# Optical Particle Counter

## :: Section 2

### Light Scattering Principles

A brief overview of light scattering from particles is provided in this section. Interaction of light waves with particles is a very important subject matter, and this interaction is responsible for many spectacular visual effects such as colored sunsets, rainbows, etc. Visibility degradation is one of the most obvious effects of air pollution. The optical phenomena is a direct result of scattering and absorption of light by aerosols.

Light is electromagnetic radiation characterized by electric and magnetic field vectors. We characterize it by its frequency or wavelength. The product of the frequency and the wavelength equals the speed of light. The wavelength of visible light is between 0.4 μm (violet) and 0.7 μm (red). The speed of light in vacuum is 3 X 108 m/s. The ratio of the speed of light in vacuum to that in a specific medium is index of refraction or the refractive index of the medium. The refractive index is expressed in general as a complex number, with the imaginary part represents the absorption coefficient. The refractive index is always greater than 1.

In a general sense, light is considered to be a stream of photons, or by a moving wave. The electric field vector can oscillate in all perpendicular directions to the direction of propagation of the wave. The source of light is then said to be unpolarized. When the electric field vector oscillates in only one plane, the light is said to be polarized. There are filters that can polarize a light beam, and laser light is typically polarized. Any light beam can be expressed as a vector sum of two perpendicular polarized components, called the horizontal and vertical polarization.

Consider that a light wave is incident on a particle. As the light wave is characterized by an oscillating electrical field vector, it induces dipoles in the particle, which are also oscillating. According to the classical electromagnetic theory, an oscillating dipole emits radiation in all directions. Thus, the induced oscillating dipoles, emit radiation in all directions. The frequency of this emission is the same as the frequency of the induced oscillating dipoles, which is the same as the frequency of the incident light wave. This phenomena is known as elastic light scattering. Thus, a key characteristic of elastic light scattering from a particle is that it happens in all directions, and is of the same frequency or wavelength as the incident light beam.

Two theories developed by Raleigh and Mie are used to determine quantitative expressions for the light scattering intensity. Rayleigh scattering theory is a molecular scattering theory and is restricted to small particles. In this regime, the electromagnetic field is uniformly distributed over the small particle, and all the induced dipoles reradiate light (the scattered light) equally in all directions. Thus, the scattered intensity is not a function of the angle with respect to the incident beam of light. Scattering by very large particles is more a geometric phenomena. In the intermediate size ranges, the Mie theory is applicable, and is typically applicable to aerosols of common interest. Here the dipoles are not uniformly distributed and a vector sum has to be carried out to determine the total scattered intensity at a certain point. This scattered intensity is a strong function of the angle with respect to the incident beam. In summary, the scattered light intensity is a function of the wavelength of incident radiation, the refractive index of the particle, the size of the particle and the angle made with respect to the incident beam.

These factors are utilized in designing instruments based on light scattering principles for measuring particle size distributions. As a single particle in the submicrometer range can produce a signal that can be detected by photodetectors, it is a sensitive tool for aerosol measurement. Furthermore, light scattering is a non-intrusive method of measurement, and instantaneous information could be obtained to allow for real time or continuous measurement. One problem to be overcome is that the signal (and hence the calibration) is dependent on the refractive index of the particle. Therefore, one has to have some idea of the refractive index of the measured aerosol to obtain reliable particle size measurements.