Fraunhofer Diffraction from Large Particles

We seek here a description of the scattering from large particles compared with the wavelength of light. In this limit the dominant scattering occurs at small angles. Furthermore, the major contribution to the scattering field arises from interactions with the particle boundary. 

The sum of the waves that result in these two experiments must equal the original plane wave incident on the particle, and the two disturbance electric fields due to diffraction are of equal magnitude, but are of opposite sign. Since the intensity is the square modulus of the electric fields, either case will produce the same answer since the sign will not affect the result. It will turn out to be simpler to calculate the scatter light intensity using the second model presented above. 

Of interest is the light intensity measured on plane II, located a distance / from plane I. Huygen s principle simply states that the field at plane II is the sum of spherical waves emanating from all points in plane I. However, the field at point A will be primarily influenced by the spherical wave at point A, with a similar relationship between the fields at points B and B. Fresnel s extension of Huygen s principle quantifies this statement. The spherical wave emanating from a differential area, dS, located at point A is 

In this case, the total field at plane II must be E = e E,. Applying Huygen s principle, the field at plane II is also the integration of all the contributions from differential areas located in plane I. In other words, 

The radial distance, r, locating a single disturbance ray on plane II is approximated as 

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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. 

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