kb/data/en.wikipedia.org/wiki/Differential_dynamic_microscopy-1.md

title	chunk	source	category	tags	date_saved	instance
Differential dynamic microscopy	2/3	https://en.wikipedia.org/wiki/Differential_dynamic_microscopy	reference	science, encyclopedia	2026-05-05T10:04:12.670972+00:00	kb-cron

Measurement speed: DDM requires extended acquisition times (minutes to hours) compared to DLS (seconds), making DLS preferred for rapid, routine measurements. Analysis time: Data analysis is computationally intensive. While traditional CPU-based processing required minutes to hours per dataset, recent GPU-accelerated implementations (e.g. fastDDM) reduce this to seconds, enabling high-throughput workflows. Commercial maturity: DLS instruments and software are mature and widely available; DDM requires custom setups or adapted commercial microscopes with specialized analysis software. Optical contrast requirement: DDM performance depends critically on signal contrast. Weakly scattering samples may require careful illumination optimization or fluorescent labeling. Dynamic range trade-offs: Lowest accessible q-values (longest length scales) correspond to very slow dynamics requiring extended acquisition; highest q-values require high magnification and frame rates, creating practical trade-offs in microscope configuration.

== Applicability and working principle == The concentration–intensity proportionality, which ensures the validity of the DDM framework, holds in two primary classes of DDM implementations: Scattering-based DDM: where image intensity arises from the interference between a strong transmitted beam and weakly scattered light, as in bright field, phase contrast, or polarized imaging. Fluorescence-based DDM: where images result from the incoherent summation of fluorescence emissions from labeled particles or structures, as in fluorescence or confocal imaging. In both classes, convolution with the PSF in real space becomes a simple product in reciprocal (Fourier) space, enabling analysis of given Fourier modes of image intensity to extract dynamics of the corresponding concentration modes. Unlike particle tracking, DDM does not require resolving individual particles, allowing characterization of the dynamics of sub-resolution features. Acquiring images in real space also offers practical advantages over traditional far-field scattering methods, such as flexible choice of imaging modality and robustness to static imaging artefacts.

== Data analysis == DDM analysis is based on the differential dynamic algorithm (DDA), developed in the context of optical fluctuation studies. In this approach, pairs of images separated by a delay

    Δ
    t
  

{\displaystyle \Delta t}

are subtracted to suppress static backgrounds and highlight changes due to motion. A two-dimensional fast Fourier transform (FFT) of the difference images yields a Fourier-space representation of the dynamics across spatial frequencies. Averaging the resulting power spectra over many image pairs with the same

    Δ
    t
  

{\displaystyle \Delta t}

(and, for isotropic samples, over wavevector directions) gives the image structure function

    D
    (
    q
    ;
    Δ
    t
    )
  

{\displaystyle D(q;\Delta t)}

. Theoretical analysis shows that for common DDM modalities

where

    f
    (
    q
    ;
    Δ
    t
    )
  

{\displaystyle f(q;\Delta t)}

is the normalized intermediate scattering function,

    I
    (
    q
    )
  

{\displaystyle I(q)}

is the static scattering intensity,

    B
    (
    q
    )
  

{\displaystyle B(q)}

is a background term associated with detection noise, and

    T
    (
    q
    )
  

{\displaystyle T(q)}

is a transfer function that depends on microscope details and imaging conditions. For simple Brownian motion, one has

    f
    (
    q
    ;
    Δ
    t
    )
    =
    exp
    ⁡
    (
    −
    D
    
      q
      
        2
      
    
    Δ
    t
    )
  

{\displaystyle f(q;\Delta t)=\exp(-Dq^{2}\Delta t)}

, where

    D
  

{\displaystyle D}

is the diffusion coefficient. Models including directed (ballistic) motion, mixtures of populations, or distributions of speeds are used for active systems such as swimming bacteria. A variant called multi-DDM analyses sub-regions of the image frame, analogous to varying the scattering volume in traditional light scattering. This variant can reveal spatial variations in dynamics and is particularly valuable for studying heterogeneous systems such as biological networks and phase-separating materials where local dynamics vary significantly with position.

== The Hitchhiker's guide to DDM == The 2025 tutorial article The Hitchhiker's guide to differential dynamic microscopy provides a step-by-step practical guide to DDM experiments and analysis, and is associated with open-source software and openly accessible datasets intended for teaching and reproducibility. An implementation of DDM analysis used in this tutorial is provided as the open-source Python package fastDDM, with documentation and source code hosted on GitHub. The fastDDM package incorporates GPU-accelerated algorithms that reduce analysis time from minutes to seconds per dataset, enabling high-throughput analysis and practical applications previously limited by computational constraints. Worked examples and tutorial notebooks are provided in a companion repository. Example open datasets used in DDM tutorials are also available via an archived dataset with DOI.