A description is given of the manner in which two and three internal reflection roof prisms bring about a deterioration in the diffraction pattern form. Assuming a rectangular limiting aperture, the deterioration consists of a doubling of the diffraction pattern in a direction perpendicular to the roof edge. Parallel to the roof edge no deterioration of the diffraction pattern takes place so that in this direction it is always of the Fraunhofer form. If plane polarized light is allowed to enter these prisms, the form of the doubling in a direction perpendicular to the roof edge can be changed by rotating the incident azimuth angle of the entering plane polarized light. Usually such a doubling of the diffraction pattern is associated with an error in the roof angle of the prism. The theory presented both in this paper and the previous paper predicts a doubling of the diffraction pattern in a direction perpendicular to the roof edge even for a prism with a perfect 90° roof angle. As compared with the earlier paper on this same subject, the theory presented in this paper is considerably simplified so that for prisms with uncoated reflecting surfaces the diffraction pattern form can now be calculated for a two or three internal reflection roof prism from a knowledge only of the angular deviation at the roof edge, the prism refractive index, and the entering azimuth angle of the plane polarized light if the prism is illuminated with plane polarized light. Experimentally it was found that silvering the roof surfaces for two different forms of prisms decreased the doubling of the diffraction pattern in a direction perpendicular to the roof edge. The theory presented in this paper makes it possible to calculate also the diffraction pattern forms for roof prisms with coated reflecting surfaces providing the refractive index and absorption index of the coating material are known. In this paper the theory will be carefully tested on the 90° deviation Amici roof prism by comparing the microphotometer tracings of the photographed diffraction patterns with those to be expected from the theory. Several conclusions about the forms of the diffraction patterns for roof prisms having a wide range in geometry will be presented both when these prisms have coated and uncoated reflecting roof surfaces.
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