Optical differentiation in a polar coordinate system

Optical analog computing prevails over digital computing in several aspects, such as processing speed and power consumption. Optical differentiation, as a main branch, can be particularly significant in image recognition. Various differentiators have been developed to realize the two-dimensional differentiation in Cartesian coordinates. Here, we propose the optical differentiation in a polar coordinate system, which can be factorized into the radial differentiation and the angular differentiation. Experimental results demonstrate that the variations along radial and angular directions can be, respectively, highlighted by the two kinds of differentiation, which suggests that employing polar coordinates may be more intuitive and informative in practical use. This work is probable to enrich the content of optical differentiation and extend potential applications in image recognition.