In this work, we extensively describe and demonstrate the structured dark-field imaging (SDFI). SDFI is a newly proposed x-ray microscopy designed for revealing the fine features below Rayleigh resolution, in which different orders of scattered x-ray photons are collected by changing the numerical aperture of the condenser. Here, the samples of single particles are discussed to extend the scope of the SDFI technique reported in a previous work (Chen J, Gao K, Ge X, et al. 2013 Opt. Lett. 38 2068). In addition, the details of the newly invented algorithm are explained, which is able to calculate the intensity of any pixel on the image plane rapidly and reliably.