Dynamic Light Scattering (DLS) Particle Size Analysis

Dynamic Light Scattering (DLS) is a widely utilized, non-invasive technique for analyzing the size distribution of particles suspended in liquid, particularly within the nanometer to submicron range. It relies on measurement of time-resolved intensity fluctuations of light scattered by particles undergoing Brownian motion in a liquid medium. These fluctuations are directly influenced by particle size: smaller particles diffuse more quickly and generate rapid fluctuations, while larger particles move more slowly, resulting in slower intensity changes. Autocorrelation analysis of the scattering intensity signal enables calculation of the translational diffusion coefficients of the particles and subsequent conversion into hydrodynamic diameters using the Stokes-Einstein equation. This provides accurate, real-time characterization of particle sizes in their native liquid environment without the need for labeling or extensive preparation. DLS is highly sensitive to nanoscale particles, positioning it as an indispensable tool across numerous scientific and industrial applications including pharmaceuticals, biotechnology, nanomaterials research, food technology, and cosmetic science.

Researchers routinely employ DLS to evaluate parameters such as particle size, distribution uniformity, colloidal stability, protein aggregation, polymer behavior, macromolecular interactions, and higher-order aggregates. DLS applications include evaluating therapeutic protein stability, tracking nanoparticle behavior in drug delivery systems, analyzing emulsion uniformity in consumer products, and detecting nanoplastics in aquatic environments.

One of the key advantages of DLS is its efficiency: it requires minimal sample volume, little preparation, and delivers results within seconds. Due to its particle size resolution across multiple orders of magnitude, DLS is the diagnostic tool of choice for identifying early signs of instability or contamination, vital for ensuring sample quality and performance over time.

A Dynamic Light Scattering (DLS) setup relies on a monochromatic laser to illuminate particles in suspension. These particles exhibit random walk, stochastically driven displacements within the sample, known as Brownian motion, which cause dynamic fluctuations in the intensity of the scattered light. A photon detector collects a small fraction of scattered light from the particles at a particular angle. The most common observation angles in DLS are the side scattering angle $(\approx 90^\circ)$ and backward scattering angle $(\approx 180^\circ)$. Analyzing the temporal fluctuations in scattered light reveals particle dynamics: smaller particles move more rapidly and diffuse faster than larger ones, causing faster intensity fluctuations.

The AutoCorrelation Function (ACF) in DLS

The detector records the scattered light as a fluctuating photon count signal, reflecting random intensity variations rather than a continuous analog trace. Accessing the overall statistical dynamics requires a mathematical transformation by an autocorrelator, which computes the intensity AutoCorrelation Function (ACF), denoted as $g^{2}(\tau)$. This function quantifies the degree of similarity (also known as “correlation”) between the intensity of scattered light at any given time t with itself after a delay time $\tau$. Importantly, $g^{2}(\tau)$ does not describe one specific moment in time. Instead, it represents an average over many detection events, in simple terms: if a photon arrives now, how likely is it that another photon will arrive after a delay 𝜏, compared to random chance?

While the ACF is primarily used to calculate particle size, it also reveals important indications about sample quality and measurement conditions. Some important characteristics of the ACF are outlined below. These features are especially important in dilute samples, where small inconsistencies can have a large impact on the correlation function:

• ACF Parameters and Decay Behavior
  

  • ACF Intercept $g^{2}(\tau = 0)$ or $g^{2}(0)$: provides insight into the signal-to-noise ratio (SNR) and the presence of potential issues such as contamination, aggregation, or optical misalignment.

    • A low intercept $\bigl[ (g^{2}(\tau) - 1) < 1 \bigr]$ often suggests low particle concentration, weak scattering intensity, insufficient laser coherence, high background noise,
    • A high intercept $\bigl[ (g^{2}(\tau) - 1) > 1 \bigr]$ can occur if particle concentration is too high (potentially causing detector saturation), with multiple scattering effects in presence of various species, from dust contamination, or from optical artifacts (e.g. reflections or incorrect cuvette positioning).
    • An intercept close to zero $\bigl[ (g^{2}(\tau) - 1) \approx 0 \bigr]$ generally indicates very low particle count, over-dilution, insufficient Brownian motion signal, or poor optical alignment that causes inadequate intersection of the scattering volume by the laser.
    • An intercept near unity $\bigl[ (g^{2}(\tau) - 1) \approx 1 \bigr]$ is considered ideal and usually reflects a well-aligned setup, appropriate concentration, and a clean, high-quality signal. It often leads to reliable and reproducible size measurements.

  • Initial Decay Time: The point at which the ACF seems to begin dropping in the logarithmic plot provides an estimate of the decay rate without further fitting.

  • Decay Profile: The shape of the ACF is indicative of the sample’s dispersity. A sharp, single-exponential decay is characteristic of a monodisperse system, while a broadened or multi-exponential decay suggests polydispersity, the presence of aggregates, or even polymodal systems.

  • Decay Rate $\Gamma$: corresponds to the speed at which particles are diffusing: maller particles with higher diffusion coefficients have a larger $\Gamma$ (faster decay), while a slower decay (smaller $\Gamma$) suggests larger particles. Two samples, one with small and one with large monodisperse particles, but otherwise identical conditions (solvent, temperature, scattering angle, …) lead to the fundamental case of a perfectly exponential decay in the ACF. Calculating the actual particle size requires further computation using the environmental parameters. The general idea, however, allows a DLS user to quickly identify differences between populations in otherwise identical conditions. The value of the decay rate ( $\Gamma$) can be calculated by fitting the exponential decay to the experimental ACF curve for monodisperse suspensions (Eqn. 1). In polodisperse suspensions, the ACF corresponds to a sum or continuous distribution of exponentials so instead of a single $\Gamma$ there is a distribution of decay rates.
    

    $$g^{(2)}(\tau) - 1 \propto e^{-\Gamma \tau}$$

    Equation 1. Characteristic exponential decay of the ACF for a monodisperse suspension. $\Gamma$ corresponds to the decay rate, and $\tau$ corresponds to the lag time.

  • ACF Baseline $g^{2} ( \tau \to \infty )$: provides diagnostic information. For a stable, monodisperse sample, the ACF should decay smoothly and level off to a flat baseline. Deviations from this behavior may indicate ¹:

    • Number fluctuations, caused by low concentrations that lead to inconsistent particle counts in the scattering volume.
    • Dust or aggregates, which introduce slowly diffusing species that distort the tail of the ACF.
    • Elevated or unstable baselines, which may appear due to contaminants or unstable systems and can push the intercept artificially higher.

• From Diffusion to Particle Size
  

  • Translational diffusion coefficient $(D_{T})$: quantifies how quickly particles move within the fluid. For a monodisperse sample, it is computed from the decay rate $\Gamma$ and scattering vector q (Eqn. 2)²

    $$D_{T} = \Gamma q^{2}$$

    Equation 2. Translational diffusion coefficient for monodisperse particlest, calculated from dividing the decay rate by the scattering vector q (which depends on the wavelength of the laser, the refractive index of the solvent, and the scattering angle)

  • Hydrodynamic radius $(R_{H})$: represents the radius of a theoretical hard sphere that diffuses through the solvent at the same rate as the actual particle. It accounts not only for the particle’s core but also any solvation layer or surface-bound structures, making it an effective measure of the particle’s behavior in its native environment. It can be calculated from the diffusion coefficient, using Stokes-Einstein (Eqn. 3). Given that $R_{H}$ is inversely proportional to $D_{T}$, faster diffusing particles (larger $D_{T}$) correspond to smaller sizes (lower $R_{H}$) and slower diffusing particles (low $D_{T}$) correspond to larger particles (bigger $R_{H}$) ³

    $$R_{H} = \frac{k_{B} T}{6 \pi\eta D_{T}}$$

    Equation 3. Stokes-Einstein formulation describes the translational diffusion coefficient $D_{T}$ as a function of $k_{B}$ (Boltzmann constant), $T$ (absolute temperature in Kelvin), $\eta$ (solvent viscosity), and $R_{H}$ (Hydrodynamic Radius).

A well-represented ACF is characteristic of a correct DLS measurement and required for accurate particle size distribution estimation. By examining both the intercept and baseline, researchers can assess sample integrity, detect issues like aggregation or optical misalignment, and ensure the reliability of the resulting particle size data. To summarize, a monomodal sample (particles of a single size or a very narrow size distribution) would result in a single-exponential decay function with a smoothly converging baseline. The y-intercept indicates if enough signal is collected and the scattering measurement is appropriate. If the intercept is low or part of the decaying correlation function seems to be missing, extending the correlation interval for short and long delays can improve the results.

Advantages of Multiple Angle Measurements in Dynamic Light Scattering

In DLS, the scattering angle significantly influences sensitivity to different particle sizes. Conventional DLS instruments typically operate at a fixed detection angle, yet this parameter directly affects the ability to resolve size differences within a sample. Forward scattering $(\approx 12-30^\circ)$ maximizes signal intensity and is suited to dilute or weakly scattering samples with predominantly small particles. Side scattering at 90° provides balanced sensitivity and a good signal-to-noise ratio, while back scattering $(\approx 160-175^\circ)$ is optimal for concentrated or optically dense samples, as the short optical path length through the dispersion minimizes multiple scattering events, thereby improving data quality.

Modern multi‑angle DLS instruments collect scattering data at several angles and use Mie theory-based weighting to integrate the measurements into a single, angle-independent particle size distribution. This approach is particularly beneficial for polydisperse or complex systems, where contributions from differently sized particles vary with angle. By leveraging information from multiple scattering geometries, multi-angle DLS enhances resolution, reduces bias, and increases confidence in results ⁴. While this used to be only feasible in a time-consuming sequential angle-by-angle fashion, advances in autocorrelator technology and decreased detector cost enable budget-friendly instruments capable of flexible and simultaneous multi-angle detection. Such devices provide a significant advantage in research, development, and Quality Assurance/Quality Control (QA/QC) environments where precision and reproducibility are essential. This capability allows measurements to be tailored to the specific characteristics of the sample such as concentration, turbidity, and size distribution, yielding a more complete and reliable characterization of both monomodal and multimodal systems.

Different Analysis Methods in DLS: Cummulant and Distribution algorithms

DLS measurements usually need to go beyond the previously discussed case of an ideal monodisperse distribution. Contemporary research requires direct measurement of polydisperse solutions, meaning that they contain a mixture of particles with various sizes. Since each particle size diffuses at its own characteristic speed, the observed ACF does follow a complex function beyond the simple exponential decay case. In DLS, particle size analysis is thus typically performed using two main approaches to interpret the ACF: Cumulant Analysis and distribution-based methods such as non-negative least squares (NNLS) or the CONTIN algorithm ⁵, ⁶.

• Cumulant Analysis applies a polynomial expansion to the ACF, using the first two moments of the decay curve to determine the intensity-weighted Z-average hydrodynamic radius and the polydispersity index (PDI). This method requires no prior assumptions about particle shape, but it does assume a single-mode size distribution. As a result, it yields only average values rather than a full distribution profile. Its simplicity and robustness make it well-suited for monomodal or nearly monodisperse systems; however, its reliability decreases for multimodal or highly polydisperse samples ⁵.

• Distribution‑based algorithms extract size information by inverting the ACF to obtain a continuous distribution of decay rates from the full curve, rather than relying solely on its initial slope. Methods such as NNLS and CONTIN make no assumptions about the underlying distribution shape, making them better suited for samples with broad or multimodal size profiles where multiple peaks and sub-populations may exist. The CONTIN algorithm, in particular, can resolve subtle differences in particle populations but requires greater computational effort, is more sensitive to noise, and relies on regularization to stabilize the inversion ⁶.

In summary: Cumulant Analysis provides a rapid, straightforward solution for routine measurements on monomodal samples, while CONTIN offers detailed distribution information essential for characterizing polydisperse or multimodal systems albeit with higher computational demands. Instruments offering both approaches allow users to switch seamlessly between high-throughput quality control and in-depth, research-grade particle size analysis.

In traditional DLS systems, the AutoCorrelation Function (ACF) of the scattered light intensity is computed using dedicated hardware correlators. While this approach was historically the first commercially viable option, it imposes several limitations that can affect measurement accuracy, data reliability, and experimental efficiency. Key challenges include high sensitivity to contaminants, limited angular detection, restricted correlator capabilities, and detector afterpulsing artifacts.

• Limited Correlator Functionality and No Access to Raw Data: The hardware correlator itself can impose fundamental limitations. Many conventional designs provide only a limited number of inputs, and offer minimal flexibility for advanced or customized data processing. These restrictions hinder the application of modern analysis techniques that could enhance resolution, compensate for noise, or extract additional information from the same dataset. By design, hardware correlators process incoming photon events into the ACF prior to transmission to a computer for further processing. While this used to be necessary given limited data rates in older computing hardware, modern personal computers are more than capable to process and store each observed photon as seen on a detector. This completely prohibits the possibility to change key parameters such as correlation time intervals, or the number of correlation bins after a measurement is complete.

• Sensitivity to Contaminants and Aggregates: Conventional hardware correlators are highly susceptible to noise introduced by dust particles, large aggregates, or other contaminants. Even rare contamination events produce irreparable intensity spikes that distort the ACF, biasing the size distribution toward larger diameters and compromising the accuracy of calculated particle sizes. Such distortions may lead to incorrect assessments of sample quality or stability, potentially delaying projects, disrupting workflows, or jeopardizing product development. Mitigation strategies typically involve manual, physical filtration and repeated measurements; however, these are prone to operator error and may be unsuitable for delicate samples. Algorithmic post-processing can remove contaminated datasets, but necessitates longer acquisition times to maintain sufficient count rates, and may inadvertently discard valuable information, further impacting data integrity.

• Angle-Dependent Scattering: Many DLS measurements involve anisotropic particles or polydisperse mixtures. In such cases, scattering intensity depends strongly on the detection angle. Larger particles or specific size fractions may dominate the scattering signal at certain angles, masking weaker contributions from other populations. Traditional DLS setups frequently measure at a single fixed angle, or sequentially across a small number of angles. For complex samples, single-angle acquisition can obscure subpopulations entirely. Sequential multi-angle measurements require repeated runs, increasing the risk of contamination, temperature drift, and experimental variability while extending overall acquisition time.

• Afterpulsing in Detectors: Although afterpulsing is a detector-related artifact rather than a correlator limitation, it remains a common issue in DLS systems employing single-photon avalanche diode (SPAD) detectors, particularly under fast intensity fluctuation conditions such as backscattering geometries. Afterpulsing originates from charge carriers trapped in defect states within the SPAD’s semiconductor structure. During an avalanche event triggered by a photon, some carriers become trapped and are released later, producing false counts that mimic real photon arrivals. This effect is amplified at backscattering angles due to higher photon flux, shorter optical paths, and the potential for detector overload with concentrated samples. Uncorrected afterpulsing distorts the temporal correlation profile, degrading the accuracy of size measurements. Some instruments attempt to mitigate afterpulsing by using two SPAD detectors at the backscattering position and applying time-coincidence filtering to reject spurious counts. While effective to some extent, this approach increases system complexity and does not completely eliminate the underlying artifact.

Hardware correlators are therefore falling behind the next-generation particle sizing platforms which incorporate high-speed, high-precision timing electronics capable of timestamping individual photon arrivals. Access to raw photon data enables flexible, experiment-specific post-processing, including complete storage of photon data, advanced noise filtering and customized correlation analysis. For anisotropic or polydisperse samples, the ability to collect and process scattering data from multiple angles simultaneously is particularly valuable. Multi-angle, time-resolved acquisition improves resolution, reveals otherwise hidden size populations, and enhances robustness across diverse sample conditions and bridging the gap between high-throughput quality control and advanced particle characterization.

Swabian Instruments provides two distinct pathways for enhancing Dynamic Light Scattering (DLS) experiments.

Replacing a Conventional DLS Correlator with a Time Tagger

For researchers designing custom systems, Swabian Instruments advances existing and new DLS configurations by replacing dedicated hardware correlators with high-performance timing electronics, also known as Time Taggers.

Time Taggers were originally developed for Time-Correlated Single Photon Counting (TCSPC) owing to their ability to record photon arrival times with exceptional precision and generate histograms from timing differences. In the context of DLS, these devices timestamp each detected photon with picosecond accuracy, allowing correlation functions to be computed entirely in software. This approach delivers flexibility in data analysis in real-time or by storing these events for post-acquisition processing tailored to the specific needs of the experiment. The advatanges of Swabian Instruments’ Time Tagger as a correlator include:

• Access to Raw Data and Real-Time Analysis: The accompanying software enables rapid correlation calculations, real-time data inspection, and full access to the photon arrival stream. This capability supports the immediate detection and filtering of artifacts caused by transient intensity fluctuations from contaminants, aggregates, or particle clusters. As a result, correlation functions can be corrected in real time, improving the reliability of particle size measurements, particularly for complex or evolving samples.

• High Precision and High Throughput: Swabian Instruments Time Taggers provide picosecond timing resolution, ensuring accurate temporal characterization of the scattered signal. Their high count-rate capacity makes them well suited to the intense photon streams often encountered in scattering experiments with multiple detectors.

• Data Reliability through Multi-Angle Simultaneous Measurement: With multiple fully independent input channels, a Time Tagger can acquire signals from several scattering angles at the same time. This allows real-time consistency checks across angles, enhancing accuracy in samples with contaminants, aggregates, or broad size distributions.

Replacing a conventional correlator in a custom DLS setup with a Swabian Instruments Time Tagger provides a cost-effective and straightforward upgrade with immediate benefits in measurement flexibility, precision, and data quality. The timestamp-based, software-driven approach enables raw data storage, advanced post-processing, simultaneous multi-angle acquisition, and enhanced robustness against noise. These capabilities are particularly valuable for analyzing polydisperse, anisotropic, or aggregation-prone samples, where conventional correlator limitations can hinder accurate characterization.

DLScat: A Turn-Key Solution with the Benefits of Time Tagger 20

DLScat is a fully integrated DLS platform built around Swabian Instruments’ Time Tagger 20. In this system, the Time Tagger 20 functions as both the photon correlator and the high-precision time-stamping engine, ensuring accurate measurement of the AutoCorrelation Function (ACF) and photon arrival statistics. By combining this timing technology with carefully selected optical and detection components, DLScat is designed to deliver precise and reproducible particle size measurements. The system offers high accuracy, flexibility, and full data transparency through the following core elements:

• High-Stability Laser Source: DLScat employs a highly collimated, monochromatic laser beam to ensure consistent scattering with excellent signal-to-noise ratio (SNR) and long-term stability. Visible-wavelength lasers are often preferred for protein sizing and nanoparticle characterization, as they provide a suitable balance between scattering efficiency and sample compatibility. Users may also select custom wavelengths to match the optical properties of their samples or to minimize absorption and fluorescence background.

• High-Performance Single-Photon Detectors: The standard configuration uses fiber-coupled Single-Photon Avalanche Diodes (SPADs), offering low dead time, high quantum efficiency, and excellent temporal resolution. These properties are essential for measuring weakly scattering samples such as dilute proteins or sub-50 nm nanoparticles. DLScat is also compatible with other detector types, including photomultiplier tubes (PMTs), to accommodate experiments that require different spectral sensitivities or enhanced detection in specific wavelength ranges.

• Multi-Angle Simultaneous Dynamic Light Scattering (MASDLS) Detection: DLScat supports simultaneous measurements at multiple scattering angles to improve accuracy in size characterization and provide internal consistency checks, particularly important for polydisperse or anisotropic samples. The system can operate with up to six single-photon detectors positioned at optimized angles $(20^\circ, 69^\circ, 90^\circ, 111^\circ$, and two detectors at $157^\circ)$. This MASDLS configuration enables more reliable determination of particle size distributions and better resolution of polydispersity or structural heterogeneities in complex samples. The backscattering angle in the DLScat system includes two detectors to mitigate afterpulsing by calculating the cross correlation instead of the auto correlation value of the signal.

• Software-Defined, Real-Time Processing: Leveraging the Time Tagger 20 as an efficient, high-throughput correlator, DLScat can acquire photon arrival times from multiple detectors simultaneously and stream them to a PC. Real-time computation and visualization of ACF allow users to adjust measurement conditions on the fly. The unique DLScat software provides direct access to raw time-tagged data from each angle, supports a range of analysis algorithms, and includes tools to suppress artifacts such as intensity spikes caused by dust or transient aggregates.

• User-driven, research-enabler, easy to use: DLScat is built with the user in mind, pairing intuitive software with plug-and-play hardware so one can go from sample to high-quality data in minutes without requiring specialized training or delicate alignment. DLScat offers advanced measurement control capabilities and optimization for a variety of adjustments: tailor detector/angle configurations, choose analysis paths (cumulants or CONTIN), and access raw time tags, correlation curves, and complete metadata - no black boxes, no lock-in. Flexibility extends to optics and detection, including custom laser wavelengths and export of raw photon streams for advanced analysis. Guided by a user-driven roadmap and frequent software enhancements, DLScat is easy on day one and expandable for years.

To summarize, a conventional hardware correlator can be easily replaced with a Time Tagger, which records photon arrival times with picosecond precision and enables software-defined correlation analysis. For those seeking a complete solution, the DLScat offers a turnkey DLS platform for real-time, multi-angle, and software-defined particle size analysis; by combining the timing precision of the Time Tagger 20 with carefully engineered optical components including laser and detectors. This integration enables high-resolution measurements, improved reliability for polydisperse samples, and unrestricted access to raw experimental data, expanding the capabilities of particle size characterization techniques.

Swabian Instruments’ Time Tagger technology provides a significant leap in precision, flexibility, and data accessibility for DLS experiments. We offer two pathways to integrate this capability: (1) DLScat as a complete, turnkey platform; and (2) Integration of Time Taggers within custom-built flexible DLS setups. In both approaches, replacing a conventional DLS correlator with a Time Tagger enables low timing jitter, minimal dead time, high data transfer rates, and direct access to raw photon arrival data. These features support more accurate, versatile, and transparent measurements.

By recording time-stamped photon arrivals across multiple detection angles simultaneously, Time Taggers enable software-defined correlation functions that can be adapted to specific experimental requirements. This approach offers high temporal resolution, precise size determination, and extensive customization in both data acquisition and analysis workflows. Built-in tools for filtering out transient intensity spikes from dust or aggregates further improve data quality, enabling cleaner correlation functions and more reliable particle size distributions. This approach lays the foundation for new possibilities in DLS data interpretation and experiment control and ensures a future-proof investment for all application scenarios.

For researchers seeking an out-of-the-box solution, the customized DLScat integrates all the benefits of Time Tagger technology into a streamlined DLS solution. The system features a clear separation between electronic and optical components, enabling extensive experimental customization in a compact form-factor. The electronics module includes the Time Tagger correlator, printed circuit boards, optical attenuators, and single-photon detectors. The optical setup, which can be independently configured by the user, allows optimization for specific measurement environments. Researchers can choose laser sources at different wavelengths, adjust optical alignment, integrate temperature control, and connect their custom optical arrangement to the electronics module via optical fibers coupled to the detectors. This modular design ensures compatibility with diverse sample types and environments, including in-situ experiments alongside Small-Angle Neutron Scattering (SANS) or Small-Angle X-ray Scattering (SAXS), in-situ irradiation studies, glove box operations, and other specialized setups. The modular design results in a versatile DLS platform that retains the precision, resolution, and real-time analysis capabilities of the DLScat system while expanding its application space far beyond conventional configurations.

Whether incorporated into a customized setup or used in its turnkey DLScat configuration, Swabian Instruments’ technology extends the capabilities of particle size analysis beyond the limits of traditional DLS; enabling faster, clearer, and more reproducible insights into particle behavior.