A technique for the in-situ localization of radioactivity is described in which the influence of γ-radiation impinging on a high-Z collimator, by which the angular response of a scintillation detector is constrained in order to identify the corresponding angular position of the radiation source, is expressed mathematically by way of a normalized sinc transform. We test this approach by examining the utility of the sinc transform to express the angular responses derived from a slot-collimated cerium bromide detector, across a variety of energy regions. Individual spectra have been acquired as a function of angle to explore how the shape of the response of the collimator-detector arrangement changes for X-rays and γ rays. A 90% improvement in localization is observed when this is defined in terms of the area described by the variance between the known location and that indicated by the response of the collimated system. This approach has the potential to improve source location accuracy and to further optimize autonomous robot exploration routines used to characterize contaminated environments associated with nuclear legacies and radiological emergencies.