The spatial resolution of microscopic images acquired via X-ray Fourier-transform holography is limited by the source size of the reference wave and by the numerical aperture of the detector. We analyze the interplay between both influences and show how they are matched in practice. We further identify, how high spatial frequencies translate to imaging artifacts in holographic reconstructions where mainly the reference beam limits the spatial resolution. As a solution, three methods are introduced based on numerical post-processing of the reconstruction. The methods comprise apodization of the hologram, refocusing via wave propagation, and deconvolution using the transfer function of the imaging system. In particular for the latter two, we demonstrate that image details smaller than the source size of the reference beam can be recovered up to the diffraction limit of the hologram. Our findings motivate the intentional application of a large reference-wave source enhancing the image contrast in applications with low photon numbers such as single-shot experiments at free-electron lasers or imaging at laboratory sources.

中文翻译：

---

在软 X 射线傅立叶变换全息术中实现衍射极限分辨率

通过 X 射线傅立叶变换全息术获得的显微图像的空间分辨率受到参考波源尺寸和探测器数值孔径的限制。我们分析了这两种影响之间的相互作用，并展示了它们在实践中是如何匹配的。我们进一步确定，在主要参考光束限制空间分辨率的全息重建中，高空间频率如何转化为成像伪影。作为解决方案，基于重建的数值后处理引入了三种方法。这些方法包括全息图的切趾、通过波传播重新聚焦和使用成像系统的传递函数去卷积。尤其是后两者，我们证明了小于参考光束源尺寸的图像细节可以恢复到全息图的衍射极限。我们的研究结果激发了有意应用大型参考波源以增强低光子数应用中的图像对比度，例如自由电子激光器的单次实验或实验室源成像。