Modeling the absorption by the passive materials (27 Feb 2004)

Spectral Model

1.  voltage
2.  sigma         : energy resolution [channel]
3.  gain_coeff    : gain_coeff * E^gain_index [channel/keV]
4.  gain_index    : 
5.  exp_lambda    : exp( (E-main_peak)/tail_length ) [channel]
6.  exp_ratio     : the ratio of counts which comes into exponential tail from photo-absorption events
7.  norm          : total photon flux [photons/sec/cm^2]
8.  src_x         : source position
9.  src_y         :
10. src_z         :

Formulating the transmission

We formulate the transmission through the passive materials such as air, the mask, and the honeycomb under the mask etc. We need to take paticular treatment on the transmission through the edge of the lead tiles. The transmission of air should be treated separately because it only depends on the distance from the source to the detector plane and also because it is better we can take the term off for flight in batdrmgen. Then, we have the transmission as products of three functions which depends on energy, angle, and the distance. 
The transmission through air :  
t1 = exp(-air_mu*air_rho*r)
r : distance from the source to the center of the detector plane
air_rho = 1.2929E-03 [g/cm^3]
air_mu = [ {A*E^(-B)}^n + {C*E^(-D)}^n ]^(1/n) [cm^2/g]
A=5307.9
B=3.028
C=0.5715
D=0.2886
n=1.182
(valid for 10-200 keV)



The transmission through the materials except for air
t2 = exp(-other_index/cos(theta));
other_index = [ {A*E^(-B)}^n + {C*E^(-D)}^n ]^(1/n)
A=407.0
B=2.60
C=0.162
D=0.262
n=1.50


The fraction that are transmitted through the edge of the lead tile:
t3 = cos(theta)/(0.1*pb_mu*pb_rho)*(1.0-exp(-0.1*pb_mu*pb_rho/cos(theta)));
pb_rho = 11.35 [g/cm^3]
pb_mu = A*E^-B [cm^2/g]
A = 199826.0
B=2.58574
(valid for 15.86-88.0 keV)


the total transmission
total = t1*t2*(1.0-0.2*tan(theta)*(1.0-t3));

Fit result

  EXT PARAMETER               
  NO.   NAME      VALUE       
   1  voltage      2.00000e+02   constant   
   2  sigma        5.42863e+00
   3  gain_coeff   3.92733e+00
   4  gain_index   1.00604e+00
   5  exp_lambda   2.90114e+01
   6  exp_ratio    1.99260e-01
   7  norm         2.50652e+01
   8  src_x       -2.95563e+01     fixed
   9  src_y        2.07454e+02     fixed
  10  src_z        3.05493e+02     fixed

*******************************************************
reducedchisq = 17.6378 (DOF=295)
d_h->Integral(rxmin, rxmax) = 2.11458
m_h->Integral(rxmin, rxmax) = 2.08765
*******************************************************
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