Optical Haar Wavelet for Extracting Edge Features along Arbitrary Directions

Abstract

A novel circular Haar wavelet (CHW), which is obtained by a radially distributed polarization state, is proposed. Optical wavelet transforms using the proposed CHW are implemented by computer simulations. The proposed CHW is shown to have remarkable features: (1) it is useful for detecting outlines of input images; (2) one polarization component is available for extracting an edge feature along a required direction; and (3) unlike the previously proposed CHW (Z. He and S. Sato: Opt. Lett. 19 (1994) 686), this one can be applied to a multi-resolution edge extraction (Y. Sheng, D. Roberge and H. H. Szu: Opt. Eng. 31 (1992) 1840).