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 5.74644 3.0442E+02 1.1832E-07 5.83939 2.9527E+02 1.1477E-07 5.93383 2.8612E+02 1.1121E-07 6.02981 2.7677E+02 1.0758E-07 6.12733 2.6700E+02 1.0378E-07 6.22644 2.5656E+02 9.9722E-08 6.32715 2.4532E+02 9.5354E-08 6.42948 2.3334E+02 9.0698E-08 6.53348 2.2097E+02 8.5889E-08 6.63915 2.0864E+02 8.1096E-08 6.74654 1.9661E+02 7.6421E-08 6.85565 1.8484E+02 7.1846E-08 6.96654 1.7307E+02 6.7271E-08 7.07922 1.6103E+02 6.2590E-08 7.19372 1.4864E+02 5.7776E-08 7.31007 1.3628E+02 5.2971E-08 7.42831 1.2468E+02 4.8461E-08 7.54845 1.1447E+02 4.4493E-08 7.67054 1.0581E+02 4.1125E-08 7.79461 9.8487E+01 3.8281E-08 7.92068 9.2230E+01 3.5849E-08 8.04879 8.6829E+01 3.3749E-08 8.17898 8.2178E+01 3.1942E-08 8.31126 7.8206E+01 3.0398E-08 8.44569 7.4811E+01 2.9078E-08 8.58229 7.1826E+01 2.7918E-08 8.72111 6.9044E+01 2.6837E-08 8.86216 6.6247E+01 2.5750E-08 9.00550 6.3210E+01 2.4569E-08 9.15116 5.9658E+01 2.3189E-08 9.29917 5.5222E+01 2.1464E-08 9.44958 4.9418E+01 1.9208E-08 9.60242 4.2007E+01 1.6328E-08 9.75773 3.3895E+01 1.3175E-08 9.91555 2.6667E+01 1.0365E-08 10.07590 2.0876E+01 8.1143E-09 10.23890 1.6227E+01 6.3072E-09 10.40450 1.2322E+01 4.7896E-09 10.57280 8.9455E+00 3.4770E-09 10.74380 6.1166E+00 2.3775E-09 10.91760 3.9156E+00 1.5219E-09 11.09420 2.2689E+00 8.8190E-10 11.21510 3.3674E-01 1.3089E-10 11.21530 3.4454E-01 1.3392E-10 11.27360 1.3821E+00 5.3722E-10 11.45590 1.5112E+00 5.8738E-10 11.64120 1.3464E+00 5.2333E-10 11.82950 1.1391E+00 4.4274E-10 12.02080 9.4021E-01 3.6545E-10 12.21530 7.6378E-01 2.9687E-10 12.41280 6.1111E-01 2.3753E-10 12.61360 4.7567E-01 1.8489E-10 12.81760 2.8490E-01 1.1074E-10 12.82400 1.9047E-01 7.4032E-11 12.82420 1.9402E-01 7.5415E-11 13.02500 3.2814E-01 1.2754E-10 13.23560 2.8542E-01 1.1094E-10 13.41840 1.9691E-01 7.6535E-11 13.41860 1.9841E-01 7.7121E-11 13.44970 2.3513E-01 9.1394E-11 13.66720 2.1834E-01 8.4867E-11 13.88830 1.9138E-01 7.4389E-11 14.11290 1.6570E-01 6.4408E-11 14.34120 1.4264E-01 5.5443E-11 14.57310 1.2242E-01 4.7582E-11 14.80890 1.0487E-01 4.0761E-11 15.04840 8.9760E-02 3.4889E-11 15.29180 7.6796E-02 2.9850E-11 15.53910 6.5703E-02 2.5538E-11 15.79040 5.6222E-02 2.1853E-11 16.04580 4.8125E-02 1.8706E-11 16.30540 4.1211E-02 1.6018E-11 16.56910 3.5311E-02 1.3725E-11 16.83710 3.0272E-02 1.1767E-11 17.10940 2.5970E-02 1.0094E-11 17.38610 2.2292E-02 8.6648E-12 17.66740 1.9147E-02 7.4423E-12 17.95310 1.6458E-02 6.3969E-12 18.24350 1.4154E-02 5.5016E-12 18.53860 1.2181E-02 4.7346E-12 18.83840 1.0490E-02 4.0773E-12 19.14310 9.0391E-03 3.5134E-12 19.45270 7.7936E-03 3.0293E-12 19.76740 6.7234E-03 2.6133E-12 20.08710 5.8037E-03 2.2558E-12 20.41200 5.0126E-03 1.9483E-12 20.74210 4.3318E-03 1.6837E-12 21.07760 3.7453E-03 1.4557E-12 21.41850 3.2399E-03 1.2593E-12 21.76500 2.8040E-03 1.0899E-12 22.11700 2.4280E-03 9.4372E-13 22.47470 2.1034E-03 8.1755E-13 22.83820 1.8230E-03 7.0856E-13 23.20760 1.5806E-03 6.1436E-13 23.58300 1.3710E-03 5.3291E-13 23.96440 1.1898E-03 4.6245E-13 24.35200 1.0329E-03 4.0146E-13 24.74590 8.9698E-04 3.4865E-13 25.14620 7.7925E-04 3.0289E-13 25.55290 6.7724E-04 2.6323E-13 25.96620 5.8877E-04 2.2885E-13 26.38610 5.1205E-04 1.9903E-13 26.81290 4.4545E-04 1.7314E-13 27.24660 3.8764E-04 1.5067E-13 27.68730 3.3743E-04 1.3115E-13 28.13510 2.9381E-04 1.1420E-13 28.59020 2.5590E-04 9.9465E-14 29.05260 2.2296E-04 8.6663E-14 29.52250 1.9428E-04 7.5515E-14 30.00000 1.7470E-04 6.7903E-14