Digital Fourier microscopy for soft matter dynamics

Abstract

Abstract. Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensembleaveraged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterised in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such Digital Fourier Microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realised in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method.

Spatially: resolved heterogeneous dynamics in a strong colloidal gel

“…Provided that the amount of scattered light is weak compared to the incident one, moreover, the intrinsic heterodyne detection scheme of the technique (field-mixing of the transmitted and scattered radiation) ensures that the imaging formation method is linear space invariant (LSI). This means that the intensity captured by the sensor can be written as a convolution integral of the form [14] i(r, t)…”

“…In the present work, we show that the application to the study of irreversible colloid aggregation of Differential Fourier Imaging (DFI) methods [14], a novel class of optical correlation techniques combining the power of scattering and microscopy, sheds new light on irreversible aggregation, arguably one of the most extensively investigated processes in colloidal science. In fact the results we present, besides providing evidence on the evolution in time of the structure factor, on sample aging and temporal heterogeneity, and on the behavior of the correlation functions that are fully consistent with those already obtained by DLS and TRC techniques, allow for a detailed analysis of the displacement field, which confirm that rearrangement events are long-ranged and that consecutive local displacements occur on average along the same direction.…”

Differential dynamic microscopy microrheology of soft materials: A tracking-free determination of the frequency-dependent loss and storage moduli

“…The latter was also studied with LB1 particles; for this sample PT is not feasible. Standard DDM analysis was based on a repeated sequence of image subtractions and image Fourier transforms [21,23,24]. In more detail, the image structure function for all the accessible two-dimensional wave vectors q = (q x ,q y ) was calculated for a set of time delays t according to…”

“…Similar to PT, it is based on real-space movies collected in microscopy experiments. These data are treated via an image processing algorithm [22] or equivalent versions of it [23] that combines image differences and spatial Fourier transformations to obtain as a result the intermediate scattering function f (q,t) that is typically probed in DLS experiments as a function of the scattering wave vector q and time t [24]. Since its introduction, DDM has been profitably used and also extended by several groups [25][26][27][28][29][30][31][32][33][34] for a variety of applications [35].…”

Giant fluctuations and structural effects in a flocking epithelium

“…A familiar but remarkable exception is represented by thermodynamic systems close to a critical point [1], such as a binary mixture close to its consolution point. Due to the vanishingly small osmotic compressibility, concentration fluctuations become so large to be visible macroscopically, opening to the possibility of accessing important thermodynamic quantities with light scattering [2,3] or quantitative microscopy [4,5] methods. Far from equilibrium, fluctuations can become anomalously large in a generic region of the phase diagram, thus without the need of fine tuning the system close to a critical point.…”