Combining Undersampled Dithered Images

Undersampled images, such as those produced by the HST WFPC-2, misrepresent fine-scale structure intrinsic to the astronomical sources being imaged. Analyzing such images is difficult on scales close to their resolution limits and may produce erroneous results. A set of ``dithered'' images of an astronomical source generally contains more information about its structure than any single undersampled image, however, and may permit reconstruction of a ``superimage'' with Nyquist sampling. I present a tutorial on a method of image reconstruction that builds a superimage from a complex linear combination of the Fourier transforms of a set of undersampled dithered images. This method works by algebraically eliminating the high order satellites in the periodic transforms of the aliased images. The reconstructed image is an exact representation of the data-set with no loss of resolution at the Nyquist scale. The algorithm is directly derived from the theoretical properties of aliased images and involves no arbitrary parameters, requiring only that the dithers are purely translational and constant in pixel-space over the domain of the object of interest. I show examples of its application to WFC and PC images. I argue for its use when the best recovery of point sources or morphological information at the HST diffraction limit is of interest.Comment: 22 pages, 9 EPS figures, submitted to PAS

The Photometry of Undersampled Point Spread Functions

An undersampled point spread function may interact with the microstructure of a solid-state detector such that the total flux detected can depend sensitively on where the PSF center falls within a pixel. Such intra-pixel sensitivity variations will not be corrected by flat field calibration and may limit the accuracy of stellar photometry conducted with undersampled images, as are typical for Hubble Space Telescope observations. The total flux in a stellar image can vary by up to 0.03 mag in F555W WFC images depending on how it is sampled, for example. For NIC3, these variations are especially strong, up to 0.39 mag, strongly limiting its use for stellar photometry. Intra-pixel sensitivity variations can be corrected for, however, by constructing a well-sampled PSF from a dithered data set. The reconstructed PSF is the convolution of the optical PSF with the pixel response. It can be evaluated at any desired fractional pixel location to generate a table of photometric corrections as a function of relative PSF centroid. A caveat is that the centroid of an undersampled PSF can also be affected by the pixel response function, thus sophisticated centroiding methods, such as cross-correlating the observed PSF with its fully-sampled counterpart, are required to derive the proper photometric correction.Comment: 20 pages, 14 postscript figures, submitted to the PAS

Destiny: A Candidate Architecture for the Joint Dark Energy Mission

Destiny is a simple, direct, low cost mission to determine the properties of dark energy by obtaining a cosmologically deep supernova (SN) type Ia Hubble diagram. Operated at L2, its science instrument is a 1.65m space telescope, featuring a grism-fed near-infrared (NIR) (0.85-1.7micron) survey camera/spectrometer with a 0.12 square degree field of view. During its two-year primary mission, Destiny will detect, observe, and characterize ~3000 SN Ia events over the redshift interval 0.4<z<1.7 within a 3 square degree survey area. In conjunction with ongoing ground-based SN Ia surveys for z<0.8, Destiny mission data will be used to construct a high-precision Hubble diagram and thereby constrain the dark energy equation of state from a time when it was strongly matter-dominated to the present when dark energy dominates. The grism-images simultaneously provide broad-band photometry, redshifts, and SN classification, as well as time-resolved diagnostic data for investigating additional SN luminosity diagnostics. Destiny will be used in its third year as a high resolution, wide-field imager to conduct a multicolor NIR weak lensing (WL) survey covering 1000 square degrees. The large-scale mass power spectrum derived from weak lensing distortions of field galaxies as a function of redshift will provide independent and complementary constraints on the dark energy equation of state. The combination of SN and WL is much more powerful than either technique on its own. Used together, these surveys will have more than an order of magnitude greater sensitivity than will be provided by ongoing ground-based projects. The dark energy parameters, w_0 and w_a, will be measured to a precision of 0.05 and 0.2 respectively.Comment: Contains full color figure

Principal Component Analysis as a Tool for Characterizing Black Hole Images and Variability

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial-domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as the Event Horizon Telescope (EHT). We also show that the simulations in the spatial domain themselves can be compactly represented with a PCA-derived basis of eigenimages allowing for detailed comparisons between variable observations and time-dependent models, as well as for detection of outliers or rare events within a time series of images. Furthermore, we demonstrate that the spectrum of PCA eigenvalues is a diagnostic of the power spectrum of the structure and, hence, of the underlying physical processes in the simulated and observed images.Comment: 16 pages, 17 figures, submitted to Ap

Luminosity Function of Faint Globular Clusters in M87

We present the luminosity function to very faint magnitudes for the globular clusters in M87, based on a 30 orbit \textit{Hubble Space Telescope (HST)} WFPC2 imaging program. The very deep images and corresponding improved false source rejection allow us to probe the mass function further beyond the turnover than has been done before. We compare our luminosity function to those that have been observed in the past, and confirm the similarity of the turnover luminosity between M87 and the Milky Way. We also find with high statistical significance that the M87 luminosity function is broader than that of the Milky Way. We discuss how determining the mass function of the cluster system to low masses can constrain theoretical models of the dynamical evolution of globular cluster systems. Our mass function is consistent with the dependence of mass loss on the initial cluster mass given by classical evaporation, and somewhat inconsistent with newer proposals that have a shallower mass dependence. In addition, the rate of mass loss is consistent with standard evaporation models, and not with the much higher rates proposed by some recent studies of very young cluster systems. We also find that the mass-size relation has very little slope, indicating that there is almost no increase in the size of a cluster with increasing mass.Comment: 22 pages, 5 figures, Accepted for publication in Ap

Brightest Cluster Galaxies at the Present Epoch

We have observed 433 z<=0.08 brightest cluster galaxies (BCGs) in a full-sky survey of Abell clusters. The BCG Hubble diagram is consistent to within 2% of a Omega_m=0.3, Lambda=0.7 Hubble relation. The L_m-alpha relation for BCGs, which uses alpha, the log-slope of the BCG photometric curve of growth, to predict metric luminosity, L_m, has 0.27 mag residuals. We measure central stellar velocity dispersions, sigma, of the BCGs, finding the Faber-Jackson relation to flatten as the metric aperture grows to include an increasing fraction of the total BCG luminosity. A 3-parameter "metric plane" relation using alpha and sigma together gives the best prediction of L_m, with 0.21 mag residuals. The projected spatial offset, r_x, of BCGs from the X-ray-defined cluster center is a gamma=-2.33 power-law over 1<r_x<10^3 kpc. The median offset is ~10 kpc, but ~15% of the BCGs have r_x>100 kpc. The absolute cluster-dispersion normalized BCG peculiar velocity |Delta V_1|/sigma_c follows an exponential distribution with scale length 0.39+/-0.03. Both L_m and alpha increase with sigma_c. The alpha parameter is further moderated by both the spatial and velocity offset from the cluster center, with larger alpha correlated with the proximity of the BCG to the cluster mean velocity or potential center. At the same time, position in the cluster has little effect on L_m. The luminosity difference between the BCG and second-ranked galaxy, M2, increases as the peculiar velocity of the BCG within the cluster decreases. Further, when M2 is a close luminosity "rival" of the BCG, the galaxy that is closest to either the velocity or X-ray center of the cluster is most likely to have the larger alpha. We conclude that the inner portions of the BCGs are formed outside the cluster, but interactions in the heart of the galaxy cluster grow and extend the envelopes of the BCGs.Comment: Accepted for publication in the Astrophysical Journa

On DESTINY Science Instrument Electrical and Electronics Subsystem Framework

Future space missions are going to require large focal planes with many sensing arrays and hundreds of millions of pixels all read out at high data rates'' . This will place unique demands on the electrical and electronics (EE) subsystem design and it will be critically important to have high technology readiness level (TRL) EE concepts ready to support such missions. One such omission is the Joint Dark Energy Mission (JDEM) charged with making precise measurements of the expansion rate of the universe to reveal vital clues about the nature of dark energy - a hypothetical form of energy that permeates all of space and tends to increase the rate of the expansion. One of three JDEM concept studies - the Dark Energy Space Telescope (DESTINY) was conducted in 2008 at the NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland. This paper presents the EE subsystem framework, which evolved from the DESTINY science instrument study. It describes the main challenges and implementation concepts related to the design of an EE subsystem featuring multiple focal planes populated with dozens of large arrays and millions of pixels. The focal planes are passively cooled to cryogenic temperatures (below 140 K). The sensor mosaic is controlled by a large number of Readout Integrated Circuits and Application Specific Integrated Circuits - the ROICs/ASICs in near proximity to their sensor focal planes. The ASICs, in turn, are serviced by a set of "warm" EE subsystem boxes performing Field Programmable Gate Array (FPGA) based digital signal processing (DSP) computations of complex algorithms, such as sampling-up-the-ramp algorithm (SUTR), over large volumes of fast data streams. The SUTR boxes are supported by the Instrument Control/Command and Data Handling box (ICDH Primary and Backup boxes) for lossless data compression, command and low volume telemetry handling, power conversion and for communications with the spacecraft. The paper outlines how the JDEM DESTINY concept instrument EE subsystem can be built now, a design; which is generally U.S. Government work not protected by U.S. copyright IEEEAC paper # 1429. Version 4. Updated October 19, 2009 applicable to a wide variety of missions using large focal planes with lar ge mosaics of sensors

The Image of the M87 Black Hole Reconstructed with PRIMO

We present a new reconstruction of the Event Horizon Telescope (EHT) image of the M87 black hole from the 2017 data set. We use PRIMO, a novel dictionary-learning based algorithm that uses high-fidelity simulations of accreting black holes as a training set. By learning the correlations between the different regions of the space of interferometric data, this approach allows us to recover high-fidelity images even in the presence of sparse coverage and reach the nominal resolution of the EHT array. The black hole image comprises a thin bright ring with a diameter of $41.5\pm0.6\,\mu$as and a fractional width that is at least a factor of two smaller than previously reported. This improvement has important implications for measuring the mass of the central black hole in M87 based on the EHT images.Comment: 7 pages, 5 figure