On Using Projective Relations for Calibration and Estimation in a Structured-Light Scanner

For structured-light scanners, the projective geometry between a projector-camera pair is identical to that of a camera-camera pair. Consequently, in conjunction with calibration, a variety of geometric relations are available for three-dimensional Euclidean reconstruction. In this paper, we use projector-camera epipolar properties and the projective invariance of the cross-ratio to solve for 3D geometry. A key contribution of our approach is the use of homographies induced by reference planes, along with a calibrated camera, resulting in a simple parametric representation for projector and system calibration. Compared to existing solutions that require an elaborate calibration process, our method is simple while ensuring geometric consistency. Our formulation using the invariance of the cross-ratio is also extensible to multiple estimates of 3D geometry that can be analysed in a statistical sense. The performance of our system is demonstrated on some cultural artifacts and geometric surfaces.

Note: Design and development of an integrated three-dimensional scanner for atomic force microscopy

A compact scanning head for the Atomic Force Microscope (AFM) greatly enhances the portability of AFM and facilitates easy integration with other tools. This paper reports the design and development of a three-dimensional (3D) scanner integrated into an AFM micro-probe. The scanner is realized by means of a novel design for the AFM probe along with a magnetic actuation system. The integrated scanner, the actuation system, and their associated mechanical mounts are fabricated and evaluated. The experimentally calibrated actuation ranges are shown to be over 1 mu m along all the three axes. (c) 2013 AIP Publishing LLC.

Variation at Diabetes- and Obesity-Associated Loci May Mirror Neutral Patterns of Human Population Diversity and Diabetes Prevalence in India

South Asian populations harbor a high degree of genetic diversity, due in part to demographic history. Two studies on genome-wide variation in Indian populations have shown that most Indian populations show varying degrees of admixture between ancestral north Indian and ancestral south Indian components. As a result of this structure, genetic variation in India appears to follow a geographic cline. Similarly, Indian populations seem to show detectable differences in diabetes and obesity prevalence between different geographic regions of the country. We tested the hypothesis that genetic variation at diabetes-and obesity-associated loci may be potentially related to different genetic ancestries. We genotyped 2977 individuals from 61 populations across India for 18 SNPs in genes implicated in T2D and obesity. We examined patterns of variation in allele frequency across different geographical gradients and considered state of origin and language affiliation. Our results show that most of the 18 SNPs show no significant correlation with latitude, the geographic cline reported in previous studies, or by language family. Exceptions include KCNQ1 with latitude and THADA and JAK1 with language, which suggests that genetic variation at previously ascertained diabetes-associated loci may only partly mirror geographic patterns of genome-wide diversity in Indian populations.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the GRAPE algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

Membrane-based deformable mirror: intrinsic aberrations and alignment issues

A deformable mirror (DM) is an important component of an adaptive optics system. It is known that an on-axis spherical/parabolic optical component, placed at an angle to the incident beam introduces defocus as well as astigmatism in the image plane. Although the former can be compensated by changing the focal plane position, the latter cannot be removed by mere optical realignment. Since the DM is to be used to compensate a turbulence-induced curvature term in addition to other aberrations, it is necessary to determine the aberrations induced by such (curved DM surface) an optical element when placed at an angle (other than 0 deg) of incidence in the optical path. To this effect, we estimate to a first order the aberrations introduced by a DM as a function of the incidence angle and deformation of the DM surface. We record images using a simple setup in which the incident beam is reflected by a 37 channel micro-machined membrane deformable mirror for various angles of incidence. It is observed that astigmatism is a dominant aberration, which was determined by measuring the difference between the tangential and sagittal focal planes. We justify our results on the basis of theoretical simulations and discuss the feasibility of using such a system for adaptive optics considering a trade-off between wavefront correction and astigmatism due to deformation. (C) 2015 Optical Society of America