Fluctuation microscopy: a probe of medium range order

Fluctuation microscopy is a hybrid diffraction-imaging technique that detects medium range order in amorphous materials by examining spatial fluctuations in coherent scattering. These fluctuations appear as speckle in images and diffraction patterns. The volume of material contributing to the speckle is determined by the point-spread function (the resolution) of the imaging optics and the sample thickness. The spatial periodicities being probed are related to the diffraction vector. Statistical analysis of the speckle allows the random and non-random (ordered) contributions to be discriminated. The image resolution that gives the maximum speckle contrast, as determined by the normalized variance of the image intensity, is determined by the characteristic length scale of the ordering. Because medium range ordering length scales can extend out to about the tenth coordination shell, fluctuation microscopy tends to be a low image resolution technique. This review presents the kinematical scattering theory underpinning fluctuation microscopy and a description of fluctuation electron microscopy as it has been employed in the transmission electron microscope for studying amorphous materials. Recent results using soft x-rays for studying nanoscale materials are also presented. We summarize outstanding issues and point to possible future directions for fluctuation microscopy as a technique.