Low-energy neutral atom (LENA) imaging promises to be a revolutionary tool for global imaging of space plasmas. The technical challenges of LENA detection include separating them from the intense ambient UV without losing information about their incident trajectories, quantifying their trajectories, and obtaining high-sensitivity measurements. Two techniques that have been proposed for this purpose are based on fundamentally different atomic interaction mechanisms between LENAs and a solid: LENA transmission through an ultrathin foil and LENA reflection from a solid surface. Both of these methods provide LENA ionization (for subsequent removal from the UV by electrostatic deflection) and secondary electron emission (for time-of-flight start pulse generation and/or coincidence). We present a comparative study of the transmission and reflection techniques based on differences in atomic interactions with solids and surfaces. Transmission methods are shown to be superior for secondary electron emission rather than reflection methods. Furthermore, transmission methods are shown to be sufficient for LENA imaging at LENA energies of approximately 1 keV to greater than 30 keV. A hybrid instrument using reflection from a low work function surface for LENA ionization and transmission for secondary electron emission is optimal for imaging of LENAs with energies less than approximately 1 keV.