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A study of Gaussian approximations of fluorescence microscopy PSF models

机译:荧光显微镜PSF模型的高斯近似研究

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Despite the availability of rigorous physical models of microscopy point spread functions (PSFs), approximative PSFs, particularly separable Gaussian approximations are widely used in practical microscopic data processing. In fact, compared with a physical PSF model, which usually involves non-trivial terms such as integrals and infinite series, a Gaussian function has the advantage that it is much simpler and can be computed much faster. Moreover, due to its special analytical form, a Gaussian PSF is often preferred to facilitate the analysis of theoretical models such as Fluorescence Recovery After Photobleaching (FRAP) process and of processing algorithms such as EM deconvolution. However, in these works, the selection of Gaussian parameters and the approximation accuracy were rarely investigated. In this paper, we present a comprehensive study of Gaussian approximations for diffraction-limited 2D/3D paraxialon-paraxial PSFs of Wide Field Fluorescence Microscopy (WFFM), Laser Scanning Confocal Microscopy (LSCM) and Disk Scanning Confocal Microscopy (DSCM) described using the Debye integral. Besides providing an optimal Gaussian parameter for the 2D paraxial WFFM PSF case, we further derive nearly optimal parameters in explicit forms for each of the other cases, based on Maclaurin series matching. Numerical results show that the accuracy of the 2D approximations is very high (Relative Squared Error (RSE) < 2% in WFFM, < 0.3% in LSCM and < 4% in DSCM). For the 3D PSFs, the approximations are average in WFFM (RSE approx= 16 - 20%), accurate in DSCM (RSE approx= 3 - 6%) and nearly perfect in LSCM (RSE approx= 0.3 - 0.5%).
机译:尽管可以使用严格的显微镜点扩散函数(PSF)物理模型,但在实际的显微镜数据处理中仍广泛使用近似PSF(尤其是可分离的高斯近似)。实际上,与通常涉及非平凡项(例如积分和无限级数)的物理PSF模型相比,高斯函数的优点是简单得多并且可以更快地进行计算。此外,由于其特殊的分析形式,通常更倾向于使用高斯PSF来简化理论模型的分析,例如光漂白后的荧光恢复(FRAP)过程和EM反卷积等处理算法。然而,在这些工作中,很少研究高斯参数的选择和近似精度。在本文中,我们对宽域荧光显微镜(WFFM),激光扫描共聚焦显微镜(LSCM)和磁盘扫描共聚焦显微镜(DSCM)的衍射受限2D / 3D近轴/非近轴PSF的高斯近似进行了全面研究使用德拜积分。除了为2D傍轴WFFM PSF情况提供最佳高斯参数外,我们还基于Maclaurin级数匹配,以显式形式为其他每种情况导出了近似最佳参数。数值结果表明,二维近似值的精度很高(相对平方误差(RSE)在WFFM中小于2%,在LSCM中小于0.3%,在DSCM中小于4%)。对于3D PSF,近似值是WFFM中的平均值(RSE大约= 16-20%),DSCM中的近似值(RSE大约= 3-6%)和LSCM(RSE大约= 0.3-0.5%)几乎是完美的。

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