Theoretical analysis on coherent optical super-resolution method for inspection of functional micro-structured surfaces with complex-amplitude-response distribution

Abstract

In case of in-line inspection of optical functional micro-structured surfaces with phase response as well as amplitude response, higher resolution than the diffraction limit and phase measurability are needed. We proposed a novel coherent super-resolution method named complex-amplitude-response SIM (structured illumination microscopy). An equation is derived that enables extraction of frequencies higher than the diffraction limit of the complex-amplitude response distribution of a sample from multiple acquired images, which had not been obtained previously. This equation was validated through theoretical analysis by using images calculated by numerical optical simulation that were assumed to be acquired. Numerical analyses using the derived equation and simulations of image acquisition revealed that the proposed method is able to measure phase- and amplitude-response distributions of samples with a resolution higher than the diffraction limit. It was demonstrated that the proposed method is able to separate two points at a submicron distance of 500 nm under conditions of visible light and long W.D. (NA 0.2) and measure the phase difference with a maximum error of approximately 0.03 rad (∼π/100). When the amplitude response distribution of a sample is uniform and consists only of phase responses, the structure of the sample cannot be observed by standard optical microscopy. Numerical simulations revealed that the proposed method is able to visualise such samples with fine periodic phase responses on the submicron scale (∼500 nm) beyond the diffraction limit. Furthermore, we have shown that the proposed method is able to detect phase defects in ultra-fine optical functional structures with periods of less than 100 nm, which is expected to characterise the next generation metasurfaces.