Fraunhofer diffraction pattern theory

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). 

Chapter 1 is concerned with the fundamental principles of image formation by a lens. These principles were first formulated by Ernst Abbe in 1873 and are basic to the chapters that follow. According to the Abbe theory, the image of an illuminated object is the result of a twofold diffraction process. First, the Fraunhofer diffraction pattern of the object is formed in the back focal plane of the lens. Second, the light waves travel... 

In principle, the diffraction patterns can be quantitatively understood within the Fraunhofer approximation of Kirchhoff s diffraction theory as described in any optics textbook (e.g., [Hecht 1994]). However, Fraunhofer s optical diffraction theory misses an important point of our experiments with matter waves and material gratings the attractive interaction between the molecule and the wall results in an additional phase of the molecular wavefunction [Grisenti 1999], Although the details of the calculations are somewhat involved2, the qualitative effect of this attractive force on far-field diffraction can be understood as a narrowing of the real slit width to an effective slit width [Briihl 2002], For our fullerene molecules the reduction can be as big as 20 nm for the unselected molecular beam and almost 30 nm for the slower, velocity selected beam. The stronger effect on slower molecules is due to the longer and therefore more influential interaction between the molecules and the wall. 

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. 

In the early days of particle size measurement, the advantage of this relatively simple theory was that it usually describes the scattering patterns of transparent particles of a few micrometers in size in liquid media better than Fraunhofer theory. Similar to the Fraunhofer theory, the anomalous diffraction theory requires no exact knowledge of the refractive index, but it should not be used for opaque particles. 

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