  A numerical method is proposed to calculate the response of detectors
measuring particle energies from incident isotropic fluxes of electrons and
positive ions. The isotropic flux is generated by injecting particles moving
radially inward on a hypothetical, spherical surface encompassing the
detectors. A geometric projection of the field-of-view from the detectors onto
the spherical surface allows for the identification of initial positions and
momenta corresponding to the clear field-of-view of the detectors. The
contamination of detector responses by particles penetrating through, or
scattering off, the structure is also similarly identified by tracing the
initial positions and momenta of the detected particles. The relative
contribution from the contaminating particles is calculated using GEANT4 to
obtain the geometric factor of the instrument as a function of the energy. This
calculation clearly shows that the geometric factor is a strong function of
incident particle energies. The current investigation provides a simple and
decisive method to analyze the instrument geometric factor, which is a
complicated function of contributions from the anticipated field-of-view
particles, together with penetrating or scattered particles.
