1 Exposure Map Development Schedule items appear below starting with item 2. 1a Responsible parties: D.Huenemoerder: lead scientist J.Davis: lead programmer, support scientist A.Dobrzycki: support scientist, background map input N.Adams: support programmer J.Flanagan: programmer: pipeline 1b Related documents: see: http://space.mit.edu/ASC/Analysis/Exposure_Maps.html 1c Document history: Created: dph 7 Oct 97 2 Specify imaging mode processing: [J.Davis, dph] Define theory fo exposure map in imaging case. 2a Forward mapping (aspect histogram convolution) The forward method maps the detector-plane image onto the sky by convolving with the aspect histogram. 2b Reverse mapping (aspect history integration) The reverse method maps a sky bin onto the detector plane, and integrates over the time history. 3 Specify spectroscopic mode processing: [J.Davis, dph] Work out theory for exposure map in case with a grating in the beam. Fundamental assumption is the relation between diffraction angle and energy, which in turn relates diffraction angle to pulse-height. As for imaging case, both forward and reverse mapping methods are required. 3a ACIS-S (HETG or LETG), with orders sorted: With ACIS-S, orders can be sorted via their PHA (or PI) values. Hence, we can derive expressions for exposure maps vs diffraction order. 3b HRC-S (LETG or HETG), all orders: With HRC as the detector, we cannot resolve orders. Hence, the exposure map at any diffraction angle will have contributions from several discrete energies. (This case should probably be done per order as for ACIS-S, but the user will typically need several orders for convolving with a model spectrum.) 4 Specify aspect solution interface: [dph, J.Davis, A.Dobrzycki, N.Adams] The aspect solution gives the time history of the boresight's (optical axis) celestial coordinates, right-ascension (alpha) and declination (delta), and spacecraft roll (gamma). The "nominal aim" is the mean (or requested) on-axis celestial coordinate, and the mean roll. The aspect solution is provided as a FITS binary table. Columns of interest here are the time, alpha, dec, roll, and uncertainties on alpha, dec, and roll. Time is nominally given in increments of 0.256 seconds. The aspect solution is differential: to determine the amount of time spent at any pointing, the solution must be integrated over that interval. 4a Specify relation of (ra,dec,roll) to p^hat: [dph,davis]: John's theory uses the vector, p^, to define the direction of a hypothetical source photon in mirror angular coordinates (???), and can be thought of as specifying a particular pixel in detector coordinates (via coordinate transformations). The aspect solution give celestial coordinates and roll. The relationship between these two needs to be specified. 4a1 Note: 971006 dph: McDowell documents are not clear on how roll=0 is defined, relative to AXAF sky, mirror, and detector coordinates. 4b Prototype aspect solutions: FITS files (w/ uncertainties). [dph] The FITS file will be a subset of the aspect solution file, which contains much more information on the solution. The header will contain nominal RA, Dec, and roll [Q. Is the dither pattern specified in sky or detector coordinates?] 4b1 Create a FITS bintable holding a nominal AXAF dither pattern at nominal time intervals. Include uncertainty values, based on T.Aldcroft error budget memo values. 4b2 Create FITS bintables for other likely dither patterns: nudge mode, slew, large-amplitude dither. 4b2a Nudge Mode: Nominal dither occurs for some time period, then nominal pointing is changed ("nudged") by a larger scale (arcminutes), and nominal dither resumes. This mode is ostensibly all one Observation ID, and useful data is obtained during the nudge. 4b2b Slew mode: Pointing changes continuously in a constant direction over a large distance at a high rate. Off-axis angle affects are large. 4b2c Large amplitude dither: The dither pattern is large enough that vignetting is not constant in time for any position in the field. 4c Specify aspect histogram FITS file [dph] The "aspect histogram" is a 3D array formed by integrating the aspect solution. Each cell of the aspect histogram is the integral of the time spent in that bin. The three coordinates are RA, Dec, and roll. N.Adams is converting ROSAT code which creates an aspect histogram. There may be an appropriate data-product. 4d Generate prototype AXAF aspect histogram: [N.Adams] Use prototype AXAF aspect solution in converted ROSAT code to create an AXAF aspect histogram. 4e Incorporate aspect solution uncertainties into aspect histogram: [J.Davis, N.Adams, dph] To incorporate the "fuzziness" of the aspect solution into the aspect histogram, the aspect histogram should be convolved with the uncertainties. This means that as time integrals are accumulated into each bin, they are distributed among neighboring bins. We assume the distribution is Gaussian and specified by the aspect solution uncertainties on the coordinates. 4f specify "compressed" aspect solution, and FITS file: [dph] In some cases (light-curves, slew, nudge-mode, or large-amplitude dither), the aspect-histogram method may not be appropriate. Instead, a time-integration over the aspect solution is needed. In order to minimize the the bins in the aspect history, the history can be compressed by binning it into "stable intervals", defined as intervals over which the pointing does not change appreciably. "Appreciably" will have different scales, depending on the desired resolution of the exposure map (low-resolution for full field, high-resolution for edges). The compressed solution will be a FITS file similar in format to the aspect solution. 4g Prototype compressed aspect solution FITS file: [dph] Use specification and prototype aspect solution to generate a compressed aspect solution for use in aspect-history integration. 5 Specify and prototype exposure map input data products: [dph] Input data products are termed, "Analysis Reference Data" (ARD), and are derived from "Calibration Interface Products" (CIP). The CIP are submitted to the ASCDS Archive by calibration scientists. They may require processing to provide the ARD, which are then also submitted to the archive. 5a Specify exposure map input data products: The ARD required for exposure map processing need to be specified in detail as FITS binary or image files. Data required have been outlined in the memo, "AXAF Exposure Maps" (D.Huenemoerder, A.Dobrzycki, 7 July 1997). 5b Prototype data products: Using specifications, create prototype products, using real or ad hoc calibration data. 6 Develop forward mapping (aspect histogram convolution) method [J.Davis, N.Adams, J.Flanagan] Develop the exposure map computation via the aspect histogram convolution. 6a Imaging mode 6a1 ACIS-I 6a2 HRC-I 6a3 ACIS-S 6a4 HRC-S 6b Spectroscopy mode 6b1 HETG/ACIS-S 6b2 LETG/HRC-S 6b3 HETG/HRC-I 6b4 LETG/ACIS-S 6b5 LETG/HRC-S/HESF 7 Develop reverse mapping (aspect history integration) method: [J.Davis, N.Adams, J.Flanagan] Develop the exposure map computation via the integration over the (binned) aspect history. 7a Imaging mode 7a1 ACIS-I 7a2 HRC-I 7a3 ACIS-S 7a4 HRC-S 7b Spectroscopy mode 7b1 HETG/ACIS-S 7b2 LETG/HRC-S 7b3 HETG/HRC-I 7b4 LETG/ACIS-S 7b5 LETG/HRC-S/HESF