Fraunhofer diffraction, particle sizing

Hirleman, E. D., Optimal Scaling of the Inverse Fraunhofer Diffraction Particle Sizing... 

Hirleman ED. Modeling of multiple scattering effects in Fraunhofer diffraction particle analysis. In Gouesbet G, Grehan G, editors. Optical Particle Sizing Theory and Practice. New York Plenum Press 1988. p 159-175. 

Particle Size Laser Refractometiy is based upon Mie scattering of particles in a liquid medium. Up until about 1985, the power of computers supplied with laser diffraction instruments was not sufficient to utilize the rigorous solution for homogeneous spherical particles formulated by Gustave Mie in 1908. Laser particle instrument manufacturers therefore used approximations conceived by Fraunhofer. 

Fraunhofer rules do not include the influence of refraction, reflection, polarization and other optical effects. Early Iziser particle analyzers used Fraunhofer approximations because the computers of that time could not handle the storage cuid memory requirements of the Mie method. For example, it has been found that the Fraunhofer-based instrumentation cannot be used to measure the particle size of a suspension of lactose (R.I. = 1.533) in iso-octane (R.I. = 1.391) because the relative refractive index is 1.10, i.e.- 1.533/1.391. This is due to the fact that diffraction of light passing through the particles is nearly the same as that passing around the particles, creating a combined interference pattern which is not indicative of the true... 

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. 

Weiner, B. B. Particle and Droplet Sizing Using Fraunhofer Diffraction. In... 

The sizing methods involve both classical and modem instrumentations, based on a broad spectrum of physical principles. The typical measuring systems may be classified according to their operation mechanisms, which include mechanical (sieving), optical and electronic (microscopy, laser Doppler phase shift, Fraunhofer diffraction, transmission electron miscroscopy [TEM], and scanning electron microscopy [SEM]), dynamic (sedimentation), and physical and chemical (gas adsorption) principles. The methods to be introduced later are briefly summarized in Table 1.2. A more complete list of particle sizing methods is given by Svarovsky (1990). 

Figure 1.6. Fraunhofer diffraction system for particle size analysis (a) Diffraction by a circular aperture (b) Diffraction by a particle cloud.

The number density function is usually obtained by using microscopy or other optical means such as Fraunhofer diffraction. The mass density function can be acquired by use of sieving or other methods which can easily weigh the sample of particles within a given size range. 

Weiner, B. B. (1984). Particle and Droplet Sizing Using Fraunhofer Diffraction. In Modem Methods of Particle Size Analysis. Ed. H. G. Barth. New York John Wiley Sons. 

D < 500 pm, Fraunhofer Diffraction Pattern Analysis (FDPA) can be employed in measuring particle size distributions (4,5). For the particles in the intermediate range, 0.7 pm < D < 10 pm, Mie theory of scattering holds and Turbidity Spectra (TS) can furnish information about particle sizes (6). 

Submicron particle size analysis employs a scatter theory not completely described by Fraunhofer diffraction. The small particle range down to about 0.1 micrometer in diameter utilizes a combination of Fraunhofer diffraction and Mie theory for the forward scattered light and 90-degree Mie scatter at three (3) wavelengths and two (2) polarizations of each wavelength. Because of its need for a technology more involved than diffraction theory, submicron measurements are influenced by the index of refraction of the material making up the particulates to be sized. 

For particulate materials with high real indices, the reported size depends less on the complex component (7). Also, as the size of particles increases, the total scattering phenomenon simplifies to Fraunhofer diffraction, and becomes a very weak function of refractive index. 

A technique for sizing monodisperse particles of unknown refractive index uses the observation that the intensity of the forward scattering lobe is mainly due to Fraunhofer diffraction and is thus independent of the refractive index of the particle. Hodkinson (1966) computed a family of curves for the ratio of intensity viewed at two different angles. This relationship is shown in Fig. 17.10. If forward angles as small as 5° can be measured, this procedure should be accurate in measuring particle sizes of a = 1 to a = 18. 

Two methods are mainly used for the determination of particle size of inorganic pigments Sedimentation methods (centrifuges) and Fraunhofer diffraction with additional correction due to Mie scattering. 

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. 

For particles in the l-200- im size range, Fraunhofer diffraction can be used to obtain particle size distributions. Owing to its relative ease of operation, this technique has become enormously popular. Samples can be dispersed in the laser beam either as suspensions in an inert fluid or as dry powders aspirated directly into the analyzing beam. It is safe to state that validation of the methodology is crucial, in that it must be verified that the method of sample handling and processing does not alter the particle size distribution of the substance. 

---