taking advantage of the fact that the Gaussian and Lorentzian components entering the definition of PSF(r) can be integrated analytically in r dr.IPSF(q) = 2 pi * integral between 0 and q of PSF(r)rdr

The resulting formula (where the fraction *f* is normalized to the detector
radius *r _{det}* (FOV radius) of 15 mm) is of the form

f(E,r) = IPSF(r)/IPSF(r_{det}) IPSF(r) = IG(r) + IL(r) IG(r) = R sigma^{2}(1 - exp[ -0.5(r/sigma)^{2}]) IL(r) = r_{l}{1 - 1 / [1 + (r/r_{l})^{2}]^{m-1}} / 2(m-1)

and depends on the same four parameters *R*, *r _{l}*,

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).

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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.