Abstract
Calibrating instruments for photon observations in space involves a number of parameters, most basic among them the pointing direction, its accuracy and stability. Wavelength accuracy is important as well. A particularly demanding and complex set of parameters to be determined concerns the responsivity (sometimes also referred to as effective area or detection efficiency) of the telescope-spectrometer combination. The responsivity is a function of wavelength, and for its determination the full set of geometric and spectro-optical properties of the system needs to be quantified. High photon arrival rates may also lead to nonlinearities that have to be assessed. The goal of astrophysics, namely a realistic physical and chemical description of astronomical objects, can only be reached with spectroradiometrically calibrated telescopes and spectrometers (combined with the use of reliable data on atoms and molecules in plasma, gaseous or condensed state). More recent aims, such as the quest for understanding dark matter and dark energy, depend on an exact characterisation of the observing instruments as well, in particular on accurate radiometry. We stress that there is no a priori celestial standard. A radiometric calibration must thus assure that observed spectral irradiances (or radiances) are measured in the units of the Système International, which in turn are defined by radiometric standards realised on Earth.
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Notes
- 1.
In astronomy, the term photometry is often used when dealing with broadband intensity measurements; and measurements with higher spectral resolution are called spectrophotometry. However, in the terminology of the Système International (SI), photometry refers to intensity determinations that are relevant to human vision. In agreement with the use of the SI throughout this book, we exclusively use the terms radiometry or spectroradiometry.
- 2.
The statement re. the Système International should be taken with a grain of salt. Actually Oke and Schild (1970) stated: “... all equipment was designed to permit a determination of the absolute flux of the standard star α Lyr at 5556 Å in units of erg sec−1 cm−2 Hz−1, since this fundamental parameter is also very uncertainly known.” At that time expressing units in the cgs system was still common, and “absolute flux” was used rather than “irradiance”. Currently, improved measurements of this kind — striving for relative accuracies of 1 % of the responsivity — are being performed in view of the requirements for the proposed SNAP mission (Smith et al 2009). Similarly, the Definition Study Report for the Euclid mission (Laureijs et al 2011) puts “a strong requirement that the relative photometric accuracy for all galaxies within the survey should be better than 1.5 %, after full data processing.” and then proceeds with the remark “At a later stage the data can be scaled to adjust the photometry to a consistent absolute calibration based on standard stars or other data sets.” (In the SI-compatible nomenclature of this book “photometric” and “photometry” should be read as “radiometric” and “radiometry”, respectively.)
- 3.
Based on interferometric observations, Peterson et al (2006) and Aufdenberg et al (2006) substantiated the suspicion of earlier spectroscopists that Vega is a fast rotator seen almost pole-on. In comparison with earlier, non-rotating Vega models, the irradiance derived for models that take rotation into account changes, for example, by a factor of about 20 at λ = 115 nm (Peterson 2012). More refined modelling of this star is still going on (cf., Monnier et al 2012, and references therein). Nevertheless, we note again that a standard star, whose spectral irradiance is based on a comparison with an Earth-based radiation standard at one wavelength and then extrapolated by use of an atmosphere model will — in spite of initial practicality — never be a true radiometric standard.
- 4.
An additional concept, viz. having emission transfer standards on the ISS, or on a small calibration satellite orbiting the Earth, with the purpose of calibrating co-orbiting satellites in the extreme ultraviolet range has been suggested (Smith et al 1991). This idea has been taken up recently, however, for the case of Earth observations: a laser mounted on the satellite helps to provide an accurate assessment of atmospheric absorption (Albert et al 2009).
- 5.
As an example we mention the calibration requirements for the PSF of Euclid: “To measure the shear from galaxy ellipticities, requirements are imposed on the PSF such that it can be reconstructed with an error ≤ 2 × 10−4 in ellipticity and its dimension varies by less than 2 × 10−3 across the FOV” (Laureijs et al 2011). Stubbs and Tonry (2006), moreover, pointed out that flat-field calibration is not necessarily straightforward: “Flat-fielding CCD images by dividing the flux detected in each pixel by a passband-dependent sensitivity array is susceptible to systematic uncertainties due to differences in the spectral energy distributions of the flat field, the sky, and the source.” (The sky was mentioned here, because the authors discussed ground-based observations.) Prospects for improved wavelength calibration by exploiting the possibilities offered by laser frequency combs are discussed by Murphy et al (2007).
- 6.
The criterion for a primary standard is that it gives results directly in SI units without the need for any calibration relative to the quantity being measured. One must be able to write the complete operating equation for the standard without any unknown or empirically determined constants or functions that depend upon the quantity being measured. There is no formal hierarchy of primary standards (Quinn 2000). However, the Bureau International des Poids et Mesures (BIPM, http://www.bipm.org) has the mandate to provide the basis for a single, coherent system of measurements – traceable to the International System of Units (SI) – throughout the world.
- 7.
- 8.
A deuterium lamp was used on the Solar Ultraviolet Spectral Irradiance Monitor (SUSIM) on UARS (Brueckner et al 1995), and electric substitution radiometers are part of total solar irradiance measurements, as discussed in Chapter 32 (Fröhlich 2013).
- 9.
http://cxc.harvard.edu/cal/, similar values apply to XMM-Newton (cf., http://xmm2.esac.esa.int/external/xmm_sw_cal/calib/). Note also that an International Astronomical Consortium for High Energy Calibration actively pursues the status of inter-calibration between the observatories RXTE, Chandra, XMM-Newton, Integral, Swift and Suzaku (cf., http://www.iachec.org/).
- 10.
In spectral regions, where the photon aspect of electromagnetic radiation is less dominant, “power” replaces “photon number per unit time”.
- 11.
Workshops on the calibration of HST are a tradition at STScI (cf., http://www.stsci.edu/institute/conference/cal13), and a recent conference on “Calibration and Standardization of Large Surveys and Missions in Astronomy and Astrophysics” (https://indico.fnal.gov/internalPage.py?pageId=10&confId=4958) held at Fermilab shows an increased interest in calibration.
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Huber, M.C.E., Pauluhn, A., Timothy, J.G., Zehnder, A. (2013). Calibration. In: Huber, M.C.E., Pauluhn, A., Culhane, J.L., Timothy, J.G., Wilhelm, K., Zehnder, A. (eds) Observing Photons in Space. ISSI Scientific Report Series, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7804-1_36
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