HRMA response versus energy at XRCF for on-axis point source at 
z_s = 518.16 meter from focus (paraboloid fronts at z_pf = 10.937 meter).

Effective area calculated using geometric ray trace developed in 
Mathematica, with reflectivity from atomic scattering factors from 
Henke, Gullikson, and Davis (1993, updated 1994).  Ray trace calculation 
for present results includes effects due to finite source distance at 
XRCF, but does not include finite source size, source-HRMA misalignments, 
mirror shell misalignments, figure errors, or scattering from the mirror 
surfaces.

Differential solid angle  d_omega subtended by area element d_area at 
axial distance d and radius r is 

	d_omega  =  d_area  cos( theta )  /  ( d^2 + r^2 ) 

		 =  d_area  d  /  ( d^2 + r^2 )^3/2 

Substitute effective area for d_area to get effective solid angle and 
use ( z_s - z_pf ) = 507.223 meter for d.  The mean radii of the annular 
paraboloid apertures are r = 60.6518, 48.8437, 43.1240, and 32.0553 cm 
for mirror shells 1, 3, 4, and 6.

----------------------------------------------------------------------

The columns are (1) energy in keV, (2) HRMA effective area in cm^2 at 
XRCF for an on-axis point source at z = 518.16 meters, (3) effective 
solid angle subtended by the HRMA for such a source.

 E ( keV )       A_eff     Eff solid angle
  0.02930     9.4960E+02     3.6910E-07
  0.02977     9.5072E+02     3.6953E-07
  0.03026     9.5201E+02     3.7004E-07
  0.03074     9.5305E+02     3.7044E-07
  0.03124     9.5406E+02     3.7083E-07
  0.03175     9.5509E+02     3.7123E-07
  0.03226     9.5637E+02     3.7173E-07
  0.03278     9.5773E+02     3.7226E-07
  0.03331     9.5870E+02     3.7263E-07
  0.03385     9.5921E+02     3.7283E-07
  0.03440     9.5926E+02     3.7285E-07
  0.03496     9.5914E+02     3.7281E-07
  0.03552     9.5904E+02     3.7277E-07
  0.03610     9.5865E+02     3.7261E-07
  0.03668     9.5790E+02     3.7233E-07
  0.03727     9.5696E+02     3.7196E-07
  0.03788     9.5618E+02     3.7166E-07
  0.03849     9.5530E+02     3.7132E-07
  0.03911     9.5440E+02     3.7096E-07
  0.03974     9.5314E+02     3.7048E-07
  0.04039     9.5169E+02     3.6991E-07
  0.04104     9.5023E+02     3.6934E-07
  0.04170     9.4890E+02     3.6883E-07
  0.04238     9.4734E+02     3.6822E-07
  0.04306     9.4579E+02     3.6762E-07
  0.04376     9.4381E+02     3.6685E-07
  0.04447     9.4190E+02     3.6610E-07
  0.04519     9.3955E+02     3.6519E-07
  0.04592     9.3709E+02     3.6423E-07
  0.04666     9.3347E+02     3.6283E-07
  0.04741     9.2821E+02     3.6078E-07
  0.04818     9.2066E+02     3.5785E-07
  0.04896     9.1749E+02     3.5662E-07
  0.04975     9.2093E+02     3.5795E-07
  0.05056     9.2558E+02     3.5976E-07
  0.05138     9.2754E+02     3.6052E-07
  0.05221     9.2877E+02     3.6100E-07
  0.05305     9.2960E+02     3.6132E-07
  0.05391     9.3020E+02     3.6156E-07
  0.05478     9.3062E+02     3.6172E-07
  0.05567     9.3090E+02     3.6183E-07
  0.05657     9.3104E+02     3.6188E-07
  0.05748     9.3104E+02     3.6188E-07
  0.05841     9.3070E+02     3.6175E-07
  0.05936     9.2986E+02     3.6143E-07
  0.06032     9.2894E+02     3.6107E-07
  0.06129     9.2845E+02     3.6088E-07
  0.06228     9.2808E+02     3.6073E-07
  0.06329     9.2812E+02     3.6075E-07
  0.06431     9.2937E+02     3.6123E-07
  0.06535     9.3148E+02     3.6206E-07
  0.06641     9.3406E+02     3.6306E-07
  0.06749     9.3717E+02     3.6427E-07
  0.06858     9.4091E+02     3.6572E-07
  0.06969     9.4401E+02     3.6692E-07
  0.07081     9.4721E+02     3.6817E-07
  0.07196     9.5031E+02     3.6937E-07
  0.07312     9.5271E+02     3.7031E-07
  0.07431     9.5478E+02     3.7111E-07
  0.07551     9.5649E+02     3.7178E-07
  0.07673     9.5805E+02     3.7238E-07
  0.07797     9.5944E+02     3.7292E-07
  0.07923     9.6069E+02     3.7341E-07
  0.08051     9.6169E+02     3.7380E-07
  0.08181     9.6233E+02     3.7405E-07
  0.08314     9.6221E+02     3.7400E-07
  0.08448     9.6231E+02     3.7404E-07
  0.08585     9.6246E+02     3.7410E-07
  0.08724     9.6262E+02     3.7416E-07
  0.08865     9.6275E+02     3.7421E-07
  0.09008     9.6284E+02     3.7424E-07
  0.09154     9.6279E+02     3.7423E-07
  0.09302     9.6240E+02     3.7407E-07
  0.09452     9.6204E+02     3.7394E-07
  0.09605     9.6173E+02     3.7381E-07
  0.09761     9.6139E+02     3.7368E-07
  0.09919     9.6106E+02     3.7355E-07
  0.10079     9.6069E+02     3.7341E-07
  0.10242     9.6033E+02     3.7327E-07
  0.10408     9.5996E+02     3.7312E-07
  0.10576     9.5952E+02     3.7296E-07
  0.10747     9.5897E+02     3.7274E-07
  0.10921     9.5829E+02     3.7248E-07
  0.11098     9.5721E+02     3.7206E-07
  0.11277     9.5583E+02     3.7152E-07
  0.11459     9.5438E+02     3.7096E-07
  0.11645     9.5274E+02     3.7032E-07
  0.11833     9.5049E+02     3.6944E-07
  0.12025     9.4754E+02     3.6830E-07
  0.12219     9.4463E+02     3.6717E-07
  0.12417     9.4162E+02     3.6600E-07
  0.12618     9.3824E+02     3.6468E-07
  0.12822     9.3404E+02     3.6305E-07
  0.13029     9.2959E+02     3.6132E-07
  0.13240     9.2520E+02     3.5961E-07
  0.13454     9.2068E+02     3.5786E-07
  0.13671     9.1610E+02     3.5608E-07
  0.13892     9.1124E+02     3.5419E-07
  0.14117     9.0604E+02     3.5217E-07
  0.14346     9.0038E+02     3.4997E-07
  0.14578     8.9491E+02     3.4784E-07
  0.14813     8.8944E+02     3.4572E-07
  0.15053     8.8410E+02     3.4364E-07
  0.15296     8.7879E+02     3.4157E-07
  0.15544     8.7365E+02     3.3958E-07
  0.15795     8.6852E+02     3.3758E-07
  0.16051     8.6360E+02     3.3567E-07
  0.16310     8.5875E+02     3.3379E-07
  0.16574     8.5427E+02     3.3205E-07
  0.16842     8.5020E+02     3.3046E-07
  0.17115     8.4657E+02     3.2905E-07
  0.17392     8.4263E+02     3.2752E-07
  0.17673     8.3871E+02     3.2600E-07
  0.17959     8.3468E+02     3.2443E-07
  0.18249     8.3057E+02     3.2283E-07
  0.18544     8.2626E+02     3.2116E-07
  0.18844     8.2227E+02     3.1961E-07
  0.19149     8.1867E+02     3.1821E-07
  0.19459     8.1554E+02     3.1699E-07
  0.19773     8.1256E+02     3.1583E-07
  0.20093     8.0968E+02     3.1471E-07
  0.20418     8.0687E+02     3.1362E-07
  0.20748     8.0430E+02     3.1262E-07
  0.21084     8.0185E+02     3.1167E-07
  0.21425     7.9972E+02     3.1084E-07
  0.21772     7.9792E+02     3.1014E-07
  0.22124     7.9653E+02     3.0960E-07
  0.22482     7.9513E+02     3.0906E-07
  0.22845     7.9376E+02     3.0852E-07
  0.23215     7.9241E+02     3.0800E-07
  0.23590     7.9131E+02     3.0757E-07
  0.23972     7.9040E+02     3.0722E-07
  0.24359     7.9011E+02     3.0711E-07
  0.24754     7.9047E+02     3.0725E-07
  0.25154     7.9082E+02     3.0738E-07
  0.25561     7.9046E+02     3.0724E-07
  0.25974     7.8990E+02     3.0703E-07
  0.26394     7.8917E+02     3.0674E-07
  0.26821     7.8840E+02     3.0644E-07
  0.27255     7.8756E+02     3.0612E-07
  0.27696     7.8673E+02     3.0579E-07
  0.28144     7.8579E+02     3.0543E-07
  0.28599     7.8492E+02     3.0509E-07
  0.29062     7.8408E+02     3.0476E-07
  0.29531     7.8320E+02     3.0442E-07
  0.30009     7.8209E+02     3.0399E-07
  0.30495     7.8092E+02     3.0353E-07
  0.30988     7.7956E+02     3.0301E-07
  0.31489     7.7800E+02     3.0240E-07
  0.31998     7.7624E+02     3.0172E-07
  0.32516     7.7473E+02     3.0113E-07
  0.33042     7.7331E+02     3.0058E-07
  0.33576     7.7201E+02     3.0007E-07
  0.34119     7.7077E+02     2.9959E-07
  0.34671     7.6965E+02     2.9915E-07
  0.35232     7.6866E+02     2.9877E-07
  0.35802     7.6802E+02     2.9852E-07
  0.36381     7.6762E+02     2.9836E-07
  0.36969     7.6708E+02     2.9816E-07
  0.37567     7.6635E+02     2.9787E-07
  0.38175     7.6561E+02     2.9759E-07
  0.38792     7.6482E+02     2.9728E-07
  0.39420     7.6408E+02     2.9699E-07
  0.40057     7.6333E+02     2.9670E-07
  0.40705     7.6267E+02     2.9644E-07
  0.41364     7.6210E+02     2.9622E-07
  0.42033     7.6188E+02     2.9613E-07
  0.42712     7.6202E+02     2.9619E-07
  0.43403     7.6215E+02     2.9624E-07
  0.44105     7.6193E+02     2.9615E-07
  0.44819     7.6160E+02     2.9603E-07
  0.45544     7.6115E+02     2.9585E-07
  0.46280     7.6068E+02     2.9567E-07
  0.47029     7.6013E+02     2.9545E-07
  0.47789     7.5958E+02     2.9524E-07
  0.48562     7.5898E+02     2.9501E-07
  0.49348     7.5841E+02     2.9479E-07
  0.50146     7.5781E+02     2.9455E-07
  0.50957     7.5727E+02     2.9434E-07
  0.51781     7.5672E+02     2.9413E-07
  0.52619     7.5626E+02     2.9395E-07
  0.53470     7.5585E+02     2.9379E-07
  0.54335     7.5560E+02     2.9369E-07
  0.55213     7.5567E+02     2.9372E-07
  0.56107     7.5645E+02     2.9403E-07
  0.57014     7.5775E+02     2.9453E-07
  0.57936     7.5849E+02     2.9481E-07
  0.58873     7.5889E+02     2.9497E-07
  0.59825     7.5920E+02     2.9509E-07
  0.60793     7.5932E+02     2.9514E-07
  0.61776     7.5941E+02     2.9517E-07
  0.62776     7.5936E+02     2.9515E-07
  0.63791     7.5930E+02     2.9513E-07
  0.64823     7.5912E+02     2.9506E-07
  0.65871     7.5895E+02     2.9500E-07
  0.66936     7.5867E+02     2.9489E-07
  0.68019     7.5843E+02     2.9479E-07
  0.69119     7.5807E+02     2.9465E-07
  0.70237     7.5776E+02     2.9453E-07
  0.71373     7.5735E+02     2.9437E-07
  0.72528     7.5701E+02     2.9424E-07
  0.73701     7.5655E+02     2.9406E-07
  0.74893     7.5619E+02     2.9392E-07
  0.76104     7.5572E+02     2.9374E-07
  0.77335     7.5537E+02     2.9360E-07
  0.78586     7.5490E+02     2.9342E-07
  0.79857     7.5463E+02     2.9331E-07
  0.81149     7.5421E+02     2.9315E-07
  0.82461     7.5411E+02     2.9311E-07
  0.83795     7.5384E+02     2.9301E-07
  0.85150     7.5433E+02     2.9320E-07
  0.86527     7.5583E+02     2.9378E-07
  0.87927     7.6106E+02     2.9581E-07
  0.89349     7.5980E+02     2.9533E-07
  0.90794     7.5946E+02     2.9519E-07
  0.92263     7.5941E+02     2.9517E-07
  0.93755     7.5959E+02     2.9524E-07
  0.95271     7.5976E+02     2.9531E-07
  0.96812     7.5991E+02     2.9537E-07
  0.98378     7.6001E+02     2.9541E-07
  0.99969     7.6012E+02     2.9545E-07
  1.01586     7.6024E+02     2.9550E-07
  1.03229     7.6053E+02     2.9561E-07
  1.04899     7.6073E+02     2.9569E-07
  1.06596     7.6088E+02     2.9574E-07
  1.08320     7.6095E+02     2.9577E-07
  1.10072     7.6096E+02     2.9578E-07
  1.11852     7.6091E+02     2.9576E-07
  1.13661     7.6081E+02     2.9572E-07
  1.15500     7.6064E+02     2.9565E-07
  1.17368     7.6043E+02     2.9557E-07
  1.19266     7.6016E+02     2.9547E-07
  1.21195     7.5984E+02     2.9534E-07
  1.23155     7.5948E+02     2.9520E-07
  1.25147     7.5912E+02     2.9506E-07
  1.27172     7.5875E+02     2.9492E-07
  1.29229     7.5836E+02     2.9477E-07
  1.31319     7.5788E+02     2.9458E-07
  1.33443     7.5731E+02     2.9436E-07
  1.35601     7.5666E+02     2.9410E-07
  1.37794     7.5591E+02     2.9381E-07
  1.40023     7.5506E+02     2.9348E-07
  1.42288     7.5410E+02     2.9311E-07
  1.44589     7.5304E+02     2.9270E-07
  1.46928     7.5188E+02     2.9225E-07
  1.49304     7.5060E+02     2.9175E-07
  1.51719     7.4924E+02     2.9122E-07
  1.54173     7.4769E+02     2.9062E-07
  1.56667     7.4594E+02     2.8994E-07
  1.59201     7.4397E+02     2.8917E-07
  1.61776     7.4173E+02     2.8830E-07
  1.64392     7.3920E+02     2.8732E-07
  1.67051     7.3631E+02     2.8620E-07
  1.69753     7.3302E+02     2.8492E-07
  1.72499     7.2926E+02     2.8345E-07
  1.75289     7.2502E+02     2.8181E-07
  1.78124     7.2002E+02     2.7986E-07
  1.81005     7.1403E+02     2.7754E-07
  1.83932     7.0668E+02     2.7468E-07
  1.86907     6.9744E+02     2.7109E-07
  1.89930     6.8541E+02     2.6641E-07
  1.93002     6.6901E+02     2.6003E-07
  1.96124     6.4470E+02     2.5059E-07
  1.99296     6.0266E+02     2.3425E-07
  2.02520     4.8872E+02     1.8996E-07
  2.04030     8.6963E+00     3.3802E-09
  2.04050     5.8660E+01     2.2801E-08
  2.05795     2.5677E+02     9.9803E-08
  2.09124     2.8863E+02     1.1219E-07
  2.11600     1.0567E+02     4.1072E-08
  2.11620     1.2917E+02     5.0208E-08
  2.12506     2.4438E+02     9.4988E-08
  2.15943     3.0852E+02     1.1992E-07
  2.19436     3.3862E+02     1.3162E-07
  2.22985     3.5915E+02     1.3960E-07
  2.26592     3.7458E+02     1.4560E-07
  2.30257     3.8670E+02     1.5031E-07
  2.33981     3.9636E+02     1.5406E-07
  2.37766     4.0401E+02     1.5703E-07
  2.41611     4.0978E+02     1.5928E-07
  2.45519     4.1345E+02     1.6070E-07
  2.49490     4.1393E+02     1.6089E-07
  2.53526     4.0428E+02     1.5714E-07
  2.55060     3.4077E+02     1.3245E-07
  2.55080     3.1222E+02     1.2135E-07
  2.57626     3.8248E+02     1.4867E-07
  2.61793     3.9875E+02     1.5499E-07
  2.66027     4.0855E+02     1.5880E-07
  2.70330     4.1581E+02     1.6162E-07
  2.74703     4.2149E+02     1.6383E-07
  2.79146     4.2586E+02     1.6553E-07
  2.83661     4.2878E+02     1.6666E-07
  2.88249     4.2870E+02     1.6663E-07
  2.90860     4.0841E+02     1.5874E-07
  2.90880     3.9269E+02     1.5264E-07
  2.92911     4.1520E+02     1.6138E-07
  2.97648     4.2337E+02     1.6456E-07
  3.02463     4.2810E+02     1.6640E-07
  3.07355     4.3151E+02     1.6772E-07
  3.12326     4.3334E+02     1.6843E-07
  3.17360     4.2109E+02     1.6367E-07
  3.17380     4.1117E+02     1.5982E-07
  3.22511     4.2848E+02     1.6654E-07
  3.27727     4.3207E+02     1.6794E-07
  3.33028     4.3475E+02     1.6898E-07
  3.38415     4.3694E+02     1.6983E-07
  3.43888     4.3876E+02     1.7054E-07
  3.49450     4.4027E+02     1.7113E-07
  3.55102     4.4152E+02     1.7161E-07
  3.60846     4.4249E+02     1.7199E-07
  3.66682     4.4323E+02     1.7228E-07
  3.72613     4.4372E+02     1.7247E-07
  3.78640     4.4399E+02     1.7257E-07
  3.84764     4.4398E+02     1.7257E-07
  3.90987     4.4371E+02     1.7247E-07
  3.97311     4.4318E+02     1.7226E-07
  4.03738     4.4239E+02     1.7195E-07
  4.10268     4.4126E+02     1.7151E-07
  4.16903     4.3985E+02     1.7096E-07
  4.23646     4.3808E+02     1.7028E-07
  4.30498     4.3594E+02     1.6944E-07
  4.37462     4.3338E+02     1.6845E-07
  4.44537     4.3038E+02     1.6728E-07
  4.51727     4.2687E+02     1.6592E-07
  4.59033     4.2282E+02     1.6434E-07
  4.66458     4.1815E+02     1.6253E-07
  4.74003     4.1280E+02     1.6045E-07
  4.81669     4.0669E+02     1.5808E-07
  4.89460     3.9977E+02     1.5539E-07
  4.97377     3.9199E+02     1.5236E-07
  5.05421     3.8335E+02     1.4900E-07
  5.13596     3.7393E+02     1.4534E-07
  5.21903     3.6391E+02     1.4145E-07
  5.30344     3.5358E+02     1.3743E-07
  5.38922     3.4322E+02     1.3341E-07
  5.47639     3.3307E+02     1.2946E-07
  5.56497     3.2322E+02     1.2563E-07
  5.65498     3.1370E+02     1.2193E-07
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