Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope

Abstract

We demonstrate the use of an ordinary white-light microscope for the study of the q-dependent dynamics of colloidal dispersions. Time series of digital video images are acquired in bright field with a fast camera and image differences are Fourier-analyzed as a function of the time delay between them. This allows for the characterization of the particle dynamics independent on whether they can be resolved individually or not. The characteristic times are measured in a wide range of wavevectors and the results are found to be in good agreement with the theoretically expected values for Brownian motion in a viscous medium. 1Microscopy and light scattering are widely used in physics, chemistry, biology and medical laboratories to access information on the structure and dynamics of mesoscopic systems.While microscopy gives direct access to real space images, scattering techniques work in reciprocal space, where information on the structure and dynamics of the system is obtained respectively from the angular and time dependence of the scattered light intensity [1]. These two complementary techniques have in general very different experimental requirements.White light sources are usual choices in microscopy, while a certain degree of coherence of the illuminating beam is required in scattering experiments; this is usually achieved by using a laser. In the past many attempts have been made to build a scattering apparatus based on a microscope; all of these attempts involved the use of a laser as an illumination source (see for example Refs. [2-6] and references therein). In some cases special care was taken to ensure the capability to perform microscopy and scattering experiments simultaneously, thereby allowing for a powerful combination of the complementary information obtained by both techniques [2,3]. More recently, microscope-based laser Dynamic Light Scattering (DLS) experiments have been developed to study the dynamic properties of samples of biological interest, such as living macrophage and red blood cells [5,6]. In practice, due to the intrinsic difficulties in building such instruments, the use of such techniques has been restricted to those laboratories, where a sufficient expertise in the realization of optical instrumentation was at hand.In this letter, we present a conceptual scheme to interpret and analyze microscopy images that are obtained from samples containing moving entities. This technique, which we term Differential Dynamic Microscopy (DDM), does not entail any special experimental requirements, being based on the use of a standard light microscope with a normal illumination source and a digital video camera. By using the tools of Fourier Optics [7] we provide the means to access information about the sample dynamics that are equivalent to the one obtained in multi-angle dynamic light scattering (DLS) experiments [8]. We test DDM by analyzing time sequences of microscopy images obtained with an aqueous dispersion of colloidal particles with diameter 73 nm, well below the resolution limit ...

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

“…We have shown here that DDM [21], a technique that retains the simplicity and flexibility of PT in terms of experimental setup and applications, can be also used for accurate microrheology experiments probing both the translational and the rotational degrees of freedom of embedded tracer particles. We also show that PT is outperformed by DDM in bright-field DDM experiments probing translational dynamics as well as in p-DDM experiments probing rotational motion.…”

“…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…”

“…Almost ten years ago, the usefulness of a technique named differential dynamic microscopy (DDM) was demonstrated for the characterization of the translational dynamics of colloidal suspensions of particles [21]. One of the main features of DDM is that it lies somehow between PT and DLS.…”

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“…Images are processed using a home-written code (MATLAB; Mathworks) based on Fourier analysis as explained in ref. 46. This yields the decorrelation time τ as a function of the wave vector q.…”

Fast, high-throughput measurement of collective behaviour in a bacterial population

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