The Extended Rayleigh resolution measure was introduced to give a generalized resolution measure that can be readily applied to imaging and resolving particles that have finite size. Here we make a detailed analysis of the influence of the particle size on this resolution measure. We apply this to scanning electron microscopy, under simple assumption of a Gaussian electron beam intensity distribution and a directly proportional emitted signal yield without detailed consideration of scattering internal to the sample, other than being proportional to the sample thickness. From this we produce beam-width normalized characteristics relating the particle diameter and resolution measure, while also taking consideration of the reduced signal yield that occurs from smaller particles. From our analysis of these characteristics, which we fit to experimental image data, we see that particle diameters < 0.7 times the beam 1/e full width, d, give agreement better than 10% with the true extended Rayleigh resolution. Further, we consider the signal current that must be collected to reliably distinguish between the mid-gap and peak intensity regions in the particle images. This leads to a practical guide that the signal to noise ratio (SNR) occurring between large area, continuous regions made of the same materials as the particle and background should typically be 10-30 times greater than the SNR that is desired to be achieved between the peak and mid-gap regions of just resolved adjacent identical particles having diameters in the size range 0.4-0.7d.

中文翻译：

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扫描电子显微镜中扩展瑞利分辨率测量的粒径、信噪比和光束要求

引入了扩展瑞利分辨率度量以提供一种广义分辨率度量，该度量可以很容易地应用于成像和解析具有有限尺寸的粒子。这里我们详细分析了粒度对这个分辨率测量的影响。我们将此应用于扫描电子显微镜，在高斯电子束强度分布和直接成比例的发射信号产量的简单假设下，没有详细考虑样品内部的散射，除了与样品厚度成正比。由此，我们产生了与颗粒直径和分辨率测量相关的光束宽度归一化特性，同时还考虑了较小颗粒产生的信号产率降低。从我们对这些特征的分析来看，我们将其拟合到实验图像数据中，我们看到粒子直径 < 0.7 倍于光束 1/e 全宽 d，与真正扩展的瑞利分辨率的一致性好于 10%。此外，我们考虑必须收集的信号电流，以可靠地区分粒子图像中的中间间隙和峰值强度区域。这导致了一个实用指南，即在由与粒子和背景相同的材料制成的大面积连续区域之间发生的信噪比 (SNR) 通常应比希望在两者之间实现的 SNR 大 10-30 倍。刚解析的直径在 0.4-0.7d 范围内的相邻相同颗粒的峰区和中隙区。与真实扩展瑞利分辨率的一致性优于 10%。此外，我们考虑必须收集的信号电流，以可靠地区分粒子图像中的中间间隙和峰值强度区域。这导致了一个实用指南，即在由与粒子和背景相同的材料制成的大面积连续区域之间发生的信噪比 (SNR) 通常应比希望在两者之间实现的 SNR 大 10-30 倍。刚解析的直径在 0.4-0.7d 范围内的相邻相同颗粒的峰区和中隙区。与真实扩展瑞利分辨率的一致性优于 10%。此外，我们考虑必须收集的信号电流，以可靠地区分粒子图像中的中间间隙和峰值强度区域。这导致了一个实用指南，即在由与粒子和背景相同的材料制成的大面积连续区域之间发生的信噪比 (SNR) 通常应比希望在两者之间实现的 SNR 大 10-30 倍。刚解析的直径在 0.4-0.7d 范围内的相邻相同颗粒的峰区和中隙区。