Active imaging radiometry—not always 1/R ²

In this paper, we derive general expressions for the signal-to-noise ratio (SNR) of active imaging systems that employ range-dependent illuminator divergence control and receiver zoom configurations. Many practical systems adjust both parameters with range, causing the received focal-plane power to deviate from the standard 1/ R 2 dependence used in conventional radiometric calculations. We show that, with an appropriate choice of receiver zoom configuration, the SNR becomes independent of range, aside from range-dependent atmospheric transmission. To illustrate these principles, we analyze a laser-range-gated imaging system that implements illuminator divergence control with two receiver zoom configurations: constant-f/# and constant aperture size. We frame the analysis as a radiometric tutorial for both resolved and unresolved targets. Ultimately, we show that the optimal configuration combines range-dependent illuminator divergence control with a constant-f/# zoom configuration. These results inform design considerations and performance requirements for active imaging systems.