Lens-less imaging of crystals with coherent X-ray diffraction offers some unique possibilities for strain-field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X-rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X-ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future.

中文翻译：

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散射幅度在相干 X 射线布拉格衍射成像中的应用

使用相干 X 射线衍射对晶体进行无透镜成像，为应变场表征提供了一些独特的可能性。它依赖于从用相干 X 射线照射的晶体中以数值方式检索散射幅度的相位。实际上，算法将此幅度编码为有效或布拉格电子密度的离散傅立叶变换。这篇简短的文章提出了从（连续）散射幅度的经典表达式到这个离散函数的详细路线。异构事件场的情况具体详述。当文献中未发现此类分析时，列出并定量讨论了六个假设。为其中两个提供了详细信息：结构因子在探测的倒易晶格向量附近变化的事实，和偏振因子，它沿着测量的衍射图案是不均匀的。随着 X 射线源、数据采集和分析的进步，相信在不久的将来，某些近似值将被证明是不合适的。