From Real to Reciprocal Space: Scattering Information from Real Space Images

This chapter introduces advanced experimental techniques for deriving scattering information from spatial Fourier analysis of time-series images acquired close to the sample, as opposed to the conventional Fraunhofer regime. It begins by reinterpreting traditional scattering experiments through a Fourier optics perspective, highlighting the transition from real to reciprocal space. We then turn to speckle patterns observed in both static and dynamic scattering experiments, with a focus on those found in the deep Fresnel regime and their implications for heterodyne near-field scattering and quantitative shadowgraphy. The chapter further describes the application of Digital Fourier Microscopy, specifically Differential Dynamic Microscopy, which utilizes common commercial microscopes to extract scattering information from deep-Fresnel images obtained with a variety of contrast mechanisms, also including fluorescence. This approach presents a straightforward entry point for studying a variety of soft and biological systems, democratizing access to sophisticated scattering analysis.