The use of optics to detect targets has been around for a long time. Early attempts at automatic target detection assumed target plus noise, which means that the targets were small compared to the pixel field of view and therefore unresolved. However, the advent of advanced focal plane technology has resulted in optical systems that can provide highly resolved target images. The intent of this paper is to develop a general solution for the detection of resolved targets in background clutter. We recognize that resolved targets obscure any background clutter that would have been visible if the targets were absent. An optimum detection algorithm is derived that compares a test statistic to a threshold and decides a target is present if the statistic is less than the threshold. We find that the detection performance depends upon (1) the apparent contrast rather than the signal to noise ratio and (2) is highly dependent on the background clutter to common system noise ratio. In fact, the target can still be detected even when the target contrast goes to zero provided the background clutter is greater than the common system noise. Computer simulations are shown to validate the theoretical detection and false alarm probabilities. The findings in this paper should be useful to engineers and scientists designing electro-optical and infrared sensors for finding resolved targets immersed in background-cluttered images.
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