclination of the Porous Gas Bearing

The influence of different surface machining states on the porous gas bearing inclination and its cause are studied in this paper. A loading experiment on the porous gas bearings of different surface processing states is conducted. The presence of tilt of the gas bearing during the working has been ascertained. The uneven distribution characteristics of the porous material permeability after surface processing are analyzed through the porous material partition experiment, thus explaining the gas bearings tilt phenomenon. The influence of milling and grinding on the inclination of the porous gas bearing is mainly studied.

Influence of tilt moiré fringe on alignment accuracy in proximity lithography

A moiré fringe alignment method based on dual gratings is proposed. This method uses the phase of moiré fringe to measure the relative linear displacement between the mask and the wafer. In practical application, the tilt moiré fringe can occur due to the incorrect positions of the mask alignment mark and the wafer alignment mark or one of them. In this work, the presence of tilt moiré fringe and its influence on the alignment accuracy are thoroughly analyzed. The analysis and discussions on the relationship between the revised linear displacement and the theoretical linear displacement reveal that moiré fringes with different tilt angles have different influences on the alignment accuracy. Experimental results are given to verify that the proposed method is accurate and feasible, which can be applied to lithography and other correlated fields.

Determination of the composition and thickness of semi-polar and non-polar III-nitride films and quantum wells using X-ray scattering

There is increasing interest in III-nitride films and multiple quantum well structures grown in non-polar or semi-polar orientations for application in light-emitting devices. We describe a method to obtain the compositions and the thicknesses of layers within III-nitride quantum well or superlattice structures grown in non-polar or semi-polar orientations, based on X-ray scattering. For each new crystallographic orientation considered, new axes were obtained and both the lengths and angles of these new axes calculated relative to the original conventional reference axes. These angles provide the coefficients of the matrix to transform the elastic constants published in the conventional setting (as used for polar c-plane oriented III-nitrides) into the appropriate new values. The new characteristic lengths and new elastic constants are then put into the general equation that relates the composition of a fully strained layer to the experimentally measured out-of-plane alloy d-spacing. Thus we have (a) determined the alloy composition from the difference between the experimentally measured alloy d-spacing and that of the substrate and (b) calculated the strained d-spacing for a given alloy composition for input to simple kinematical simulation software. In addition for quantum well structures the thickness ratio of well-to-barrier must be determined. Here we use the minima in the low angle reflectivity data. The repeat thickness and thus the thicknesses of the well and barrier layers, can be obtained from either the low or the high-angle data. We then cross-check by comparing the experimental and the simulated high-angle diffraction data. This method has been applied successfully to heteroepitaxial non-polar and semi-polar GaN/AlGaN and InGaN/GaN multiple quantum well structures and may also be used to find the composition of epilayers. The method works even in the presence of tilt between the superlattice and the GaN “template’, although in this case additional high-angle diffraction data at different settings must be collected.

Cone over Guide Wire Technique for Difficult IVC Filter Retrieval

Retrievable inferior vena cava (IVC) filters are placed in patients who are at temporary increased risk for pulmonary embolism, with or without contraindication for anticoagulation, with the expectation of subsequent removal. The failure to retrieve nonpermanent IVC filters is an increasingly encountered dilemma for vascular interventionalists. One of the more common causes of technical failure of retrieval is the presence of tilt in the orientation of the IVC filter, which may result in the retrieval hook abutting the wall of the IVC, preventing contact with the removal system [1]. This issue may be compounded by endothelialization of the filter hook [2]. We describe a nonconventional method for the retrieval of tilted IVC filters in two patients. This method uses a femoral access site that is contralateral to the direction of filter tilt in addition to the right internal jugular vein (IJV) access site. A cone-over-guide wire is then used to retrieve the filter, which has been realigned to the caval axis by the gentle application of tension on the guide wire ends. This technique can be used for filters of both the half-basket and double-basket design, when conventional and other nonconventional techniques fail and may make retrieval difficulties pertaining to filter hook endotheliazliation less relevant.

Dielectric Spectroscopy of a Newly Synthesized Chlorinated Analogue of MHPOBC Antiferroelectric Liquid Crystals

Temperature and bias field dependent dielectric characterization of an antiferroelectric liquid crystal (AFLC) derived from chlorination of prototype MHPOBC has been carried out over the frequency range of 1 Hz to 10 MHz. In addition to orthogonal SmA* phase, this material has four narrow tilted phases at considerably lower temperature in comparison to MHPOBC, including one broad antiferroelectric (SmC A *) phase (85°C to below room temp). The dielectric studies show the presence of tilt and phase fluctuation modes of relaxation in SmCα*, SmC* and SmCγ* phases. The presence of phase fluctuation (Goldstone) mode confirms the tilted and helical nature of these phases. It has been possible to suppress Goldstone mode in chiral SmC subphases by applying bias electric field. With respect to molecular modes, the reorientation around short axis has also been studied.

Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis

We propose a distance measuring system based on lateral shearing interferometer (LSI) with extended range of measurement and improved resolution. The sensor is based on a wedge-shaped plate LSI and due to the presence of tilt, a finite number of fringes parallel to the direction of shear appear and hence significant spatial carrier frequency is generated at the focus position. On varying the distance of the object surface from the focus position, the orientation, fractional and integer order, and the width of the interference fringes change. It is shown that the orientation of the fringes is the most sensitive parameter, by means of which one can detect small changes in distance. The Fourier transform method for fringe analysis is used, and from the position of the maxima of the first-order Fourier spectrum the orientation of the fringes and hence the distance is measured. Experimental results of distance measurement by changing the focal length of the lens are presented. A large range of measurement without any fringe ambiguity problem can be achieved using the system.

Sensitivity of off-axis performance of aspheric spectacle lenses to tilt and decentration.

Apparatus was modified to measure, and theoretical raytracing was used to predict, off-axis powers of spectacle lenses in the presence of tilt or decentration. In response to poor fitting in the form of tilt or decentration, lenses with aspheric front surfaces were found to have greater off-axis power errors than best-form lenses with spherical surfaces. This is attributable to the aspheric lenses having flatter surfaces than the spherical lenses. The errors are up to twice those occurring for the spherical lenses, and can be quite high, e.g. 0.9 D astigmatism for +6D power with 10 degrees tilt in 20 degrees upgaze. Negative lenses are more sensitive to poor fitting than are positive lenses of the same power. The errors for straight ahead vision associated with tilt are approximately proportional to the square of the angle of tilt, and the errors for straight ahead vision associated with decentration are approximately proportional to the square of decentration. It is most important that aspheric lenses be correctly fitted, which means that each 2 degrees of pantascopic tilt should be accompanied by approximately 1 mm decentration.

Realistic requirements for inverting ionograms to profiles

The requirements for an accurate ionogram inversion are discussed briefly and quantitative estimates of possible accuracy are made using Dynasonde data. The presence of tilts in the ionosphere seriously limits the accuracy with which the effects of missing data (valleys, D-region) can be estimated. The very accurate range estimates from stationary phase [ca 60m] and evaluations of prevailing tilts are essential for reliable valley and underlying ionization corrections.

Optical beam wave propagation through complex optical systems

20We describe a novel formulation of light beam propagation through any complex optical system that can be described by an ABCD ray-transfer matrix. Within the paraxial approximation, optical propagation can be formulated in terms of a Huygens principle expressed in terms of the ray-transfer ABCD matrix elements of the optical system. We extend and generalize previous treatments to include the effects of finite-sized limiting apertures (i.e., diffractive screens) in the optical train, tilt and random jitter of the optical elements, and distributed random inhomogeneities along the optical path (e.g., clear air turbulence and aerosols). In the presence of limiting apertures the ABCD matrix elements of the optical system are complex. For the case of laser beam propagation and Gaussian-shaped limiting apertures in the optical train, we obtain analytical expressions for both the spot radius and the wave-front radius of curvature at an arbitrary observation plane and give illustrative examples of practical concern. In particular, analytical expressions for the fringe visibility obtained in a coherent laser interferometric system are presented. An analytical expression for the mean spot radius of a laser beam propagating through an optical system in the presence of tilt and random jitter is obtained. We also consider the propagation of partially coherent light through optical systems. In particular, we derive a generalized van Cittert–Zernike theorem that is valid for an arbitrary optical system that can be characterized by an ABCD ray-transfer matrix. Finally, the propagation of laser beams through a general optical system in the presence of distributed random inhomogeneities is considered. An explicit expression for the mean irradiance distribution of a Gaussian-shaped beam is derived that is valid for an arbitrary optical system. In addition, we derive an expression for the mutual-coherence function for wave propagation through an arbitrary optical system. In all cases the results are expressed in terms of the ABCD matrix elements of the complete optical system. The formulation of optical propagation presented here is a rather simple and straightforward way of determining the effects of finite-sized optical elements, tilt and random jitter, and distributed random inhomogeneities along the optical path. It is merely necessary first to multiply the relevant ray matrices together to find the complete system matrix and then to substitute this matrix into the expressions given in this paper.