text: Once the autocorrelation data have been generated, different mathematical approaches can be employed to obtain information from it.  Analysis of the scattering is facilitated when particles do not interact through collisions or electrostatic forces between ions. Particle-particle collisions can be suppressed by dilution, and charge effects are reduced by the use of salts to collapse the electrical double layer.
  The simplest approach is to treat the first-order autocorrelation function as a single exponential decay.  This is appropriate for a monodisperse population.
  where  is the decay rate.  The translational diffusion coefficient  may be derived at a single angle or at a range of angles depending on the wave vector .
  with
  where  is the incident laser wavelength,  is the solvent refractive index and  is the angle at which the detector is located with respect to the sample cell.
  The refractive index of the solvent plays a crucial role in light scattering and is important to calculate the Stokes radius from the Stokes-Einstein equation. Therefore, previous refractive index data from the scattering medium should be evaluated with dedicated instruments, known as refractometers. Alternatively, DLS instruments containing a refractive index measurement module allow a good estimative for this important parameter within ±0.5%, which is the accuracy defined by ISO 22412:2017 for refractive index values required for DLS. Besides the refractive index of the medium, the refractive index of the particles is only necessary when analyzing larger particle size (usually above 100 nm) and volume- or number-weighted size distributions are needed. In these cases, prior knowledge of the refractive index and absorbance of the material is required in order to apply the Mie scattering.
  Depending on the anisotropy and polydispersity of the system, a resulting plot of  vs.  may or may not show an angular dependence. Small spherical particles will show no angular dependence, hence no anisotropy. A plot of  vs.  will result in a horizontal line. Particles with a shape other than a sphere will show anisotropy and thus an angular dependence when plotting   vs. . The intercept will be in any case the D. Thus, there is an optimum angle of detection  for each particle size. A high-quality analysis should always be performed at several scattering angles (multiangle DLS). This becomes even more important in a polydisperse sample with an unknown particle size distribution. At certain angles the scattering intensity of some particles will completely overwhelm the weak scattering signal of other particles, thus making them invisible to the data analysis at this angle. DLS instruments which only work at a fixed angle can only deliver good results for some particles. Thus, the indicated precision of a DLS instrument with only one detection angle is only ever true for certain particles.
   is often used to calculate the hydrodynamic radius of a sphere through the Stokes–Einstein equation.  It is important to note that the size determined by dynamic light scattering is the size of a sphere that moves in the same manner as the scatterer.  So, for example, if the scatterer is a random coil polymer, the determined size is not the same as the radius of gyration determined by static light scattering.  It is also useful to point out that the obtained size will include any other molecules or solvent molecules that move with the particle.  So, for example, colloidal gold with a layer of surfactant will appear larger by dynamic light scattering (which includes the surfactant layer) than by transmission electron microscopy (which does not "see" the layer due to poor contrast).
  In most cases, samples are polydisperse.  Thus, the autocorrelation function is a sum of the exponential decays corresponding to each of the species in the population.
  It is tempting to obtain data for  and attempt to invert the above to extract .  Since  is proportional to the relative scattering from each species, it contains information on the distribution of sizes.  However, this is known as an ill-posed problem.  The methods described below (and others) have been developed to extract as much useful information as possible from an autocorrelation function.