Fraunhofer diffraction instrument

For comparison. Fig. 10 shows measurements made by a Fraunhofer Diffraction instrument on the same four materials. Only eleven channels of data are registered on this distribution, so the size resolution is limited. Even for large particles, the direct measurement of concentration in this type of instrument is affected by the scattering... 

Instrument Based on Fraunhofer Diffraction of Laser Light... 

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 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). 

In practical appHcations, diffraction instruments may exhibit certain problems. For example, there maybe poor resolution for the larger droplets. Also, it is not possible to obtain an absolute measure of droplet number density or concentration. Furthermore, the Fraunhofer diffraction theory cannot be appHed when the droplet number density or optical path length is too large. Errors may also be introduced by vignetting, presence of nonspherical... 

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. 

The Crystalsizer is based on the principle of incoherent light diffraction thus turning the traditional optical structure back to front. Thus the same physical effect is measured as with traditional devices, but without using coherent laser light. The size distribution is determined using Fraunhofer diffraction theory. The robust construction of the instrument makes it suitable for use on-site . Typically, samples are removed from the process and fed to the Crystallizer sequentially. 

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. 

As indicated, Fraunhofer diffraction is a special case of Mie theory that can be used to obtain the volume of particles. The Malvern Instruments Model 2600c series of sizers (Malvern Instruments, Southborough, MA) use a laser diffraction method. The instruments are equipped with an IBM-compatible computer that controls the collection, manipulation, and presentation of data. The principle of operation is illustrated in Fig. 18. The instruments consist of a low-power laser transmitter and receiver detector units mounted 50 cm apart. Particles or spray... 

Figure 18 Principle of operation of a Fraunhofer diffraction laser particle sizer. (With permission of Malvern Instruments, Inc.)...

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-... 

Another widely used particle size analyser is based on the forward scattering of laser light through a dilute (< 1 % by volume) suspension of crystals retained in a small ( 10mL) agitated cell. The resulting Fraunhofer diffraction pattern is detected and translated, by means of the instrument software, into a particle size distribution (BS ISO 13320, 2000). 

The powder can be analyzed in the dry state or, more commonly, as a dilute suspension. The measurements can be made accurately and fairly rapidly. For instruments based on the Fraunhofer diffraction theory, a reliable size range is 2-100 xm. However, the use of special light collection systems and the Mie theory can extend the range to —0.1-1000 xm. 

In most modern instruments, the measurement is performed by an array of N detectors. Also, Mie scattering theory is used in many instruments instead of Fraunhofer diffraction theory. In one popular approach the particles are divided into size intervals and each interval is assumed to generate an intensity distribution according to the average size. In this case, the preceding equation becomes... 

Particle sizing instruments can be categorized by the method qjplied to determine a size distribution. Integral optical methods like Fraunhofer Diffraction or Dynamic Light Scattering require extensive mathematics to extract the particle size distribution from samples. The general shape of this distribution is ordinarily assumed and a few parameters of this assumed distribution are adjusted to represent features of the data. Because of these restrictions, integral optical methods are not able to resolve all fine details of a particle size distribution. 

A CCD based approach to high-precision size and refractive index determination of levitated microdroplets using Fraunhofer diffraction. Review of Scientific Instruments 68 2287-2291. 

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