光学亚像素定位技术常被用来计算类点目标在像素化图像探测器上的成像位置，已被广泛应用于多种光学测量领域。由于成像过程中存在不可避免的噪声，估计目标的亚像素位置存在理论精度极限，其取决于探测光子数、噪声水平、点扩散函数（PSF）半径和PSF位于的像素相位（即像素内位置）。以往研究已充分阐明了前三个参数对于定位精度极限的影响效应，但忽略了PSF像素相位信息。本文提出一种用以揭示小PSF像素相位效应的定位精度极限分析方法。为准确估计实际应用中的定位精度极限，首先提供目标有效点扩散函数（ePSF）建模方法，并应用克拉美罗下界（CRLB）理论。基于小PSF 的特性，推导了揭示任意非理想小PSF的最优精度极限和最佳像素相位的简化公式，并在真实PSF上验证了其有效性与准确性。其次，使用典型高斯PSF 作进一步推导，揭示了最优定位精度极限在PSF 高斯半径尽可能小且位于像素边缘时实现，这表明最优定位精度极限最终受限于光的衍射极限。最后，利用最大似然估计（MLE）方法拟合ePSF 模型，使真实PSF 的定位精度达到理论精度极限。本文启发了一种将探测器位置调制和PSF 工程结合的新视角，以充分利用信息论蕴含的提升潜力，为彻底理解和实现光学亚像素定位的最优精度极限奠定重要基础。

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 (ePSF) 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 ePSF 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.