Theoretically-Efficient and Practical Parallel DBSCAN

The DBSCAN method for spatial clustering has received significant attention due to its applicability in a variety of data analysis tasks. There are fast sequential algorithms for DBSCAN in Euclidean space that take $O(n\log n)$ work for two dimensions, sub-quadratic work for three or more dimensions, and can be computed approximately in linear work for any constant number of dimensions. However, existing parallel DBSCAN algorithms require quadratic work in the worst case, making them inefficient for large datasets. This paper bridges the gap between theory and practice of parallel DBSCAN by presenting new parallel algorithms for Euclidean exact DBSCAN and approximate DBSCAN that match the work bounds of their sequential counterparts, and are highly parallel (polylogarithmic depth). We present implementations of our algorithms along with optimizations that improve their practical performance. We perform a comprehensive experimental evaluation of our algorithms on a variety of datasets and parameter settings. Our experiments on a 36-core machine with hyper-threading show that we outperform existing parallel DBSCAN implementations by up to several orders of magnitude, and achieve speedups by up to 33x over the best sequential algorithms

Optimal pre-scheduling of problem remappings

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal

Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis

Spatial Heterodyne Observations of Atmospheric Water Vapour from a High Altitude Aircraft

The atmosphere of the Earth is divided into layers, and the boundaries of these layers are positioned at altitudes where inversions in the atmospheric temperature lapse rate occur. The content of the present work is concerned with water vapour within the upper troposphere - lower stratosphere (UTLS) which is a region of the atmosphere within five kilometres of the tropopause - the boundary between the troposphere and stratosphere. The behaviour of this region is very important in the formation of both the troposphere and stratosphere with water vapour being a principle factor. While broad characteristics of the UTLS, and the role of water vapour within, are well understood questions do remain. To get a better understanding of the answers to these questions there is a need for a continuous high resolution scientific data set of UTLS constituents like water vapour. The Spatial Heterodyne Observation of Water (SHOW) is a scientific instrument designed to measure atmospheric water vapour. The premise of the SHOW measurement technique is Spatial Heterodyne Spectroscopy (SHS) which performs a frequency decomposition on input light to create an interferogram. SHOW measures the atmosphere by observing the UTLS region in the limb. The measurements of SHOW can be combined with a radiative transfer model, a SHS instrument model, and an inversion technique to infer the water content of the observed atmosphere. Due to the nature of the SHS technique, SHOW has the ability to obtain measurements at a high spatial and altitude resolution. This gives SHOW, and SHS technology, the potential to obtain the desired high resolution data sets of the UTLS. However, SHS based instruments, including SHOW, are largely unproven for the application of atmospheric research like measuring water vapour. As a demonstration to validate SHOW, and SHS technology, as applicable to atmospheric science, SHOW was deployed on NASA's ER-2 high altitude science aircraft in July of 2017 for a scientific campaign. The goal of this campaign was to determine the abilities of SHOW with the desired results being to measure atmospheric water vapour to within 1 ppm, with a vertical resolution of less than five hundred meters, and with high spatial sampling. To provide a comparison for the assessment of SHOW, a Vaisala RS41 radiosonde was launched from the Jet Propulsion Laboratory facility located close to Table Mountain. This radiosonde was launched in-situ with some SHOW measurements taken during the engineering flight on July 18th, 2017 and measured the atmospheric water vapour within the region above the facility The SHOW data which corresponded to the radiosonde measurements was analyzed and found that the measurements between the two instruments agreed largely within the goal of 1 ppm. Furthermore, SHOW was able to do so at a vertical resolution of two hundred and fifty meters and achieved a spatial resolution of 0.005 to $0.01 degrees in latitude (roughly 500 m to 1000 m) along a north-south flight track when deployed on the ER-2 platform. These results lend strong supporting evidence that SHOW is capable of providing the desired high resolution UTLS water vapour data set and should be considered for further development and deployment in the future. Furthermore, SHS based instruments should be considered viable atmospheric instruments, and should potentially be used to measure other atmospheric constituents within the UTLS

Investigating block mask lithography variation using finite-difference time-domain simulation

Simulation work has long been realized as a method for analyzing semiconductor processing expediently and cost-effectively. As technology advancements strive to meet increasingly stringent parameter constraints, difficult issues arise. In this paper, challenges in block mask lithography will be discussed with the aid of using simulation packages developed by Panoramic Technology®. Halo formation utilizes a 20-30° tilt-angle implantation [1]. The block mask defines the geometries of the resist opening to allow implantation of atoms to extend into the channel region. Due to designed resolution scaling and tolerance in conjunction with substrate topography, there can be undesired influence on the electrical device characteristics due to block variations. Although the block mask pattern definition is relatively simple, additional investigation is required to understand the sensitivities that drive the implant resist CD variation. In this study, block mask measurements processed using 248 nm and 193 nm illumination sources were used to calibrate the simulation work. Addition of optical proximity correction (OPC) and wafer topography geometry parameters have been shown to improve modeling capabilities. The modeling work was also able to show the benefits of a developable bottom anti-reflection coating (dBARC) process over a single layer resist (SLR) process in the resist intensity profiles as gate pitch is decreased. The goal of this work was to develop an accurate simulation model that characterizes the lithographic performance needed to support the transition into future technology nodes

Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE)

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at an unprecedented, speckle-scale lateral resolution of ~5 µm