Fraunhofer diffraction and interference

Abstract

The difference between Fresnel and Fraunhofer diffraction has been discussed in Chapter 7, where we showed that Fraunhofer diffraction is characterized by a linear change of phase over the diffracting obstacle, contrasting the quadratic phase change responsible for Fresnel diffraction. Basically, Fraunhofer diffraction is the limit of Fresnel diffraction when the source and the observer are infinitely distant from the obstacle . When the wavelength is very short and the obstacles are very small, such conditions can be achieved in the laboratory; for this reason Fraunhofer diffraction is naturally observed with X-rays, electrons, neutrons, etc., which generally have wavelengths less than 1A. The study of Fraunhofer diffraction has been fuelled by its importance in understanding the diffraction of these waves, particularly by crystals. This has led to our present-day knowledge of the crystalline structures of materials and also of many molecular structures. Figure 8.1 shows a famous X-ray diffraction pattern of a crystal of haemoglobin, from about 1958, whose interpretation was a milestone in visualizing and understanding biological macromolecules. The techniques used in interpreting such pictures will be discussed in the later parts of the chapter. In optics, using macroscopic objects in a finite laboratory, the linear phase change can be achieved by illuminating the object with a beam of parallel light. It is therefore necessary to use lenses, both for the production of the parallel beam and for the observation of the resultant diffraction pattern.