Pseudo-Cross Correlation
The smallest particle size measurable with Dynamic Light Scattering (DLS) is typically specified as 0.3 nm in diameter, primarily limited by the shortest accessible lag time of the correlator. This lower limit, however, does not consider other hardware limitations that hinder the measurement of such small sizes.
One of such limitations is the sensitivity of the instrument, defined by the ratio of the measured scattered intensity to the incident intensity at the sample. To ensure the collection of most of the scattered light, a highly efficient detection system is essential: Avalanche Photodiodes (APDs) are commonly used for this purpose thanks to their high signal-to-noise ratio and optimal time resolution. In ideal conditions, APDs are designed to generate one electronic pulse for each incident photon.
After-pulsing is an effect observed in APDs where a single detected photon can trigger subsequent electronic pulses. For high-performance detectors, the likelihood of after-pulsing is typically around 2%. This effect becomes visible in DLS experiments through the intensity correlation function (ICF): at short lag times, an artificial decay appears. This decay poses a significant challenge when measuring small particle sizes (typically below 5 nanometers in diameter) as it mixes with the true measured signal and prevents an accurate fitting of the ICF, therefore leading to inaccurate sizing results.
Figure 1: After-pulsing effect visible in the ICF through a spurious decay at low lag times.
To effectively suppress the after-pulsing effect, the Pseudo-Cross Correlation technique can be employed. The principle of this technique involves using two APDs in conjunction with a Y-shaped fiber that collects the optical signal and splits it into two parts of equal intensity.
Figure 2: Pseudo-Cross Correlation scheme
The output signals from both detectors are then cross-correlated using a correlator. The true scattering signal, which is common to both channels, will be preserved, while each detector generates a different, random after-pulsing signal. Consequently, the after-pulsing contribution is effectively suppressed, and only the true scattering signal is recovered. For the DLS user, this means that there is full reliability on the signal obtained with no after-pulsing artefacts present: all decays in the ICF will be related to true diffusion events.
Figure 3: Illustration of ICFs obtained using different correlation schemes.
By implementing the Pseudo-Cross Correlation technique, researchers can obtain more accurate measurements, especially when targeting small particle sizes. This approach improves the reliability and precision of light scattering measurements, allowing for a better understanding of nanoparticle systems.