Light scattering Fraunhofer theory

The vesicle size is an important parameter not only for in-process control but particularly in quality assurance, because the physical stability of the vesicle dispersion depends on particle size and particle size distribution. An appropriate and particularly quick method is laser light scattering or diffraction. Laser light diffraction can be applied to particles > 1 pm and refers to the proportionality between the intensity of diffraction and the square of the particle diameter according to the diffraction theory of Fraunhofer. 

The Mie theory (actually Mie s solution to Maxwell s equations for spheres) can be applied to spherical particles that are smaller than, similar in size to, and larger than the wavelength of light used (Mie, 1908). With particles much larger than the wavelength, the Mie theory can be simplified to the Fraunhofer theory. The mathematics of scattering is complicated for other than spherical shapes, and that is why the assumption that particles are spherical is often made. 

Fraunhofer diffraction theory combines the above results to compute the light scattered at small angles from large particles. Such a particle is pictured in Figure 4.15. 

The more complex Mie Theory (lj must be invoked to analyze particles with dimensions near the wavelength of light. Fraunhofer theory is an interference phenomenon, and is described in various optics text books (.2,3.). It is adequate for most particle sizing applications and will be discussed in detail. Mie Theory requires a knowledge c the refractive index of the material. A unique use of polarized side scatter at several wavelengths is employed to obtain particle size channels in the submicron region. 

Early instruments employed low (forward) angle laser light scattering (LALLS) but these have been replaced by multi-angle instruments. MALLS instruments use Lorenz-Mie (often referred to as Mie) theory or Fraunhofer diffraction theory. 

Refractive index consists of two parts, a real part that describes the refracted light and an imaginary (complex) part that describes absorption. In the case of very small particles, or particles where the complex part of the refractive index is near zero, light is transmitted through the partieles and interferes with the diffracted radiation. The interaction between the transmitted and diffracted radiation results in anomolous scattering and can be catered for in the Fraunhofer theory if both parts of the refractive index are known. 

Beckman Coulter LS series uses a dark-field reticule having an array of 500 pm holes for automatic alignment purposes. The LS uses reverse Fourier lens optics incorporated in a binocular lens system to optimize light scattering over the widest dynamic size range. Results are calculated from either Fraunhofer or Mie theories. An application of this instrument to the measurement of micro-silica mixtures has been presented [154]. 

The newer la.ser diffraction instrument allows measurement for particle sizes ranging from 0.1 pm to 8 mm (7). Most of the laser diffraction instruments in the pharmaceutical industry use the optical model based on several theories, either Fraunhofer, (near-) forward light scattering, low-angle laser light scattering, Mie, Fraunhofer approximation, or anomalous diffraction. These laser diffraction instruments assume that the particles measured are spherical. Hence, the instrument will convert the scattering pattern into an equivalent volume diameter. A typical laser diffraction instrument consists of a laser, a sample presentation system, and a series of detectors. 

Two theories dominate the theory of light scattering the Fraunhofer and Mie. In the former, each particle is treated as spherical and essentially opaque to the impinging laser light. The... 

Most commercial instruments use optical models in tlicir analysis software that arc based on Mie scattering theory or Fraunhofer diffraction. Mie theory provides a complete soluuon to the problem of light scattering by a sphere, including the eiTccis of transmitted and absorbed light. On the other hand, the Fraunhofer dif-... 

Laser has been widely used for the measurement of particle size through light scattering [30]. Laser scattering measurements are very accurate and fast. The techniques based on the Fraunhofer diffraction theory can measure the size of particles in the range of 2-100 pm. The Mie theory can extend the measurable size range to 0.1-1000 pm, if special light collection systems are used. 

A particle size analyzer determines the particle size distribution of powders either dry or dispersed in solvent by laser light scattering based on the Fraunhofer scattering theory. This type of equipment has an optical bench whose combined dynamic range is nominally 0.7-2000 pm. The instrument calculates mean diameters and distribution data. An interfaced computer generates sample histograms. This technique has been applied to the study of particle size and particle size distributions for polymer powders and polymer suspensions in a variety of solvents. 

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