Based on the AdS/CFT correspondence, this study employs an oscillating Gaussian source to numerically study the holographic images of an AdS black hole under f(R) gravity using wave optics. Due to the diffraction of scalar wave, it turns out that one can clearly observed the interference patten of the absolute amplitude of response function on the AdS boundary. Furthermore, it is observed that its peak increases with the f(R) parameter α but decreases with the global monopole η, frequency ω, and horizon r_h. More importantly, the results reveal that the holographic Einstein ring is a series of concentric striped patterns for an observer at the North Pole and that their center is analogous to a Poisson–Arago spot. This ring can evolve into a luminosity-deformed ring or two light spots when the observer is at a different position. According to geometrical optics, it is true that the size of the brightest holographic ring is approximately equal to that of the photon sphere, and the two light spots correspond to clockwise and anticlockwise light rays. In addition, holographic images for different values of black holes and optical system parameters were obtained, and different features emerged. Finally, we conclude that the holographic rings of the AdS black hole in modified gravities are more suitable and helpful for testing the existence of a gravity dual for a given material.

基于AdS/CFT对应关系，本研究采用振荡高斯源，利用波动光学对f ( R )重力下AdS黑洞的全息图像进行数值研究。由于标量波的衍射，可以清楚地观察到响应函数绝对幅值在AdS边界上的干涉图样。此外，观察到其峰值随着f ( R ) 参数α的增加而增加，但随着全局单极子η、频率ω和视界r _{h 的}增加而减少。更重要的是，结果表明，对于北极的观察者来说，全息爱因斯坦环是一系列同心条纹图案，它们的中心类似于泊松-阿拉戈斑。当观察者处于不同位置时，该环可以演变成光度变形环或两个光点。根据几何光学，确实最亮的全息环的尺寸约等于光子球的尺寸，并且两个光斑对应于顺时针和逆时针的光线。此外，还获得了不同黑洞值和光学系统参数的全息图像，并出现了不同的特征。最后，我们得出结论，修正重力下的 AdS 黑洞的全息环更适合且有助于测试给定材料的重力对偶是否存在。