Magnetoresistive transducer for absolute position detection

In this paper a new method is presented for the measurement of absolute linear or angular position. The digital position information is recorded serially into one track of a suitable hard-magnetic medium. The stray field of this information layer determines the angular magnetisation distribution in a ferromagnetic (permalloy) detection strip which is positioned parallel to the track but with its plane perpendicular to the hard-magnetic layer. The bit pattern representing the position co-ordinate is regained by detection of the planar magnetoresistance effect in the sensor strip. Experiments have been performed using sensors with a resolution of 250 ¿m and 1 mm respectively and longitudinally recorded audio tape. Suitable sensor output signals could be measured without hysteresis

The absolute position of a resonance peak

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible

The absolute position of a resonance peak

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible

Absolute Position Total Internal Reflection Microscopy with an Optical Tweezer

A non-invasive, in-situ calibration method for Total Internal Reflection Microscopy (TIRM) based on optical tweezing is presented which greatly expands the capabilities of this technique. We show that by making only simple modifications to the basic TIRM sensing setup and procedure, a probe particle's absolute position relative to a dielectric interface may be known with better than 10 nm precision out to a distance greater than 1 $\mu$m from the surface. This represents an approximate 10x improvement in error and 3x improvement in measurement range over conventional TIRM methods. The technique's advantage is in the direct measurement of the probe particle's scattering intensity vs. height profile in-situ, rather than relying on calculations or inexact system analogs for calibration. To demonstrate the improved versatility of the TIRM method in terms of tunability, precision, and range, we show our results for the hindered near-wall diffusion coefficient for a spherical dielectric particle.Comment: 10 pages. Submitted for peer review 8/20/201

Position and Orientation Estimation of a Rigid Body: Rigid Body Localization

Rigid body localization refers to a problem of estimating the position of a rigid body along with its orientation using anchors. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known, but, the relative position of the sensors or the topology of the sensors on the rigid body is known. We express the absolute position of the sensors as an affine function of the Stiefel manifold and propose a simple least-squares (LS) estimator as well as a constrained total least-squares (CTLS) estimator to jointly estimate the orientation and the position of the rigid body. To account for the perturbations of the sensors, we also propose a constrained total least-squares (CTLS) estimator. Analytical closed-form solutions for the proposed estimators are provided. Simulations are used to corroborate and analyze the performance of the proposed estimators.Comment: 4 pages and 1 reference page; 3 Figures; In Proc. of ICASSP 201

The Position of Sgr A∗^* at the Galactic Center

The absolute position of the compact radio source at the dynamical center of the Galaxy, Sgr A$^*$, was known only to an accuracy of $0.2''$ in spite of its accurate location with respect to near-IR stellar sources to within 30 milliarcsecond (mas). To remedy this poor positional accuracy, we have selected 15 high-resolution, high-frequency VLA observations of Sgr A$^*$ carried out in the last 13 years and determined the weighted average position with the average epoch 1992.4 to be at $\alpha$, $\delta$[1950] = $17^{\rm h} 42^{\rm m}$ 29\dsec3076$\pm0.0007$, $-28^\circ 59^\prime 18.484\pm0.014^{\prime\prime}$, or $\alpha$, $\delta$[2000] = $17^{\rm h} 45^{\rm m}$ 40\dsec0383$\pm0.0007$, $-29^\circ 00^\prime 28.069\pm0.014^{\prime\prime}$ which agrees with earlier published values to within the $0.2''$ error bars of the earlier measurements. An accurate absolute position of Sgr A$^*$ can be useful for its identification with sources at other wavelengths, particularly, in soft and hard X-rays with implications for the models of a massive black hole at the Galactic center.Comment: 11 pages, one figure and one table. ApJL (in press