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Appendix 9 Geometric Factor Study for the Deflected and Unscattered Electrons of HISCALE (Buckley MS Thesis continued)

A9.2  Chapter 2 - The Geometric Factor and Fluxes

Space scientists are interested in particle fluxes for a given particle type at a given energy and location in time and space.  This integral flux J is therefore a function of energy E, particle type a, position x, and time t.

Raw data comes in the form of R counts/second.  Space scientists need to convert these count rates into particle fluxes.  Part of this conversion involves the geometric factor G.  The raw count rate R is related to the intensity I of the particle stream by G, the gathering power of the telescope involved:

R =GI

For a telescope which is able to distinguish a single particle species over a given energy passband DE, we have for I isotropic that G = G, hence

R = GI₀,      I₀ Isotropic intensity.

Figure A9-3 Calculating G for simple geometries.

To calculate this G for a simple geometry, imagine that you have a telescope with a detector near the bottom, as in Figure A9-3.  The detector has surface area S, and is broken up into surface elements ds.  An excellent formulation in calculating G for simple geometries is given by J. D. Sullivan₂

where W is the domain of solid angle w, which is determined from the telescope geometry, dw=dfdcosq, and ds×r is the effective element of area looking into w.

So, roughly speaking we can think of G as being an area times an effective solid angle W:

G=DADW

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