Comparison of IRST systems by SNR

Infrared (IR) cameras are widely used in systems to search and track. IR search and track (IRST) systems are most often available in one of two distinct spectral bands: mid-wave IR (MWIR) or long-wave IR (LWIR). Many have compared both systems in a number of ways. The comparison included field data and analysis under different scenarios. Yet, it is a challenge to make a right decision in choosing one band over the other band for a new scenario. In some respects, the attempt is like choosing between an apple and an orange. The signal-to-noise ratio (SNR) of a system for a point-like target is one criterion that helps one to make an informed decision. The formula for SNR commonly uses noise equivalent irradiance (NEI) that requires front optics. Such formalism cannot compare two bands before a camera is built complete with front optics. We derive a formula for SNR that utilizes noise equivalent differential temperature (NEDT) that does not require front optics. The formula is further simplified under some assumptions, which identifies critical parameters and provides an insight in comparing two bands. We have shown an example for a simple case.