Edge detector tolerant to object defocusing

Different methods for edge extraction have been studied in the past years. In a recent paper we have presented a rotation-invariant edge extractor based on a spiral phase filter placed in the frequency plane of a convergent correlator. In this architecture, the axial position of the output plane strongly depends on the axial position of the object. This condition limits the processing of three dimensional objects, because only a narrow axial region of the object would be correctly imaged to the output. The other axial regions of the target yield defocused results. Likewise, a rather small axial misalignment of planar scenes could produce completely inaccurate correlations. Besides, annular pupils have been widely used to regulate the depth of focus (DOF) and the transversal resolution of optical systems. In this paper we present a novel filter that combines the advantages of a spiral phase-based edge extractor and those of an axial-apodizing annular pupil. This design allows edge extraction of objects in a widened axial range. Numerical simulations and experimental results that demonstrate edge extraction with improved tolerance to defocusing are presented.