We present a new design of a fast-neutron camera based on SiPM array readout. This design has advantages over previous optical-readout designs, such as compactness and modularity. In this Part I contribution we evaluate by Geant4 Monte-Carlo simulations the hierarchy and neutron-energy-dependence of the contribution of various fast-neutron interactions and secondary processes to the creation of light and their influence on the intrinsic spatial resolution and radiographic contrast in a 200 × 200 × 50 mm3 organic scintillator screen. Specifically, the contribution of proton recoils, delta electrons, carbon recoils, high-energy electrons, positrons, alpha particles and Cherenkov radiation to the total light and their influence on the intrinsic spatial resolution was evaluated in the 2.5–14-MeV neutron energy range. In a 50-mm-thick scintillator camera the limiting intrinsic spatial resolution was about 450 μm for 14-MeV neutrons and appreciably better for lower neutron energies.