用傅里叶角谱衍射理论推导了光子扫描隧道显微镜的标量和矢量角谱传递函数。计算表明,光子扫描隧道显微镜的角谱传递函数鲜明地分成两个区,即远场区和近场区。随着探针样品间距增大,近场区内的角谱其振幅迅速衰减,频率越高衰减越快,而相位保持不变;相反远场区内的角谱其振幅保持不变,而相位非均匀线性增加,频率越低增加越快。光子扫描隧道显微镜对近场角谱的采集能力是其突破瑞利衍射极限的关键。进一步根据角谱传递函数计算了不同样品的光子扫描隧道显微镜理论图像,分析了探针与样品的间距、探针孔径大小、照明光入射角等对光子扫描隧道显微镜成像的影响。

Analytical expressions for scalar/vector angular spectrum transfer function (scalar-/vector-ASTF) of photon scanning tunneling microscope (PSTM) were derived using Fourier angular spectrum diffraction theorem. The numerical results show that the ASTF of a PSTM consists of two distinct components, the propagating component and evanescent component. For evanescent component, their amplitudes decrease dramatically, and the higher the frequency the faster the amplitudes decreasing, while the phases remain constant as tip-sample distance d increases. For propagating component, their phases increase linearly but not uniformly with d, and the lower the frequency the faster the phases increasing, while the amplitudes remain constant. It is the ability of a PSTM to collect evanescent component that makes it possible to break through the Rayleigh diffraction limit. Based on ASTF the influence of such parameters as tip-sample distance, tip aperture diameter and the incident angle of illuminating laser beam on PSTM image has been discussed.