Enclosed Count Fractions ------------------------ These data parameterize the Chandra PSF using circles. The circle parameters are a function of energy, off-axis angle, azimuth, and enclosed count fraction (ECF). The ECF is simply the fraction of the total number of counts contained within a given circle. The ECF is measured in a plane perpendicular to the telescope's optical axis. Determination of the circles ---------------------------- The circles are generated from simulations of the PSF using SAOsac. The center of the rays is determined by an iterative sigma-clipping algorithm. This center is used for all of the enclosing circles. The rays are then sorted by their distance from this center, and the radii which enclose the fractions in the list of ECFs are interpolated. File Format ----------- The FITS file structure follows the general directions of the OGIP Calibration Memo CAL/GEN/92-020 for radial encircled energy functions (REEF). That document has several inconsistencies which prevent following it to the letter. Here's a practical summary of the format. The FITS file contains a binary table HDU, consisting of a single row. Each column in the row is a vector. The columns ECF, THETA, PHI, ENERGY, ENERG_LO, and ENERG_HI contain 1D vectors. The columns RADIUS, RADIUS_SMIN and RADIUS_SMAX contain 4D matrices. The matrix shape is given by the TDIMm parameters. The order in which the coordinates vary, from most frequently to least frequently, is given by the nCTYPEm keywords (summarized in CREFm). The input parameters are specified in the 1D vectors. To determine the ranges of input parameters, simply display the contents of the ECF, THETA, PHI, and ENERGY columns. dmlist hrmaD1996-12-20hrci_ecf_N0002.fits'[cols theta,phi,energy,ecf]' \ opt=array The contents of the columns are as follows: ECF: The enclosed count fraction; the fraction of the total counts in the circle. ENERG_LO, ENERG_HI: The energy range in keV for which the circles are valid. ENERGY: The midpoint of the valid energy range, in keV. THETA: The off-axis angle of the source in minutes of arc. PHI: The azimuthal angle of the source in degrees (oriented in Mirror Spherical Coordinates) RADIUS: The radius of the circle in seconds of arc. The column RADIUS is the median of the 100 realizations for the values of ECF, THETA, PHI, and ENERGY. RADIUS_SMIN and RADIUS_SMAX contain the values bounding the central 68.26% of the realizations. These indicate the variation in the radius due to randomly sampling the model. No systematic errors are yet included. To determine the ranges of parameters, simply display the contents of the ECF, THETA, PHI, and ENERGY columns. dmlist hrmaD1996-12-20hrci_ecf_N0002.fits'[cols theta,phi,energy,ecf]' \ opt=array Usage ----- The parameterization is given as RADIUS(ECF,THETA,PHI,ENERGY) How to use this mess? Look up your favorite values in the ECF, THETA, PHI, ENERG_LO/ENERG_HI vectors and save their indices into those vectors. Use those indices to calculate an offset into the RADIUS matrix. C: If you read the 4D matrices directly in C, the matrix looks like this: RADIUS[iENERGY][iPHI][iTHETA][iECF] Or, dealing with pointers: radius + iECF + iTHETA * ( nECF ) + iPHI * ( nECF * nTHETA ) + iENERGY * ( nECF * nTHETA * nPHI ) Fortran: RADIUS(iECF,iTHETA,iPHI,iENERGY) PDL: After reading in the RADIUS data, reshape it: $radius->reshape( $ecf->nelem, $theta->nelem, $phi->nelem, $energy->nelem); and read it in: $radius($iECF, $iTHETA, $iPHI, $iENERGY); # using NiceSlice $radius->at($iECF, $iTHETA, $iPHI, $iENERGY); # standrad PDL