Combined calculi for photon orbital and spin angular momenta

Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital angular momentum (POAM), completely describe the state of a photon or an electric field (an ensemble of photons). Wavelength relates directly to energy and linear momentum, the corresponding kinetic quantities. PSAMand POAM, themselves kinetic quantities, are colloquially known as polarization and optical vortices, respectively. Astrophysical sources emit photons that carry this information. Aims. PSAM characteristics of an electric field (intensity) are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I created calculi to represent POAM characteristics of electric fields and intensities in an astrophysical context. Adding wavelength dependence to all of these calculi is trivial. The next logical steps are to 1) form photon total angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using operators and expectation values; and 3) show that instrumental PSAM can affect measured POAM values for certain types electric fields. Methods. I derive the PTAM calculi of electric fields and intensities by combining the POAM and PSAM calculi. I show how these quantities propagate from celestial sphere to image plane. I also form the PTAMoperator (the sum of the POAMand PSAMoperators), with and without instrumental PSAM, and calculate the corresponding expectation values. Results. Apart from the vector, matrix, dot product, and direct product symbols, the PTAM and POAM calculi appear superficially identical. I provide tables with all possible forms of PTAM calculi. I prove that PTAM expectation values are correct for instruments with and without instrumental PSAM. I also show that POAM measurements of "unfactored" PTAM electric fields passing through non-zero instrumental circular PSAM can be biased. Conclusions. The combined PTAM calculi provide insight into how to mathematically model PTAM sources and calibrate POAMand PSAM- induced POAM measurement errors

The 2012 Interferometric Imaging Beauty Contest

We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thi\'ebaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiRA entries; Rengaswamy with an original method; and Elias with the radio-astronomy package CASA. The contest model images, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm

World Health Organization cardiovascular disease risk charts: revised models to estimate risk in 21 global regions

BACKGROUND: To help adapt cardiovascular disease risk prediction approaches to low-income and middle-income countries, WHO has convened an effort to develop, evaluate, and illustrate revised risk models. Here, we report the derivation, validation, and illustration of the revised WHO cardiovascular disease risk prediction charts that have been adapted to the circumstances of 21 global regions. METHODS: In this model revision initiative, we derived 10-year risk prediction models for fatal and non-fatal cardiovascular disease (ie, myocardial infarction and stroke) using individual participant data from the Emerging Risk Factors Collaboration. Models included information on age, smoking status, systolic blood pressure, history of diabetes, and total cholesterol. For derivation, we included participants aged 40-80 years without a known baseline history of cardiovascular disease, who were followed up until the first myocardial infarction, fatal coronary heart disease, or stroke event. We recalibrated models using age-specific and sex-specific incidences and risk factor values available from 21 global regions. For external validation, we analysed individual participant data from studies distinct from those used in model derivation. We illustrated models by analysing data on a further 123 743 individuals from surveys in 79 countries collected with the WHO STEPwise Approach to Surveillance. FINDINGS: Our risk model derivation involved 376 177 individuals from 85 cohorts, and 19 333 incident cardiovascular events recorded during 10 years of follow-up. The derived risk prediction models discriminated well in external validation cohorts (19 cohorts, 1 096 061 individuals, 25 950 cardiovascular disease events), with Harrell's C indices ranging from 0·685 (95% CI 0·629-0·741) to 0·833 (0·783-0·882). For a given risk factor profile, we found substantial variation across global regions in the estimated 10-year predicted risk. For example, estimated cardiovascular disease risk for a 60-year-old male smoker without diabetes and with systolic blood pressure of 140 mm Hg and total cholesterol of 5 mmol/L ranged from 11% in Andean Latin America to 30% in central Asia. When applied to data from 79 countries (mostly low-income and middle-income countries), the proportion of individuals aged 40-64 years estimated to be at greater than 20% risk ranged from less than 1% in Uganda to more than 16% in Egypt. INTERPRETATION: We have derived, calibrated, and validated new WHO risk prediction models to estimate cardiovascular disease risk in 21 Global Burden of Disease regions. The widespread use of these models could enhance the accuracy, practicability, and sustainability of efforts to reduce the burden of cardiovascular disease worldwide. FUNDING: World Health Organization, British Heart Foundation (BHF), BHF Cambridge Centre for Research Excellence, UK Medical Research Council, and National Institute for Health Research

Imaging Stars by Performing Full-Stokes Optical Interferometric Polarimetry

Optical interferometry and polarimetry have separately provided new insights into stellar astronomy, especially in the fields of fundamental parameters and atmospheric models. We present: scientific justifications for “full-Stokes” optical interferometric polarimetry (OIP); updated instrument requirements; preliminary beam combiner designs; polarimeter design; end-to-end OIP data reduction; and realistic reimaged full-Stokes models of Be stars with a suitable number of telescopes plus noise sources. All of this work represents preliminary research to construct an OIP beam combiner

The Penn Polarimeters

This report describes the inception, development and extensive use over 30 years of elliptical polarimeters at the University of Pennsylvania. The initial Mark I polarimeter design utilized oriented retarder plates and a calcite Foster-Clarke prism as the analyzer. The Mark I polarimeter was used on the Kitt Peak 0.9 m in 1969-70 to accomplish a survey of approximately 70 objects before the device was relocated to the 0.72 m reflector at the Flower and Cook Observatory. Successive generations of automation and improvements included the early-80’s optical redesign to utilize a photoelastic modulated wave plate and an Ithaco lock-in amplifier–the photoelastic modulating polarimeter. The final design in 2000 concluded with a fully remote operable device. The legacy of the polarimetric programs includes studies of close binaries, pulsating hot stars, and luminous late-type variables

Imaging Stars by Performing Full-Stokes Optical Interferometric Polarimetry

Optical interferometry and polarimetry have separately provided new insights into stellar astronomy, especially in the fields of fundamental parameters and atmospheric models. We present: scientific justifications for “full-Stokes” optical interferometric polarimetry (OIP); updated instrument requirements; preliminary beam combiner designs; polarimeter design; end-to-end OIP data reduction; and realistic reimaged full-Stokes models of Be stars with a suitable number of telescopes plus noise sources. All of this work represents preliminary research to construct an OIP beam combiner