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XMM-Newton Science Analysis System


rgsrmfgen (rgsrmfgen-1.10) [xmmsas_20070708_1801-7.1.0]

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Algorithm

• The following algorithm defines how certain filenames are inferred when not explicitly provided. This mechanism will work nicely when the task is run with product files from the PPS or from rgsproc. Note also that when the template filename is shorter than the PPS convention allows, an alternate convention is assumed, which the user may find more convenient under special circumstances.

  IF *newrmf
    IF *withspectrum
      template = *spectrumset
    ELSE
      template = *evlist OR *srclist
  ELSE
    template = *rmfset
  
  IF *srclist == ""
    IF template.root.length >= 10
      *srclist = template with "SRCLI_0000" substituted
    ELSE
      *srclist = "srcli." + template.suffix
  
  IF *evlist == ""
    IF template.root.length >= 10
      *evlist = template with "EVENLI0000" substituted
    ELSE
      *evlist = "evenli." + template.suffix
  
  IF *newrmf AND *rmfset == ""
    IF template.root.length >= 10
      *rmfset = template with ("RSPMAT",*order,*source) substituted
    ELSE
      *rmfset = "rspmat." + template.suffix
  

• NarrowLSF
  The following algorithm defines the narrow-feature line-spread-function for a given source position, reflection order, and incident energy bin. The large-angle-scattering distribution is not included here because, in principle at least, it could be computed on a much coarser channel grid and thus consume much less space in the output. However, OGIP does not currently support a response matrix file format with both a fine-grid matrix and a coarse-grid matrix, and so the broad and narrow line-spread-functions are currently just added together as the response matrix is assembled.

  IF GratingDataServer::beta(source,order,energy) within matrix channel space
  
    // prepare various distributions in wrap-around order for convolution
  
      // small angle scattering distribution
        D = GratingDataServer::scatteringDistribution(source,order,energy)
        (a,b) = GratingDataServer::scatteringDistributionContribs
        D[peak] += (1-a)*(1-b)
  
      // mirror point spread distribution
        IF *withmirrorpsf
          PsfDataServer::dispersionFigureDistribution(source,order,energy)
  
      // custom angular distribution
        IF *withangdist
          customFigureDistribution(order,energy)
  
      // grating bow induced misalignment distribution
        GratingDataServer::bowingFigureDistribution(source,order,energy)
  
      // geometric defocus approximation distribution
        GeometryDataServer::lsfDefocusDistribution(source,order,energy)
  
      // finite energy band broadening distribution
        GratingDataServer::broadeningDistribution(source,order,energy)
  
    // prepare the primary distribution on the matrix channel grid
  
      GratingDataServer::misalignmentFigureDistribution(source,order,energy)
  
    LSF = convolution(primary,various...)
  
  ELSE
  
    // distributions peak outside the matrix channel space, so skip
    // convolutions, and instead just use the tail of the small angle
    // scattering distribution where it overlaps the channel space
  
      LSF = GratingDataServer::scatteringDistribution(source,order,energy)
  
  // scale the LSF by the effective area
  
    IF dyneffarecorr
      scale = EffectiveAreaDataServer::realisticEffectiveAreaCurve(source,order)::area(energy)
    ELSE
      scale = EffectiveAreaDataServer::intrinsicEffectiveAreaCurve(source,order)::area(energy)
    NarrowLSF = scale * LSF
  

• BroadLSF
  The broad-feature line-spread-function is uncomplicated.

  // place the large angle scattering distribution on the matrix channel
  // grid and scale it by the effective area
  
    LSF = GratingDataServer::scatteringDistribution(source,order,energy)
    scale = EffectiveAreaDataServer::intrinsicEffectiveAreaCurve(source,order)::area(energy)
    BroadLSF = scale * LSF
  

• empiricalCrossLA
  The following calibration formula should eventually be transfered to the CAL. Input parameters are: a one-dimensional selection region in cross-dispersion channels, the source position, and the incident energy in keV.

  dpsi = source.DELTA_XDSP * pi/10800
  k = (energy * 10800) / (0.678 * pi)
  
  FOREACH span = interval [min,max] of cross-dispersion channels
    s += (atan(k*(xdsp(max+0.5)+dpsi)) - atan(k*(xdsp(min-0.5)+dpsi))) / pi
    n += span.length
  
  empiricalCrossLA = s/n
  

• The above two line-spread-functions are computed for each reflection order, including the zeroth, and combined with various response-suppressing factors to produce the output response matrix. The following algorithm shows the rough details of these calculations. Here the arrays prefixed with src and bkg refer, respectively, to the source and background spatial selection regions. In particular the arrays src.spans and bkg.spans are the selection regions themselves, converted to an image mask, and represented as a list of cross-dispersion channel intervals at each dispersion channel. Similarly the energy selection region for the reflection order of the output matrix is converted to the array called banana.

  // analyze the exposure maps within the spatial selection regions
  
  FOREACH node
    FOREACH b = dispersion channel of node
      src.exposure[node,b] = EXPMAP<node>[b] summed over src.spans[node,b]
      bkg.exposure[node,b] = EXPMAP<node>[b] summed over bkg.spans[node,b]
      D = EXPMAP<node>[b] * CanonicalCrossPsf::probability(beta(b),source)
      src.crossPSF[node,b] = D summed over src.spans[node,b]
      bkg.crossPSF[node,b] = D summed over bkg.spans[node,b]
  
  // compute the response matrix
  
  FOREACH incident energy bin
  
    // compute the loss factors specific to the narrow-featured LSF
  
    loss = 0
    FOREACH node
      FOREACH b = dispersion channel of node
        y = src.crossPSF[node,b]
        IF *bkgcorrect AND bkg.exposure[node,b]
          y -= bkg.crossPSF[node,b] * src.exposure[node,b] / bkg.exposure[node,b]
        loss[b] += y * ccdQuantumDataServer(node)::efficiency(energy)
  
    // combine with the narrow-featured LSF for each reflection order
  
    LSF = 0
    FOREACH order in [0,5]
      LSF += NarrowLSF(source,order,energy)
    response = LSF * loss
  
    // compute the loss factors specific to the broad-featured LSF
  
    loss = 0
    FOREACH node
      FOREACH b = dispersion channel of node
        y = empiricalCrossLA(src.spans[node,b],source,energy)
        IF *bkgcorrect
          y -= empiricalCrossLA(bkg.spans[node,b],source,energy)
        loss[b] += y * src.exposure[node,b] * ccdQuantumDataServer(node)::efficiency(energy)
  
    // combine with the broad-featured LSF for each reflection order
  
    LSF = 0
    FOREACH order in [0,5]
      LSF += BroadLSF(source,order,energy)
    response += LSF * loss
  
    // apply loss factors that are not specific to the type of LSF;
    // the redistribution function varies slowly with incident energy
    // and so it is recomputed no more often than every .02 keV
  
    IF redistLoss is stale
      FOREACH b = response channel
        redistLoss[b] = CanonicalRedist::spectrum(energy) summed over banana[b]
    response *= redistLoss * GratingDataServer::selfVignettingEfficiency
  
    // copy all response channels above LO_THRES to the output matrix