The autumnal decay in Cambridge sometimes appears to extend from deciduous tree foliage to all things living. This year however, the falling leaves were outnumbered by leaves of white, with mysterious squiggly black lines on them. These leaves spewed from printers and photocopiers, born from the spoils of ravaged forest to festoon the halls of 60 Garden Street. They formed into groups and were both welcomed and feared by man. (Watch that gender thing. Ed.) They were the Chandra instrument calibration reports. Welcomed for the information and summary of knowledge they would contain, feared as harbingers of information and knowledge still to be gathered.
The Low Energy Transmission Grating (LETG) report was put together by the instrument teams at MPE, Garching, and SRON, Utrecht. It comprises 126 pages, 37 of which are appendices, and is based on an extensive (but not all-inclusive) collection of analyses of subassembly and XRCF calibration data by these groups and by the LETG group at the Chandra X-ray Center. As with the other instruments on Chandra, the LETG calibration consisted of two different parts: subassembly characterization of individual grating elements and ensemble testing of the whole grating assembly of 540 elements at the Marshall Space Flight Center X-ray Calibration Facility (XRCF). The former was undertaken by the instrument teams, while the latter was largely planned by CXC calibration scientists and was executed by CXC, Project Science,and Mission Support Team scientists.
and instrument team scientists.
The calibration of a transmission grating can be roughly broken into two aspects: the diffraction efficiency, describing the intensity diffracted into the various orders with respect to the incident intensity; and the spatial characteristics of the diffracted light--the point spread function (PSF) and its related line spread function (LSF), the ``plate scale'', and scattered light. In the case of the LETG, the support structure obscuration and diffraction also require consideration since it can modify the effective diffraction efficiency as well as the spatial character of diffracted light. The MPE team have been concentrating on the diffraction efficiency, the SRON team on the spatial characteristics. Appropriately enough, the calibration report is divided equally between these two aspects.
The report commences with a brief description of the LETG itself, then goes on to describe the subassembly characterization by means of near infra-red (NIR) metrology of all the elements and direct X-ray measurements of a sample of grating elements at the BESSY synchrotron storage ring in Berlin, and at the MPE ZETA beamline. The grating bars themselves are assumed to have a trapezoidal cross-section, from which an analytical model of the X-ray diffraction efficiency as a function of energy can be readily derived for a given set of optical constants appropriate to the grating material (gold). The NIR tests characterize the average grating bar parameters for a given element, while the X-ray measurements can be used to test and verify the diffraction model. Following the subassembly calibration overview, the report describes the XRCF tests and some of the subsequent data analysis. The ensemble grating model efficiency is compared with efficiencies derived at different energies from the XRCF tests for 0th, 1st and some higher orders.
The section of the report dealing with spatial analysis commences with an overview of the different terms entering into the expression describing the blurring of a monochromatic spectral line. The dominant term in the equation is the PSF of the main mirror assembly. However, a key question to answer is: does the LETG itself add significant broadening to an observed spectral line? The report covers the more important of the measurements made at XRCF in order to probe the LSF, deals with the plate scale and linearity of the HRC-S flight detector, and includes a nice piece on scattered light.
By now, the reader is possibly suspicious of mere descriptions of a calibration report with no mention of results. Perhaps appealing to an inner sense of optimism that current astrophysical and modelling problems possibly related to uncertainties in knowledge of X-ray instrument performance will be ameliorated by the launch of Chandra, words to the effect of ``...But Chandra will be calibrated to one percent, won't it?'' seem to have been a common conception and a common remark in the last year or two made by colleagues not directly associated with the project. And why not? After all, in theory the process is simple: throw the instrumentation--mirror, grating and detector--in front of a source of X-rays of a given energy and known flux, obtain 10,000 counts in the detector, or 20,000 for good measure, and bingo, 1% calibration.
As stated in the LETG calibration report, the target accuracy for the calibration of the LETG Spectrograph (referring to the mirror + grating + detector combination) was actually specified as ``only'' 10% absolute and 3% relative. Articles referring to the calibration reports of the HRMA and HRC-S can be found elsewhere in this Newsletter. For the LETG itself, the current calibration is still slightly shy of the target. Unfortunately, in X-ray calibration, theory and experiment are only cousins, often distant ones at that, and several times removed. As with calibration of the other Chandra instruments, systematic effects and uncertainties dominate the process, and accounting properly for these effects is where the bulk of the effort to analyze and interpret the calibration experiments is being, and has been, aimed.
At the subassembly level, the agreement between modelled and measured X-ray efficiency for individual elements is generally no better than 10% or so. Sources of such discrepancies lie in the approximation that each element can be described by a trapezoidal bar cross-section (more complex descriptions are possible but cannot be uniquely constrained by feasible calibration strategies), uncertainties in the gold optical constants and in the appropriate gold density to assume for the grating bars, and systematic uncertainties arising in the X-ray measurements. Uncertainties such as those of the gold optical constants are very difficult to assess properly, since data that cover a sufficient energy range (e.g. the ``Henke Tables'') are based on compilations of results from the literature which themselves often do not include any proper assessment of experimental error.
The uncertainties in the model diffraction efficiency of a single
grating element is offset partly by the fact that the flight LETG
comprises 540 different elements; the efficiency of the ensemble is an
average of these individual efficiencies. The bad news is then that
the characterization of the entire ensemble is experimentally rather
tricky. The XRCF experiments to calibrate the Chandra HRMA, gratings, and
detectors provide a somewhat comprehensive lesson in the
difficulties and different sources of error that are
involved in such X-ray measurements. Starting with the X-ray source,
one must account for effects such as broad-band continuum emission,
non-uniformities in the X-ray beam itself over the aperture of the
HRMA, and sometimes variability in the source flux. Focal plane measurements
required accurate (to a few 
m) three-dimensional placement of
entrance apertures. Subsequent analysis requires modelling of the
diffracted source
spectrum (including cross-dispersion by support structures)
on entrance apertures, including all misalignments of grating
and facility optical and dispersion axes. Complex responses of flow
proportional counter (FPC) focal plane detectors with low intrinsic
energy resolution to the often complicated incident spectra
have to be accurately modelled, including the effects of obscuration
by mesh structures supporting the FPC entrance windows and
bowing in the windows themselves.
Icing for this over-spiced cake is provided by the often arcane, byzantine nature of the data themselves. The seething multitude of different contractors and groups involved in executing the XRCF experiments tended to speak their own different computer languages, or to only speak to themselves. Consequently, assembling the appropriate information to tell one exactly what the X-ray source, mirror, and focal plane detector and mount were doing exactly at any given time has infinite capacity for turning a jolly pleasant afternoon bad.
At the time of its writing, the LETG calibration report indicates differences of typically 10% between the ensemble model and measured diffraction efficiency in 0th and 1st orders. At energies above 1.5-2 keV or so these uncertainties tend to be a bit higher; uncertainties in higher spectral orders are also inevitably higher. Progress has, however, been made since the minting of the calibration report, and further sources of modelling error and measurement uncertainty have been accounted for. It is expected that significant improvements in the calibration uncertainty will result from this effort.
In terms of the LSF, no sources of broadening attributable to the LETG itself have been found in the data. At the most detailed level, quantification of the PSF and LSF cores as measured at XRCF is complicated by gravity deformation of the HRMA, by the finite size and distance of the X-ray sources, and by some slight but significant misalignments of the gratings, and focal plane detectors with respect to each other and the XRCF for some of the tests. As we continue to perfect our understanding of these effects, however, our conclusion remains that the PSF and LRF of the system are dominated by the intrinsic HRMA blur and detector broadening, with any contributions from the LETG being relatively small.
In scientific terms, an accurate determination of LSF of the LETGS is generally much more important than determining the absolute effective area of the system to better than 10%. (In this author's subjective and humble opinion!) The LSF enters crucially into spectral line deblending and flux measurement, and into studies of line profiles broadened by thermal or non-thermal velocities. In contrast, existing X-ray spectral models generally include intrinsic uncertainties at levels larger than 10% , such as the gaunt factors that enter into the computation of bound-free and free-free continuum emission, ion populations, line excitation rates etc. At least for our purposes this situation is not too inconvenient: calibration of the core of the LSF can be verified (and possibly improved upon) in-flight by looking at point sources with fairly narrow spectral lines (e.g. stellar coronae). Effective area calibration in flight is much more difficult, requiring constant sources with reasonably accurate spectral models (e.g. white dwarfs).
At the CXC, and SRON and MPE, we continue our attrition of the flesh, blood and souls of mortal man for each minute quantum of information wrestled from the ruthless clawed monster of ground calibration data. The monster still has appetite for such humble victuals, though over the next several months we hope largely to sate it and to cap it off with the after dinner mint of in-flight calibration, wafer thin of course.
When the Instrument team calibration report is finalized, it can be found from the CXC LETG team web page:
http://asc.harvard.edu/cal/Links/Letg/WWWletg_cal.html
- Jeremy J. Drake