Width Of Point Spread Function Research Articles

Refraction by Earth’s Atmosphere near 12 Microns

ABSTRACTWe have measured chromatic differential refraction of astronomical images by the Earth’s atmosphere, comparing visible light at 500–600 nm with infrared near 12 μm, and found the index of refraction near 12 μm to be greater than predicted by the dispersion relation in common use. The differential refraction between visible and 12 μm thus is smaller than the extrapolated difference. At Mauna Kea, the empirical differential refraction at 45° from zenith was measured at 0.″ 28 ± 0.″28 (3 σ) on one occasion, compared to an expected differential refraction of 0.″63–0.″69. Refractivity scales linearly with barometric pressure, and thus the inaccuracy is more severe at lower altitude observatories. The pointing error from inaccurate correction for differential refraction is comparable to the point spread function width of an 8–10 m telescope in this wavelength range. Even on smaller telescopes, accurate correction for differential refraction is necessary to guide small‐aperture spectrophotometry or to register mid‐infrared imaging with visible‐light structures.

Pile-up on X-ray CCD instruments

This paper presents a statistical and analytical analysis of the pile-up phenomenon on X-ray CCD detectors, whereby two incoming X-rays are counted as one. The probability of measuring configurations involving 1, 2, 3 or 4 pixels is written down for a uniform incoming flux, thus allowing the computation of the flux loss (fraction of photons rejected because of pile-up) and of the pile-up fraction (fraction of events with wrong energy). For detectors with pixels which are small compared to the point spread function (PSF) of the telescope (such as XMM/EPIC-MOS or ASCA/SIS ) the formulae can be readily integrated over space to predict and account for pile-up on the total flux of point sources. It is shown that if only single events are selected the total pile-up fraction can never get very high for usual PSF shapes. The main effect is a loss of efficiency which is perfectly quantifiable. It is concluded that taking extreme care to avoid pile-up by adapting the instrument setting (for example restricting the useful area of the CCD) may not be so important after all, although it remains necessary if it is important to collect as many photons as possible from the source. An extension to the theory is proposed for detectors with pixels comparable to the PSF width (such as AXAF/ACIS ), and for extended sources.

On sampling with account of noise

Abstract The optimum pixel size ϵ of a detector under given observational conditions depends on a priori information about the object in focus, the Point Spread Function (PSF), the signal-to-noise ratio, etc. The Rayleigh criterion, according to which the theoretically attainable resolution is of the order of the PSF width Δ, leads to the generally accepted value of ϵ= Δ/2. It is shown that this conventional approach does not take into account important information concerning the image smoothing. Image restoration technique allows to reach much higher resolving power under typical conditions of observations, so that much smaller pixel size should be chosen to provide the theoretically attainable resolving power. Unmatched telescope and detector have significant losses in the resolving power and limiting magnitude. The formulae are given for approximate calculation of the corresponding parameters. As an example, the problem of the resolving power of the Hubble Space Telescope is discussed.