Reimer L, Gentsch P
Ultramicroscopy. 1975 Jul;1(1):1-5. doi: 10.1016/s0304-3991(75)80003-9.
The chromatic error is calculated using our scattering cross sections obtained from contrast experiments and a distribution function of energy losses from Misell and Burge. The assumed ratio of total inelastic and elastic cross sections was 3.5. Monte-Carlo calculations were performed for the multiple scattering problem of thick carbon specimens using these values for single scattering. As expected, a minimum confusion of the chromatic error disc exists at underfocusing. The half width broadening of an edge is in good agreement with experiments at 100 keV if the experimental method of determining the half width is also taken into consideration theoretically. The lateral displacements of electron paths normal to the direction of the electron incidence, which give rise to poorer resolution at the bottom of a thick specimen in scanning transmission electron microscopy, cannot simply be added to the chromatic error in the normal mode of transmission electron microscopy. Calculations show that there is no difference in edge resolution at 100 keV to be expected, in agreement with experiment. With increasing energy, the influence of beam broadening increases relative to the chromatic error. Considering only the chromatic error (1-2 nm), at 1 MeV and optimum defocus details on the top of a 2 micron specimen will be imaged with nearly twice the value of edge half width as they will at the bottom.
色差是利用我们从对比度实验中获得的散射截面以及米塞尔和伯奇的能量损失分布函数来计算的。假设的总非弹性和弹性截面之比为3.5。使用这些单散射值对厚碳样品的多重散射问题进行了蒙特卡罗计算。正如预期的那样，在欠聚焦时色差圆盘的混淆最小。如果从理论上也考虑确定半高宽的实验方法，那么在100 keV时边缘的半高宽展宽与实验结果吻合良好。在扫描透射电子显微镜中，垂直于电子入射方向的电子路径横向位移会导致厚样品底部分辨率变差，而在常规透射电子显微镜模式下，不能简单地将其加到色差中。计算表明，与实验结果一致，在100 keV时边缘分辨率预计没有差异。随着能量增加，束展宽相对于色差的影响增大。仅考虑色差（1 - 2纳米），在1 MeV且最佳散焦条件下，2微米厚样品顶部的细节成像时边缘半高宽的值将几乎是底部的两倍。
