The Hitchhiker's Guide to Differential Dynamic Microscopy

TL;DR

DDM addresses the challenge of extracting dynamics from time-lapse microscopy by analyzing temporal fluctuations in Fourier space, bridging microscopy and light scattering. The paper surveys the theory, practical considerations, and introduces fastDDM to enable rapid, high-throughput analyses across diverse systems, including protein solutions, bacteria, microrheology, and cell monolayers. It provides a detailed, end-to-end tutorial with worked examples and publicly available datasets to facilitate adoption, and discusses how to extend DDM to 3D, non-stationary dynamics, and advanced applications. The work demonstrates that DDM can deliver quantitative dynamical information across length and time scales while lowering the barrier to entry for new users.

Abstract

Over nearly two decades, Differential Dynamic Microscopy (DDM) has become a standard technique for extracting dynamic correlation functions from time-lapse microscopy data, with applications spanning colloidal suspensions, polymer solutions, active fluids, and biological systems. In its most common implementation, DDM analyzes image sequences acquired with a conventional microscope equipped with a digital camera, yielding time- and wavevector-resolved information analogous to that obtained in multi-angle Dynamic Light Scattering (DLS). With a widening array of applications and a growing, heterogeneous user base, lowering the technical barrier to performing DDM has become a central objective. In this tutorial article, we provide a step-by-step guide to conducting DDM experiments -- from planning and acquisition to data analysis -- and introduce the open-source software package fastDDM, designed to efficiently process large image datasets. fastDDM employs optimized, parallel algorithms that reduce analysis times by up to four orders of magnitude on typical datasets (e.g., 10,000 frames), thereby enabling high-throughput workflows and making DDM more broadly accessible across disciplines.

Figures (22)

• Figure 1: a) In a DLS experiment, a monochromatic plane wave with wavevector $\mathbf{k}_\mathrm{i}$ illuminates the sample. Scattered light with wavevector $\mathbf{k}_\mathrm{s}$ is collected at angle $\theta$ in the far field using, e.g., a photomultiplier tube (PMT) or another point detector. This arrangement is effectively equivalent to detecting light in the back focal plane (BFP) of a microscope, making explicit the geometric correspondence between scattering and imaging. The scattering vector $\mathbf{Q}$ can be decomposed using $\mathbf{q}_z$ along the incident beam direction and a transverse one $\mathbf{q}$. b) In microscopy, the sample is illuminated by a monochromatic plane wave, and the objective lens (OL) of focal length $f$ and numerical aperture $\mathrm{NA_o}$ collects the scattered light. Geometrical optics maps each scattering direction to a point in the BFP, while each object point is reconstructed in the image plane. In practice, diffraction blurs the image $\psi(\mathbf{x},t)$ over a finite region determined by the point spread function $\kappa(\mathbf{x})$ [Eq. \ref{['eq:psf']}]. c) According to the Abbe–Fourier theory, an object can be represented as a superposition of sinusoidal gratings, each diffracting light into plane waves at angles $\pm\Theta$ (only $+\Theta$ shown). The lens focuses these into the BFP, and their interference reconstructs the spatial modulations in the image plane. Thus, the image is the sum of sinusoidal contributions (smeared by Eq. \ref{['eq:convo2D']}) that correspond one-to-one with modulations in the sample.
• Figure 2: First row: Bright-field microscopy images of Brownian particles (diameter $240~ \mathrm{\,nm}$) acquired at different times. Each panel spans approximately $166~ \mathrm{\,\mu m}$. The weak signal $\psi$ from the particles is masked by a dominant static contribution $i_{0}$ from dust and other imperfections on optical surfaces and the detector. Second row: Difference images $\Delta i(\mathbf{x},t,\Delta t)$ obtained by subtracting a reference image acquired at $t=0$ from subsequent frames at delays $\Delta t=0.1,1.0,10.0$ s. This subtraction removes $i_0$ and highlights the contribution from particle motion. The increasing contrast with $\Delta t$ reflects the Brownian displacements. The average size of the granularity (speckles) visible in the last difference image ($\Delta t=10$ s) gives an estimate of the microscope resolution, as the particle size lies below the resolution limit. Third row: Structure functions $D(\mathbf{q},\Delta t)$ computed for $\Delta t=0.1,1.0,10.0$ s, by averaging over 5980, 5800, and 4000 difference images, respectively, characterized by the same $\Delta t$ but different $t$. The contrast increases with $\Delta t$, consistent with enhanced decorrelation due to the particle dynamics. The central black cross masks processing artifacts. The white line on the color bar indicates the estimated noise floor $B$.
• Figure 3: Top row: Wide-field fluorescence (left), confocal fluorescence (center), and bright-field (right) microscopy images of fluorescent polystyrene particles suspended in water (nominal diameter $1.9~ \mathrm{\,\mu m}$, volume fraction $\phi_0 \simeq 2 \times 10^{-5}$; Fluoro-Max G0200, Thermo Scientific). These three modalities differ in how they weigh contributions along the optical axis, thus affecting the effective depth from which signal is collected. Scale bars: $32.5~ \mathrm{\,\mu m}$. Bottom row: Magnified views of regions containing two closely spaced particles. The visibility, contrast, and apparent size of the particles differ across modalities, illustrating the varying axial and transverse point spread functions. White (fluorescence) and red (bright-field) circles indicate particle positions. These differences reflect the varying axial response of each technique and motivate the formal treatment of axial averaging discussed in this section. Scale bars: $6.2~ \mathrm{\,\mu m}$.
• Figure 4: a) Structure function $d(q, \Delta t)$ (symbols) as a function of the delay time $\Delta t$ for three different values of $q$ (see legend), obtained from the analysis of the $240~ \mathrm{\,nm}$ PS particles sample of Ref. bradley2023sizing. The solid lines show the corresponding fits to Eq. \ref{['eq:dqt-model']}, as discussed in the text. b) Intermediate scattering functions $f_{R}(q, \Delta t)$ (symbols) and best fits (solid lines) derived using the same parameters as in panel a).
• Figure 5: a) Relaxation rate $\Gamma(q)$ (open symbols) as a function of wavevector $q$ for different particle sizes, as indicated in the legend. Colored dashed lines are weighted fits of the form $\Gamma(q) = D_0 q^2$, used to extract the diffusion coefficient $D_0$ and the corresponding hydrodynamic radius $R_\mathrm{h}$. The gray dashed horizontal lines mark the accessible relaxation rate range ($\gamma_T \leq \Gamma \leq \gamma_0$), while the gray vertical lines indicate the accessible wavevector window ($q_{\min} \leq q \leq q_{\max}$) for this dataset. Transparent data shows discareded data outside the reliable $q$ range by using the intersection of $D_0 q^2$ with $\gamma_T$ as a lower limit cutoff) b) Static amplitude $A(q)$ (symbols) and noise floor $B(q)$ (dashed lines) obtained from the fits in panel a. Color coding matches panel a.