A Modeling Approach for Predicting the Resolution Capability in Terrestrial Laser Scanning

The minimum size of objects or geometrical features that can be distinguished within a laser scanning point cloud is called the resolution capability (RC). Herein, we develop a simple analytical expression for predicting the RC in angular direction for phase-based laser scanners. We start from a numerical approximation of the mixed-pixel bias which occurs when the laser beam simultaneously hits surfaces at grossly different distances. In correspondence with previous literature, we view the RC as the minimum angular distance between points on the foreground and points on the background which are not (severely) affected by a mixed-pixel bias. We use an elliptical Gaussian beam for quantifying the effect. We show that the surface reflectivities and the distance step between foreground and background have generally little impact. Subsequently, we derive an approximation of the RC and extend it to include the selected scanning resolution, that is, angular increment. We verify our model by comparison to the resolution capabilities empirically determined by others. Our model requires parameters that can be taken from the data sheet of the scanner or approximated using a simple experiment. We describe this experiment herein and provide the required software on GitHub. Our approach is thus easily accessible, enables the prediction of the resolution capability with little effort and supports assessing the suitability of a specific scanner or of specific scanning parameters for a given application.

The Set Increment with Limited Views Encoding Ratio (SILVER) Method for Optimizing Radial Sampling of Dynamic MRI

PurposeTo present and assess a method for choosing the increment between spokes in radially sampled MRI that can produce higher SNR than golden ratio derived methods.Theory and MethodsSampling uniformity determines image SNR when reconstructed using linear methods. Thus, for a radial trajectory, uniformly spaced sampling is ideal. However, uniform sampling lacks post-acquisition reconstruction flexibility, which is often needed in dynamic imaging. Golden ratio-based methods are often used for this purpose. The method presented here, Set Increment with Limited Views Encoding Ratio (SILVER), optimizes sampling uniformity when the number of spokes per frame is approximately known a-priori. With SILVER, an optimization algorithm finds the angular increment that provides the highest uniformity for a pre-defined set of reconstruction window sizes. The optimization cost function was based on an electrostatic model of uniformity. SILVER was tested over multiple sets and assessed in terms of uniformity, analytical g-factor, and SNR both in simulation and applied to dynamic arterial spin labeling angiograms in three healthy volunteers.ResultsAll SILVER optimizations produced higher or equal uniformity than the golden ratio within the predefined sets. The SILVER method converged to the golden ratio for broad optimization sets. As hypothesized, the g-factors for SILVER were higher than for uniform sampling, but, on average, 26% lower than golden ratio. Image SNR followed the same trend both in simulation and in vivo.ConclusionSILVER is a simple addition to any sequence currently using golden ratio sampling and it has a small but measurable effect on sampling efficiency.

A posterioridetermination of the useful data range for small-angle scattering experiments on dilute monodisperse systems

Small-angle X-ray and neutron scattering (SAXS and SANS) experiments on solutions provide rapidly decaying scattering curves, often with a poor signal-to-noise ratio, especially at higher angles. On modern instruments, the noise is partially compensated for by oversampling, thanks to the fact that the angular increment in the data is small compared with that needed to describe adequately the local behaviour and features of the scattering curve. Given a (noisy) experimental data set, an important question arises as to which part of the data still contains useful information and should be taken into account for the interpretation and model building. Here, it is demonstrated that, for monodisperse systems, the useful experimental data range is defined by the number of meaningful Shannon channels that can be determined from the data set. An algorithm to determine this number and thus the data range is developed, and it is tested on a number of simulated data sets with various noise levels and with different degrees of oversampling, corresponding to typical SAXS/SANS experiments. The method is implemented in a computer program and examples of its application to analyse the experimental data recorded under various conditions are presented. The program can be employed to discard experimental data containing no useful information in automated pipelines, in modelling procedures, and for data deposition or publication. The software is freely accessible to academic users.

Dynamic Bending Mathematical Model of Vehicle Adaptive Front-Lighting System Based on Rolling Characteristics

When the vehicle is turning, the vehicle body will tend to roll because of centrifugal force, which will lead to the change of headlamps' space location and the mismatch between light type and the regulation GB4599-2007. Directing at this problem, first the relationship among the rolling characteristics of vehicle, light distribution characteristics of AFS headlamps and dynamic light angle of AFS was analyzed in the article. Then a dynamic bending mathematical model of AFS based on rolling characteristics was proposed. Based on the three degrees of freedom of manipulation model, the interaction mechanism between the roll angle and light distribution characteristics of AFS was analyzed, and the dynamic bending mathematical model of AFS based on rolling characteristics which can amend the illumination direction of AFS was built afterwards. After analysis in Matlab and Tracepro, the results show that the dynamic AFS headlamp angle determines the maximum of 1.75° angular increment in the xy plane and 2.25° in the yz plane, and solves the problem of the mismatch between light type and regulation GB4599-2007.

A Generalized Coning Correction Structure for Attitude Algorithms

A new coning correction structure is presented for attitude update coning correction. Different from the previous rate-based and increment-based coning correction structures, the new structure contains cross-product of angular rates, cross-product of angular increments, and cross-product of angular rate and increment (an angular increment may be approximated from angular rate samples). Two types of optimization methods including time Taylor-series method and frequency Taylor-series method were utilized to design the structure coefficients including the uncompressed and the compressed. Two types of algorithm error models including one applicable to coning environments and the other two applicable to maneuver environments were defined and used for analyzing or evaluating the algorithm performance. The derivation procedure of a rotation vector magnitude extraction method is included. Analysis and simulation results indicate that the new structure-based algorithm with the compressed coefficients designed by using frequency Taylor-series method gives a superior algorithm performance in coning environments and maneuver environments.

Mechanical Design on Finite Element Method for Ring Laser Gyroscope

The gyroscopes have been used as a suitable inertial instrument for the navigation guidance and attitude controls. The accuracy as very sensitive sensor is limited by the lock-in region (dead band) due to the frequency coupling between two counter-propagating waves at low rotation rates. This frequency coupling gives no phase difference, and an angular increment is not detected. This problem can be overcome by mechanically dithering the gyroscope. This paper presents the design method of mechanical dither by the theoretical considerations and the verification of the theoretical equations through FEM applications. As a result, comparing to the past result, the maximum prediction error of resonant frequency was within 3 percent and peak dither rate was within 5 percent. It was found that the theoretical equations can be feasible for the mechanical performance of dither.