AXAF Transmission Grating Data Processing Overview
(Level 1.5)

David Huenemoerder

20 June 1997

The AXAF transmission gratings, HETG or LETG, are typically used with the ACIS-S and HRC-S detector arrays, respectively. The data can be processed to a point without any dependence upon the gratings. This is referred to as "Level 1": it is primarily a scaling and formatting of the event data and ancillary descriptive information about the observation ("meta-data"). After Level 1, "Level 2" processing is defined as analysis of source properties, such as source detection, fluxes, or extent. Grating data require a bit of analysis in order to provide the basic spectral properties of each photon: its diffraction angle, wavelength, and if possible, a diffraction order. This is referred to as "Level 1.5", since it must be done before spectral analysis. This document is intended to provide a basic overview of these steps.

Figure 1below shows a block diagram of the fundamental steps, of which boxes 3-6 comprise Level 1.5 processing.

Much of the processing has been implemented for XRCF. However, XRCF and flight processing are somewhat different, primarily in the use of aspect dither in which the spacecraft pointing is driven on a Lissajous pattern on the sky, and in the possibility of multiple sources in the field. One XRCF observation, that of a continuum source ("Molecular Contamination" test) observed with the HETG and ACIS-S has been used to prototype flight processing. Each of the boxes in the block diagram will be described in more detail, with accompanying graphical examples derived from the test data.

AXAF spectroscopic data are obtained as event lists. Each step in the processing maintains the event-list format, and the final Level 1.5 product is an event list. Furthermore, an effort is being made to avoid truncation of data by imposing grids; since the pointing is moving continuously during an observation, there is no well defined "pixel" size for the resulting data. Analysis may follow by binning event-lists into counts spectra, or may be used in maximum-likelihood methods.

  • 1- Standard ACIS/HRC event processing: Here telemetry is processed by de-commutation, scaling and formatting into FITS binary tables. The aspect solution is applied to give sky coordinates for the photons, but without knowledge of whether a photon has been diffracted by a grating. The result has columns in the data such as time, chip id, chip x, chip y, detector x, detector y, sky x, sky y, PHA, and PI. A sample field image, as if made from the sky x and sky y (usually parallel to right ascension and declination) are shown in Figure 2. A slight rotation has been applied to simulate an arbitrary angle of the detector axes on the sky.

    • This is a scatterplot of photon positions, and not an intensity image. The zero-order photons lie in the dense region near the center of the image. The two arms of the "X" are the HEG and MEG parts of the HETG spectrum. The aspect ratio is approximately 1:1. This was a heavily exposed image and suffers from some problems: bright lines leave tails (approximately vertical stripes) due to exposure during frame-transfer (an ACIS PSF "feature"!) , and no event-grade filtering has been done.

  • 2- Detect Sources: Before attributes pertaining to the diffraction can be assigned, the zero-order source position on the sky must be determined. This is the origin of the spectral coordinates, and so each source in the field will have its own origin for diffraction coordinates. Source detection must not be fooled by bright lines away from the center of the field. There are a couple ways to discriminate bright emission lines from off-axis sources. Primarily, off-axis sources will be blurred by being out-of-focus, while emission lines from an on-axis source will have an on-axis PSF. Another diagnostic which can be applied for ACIS is to use the PHA variance of a candidate source: a line will have small variance while a zero-order will have large variance, since it has photons from the entire spectrum. (This simulation does not contain source detection - a zero-order source position was determined a priori.)
  • 3- Identify spectrum parts geometrically: From purely geometrical considerations, given a few geometrical calibration parameters of the observatory, we can group events by part of the spectrum. For HETGS, the relevant parts for each source are: zero-order, MEG photons, HEG photons, or background photons. For LETG, there is only one grating type, so the parts are zero-order, LEG, or background. (The Drake Flat adds several more parts: straight-through, plus two more parts, one for each of the two segments of the flat.) We can define regions as rectangles in diffraction coordinates, in which the zero-order is the origin, and one axis is parallel to the spectrum, and the other perpendicular to it. The width of the rectangle is specified by the effective PSF (mirror, Rowland geometry astigmatism, de-focus, aspect). The region can be applied simply by translating the sky coordinates source position to the origin and then rotating by the grating angle plus the mean roll angle. Any event inside the rectangle is then assigned to that part of the spectrum (HEG or MEG, or LEG). Zero-order photons are assigned by being within some radius of the zero-order centroid. Figure 3 shows a color-coded result of such an assignment for the center of the field shown in Figure 2. In this case, the HEG and MEG rectangles have collided near zero-order. Photons in the overlap region have also been assigned a tag. (Some peculiarities of the data can also be seen: the "hour-glass" effect at zero-order is due to HRMA shutters closing part of the beam, and the black square in zero-order is blocking of the zero-order in ACIS software.)

  • 4- Compute linear diffraction coordinates: Photons have been selected geometrically by their sky coordinates. Now the fully detailed transformation can be done from chip pixel to diffraction coordinate along the dispersion (tg_r, or r for short) and cross-dispersion coordinate (tg_d, or just d for short), using the aspect solution to specify the position of the zero-order on the detector at any time, and all the geometric parameters necessary to compute diffraction angles of the photon relative to the grating node and pole. Photons are shown in these coordinates in Figure 4.

  • 5- Compute "first order" wavelengths: Now that diffraction angles have been determined parallel to the dispersion, it is a simple matter to apply the basic grating equation,

    • m*lambda = P*sin(tg_r)

    to determine m*lambda for each photon. Here, m is the integral diffraction order, and P is the mean period of the set of gratings (MEG, HEG, LEG). A picture in m*lambda space looks much like the above (Figure 5).

  • 6- Resolve Orders (if ACIS): ACIS provides moderate spectral resolution via a pulse-height (PH, PHA, or PI) for every photon. This resolution is enough to determine with high confidence what the spectral order is at any tg_r or tg_mlam, since only integral multiples are allowed at any given position (see the basic grating equation). In practice, one must apply a range of PI (Pulse Invariant - i.e., PHAs from different CCDs are offset and scaled to a common scale) for each order which is dependent upon energy. The first-order coordinate specifies what the minimum energy should be, and the spread in PI for any order can be determined from the CCD resolution at those energies. A sample is shown in Figure 6, in which the PI for MEG photons are shown against tg_mlam, and orders have been color-coded as determined from a CCD response. After determining the orders, m*lambda can be converted into lambda; both m and lambda are added to the event file, and this concludes Level 1.5 processing. (For HRC, we will fill the m column with +1 or -1, and the lambda column with m*lambda, since HRC has no order-sorting capability. This will allow permit identical use of analysis tools.) Since only a theoretical CCD resolution was used here, order-sorting is not ideal, but only illustrative of the process. Some chip-to-chip differences are visible, such as discontinuities in the PI and wiggles in the PI vs wavelength. These will be addressed with actual calibration results for the CCDs. Pileup is also visible in this spectrum (which was exposed for the continuum and so saturated lines) as vertical streaks.

  • 7- Bin into 1D spectra: Now that the Level 1.5 data are complete with identifiers for the part of the spectrum, the diffraction angles, first order wavelengths, orders, and wavelengths, counts spectra vs wavelength can be created. The picture below (Figure 7), shows such spectra, but not a very good example, since the data were very degraded by pileup and have not been grade filtered.
    •

Data Product

    The prototype final product is an event-list with the following columns:

TIME DOUBLE
CCD_ID INT
CHIPX INT
CHIPY INT
TDETX INT
TDETY INT
DETX INT
DETY INT
X FLOAT
Y FLOAT
PHA LONG
PI LONG
GRADE INT
FLTGRADE INT
TG_PART_MAP LONG
TG_R FLOAT
TG_D FLOAT
TG_MLAM FLOAT
TG_ORDER INT
TG_LAM FLOAT

    The Level 1.5 additions begin with "TG_PART_MAP". Some ofthese definitions are subject to change. There are currently issues pending resolution on the use of floats vs longs. A sample FITS bintable can befound in TBS.

David Huenemoerder
(617-253-4283; fax: -0861)
Center for Space Research /AXAF Science Center
MIT 37-667, Cambridge, MA 02139
dph@space.mit.edu