# DLS FAQ: The Baseline Index

Jan 26, 2021
Applications: DLS
Instruments: NanoBrook SeriesParticle ExplorerParticle Solutions

#### Introduction

The baseline index, abbreviated as BI, is a metric that can be used to quantify the impact of dust contamination on a given DLS measurement. Within the vernacular of light scattering, dust is often loosely defined, referring to any minor component too large to properly disperse, moving due to gravity, rather than Brownian motion. These large dust particles will often appear only transiently and can distort a measured autocorrelation function. A high baseline index, say BI = 10, would be expected for a perfectly dust-free sample, whereas a very low or near zero baseline index would be expected for a sample containing a noticeable amount of dust.  This nomenclature is used across all Brookhaven Instruments DLS instruments.

#### What is the baseline index?

During data analysis, the experimental autocorrelation function must be normalized. In theory, one should use the infinite time baseline Bobtained from the square of the average counts per sampling time. However, in order to eliminate the effect of a small number of very large particles, or dust, a baseline obtained from the measured correlation function at some long delay time is a better choice for normalization. During measurement, this constant background term is measured using a variety of possible methods (see below) to obtain a measured baseline, Bm. The index is defined as follows:

BI = 10 [ 1 – 100 |(Bm/B-1)| ]

If the baselines agree perfectly, the baseline index equals 10. If for instance BI ≥8, it means that the two measures of the correlation function baseline are in good agreement. If the measured baseline is 1% or more above the infinite time baseline, or the measured baseline is below the infinite time baseline, the baseline index is 0.

#### Why do baselines matter?

Proper normalization of the autocorrelation function is a prerequisite for accurately calculating an effective particle size. These normalized correlation functions are then fit by one of several models to obtain the hydrodynamic particle size. A good baseline index indicates that the data is of high quality, implying that the sample is free of dust. Note that a correctly normalized autocorrelation function, C(τ), should only have coefficients between 0 and 1.

A low baseline index does not necessary mean that an autocorrelation function is unusable, as the software also makes use of a so-called dust filter, a sophisticated dust rejection algorithm that can be used with anomalously dusty samples.

#### Methods for estimating baselines

Three common methods exist in software for estimating the baseline of an autocorrelation function, Autoslope, Last Channels, and Calculated. For the majority of clean monomodal samples this option works nicely. However, when dealing with samples that produce correlation functions that are either noisy or have multiple distinct components, this option may be insufficient. In these cases, the Autoslope analysis may assign the baseline prematurely. In such cases using either Last Channels or Calculated may produce better baseline estimates.

#### Summary

Having an accurate estimate of the baseline is necessary to normalize the correlation function, which is a prerequisite to data analysis and correlation function fitting. If the correlation function is very clean, all three methods should produce similar — if not identical – results. If the correlation functions are noisy or otherwise ambiguous the results will diverge. This is the reason that the Baseline Index, which compares measured and calculated baselines, is an effective indicator of DLS measurement quality.

#### Recap

The meaning of the three options presented in the data analysis section of the Particle Solutions SOP editor are as follows:

1. Auto (Slope Analysis) – in which the baseline is determined by identifying a region of low or zero slope.
2. Last Channels – assigns the average of the last 8 measured channels as the baseline
3. Calculated – uses the infinite time baseline for normalization