Achromatizing a liquid-crystal spectropolarimeter: Retardance vs Stokes-based calibration of HiVIS

Astronomical spectropolarimeters can be subject to many sources of systematic error which limit the precision and accuracy of the instrument. We present a calibration method for observing high-resolution polarized spectra using chromatic liquid-crystal variable retarders (LCVRs). These LCVRs allow for polarimetric modulation of the incident light without any moving optics at frequencies >10Hz. We demonstrate a calibration method using pure Stokes input states that enables an achromatization of the system. This Stokes-based deprojection method reproduces input polarization even though highly chromatic instrument effects exist. This process is first demonstrated in a laboratory spectropolarimeter where we characterize the LCVRs and show example deprojections. The process is then implemented the a newly upgraded HiVIS spectropolarimeter on the 3.67m AEOS telescope. The HiVIS spectropolarimeter has also been expanded to include broad-band full-Stokes spectropolarimetry using achromatic wave-plates in addition to the tunable full-Stokes polarimetric mode using LCVRs. These two new polarimetric modes in combination with a new polarimetric calibration unit provide a much more sensitive polarimetric package with greatly reduced systematic error.Comment: Accepted in PAS

Calibrating and Stabilizing Spectropolarimeters with Charge Shuffling and Daytime Sky Measurements

Well-calibrated spectropolarimetry studies at resolutions of $R>$10,000 with signal-to-noise ratios (SNRs) better than 0.01\% across individual line profiles, are becoming common with larger aperture telescopes. Spectropolarimetric studies require high SNR observations and are often limited by instrument systematic errors. As an example, fiber-fed spectropolarimeters combined with advanced line-combination algorithms can reach statistical error limits of 0.001\% in measurements of spectral line profiles referenced to the continuum. Calibration of such observations is often required both for cross-talk and for continuum polarization. This is not straightforward since telescope cross-talk errors are rarely less than $\sim$1\%. In solar instruments like the Daniel K. Inouye Solar Telescope (DKIST), much more stringent calibration is required and the telescope optical design contains substantial intrinsic polarization artifacts. This paper describes some generally useful techniques we have applied to the HiVIS spectropolarimeter at the 3.7m AEOS telescope on Haleakala. HiVIS now yields accurate polarized spectral line profiles that are shot-noise limited to 0.01\% SNR levels at our full spectral resolution of 10,000 at spectral sampling of $\sim$100,000. We show line profiles with absolute spectropolarimetric calibration for cross-talk and continuum polarization in a system with polarization cross-talk levels of essentially 100\%. In these data the continuum polarization can be recovered to one percent accuracy because of synchronized charge-shuffling model now working with our CCD detector. These techniques can be applied to other spectropolarimeters on other telescopes for both night and day-time applications such as DKIST, TMT and ELT which have folded non-axially symmetric foci.Comment: Accepted to A&

Spitzer 24-micron Time-Series Observations of the Eclipsing M-dwarf Binary GU Bootis

We present a set of {\it Spitzer} 24$\mu$m MIPS time series observations of the M-dwarf eclipsing binary star GU Bo\"otis. Our data cover three secondary eclipses of the system: two consecutive events and an additional eclipse six weeks later. The study's main purpose is the long wavelength (and thus limb darkening-independent) characterization of GU Boo's light curve, allowing for independent verification of the results of previous optical studies. Our results confirm previously obtained system parameters. We further compare GU Boo's measured 24$\mu$m flux density to the value predicted by spectral fitting and find no evidence for circumstellar dust. In addition to GU Boo, we characterize (and show examples of) light curves of other objects in the field of view. Analysis of these light curves serves to characterize the photometric stability and repeatability of {\it Spitzer's} MIPS 24\micron array over short (days) and long (weeks) timescales at flux densities between approximately 300--2,000$\mu$Jy. We find that the light curve root mean square about the median level falls into the 1--4% range for flux densities higher than 1mJy. Finally, we comment on the fluctuations of the 24\micron background on short and long timescales.Comment: ApJ accepted. 10 pages, 12 figure

A framework for the statistical analysis of mass spectrometry imaging experiments

Mass spectrometry (MS) imaging is a powerful investigation technique for a wide range of biological applications such as molecular histology of tissue, whole body sections, and bacterial films , and biomedical applications such as cancer diagnosis. MS imaging visualizes the spatial distribution of molecular ions in a sample by repeatedly collecting mass spectra across its surface, resulting in complex, high-dimensional imaging datasets. Two of the primary goals of statistical analysis of MS imaging experiments are classification (for supervised experiments), i.e. assigning pixels to pre-defined classes based on their spectral profiles, and segmentation (for unsupervised experiments), i.e. assigning pixels to newly discovered segments with relatively homogenous and distinct spectral profiles. To accomplish these goals, this research provides both statistical methods and statistical computing tools. First, we propose a novel spatial shrunken centroids framework for performing classification and segmentation of MS imaging experiments with feature selection. Spatial shrunken centroids combines spatial smoothing with statistical regularization in a model-based framework appropriate for both supervised and unsupervised settings. Second, we provide Cardinal, a free and open-source R package for processing, visualization, and statistical analysis of MS imaging experiments. Cardinal is the first R package designed specifically for MS imaging, and the first software for MS imaging that focuses specifically on experiments and statistical analysis. In addition to providing tools for statistical analysis, it also provides infrastructure to enable other statisticians to more easily develop new methods for MS imaging experiments. Lastly, to enable scalability of Cardinal to larger-than-memory datasets, we provide matter, a free and open-source R package for statistical computing with structured datasets-on-disk, such as MS imaging data files. Together, spatial shrunken centroids, Cardinal, and matter aim to allow scalable statistical analysis for high-resolution, high-throughput MS imaging experiments

Compact spaces generated by retractions

We study compact spaces which are obtained from metric compacta by iterating the operation of inverse limit of continuous sequences of retractions. We denote this class by R. Allowing continuous images in the definition of class R, one obtains a strictly larger class, which we denote by RC. We show that every space in class RC is either Corson compact or else contains a copy of the ordinal segment $[0,\omega_1]$. This improves a result of Kalenda, where the same was proved for the class of continuous images of Valdivia compacta. We prove that spaces in class R do not contain cutting P-points (see the definition below), which provides a tool for finding spaces in RC minus R. Finally, we study linearly ordered spaces in class RC. We prove that scattered linearly ordered compacta belong to RC and we characterize those ones which belong to R. We show that there are only 5 types (up to order isomorphism) of connected linearly ordered spaces in class R and all of them are Valdivia compact. Finally, we find a universal pre-image for the class of all linearly ordered Valdivia compacta.Comment: Minor corrections; added two statements on linearly ordered compacta. The paper has 21 pages and 2 diagram