Challenges in using GPUs for the real-time reconstruction of digital hologram images

This is the pre-print version of the final published paper that is available from the link below.In-line holography has recently made the transition from silver-halide based recording media, with laser reconstruction, to recording with large-area pixel detectors and computer-based reconstruction. This form of holographic imaging is an established technique for the study of fine particulates, such as cloud or fuel droplets, marine plankton and alluvial sediments, and enables a true 3D object field to be recorded at high resolution over a considerable depth. The move to digital holography promises rapid, if not instantaneous, feedback as it avoids the need for the time-consuming chemical development of plates or film film and a dedicated replay system, but with the growing use of video-rate holographic recording, and the desire to reconstruct fully every frame, the computational challenge becomes considerable. To replay a digital hologram a 2D FFT must be calculated for every depth slice desired in the replayed image volume. A typical hologram of ~100 μm particles over a depth of a few hundred millimetres will require O(10^3) 2D FFT operations to be performed on a hologram of typically a few million pixels. In this paper we discuss the technical challenges in converting our existing reconstruction code to make efficient use of NVIDIA CUDA-based GPU cards and show how near real-time video slice reconstruction can be obtained with holograms as large as 4096 by 4096 pixels. Our performance to date for a number of different NVIDIA GPU running under both Linux and Microsoft Windows is presented. The recent availability of GPU on portable computers is discussed and a new code for interactive replay of digital holograms is presented

Systematic Errors in Cosmic Microwave Background Interferometry

Cosmic microwave background (CMB) polarization observations will require superb control of systematic errors in order to achieve their full scientific potential, particularly in the case of attempts to detect the B modes that may provide a window on inflation. Interferometry may be a promising way to achieve these goals. This paper presents a formalism for characterizing the effects of a variety of systematic errors on interferometric CMB polarization observations, with particular emphasis on estimates of the B-mode power spectrum. The most severe errors are those that couple the temperature anisotropy signal to polarization; such errors include cross-talk within detectors, misalignment of polarizers, and cross-polarization. In a B mode experiment, the next most serious category of errors are those that mix E and B modes, such as gain fluctuations, pointing errors, and beam shape errors. The paper also indicates which sources of error may cause circular polarization (e.g., from foregrounds) to contaminate the cosmologically interesting linear polarization channels, and conversely whether monitoring of the circular polarization channels may yield useful information about the errors themselves. For all the sources of error considered, estimates of the level of control that will be required for both E and B mode experiments are provided. Both experiments that interfere linear polarizations and those that interfere circular polarizations are considered. The fact that circular experiments simultaneously measure both linear polarization Stokes parameters in each baseline mitigates some sources of error.Comment: 19 pages, 9 figures, submitted to Phys. Rev.

Mosaicking with cosmic microwave background interferometers

Measurements of cosmic microwave background (CMB) anisotropies by interferometers offer several advantages over single-dish observations. The formalism for analyzing interferometer CMB data is well developed in the flat-sky approximation, valid for small fields of view. As the area of sky is increased to obtain finer spectral resolution, this approximation needs to be relaxed. We extend the formalism for CMB interferometry, including both temperature and polarization, to mosaics of observations covering arbitrarily large areas of the sky, with each individual pointing lying within the flat-sky approximation. We present a method for computing the correlation between visibilities with arbitrary pointing centers and baselines and illustrate the effects of sky curvature on the l-space resolution that can be obtained from a mosaic.Comment: 9 pages; submitted to Ap

Fast directional continuous spherical wavelet transform algorithms

We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al. Fast algorithms for performing the directional continuous wavelet analysis on the unit sphere are presented. The fast directional algorithm, based on the fast spherical convolution algorithm developed by Wandelt and Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature implementation for Npix pixels on the sphere, and allows one to perform a directional spherical wavelet analysis of a 10^6 pixel map on a personal computer.Comment: 10 pages, 3 figures, replaced to match version accepted by IEEE Trans. Sig. Pro

Markov chain Monte Carlo analysis of Bianchi VII_h models

We have extended the analysis of Jaffe et al. to a complete Markov chain Monte Carlo (MCMC) study of the Bianchi type ${\rm VII_h}$ models including a dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalised parameter constraints and the comparative Bayesian evidence. Treating the left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot' in the southern hemisphere, the parameter estimates derived for the total energy density, `tightness' and vorticity from 3-year data are found to be: $\Omega_{tot} = 0.43\pm 0.04$, $h = 0.32^{+0.02}_{-0.13}$, $\omega = 9.7^{+1.6}_{-1.5}\times 10^{-10}$ with orientation $\gamma = {337^{\circ}}^{+17}_{-23}$). This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. A Bianchi type template is supported by the data only if its position on the sky is heavily restricted. The low total energy density of the preferred template, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. found that extending the Bianchi model to include a term in $\Omega_{\Lambda}$ creates a degeneracy in the $\Omega_m - \Omega_{\Lambda}$ plane. We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1 or 3 year WMAP data would prefer at any significance above $2\sigma$. Thus we can confirm that a physical Bianchi ${\rm VII_h}$ model is not responsible for this signature.Comment: 8 pages, 10 figures, significant update to include more accurate results and conclusions to match version accepted by MNRA