Analyzing the Effect of the Intra-Pixel Position of Small PSFs for Optimizing the PL of Optical Subpixel Localization

Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.

Geometrical condition for observing Talbot effect in plasmonics infinite metallic groove arrays

The plasmonics Talbot effect in metallic layer with infinite periodic grooves is presented in this study. Numerical approach based on the finite element method is employed to verify the derived Talbot carpet on the non-illumination side. The groove depth is less than the metallic layer thickness; however, for specific conditions, surface plasmons polaritons(SPPs)can penetrate through grooves, propagate under the metallic layer, and form Talbot revivals. The geometrical parameters are specified via groove width, gap size, period, and wavelength, and their proper values are determined by introducing two opening ratio parameters. To quantitatively compare different Talbot carpets, we introduce new parameters such as R-square that characterizes the periodicity of Talbot images. The higher the R-square of a carpet, the more coincident with non-paraxial approximation the Talbot distance becomes. We believe that our results can help to understand the nature of SPPs and also contribute to exploring this phenomenon in Talbot-image-based applications, including imaging, optical systems, and measurements.