Best linear unbiased axial localization in three-dimensional fluorescent bead tracking with subnanometer resolution using off-focus images.
Best linear unbiased axial localization in three-dimensional fluorescent bead tracking with subnanometer resolution using off-focus images.
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DOI：
10.1364/josaa.26.001484
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
Zhipeng Zhang;C. Menq
中科院分区：
文献类型：
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作者：
Zhipeng Zhang;C. Menq
介绍了一种基于显微镜离焦图像的三维粒子跟踪技术。Zhang和C.- H. Menq，Appl.Opt.47，2361（2008）中描述的方法，并应用于亮场成像。本文提出了两个主要的改进的轴向定位算法的三维粒子跟踪技术。首先，它扩展的算法来测量荧光粒子的存在下，光漂白和激发变化。第二，它通过实现粒子轴向位置的最佳线性无偏估计来提高测量分辨率。与原始算法类似，首先从颗粒的离焦2D图像转换半径矢量，并通过将半径矢量与在每次实验之前自动校准的对象特定模型进行比较来估计轴向位置。虽然它是一个基于强度的方法，通过规范化的半径矢量的改进算法成为一个基于形状的方法，从而不受图像强度变化和光漂白的鲁棒性。此外，当考虑到半径向量中每个点的噪声方差及其相关性时，基于线性化模型获得了最佳线性无偏估计。结果表明，方差均衡和相关加权优化大大降低了估计方差，并导致在整个测量范围内的近均匀的定位分辨率。对估计分辨率进行了理论分析和实验验证。理论分析使得能够基于校准数据预测测量分辨率。最后，实验结果表明，该测量方法在测量精度和范围方面的性能，以及其对强度变化的鲁棒性。
A three-dimensional particle tracking technique, based on microscope off-focus images, was introduced in Z. Zhang and C.-H. Menq, Appl. Opt.47, 2361 (2008) and applied to bright-field imaging. This paper presents two major improvements to the axial localization algorithm of the 3D particle tracking technique. First, it extends the algorithm to measure fluorescent particles in the presence of photobleaching and excitation variation. Second, it enhances the measurement resolution by achieving the best linear unbiased estimation of the particle's axial position. Similarly to the original algorithm, a radius vector is first converted from the off-focus 2D image of the particle, and the axial position is estimated by comparing the radius vector with an object-specific model, calibrated automatically prior to each experiment. Although it was an intensity-based method, by normalizing the radius vectors the improved algorithm becomes a shape-based method, thus invariant to image intensity change and robust to photobleaching. Moreover, when considering the noise variance of each point in the radius vector and their correlations, the best linear unbiased estimation based on a linearized model is achieved. It is shown that variance equalization and correlation-weighted optimization greatly reduce the estimation variance and lead to near-uniform localization resolution over the entire measurement range. Estimation resolution is theoretically analyzed and validated by experiments. Theoretical analysis enables the prediction of measurement resolution based on calibration data. Finally, experimental results are presented to illustrate the performance of the measurement method in terms of measurement precision and range, as well as its robustness to intensity variation.