Cross-Spectral Analysis For Spatial Point-Lattice Processes

In this study, we explore the relationship between the components of a hybrid process consisting of a spatial point process arid a lattice process using two-dimensional spectral techniques. Simulated spatial point-lattice patterns are used to demonstrate how the different cross-spectral statistics can reveal correlation between the two components. A method to adjust for jumps that normally occur in the cross-spectral phase statistic is then proposed. Such adjustment is needed to enable us to calculate the slope of the phase spectrum which measures the shift between the two components. Several methods to calculate the slope are investigated. Asymptotic properties of the cross-spectral statistics are derived and their confidence intervals estimated. A test that the components are independent is described. In a study region, lattice processes are observed at regular grids whereas point, processes can be observed anywhere. In order to account for discrepancies that. might arise due to this, methods to discretise the point pattern are suggested. Cross-spectral techniques are then applied to analyse the joint process of the discretised point pattern and the lattice pattern. Finally, we apply the techniques suggested above to study the joint properties of two data sets. The first consists of altitude data of a region in a rain forest in French Guyana together with the locations of a number of tree species in that region. The second set consists of altitude data of the Sahel region of Africa together with location of storms and some of their characteristics. In order to incorporate the storm characteristics in the analysis, cross-spectral tools used to analyse two components are extended to three components

Gemini Planet Imager: Preliminary Design Report

For the first time in history, direct and indirect detection techniques have enabled the exploration of the environments of nearby stars on scales comparable to the size of our solar system. Precision Doppler measurements have led to the discovery of the first extrasolar planets, while high-contrast imaging has revealed new classes of objects including dusty circumstellar debris disks and brown dwarfs. The ability to recover spectrophotometry for a handful of transiting exoplanets through secondary-eclipse measurements has allowed us to begin to study exoplanets as individual entities rather than points on a mass/semi-major-axis diagram and led to new models of planetary atmospheres and interiors, even though such measurements are only available at low SNR and for a handful of planets that are automatically those most modified by their parent star. These discoveries have galvanized public interest in science and technology and have led to profound new insights into the formation and evolution of planetary systems, and they have set the stage for the next steps--direct detection and characterization of extrasolar Jovian planets with instruments such as the Gemini Planet Imager (GPI). As discussed in Volume 1, the ability to directly detect Jovian planets opens up new regions of extrasolar planet phase space that in turn will inform our understanding of the processes through which these systems form, while near-IR spectra will advance our understanding of planetary physics. Studies of circumstellar debris disks using GPI's polarimetric mode will trace the presence of otherwise-invisible low-mass planets and measure the build-up and destruction of planetesimals. To accomplish the science mission of GPI will require a dedicated instrument capable of achieving contrast of 10{sup -7} or more. This is vastly better than that delivered by existing astronomical AO systems. Currently achievable contrast, about 10{sup -5} at separations of 1 arc second or larger, is completely limited by quasi-static wave front errors, so that contrast does not improve with integration times longer than about 1 minute. Using the rotation of the Earth to distinguish companions from artifacts or multiwavelength imaging improves this somewhat, but GPI will still need to surpass the performance of existing systems by one to two orders of magnitude--an improvement comparable to the transition from photographic plates to CCDs. This may sound daunting, but other areas of optical science have achieved similar breakthroughs, for example, the transition to nanometer-quality optics for extreme ultraviolet lithography, the development of MEMS wave front control devices, and the ultra-high contrast demonstrated by JPL's High Contrast Imaging Test-bed. In astronomy, the Sloan Digital Sky Survey, long baseline radio interferometry, and multi-object spectrographs have led to improvements of similar or greater order of magnitude. GPI will be the first project to apply these revolutionary techniques to ground-based astronomy, with a systems engineering approach that studies the impact of every design decision on the key metric--final detectable planet contrast