In the electro-optical target detection community, there is considerable interest in finding quantitative measures of detection performance, such as the (Delta) (Tau) metric of contrast between a target and background. As a measure of target detectability against a variety of backgrounds, this paper discusses a new, generalized signal-to-clutter ratio (SCR), which has many attractive features, such as detailed quantification of the role of target shape, clutter spatial statistics, and interchannel correlation (including color) on detectability. Using this measure of performance, it is easy to produce plots showing detection probability in terms of false alarm rate using a standard probability curve. To provide insight, some intuitive examples are presented of the role played by spatial/frequency matrix blocks in the generalized SCR. Finally, it is shown that when certain approximations or simplifications are made, the generalized signal-to-clutter metric discussed here does specialize to other, simpler and more familiar measures of detectability.