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The optical memory effect is a well-known type of tilt/tilt wave correlation that is observed in coherent fields, allowing control over scattered light through thin and diffusive materials. Here we show that the optical memory effect is a special case of a more general class of combined shift/tilt correlations occurring in media of arbitrary geometry. We experimentally demonstrate the existence of these correlations, and provide an analytical framework that allows us to predict and understanddoi:10.1364/optica.4.000886 fatcat:ta5p2e72lfc3hmgvzuzjpu4mzu