Abstract

It has been possible, using Kirchhoff-type integrals, to develop some optical equations for evaluating the form of the Fraunhofer diffraction patterns characteristic of a plane-parallel plate and rectangular diffracting aperture, when the plane-parallel plate has arbitrary positions and orientations in front of the rectangular diffracting aperture. The solution is an optical one, because the rectangular diffracting aperture is assumed to be large compared to the wavelength, diffraction effects in the plane of the rectangular diffracting aperture due to the edges of the plane-parallel plate are negligible, and multiple reflections between the edges of the rectangular diffracting aperture and plane-parallel plate have been neglected. Within these initial assumptions it is rigorous, for the directly transmitted and all the higher-order internally reflected wavefronts which make contributions to the amplitude and phase in the plane of the diffracting aperture have been considered. A UNIVAC 1103A-type computer has been used to calculate the forms of many of these diffraction patterns for particular choices of the nine possible variables. Attempts were also made with a 21-ft Jarrell-Ash Spectrograph to observe the corresponding experimental forms of these diffraction patterns. When an interferometer plate was moved across, and in front of, the rectangular diffracting aperture, the changes in form of the diffraction pattern were slow and could be followed in detail by corresponding theoretically calculated diffraction patterns. When, however, the interferometer plate was rotated in front of the rectangular diffracting aperture about an axis passing through its center, the changes became very rapid and required a very large number of calculated diffraction patterns to follow all the detailed changes. The theory in general seems to be quite useful in predicting the possible forms of the corresponding experimentally observed diffraction patterns.

© 1960 Optical Society of America

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References

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Figures (12)

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Equations (19)

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