IPSF(q) = 2 pi * integral between 0 and q of PSF(r)rdrtaking advantage of the fact that the Gaussian and Lorentzian components entering the definition of PSF(r) can be integrated analytically in r dr.
The resulting formula (where the fraction f is normalized to the detector radius rdet (FOV radius) of 15 mm) is of the form
f(E,r) = IPSF(r)/IPSF(rdet)
IPSF(r) = IG(r) + IL(r)
IG(r) = R sigma2 (1 - exp[ -0.5(r/sigma)2])
IL(r) = rl {1 - 1 / [1 + (r/rl)2]m-1} / 2(m-1)
and depends on the same four parameters R, rl, sigma and m already described for the differential PSF(r). As already explained, each one of them in turn depends on energy via five coefficients
The relevant coefficients are kept in files
m{1,2,3}_psf.coeff
while
their energy dependency
is shown elsewhere.
We report here some examples of the PSF correction factor (normalized integral PSF).
Fig. 4.11.3-I : MECS integral PSF (analytical form) at 2 (solid) and 8 keV (dotted)
while additional representations of (analytically-generated) integral PSF's can be obtained via the following form.