An application of optical interference to dynamic position measurement in three dimensions
This thesis is concerned with the measurement of the positions of points and bodies moving in trajectories in three dimensions, and the use of a new technique of optical interference which allows such measurements to be made dynamically. A variety of existing techniques for both static and dynamic three-dimensional position measurement are discussed, and the design of the new interferometer is introduced. The geometry of points, curves and surfaces in three dimensions is examined, with emphasis on the intersection of the point loci represented by the coordinate output of measuring instruments. The coordinates output by the interferometer represent surface loci which are quadric surfaces. A method of calculating the position and orientation of a body using three quadric surface intersection curves is presented. Diffraction of monochromatic light at an aperture is considered and it is shown that an interferometer working by division of wavefront can be used to obtain continuous information about the movement of the source of radiation, with that source free to move in up to three dimensions. A lens may be used to produce a compact instrument based on these principles. The diffraction integral equations are modified to incorporate the effect of a lens in the diffraction field. It is shown that even complex lenses can be represented by a few parameters in the diffraction equations. From the evaluation of these diffraction integrals, it is shown how the movement of interference fringes provides a coordinate output and how this is related to the locus of the radiation source. A method of obtaining very high resolution measurements of interference fringe pattern movement is presented. The interferometer was built and tested and the above theory verified in practice in a series of optical bench tests. The implementation of a system which uses this interferometer to measure the dynamic performance of industrial robots is considered. The optimum positions for the instruments are derived, and the method of designing the interferometer to give the required resolution is presented.