MECS calibration parameters (cont. ; part 10/19) : non-gaussian tail

[continues from 4.7.1]

4.7.2 Low energy tail

A monochromatic line gives rise not only to a Gaussian line, but shows also a tail on the low energy side (extending below 1 keV where the Be window is not transparent). The physical reason is that part of the electrons generated by an X-ray may attach to the Be window itself instead of propagating in the drift region (see GSPC operation).

Fig. 4.7.2-I : Example of the spread of a simulated spectrum generated by a 3 keV and 7 keV monochromatic line. The gaussian and tail components (unnormalized) are shown, as well as their (normalized) combination.

The tail is empirically modelled by a complex function (defined only above 1.255 keV) :


	T_i(E_j) = D₄ + D₅ exp( (PI-D₆)/D₇) 			if PI<D₆

	T_i(E_j) =   D₅ exp(-0.5 [3(PI-D₆)/(D₂-D₆)]²) 	 	otherwise

where the symbols are as follows :

PI indicates the i-th output channel

D₂ is the peak of the gaussian component of given energy, given by the gain relation
D₄ is computed indirectly as a function of energy as a quadratic polynomial of the Xenon absorption efficiency (3 coefficients L_1,1, L_1,2, L_1,3 necessary)
D₅ depends on other terms and is given by formula
```
     D₅ =(C/D₇)/(1-exp[(L₄-D₆)/D₇)])
```
where C is a quadratic polynomial of energy up to 8.04 keV, then remains constant (3 coefficients L_2,1, L_2,2, L_2,3 necessary)
D₆ is given by a linear function of energy in two separate stretches (of same slope L_5,3, but with two different intercepts L_5,1 and L_5,2 below and above the Xenon L-edge)
D₇ is computed via the gain relation from a single coefficient L₃
L₄ is an independent coefficient giving the start channel above which the tail is defined

The values of the coefficients L are kept in files m{1,2,3}_tail.coeff
The notation L_i,j refers to the i-th line and j-th position in line in the file.

Fig. 4.7.2-II : Energy dependency of tail parameters D₄ and D₅. The values for the different MECS units (colours) are quite similar. Note that coefficients are meaningless (dotted line) below 1.25 keV where the tail is not defined.

Additional representations of simulated spectra can be obtained via the following form. Data is always generated for the three MECS units.

Select energy keV, representation and type of spectral component

Gaussian component (unnormalized)
Tail component (unnormalized)
Their combination (normalized)

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