Angular Uncertainty Research Articles

Two methods for determining geophone orientations from VSP data

Vertical seismic profile (VSP) data are usually acquired with three-component geophones of unknown azimuthal orientation. The geophone orientation must be estimated from the recorded data as a prerequisite to processing such as P- and S-wave separation, calculation of wave-incident directions, and 3D migration. We compare and combine two methods for estimating azimuthal orientation by least-squares fitting over a large number of shots. Combining the two methods can be done in an automated manner, which provides more accurate estimates of the geophone orientations than previous methods. In the polarization-plane method, we calculate the polarization plane of the first P-wave arrival. Then we subtract the source azimuth to determine the geophone orientation, independently for each geophone, with an angular uncertainty of [Formula: see text], and with no accumulated errors. In the relative-angle method, we obtain relative angles between adjacent geophone pairs using trace crosscorrelations, and operate on all coherent signals (even noise). Swapped geophone components can be detected automatically using the polarization-plane method. The main limitation of these (and all other known) methods is that uncertainties associated with path refraction are not estimated, unless some geophones have a priori known orientations, or we have a known earth model to correct for refraction.

Angular minimum uncertainty states with large uncertainties

The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for a given uncertainty in the angle or in the angular momentum. We show that, if the given angle uncertainty is close to its maximum value, the lowest possible uncertainty product tends to infinity.

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

Large-uncertainty intelligent states for angular momentum and angle

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.

Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks

Cultural heritage recording and engineering surveying are prime applications for terrestrial laser scanners (TLSs) because of the high spatial resolution, high accuracy, and fast data capture rates this technology offers. To date, insufficient attention has been given to the many error sources contributing to the uncertainty of scanner datasets. A full error budget for directly georeferenced terrestrial laser scanner networks that considers both relevant error sources fundamental to surveying and those unique to sampled laser scanner systems is derived. In the case of the latter, new probabilistic models are proposed for angular positional uncertainty due to laser beamwidth and centroid-based target pointing. Analysis of a cultural heritage-recording project in Ayutthaya, Thailand, highlights the disparity between “expected” precision and the more realistic precision indicated by the error budget and demonstrates that the beamwidth error can be a significant factor. The causes and effects of several syste...

Use of HRSC-A for sampling bidirectional reflectance

This paper describes a method for sampling bidirectional reflectance information from multiangular airborne images. The method uses high resolution surface models to determinate the location of the imaged point on the ground and the orientation of the measured surface fragment. Since natural surfaces scatter incident radiation anisotropically, viewing and illumination conditions play a critical role in the interpretation of remotely sensed images. Thus, directionally defined reflectance data are needed for the modelling and correction of bidirectional effects on airborne optical images. Two test sites were imaged with a wide range of viewing azimuth angles at two different times. A high resolution HRSC-A stereo camera was used for image acquisition. Algorithms were implemented to reconstruct the image acquisition and retrieve the image samples from the HRSC-A image data. Combined with GPS and INS data, automatically derived high resolution digital surface models, including vegetation canopies, houses, etc., were used to determine the viewing and illumination geometry on the target surface. The brightness of a sample point was recorded as a measure for reflectance. A large number of directionally defined samples and a wide angular range of sample geometry were obtained. The images were first classified. Sampled reflectance data were verified by investigating the bidirectional reflectance of five agricultural and forest targets. Errors affecting the data quality, such as angular uncertainty, were studied. The multiangular image data, the developed sampling methods and the obtained bidirectional dataset proved to be applicable in investigations of bidirectional reflectance effects of natural targets. Airborne imagery combined with high resolution digital surface models permit extensive investigation of the bidirectional reflectance of a wide range of natural objects and large habitats.

Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain

High b value diffusion-weighted images sampled at high angular resolution were analyzed using a composite hindered and restricted model of diffusion (CHARMED). Measurements and simulations of diffusion in white matter using CHARMED provide an unbiased estimate of fiber orientation with consistently smaller angular uncertainty than when calculated using a DTI model or with a dual tensor model for any given signal-to-noise level. Images based on the population fraction of the restricted compartment provide a new contrast mechanism that enhances white matter like DTI. Nevertheless, it is assumed that these images might be more sensitive than DTI to white matter disorders. We also provide here an experimental design and analysis framework to implement CHARMED MRI that is feasible on human clinical scanners.

Canadian surveillance of space concept demonstrator—metric accuracy and limiting magnitude assessment

Defence R&D Canada (DRDC), in partnership with the Canadian Forces’ Surveillance of Space Project, is developing an array of three remotely operated, ground-based optical observatories for space surveillance (the Concept Demonstrator, CD). Manual metric accuracy testing of the CD, performed using a single sensor, began in December 2003, and focused on GPS calibration satellites. Results from this study are promising, with angular residual uncertainties less than 3 ″ with arcsec level biases. This short metric accuracy campaign also permitted a rough sensitivity performance check. This paper summarizes these metric accuracy and sensitivity performance checks of the CD.

Minimum uncertainty states of angular momentum and angular position

The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

Uncertainty principle for angular position and angular momentum

The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry.

Effect of compensation for scattering angular uncertainty in analytical Compton camera reconstruction

In Compton cameras, the measured scattering angle is associated with an uncertainty which becomes larger as the incident gamma-ray energy decreases. Since this uncertainty degrades the spatial resolution of reconstructed images, Hirasawa and Tomitani (2003 Phys. Med. Biol. 48 1009–26) previously revised their analytical reconstruction algorithm to compensate for it. As the new algorithm improved the spatial resolution in effect, they expected an enhancement of the statistical noise. In this paper, the effect of this compensation has been analysed in view of spatial resolution (the FWHM of the noise-free reconstructed image for a point source distribution), statistical noise (the relative standard deviation of reconstructed images for an isotropic source distribution) and image quality (the roughness of reconstructed images for a phantom). The results describe not only the effect of the compensation, but also the relation between the statistical noise and three parameters, i.e., the incident gamma-ray energy, the spatial resolution and the measured total event numbers, in reconstruction with compensation. This relation should be taken into account for the design of Compton cameras with good quality images, i.e., useful image, output.

On the Cross-Correlation between the Arrival Direction of Ultra-High-Energy Cosmic Rays, BL Lacertae Objects, and EGRET Detections: A New Way to Identify EGRET Sources?

With the aim of testing recent claims for a particularly strong correlation between ultra-high-energy cosmic rays (UHECRs), observed with the AGASA and Yakutsk experiments, and a sample of BL Lacertae objects, we conduct a blind statistical assessment. We search for associations between the same set of BL Lac objects and the arrival directions of 33 relevant UHECRs observed with the Haverah Park and Volcano Ranch experiments. Within the accuracy of the angle determination, there are no positional coincidences. The probability that this null result arises as a statistical fluctuation from the strongly correlated case is less than 5%. This implies that the possible correlation between the arrival directions of UHECRs and BL Lac objects is not statistically sustained. We discuss the impact of our findings on the proposed additional connection among UHECRs, BL Lac objects, and EGRET γ-ray blazars. Recently, such an association was used as a classification technique for EGRET sources. Here we show that its main underlying hypothesis (i.e., the EGRET angular uncertainty is twice that quoted in the third EGRET catalog) grossly underestimates the goodness of existing γ-ray data.

A Feasibility Study of Using Hybrid Collimation for Nuclear Environment.

This paper presents a feasibility of a gamma ray imager using combined electronic and mechanical collimation methods. This detector is based on the use of a multiple pinhole collimator, a position sensitive scintillation detector with Anger logic readout. A pixelated semiconductor detector, located between the collimator and the scintillation detector, is used as a scattering detector. For gamma rays scattered in the first detector and then stopped in the second detector, an image can also be built up based on the joint probability of their passing through the collimator and falling into a broadened conical surface, defined by the detected Compton scattering event. Since these events have a much smaller angular uncertainty, they provide more information content per photon compared with using solely the mechanical or electronic collimation. Therefore, the overall image quality can be improved. This feasibility study adapted a theoretical approach, based on analysing the resolution-variance trade-off in images reconstructed using Maximum a priori (MAP) algorithm. The effect of factors such as the detector configuration, Doppler broadening and collimator configuration are studied. The results showed that the combined collimation leads to a significant improvement in image quality at energy range below 300keV. However, due to the mask penetration, the performance of such a detector configuration is worse than a standard Compton camera at above this energy.

Fuzzy dynamic localization for mobile robots

In this paper, we introduce a new fuzzy logic-based approach for dynamic localization of mobile robots equipped with a ring of sonar sensors. In this approach, the angular uncertainty and radial imprecision of sonar data are modeled by possibility distributions. From sonar data, a local fuzzy composite map is constructed and fitted to the given global map of the environment to identify robot's location. As a result of this fit, either a unique fuzzy location or multiple candidate fuzzy locations are obtained. To reduce the multiple candidate locations, the robot is moved to a new location and a new local fuzzy composite map is constructed. Then, a new set of candidate fuzzy locations is obtained. By considering the robot's movement, a set of hypothesized locations is identified from the old set of candidate locations. The hypothesized locations are matched with the new candidate locations and the candidates with low degree of match are eliminated. This process is continued until a unique location is obtained. The matching process is performed by using the fuzzy pattern matching technique. The proposed method is implemented on a Nomad 200 robot and the results are reported.

Uncertainty estimation for multiposition form error metrology

We analyze a general multiposition comparator measurement procedure that leads to partial removal of artifact error for a class of problems including roundness metrology, measurement of radial error motions of precision spindles, and figure error metrology of high-accuracy optical components. Using spindle radial error motion as an explicit example, we present a detailed analysis of a complete test with N orientations of a test ball with respect to the spindle. In particular, we show that (1) all components of the ball roundness error average to zero except those with frequencies of kN cycles/revolution, where k is a positive integer; and (2) the combined standard uncertainty of the measurement is proportional to 1/√N. We then show how a complete set of measurements for an N-position test can be synthesized from only two measurements, and we derive a general expression for the combined standard uncertainty as a function of the number of positions n (2 ≤ n ≤ N) actually measured in an N-position test. This uncertainty can serve as a useful guide to measurement design, involving trade-offs between multiple setup cost and complexity and required levels of angular harmonic resolution and combined standard measurement uncertainty.

POSSIBILISTIC SONAR DATA MODELING FOR MOBILE ROBOTS

Sonar sensors are widely used in mobile robots applications such as navigation, map building, and localization. The performance of these sensors is affected by the environmental phenomena, sensor design, and target characteristics. Therefore, the readings obtained from these sensors are uncertain. This uncertainity is often modeled by using Probability Theory. However, the probablistic approach is valid when the available knowledge is precise which is not the case in sonar readings. In this paper, the behavior of sonar readings reflected from walls and corners are studied, then new models of angular uncertainty and radial imprecision for sonar readings obtained from corners and walls are proposed. These models are represented by using Possibility Theory, mainly possibility distributions.

Angular uncertainties due to geometry and spatial resolution in Compton cameras

In this paper, we investigate the effects of spatial resolution and relative orientation of detectors on the accuracy of the directional localization in two-detector Compton cameras. We derive a general expression that relates the angular uncertainty to spatial resolution and geometry. Appropriate expressions for specific configurations are obtained as special cases of the general expression. Finally, we present a simple formula for estimating the position uncertainty of Compton cameras in terms of relative spatial resolution and distances.

Discrete uncertainty relations

Generalized uncertainty relations based upon Fourier transforms of both discrete and continuous functions are briefly reviewed. We extend these results in order to establish discrete versions of the angular momentum uncertainty relations, based upon SU(2) transformations. Possible applications in quantum signal processing and computations are briefly discussed.

C-SPRINT: a prototype Compton camera system for low energy gamma ray imaging

An electronically-collimated imaging system is being built using pixellated, low-noise, position-sensitive silicon as the first detector, and a sodium iodide scintillation detector ring as the second detector. The system consists of a single 3/spl times/3/spl times/0.1 cm/sup 3/ silicon pad detector module with 1 keV FWHM (noise-limited) energy resolution centered at the front face of a 50 cm diameter, 10 cm long NaI detector annulus. Custom acquisition and timing electronics have been manufactured to minimize system dead time. Monte Carlo modeling is used to predict system sensitivity and position resolution. Simulations using the existing setup show angular uncertainties of 4.1/spl deg/ and 2.1/spl deg/ FWHM for /sup 99m/Tc and /sup 131/I point sources, respectively (7.2 mm and 3.7 mm at 10 cm). Sensitivity can be improved by more than a factor of a hundred over the existing setup by stacking five 1 mm thick 9/spl times/9 cm/sup 2/ silicon arrays and redesigning the second detector geometry to accept a wider range of scattering angles. Lower bound calculations show that our electronically-collimated camera system challenges current mechanically-collimated systems for both /sup 99m/Tc and /sup 131/I despite the deleterious effects of Doppler broadening. Preliminary measurements show a timing resolution of 41 ns FWHM between the silicon detector and a single SPRINT module.

Angular Range and Uncertainty Analysis of Nonorthogonal Crossed Hot Wire Probes

Crossed hot wire probes are widely used for measuring two-dimensional flows. Many applications in fluid mechanics like turbomachinery require an angular range as large as possible and a reasonable uncertainty in both direction and velocity values. The classic design places the wires orthogonally, while an angle between the probe wires allows a wider angular range to be obtained. The paper shows an experimental and a theoretical study of the response of this kind of probes, by analyzing the dependence of the calibration procedure and uncertainties of flow angle and velocity with the angle between the wires.