Turbidity describes the cloudiness of a solution due to scattering of light by suspended particles. In contrast to measuring the scattered light directly, turbidity measurements analyze the transmitted light - meaning the non-scattered portion of the incident light.

The Prometheus Panta system measures turbidity using the backreflection optics in order to understand a sample's aggregation behavior.

There are different types of scattering. The main source of scattering for molecules with a diameter below 1/10 the wavelength of the incident light is Rayleigh scattering, and the light collected at a specific angle Iθ can be expressed as a function of the source intensity I0:

In the case of backreflection technology, most of the parameters are constants, such as θ, the angle between the detector and the light source, r, the distance between the detector and the particle, k, the wave number, and I0, the original intensity. The only parameter which is not constant is the polarizability α. Therefore, each particle will alter the light intensity depending on α, which is expressed by:

Here, m is the refractive index of the particle and v is the volume of the particle. Thus, the residual light collected by backreflection, after the scattering of a single particle, can be expressed as:

This intensity will depend on the refractive index of the particle, m, to the power of 4 and on its diameter, dp, to the power of 6.

If protein aggregates are present, each aggregate scatters an amount of light according to the parameters described above. Therefore, the remaining light will decrease proportionally to the number of aggregates encountered by the light beam (i.e. the concentration of aggregates in the sample).

This means that the measurement from the backreflection optics is influenced by three main parameters: the concentration of aggregates cagg, the refractive index m, and the particle diameter dp.

However, Rayleigh scattering is not the only kind of scattering that the backreflection optics detect. Aggregates between 1/10 the wavelength of light and approximately equal to the wavelength of light induce the so-called Mie scattering, which cannot be expressed by a single mathematical equation.

The equations above explain why the signal recorded by the Prometheus backreflection optics depends on three parameters (size, concentration, and refractive index), and therefore does not allow for precisely determining aggregate size or number. Nevertheless, an increase in mAU typically corresponds to an increase in the size of the particles and a decrease in the concentration, as aggregation depicts a balance between caggand dp.