Moiré Patterns: Their Application to Refractive Index and Refractive Index Gradient Measurements

The general theory of moiré patterns obtained from parallel rulings and concentric circles is presented. Near superposition of a regular ruling on to parallel rulings of variable spacings results in a curved moiré pattern which is functionally related to the deviation in spacings. When two figures consisting of uniformly spaced concentric circles are overlapped, the resulting moiré patterns are hyperbolas defined by the center-to-center distance of the figures and the inter-ring spacing.Since very small relative displacements of the figures result in large changes in the moiré pattern, this technique can be a sensitive detector of minute changes in refractive index and in refractive index gradient which bring about apparent relative displacement of the figures. The technique is demonstrated for the case of a constant refractive index gradient and for a variable refractive index gradient as encountered in diffusion measurements. Birefringence and dispersion can also be determined utilizing the moiré method. Demonstration of the use of the moiré technique for the evaluation of lenses is also presented.