Optical computation of Laplace operator using Pancharatnam-Berry lens of large focal length

Abstract

We propose an optical Laplace operator consisting of a large-focal-length Pancharatnam-Berry lens placed on the Fourier plane of an optical imaging system and sandwiched with two orthogonal linear polarizers. Theoretical analysis reveals that the isotropic second-order differentiation derives from the quadratic phase attached to the left-handed and right-handed circularly polarized light. The Pancharatnam-Berry lens made of liquid crystal with high transmittance and diffraction efficiency is integrated into different imaging systems to realize edge detection for both amplitude and phase objects, and the results conform to the theory well. This work paves the way to implement Laplace operator in practical applications such as image processing and high-contrast microscopy.