PurposeThe purpose is to develop search and detection strategies that maximize the probability of detection of mine-like objects.Design/methodology/approachThe author have developed a methodology that incorporates variational calculus, number theory and algebra to derive a globally optimal strategy that maximizes the expected probability of detection.FindingsThe author found a set of look angles that globally maximize the probability of detection for a general class of mirror symmetric targets.Research limitations/implicationsThe optimal strategies only maximize the probability of detection and not the probability of identification.Practical implicationsIn the context of a search and detection operation, there is only a limited time to find the target before life is lost; hence, improving the chance of detection will in real terms be translated into the difference between success or failure, life or death. This rich field of study can be applied to mine countermeasure operations to make sure that the areas of operations are free of mines so that naval operations can be conducted safely.Originality/valueThere are two novel elements in this paper. First, the author determine the set of globally optimal look angles that maximize the probability of detection. Second, the author introduce the phenomenon of concordance between sensor images.