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Kepler seeks to detect sequences of transits of Earth-size exoplanets orbiting Solar-like stars. Such transit signals are on the order of 100 ppm. The high photometric precision demanded by Kepler requires detailed knowledge of how the Kepler pixels respond to starlight during a nominal observation. This information is provided by the Kepler pixel response function (PRF), defined as the composite of Keplers optical point spread function, integrated spacecraft pointing jitter during a nominal cadence and other systematic effects. To provide sub-pixel resolution, the PRF is represented as a piecewise-continuous polynomial on a sub-pixel mesh. This continuous representation allows the prediction of a stars flux value on any pixel given the stars pixel position. The advantages and difficulties of this polynomial representation are discussed, including characterization of spatial variation in the PRF and the smoothing of discontinuities between sub-pixel polynomial patches. On-orbit super-resolution measurements of the PRF across the Kepler field of view are described. Two uses of the PRF are presented: the selection of pixels for each star that maximizes the photometric signal to noise ratio for that star, and PRF-fitted centroids which provide robust and accurate stellar positions on the CCD, primarily used for attitude and plate scale tracking. Good knowledge of the PRF has been a critical component for the successful collection of high-precision photometry by Kepler.
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Space missions designed for high precision photometric monitoring of stars often under-sample the point-spread function, with much of the light landing within a single pixel. Missions like MOST, Kepler, BRITE, and TESS, do this to avoid uncertainties due to pixel-to-pixel response nonuniformity. This approach has worked remarkably well. However, individual pixels also exhibit response nonuniformity. Typically, pixels are most sensitive near their centers and less sensitive near the edges, with a difference in response of as much as 50%. The exact shape of this fall-off, and its dependence on the wavelength of light, is the intra-pixel response function (IPRF). A direct measurement of the IPRF can be used to improve the photometric uncertainties, leading to improved photometry and astrometry of under-sampled systems. Using the spot-scan technique, we measured the IPRF of a flight spare e2v CCD90 imaging sensor, which is used in the Kepler focal plane. Our spot scanner generates spots with a full-width at half-maximum of $lesssim$3 microns across the range of 400 nm - 850 nm. We find that Keplers CCD shows similar IPRF behavior to other back-illuminated devices, with a decrease in responsivity near the edges of a pixel by $sim$50%. The IPRF also depends on wavelength, exhibiting a large amount of diffusion at shorter wavelengths and becoming much more defined by the gate structure in the near-IR. This method can also be used to measure the IPRF of the CCDs used for TESS, which borrows much from the Kepler mission.
Space missions designed for high precision photometric monitoring of stars often under-sample the point-spread function, with much of the light landing within a single pixel. Missions like MOST, Kepler, BRITE, and TESS, do this to avoid uncertainties due to pixel-to-pixel response nonuniformity. This approach has worked remarkably well. However, individual pixels also exhibit response nonuniformity. Typically, pixels are most sensitive near their centers and less sensitive near the edges, with a difference in response of as much as 50%. The exact shape of this fall-off, and its dependence on the wavelength of light, is the intra-pixel response function (IPRF). A direct measurement of the IPRF can be used to improve the photometric uncertainties, leading to improved photometry and astrometry of under-sampled systems. Using the spot-scan technique, we measured the IPRF of a flight spare e2v CCD90 imaging sensor, which is used in the Kepler focal plane. Our spot scanner generates spots with a full-width at half-maximum of $lesssim$5 microns across the range of 400 nm - 900 nm. We find that Keplers CCD shows similar IPRF behavior to other back-illuminated devices, with a decrease in responsivity near the edges of a pixel by $sim$50%. The IPRF also depends on wavelength, exhibiting a large amount of diffusion at shorter wavelengths and becoming much more defined by the gate structure in the near-IR. This method can also be used to measure the IPRF of the CCDs used for TESS, which borrows much from the Kepler mission.
We employ electrostatic conversion drift calculations to match CCD pixel signal covariances observed in flat field exposures acquired using candidate sensor devices for the LSST Camera. We thus constrain pixel geometry distortions present at the end of integration, based on signal images recorded. We use available data from several operational voltage parameter settings to validate our understanding. Our primary goal is to optimize flux point-spread function (FPSF) estimation quantitatively, and thereby minimize sensor-induced errors which may limit performance in precision astronomy applications. We consider alternative compensation scenarios that will take maximum advantage of our understanding of this underlying mechanism in data processing pipelines currently under development. To quantitatively capture the pixel response in high-contrast/high dynamic range operational extrema, we propose herein some straightforward laboratory tests that involve altering the time order of source illumination on sensors, within individual test exposures. Hence the word {it hysteretic} in the title of this paper.
We have been developing the X-ray silicon-on-insulator (SOI) pixel sensor called XRPIX for future astrophysical satellites. XRPIX is a monolithic active pixel sensor consisting of a high-resistivity Si sensor, thin SiO$_2$ insulator, and CMOS pixel circuits that utilize SOI technology. Since XRPIX is capable of event-driven readouts, it can achieve high timing resolution greater than $sim 10{rm ~mu s}$, which enables low background observation by adopting the anti-coincidence technique. One of the major issues in the development of XRPIX is the electrical interference between the sensor layer and circuit layer, which causes nonuniform detection efficiency at the pixel boundaries. In order to reduce the interference, we introduce a Double-SOI (D-SOI) structure, in which a thin Si layer (middle Si) is added to the insulator layer of the SOI structure. In this structure, the middle Si layer works as an electrical shield to decouple the sensor layer and circuit layer. We measured the detector response of the XRPIX with D-SOI structure at KEK. We irradiated the X-ray beam collimated with $4{rm ~mu mphi}$ pinhole, and scanned the device with $6{rm ~mu m}$ pitch, which is 1/6 of the pixel size. In this paper, we present the improvement in the uniformity of the detection efficiency in D-SOI sensors, and discuss the detailed X-ray response and its physical origins.
Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called binary stars. While long anticipated, the existence of a circumbinary planet orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses (transits) of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Suns mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.
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