1. Field of the Invention
This invention relates to a method of measuring refractive index profile of a cylinder having a circular cross section with distributed refractive index, such as optical fibers and lenses. The method of the invention has a high resolution and it is particularly useful for accurately determining the refractive index profile of a cylinder having a large difference of refractive index between the central and peripheral portions thereof.
2. Description of the Prior Art
In general, a cylindrical optical element (to be referred to as "cylinder", hereinafter) having a circular cross section with distributed refractive index, such as optical fibers and lenses with distributed refractive index, has a very wide range of application in optical technology and it is highly useful. With such cylinders, the distribution pattern of their internal refractive index exerts critical influence on the optical characteristics and performance of the cylinders. Accordingly, various methods for measuring the refractive index profile of the cylinder have been developed heretofore. Typical non-destructive methods of measuring the refractive index profile of the cylinder by using incident rays perpendicular to its longitudinal axis will be briefly reviewed.
Referring to FIG. 6, a three-dimensional orthogonal coordinate system is considered with the x-axis aligned with the longitudinal axis of a cylinder E. When a ray of light (to be referred to as the ray) U is applied to the cylinder E at right angles to the longitudinal axis, i.e., in parallel to the z-axis, with a distance y to the z-axis, the ray U proceeds through the cylinder E along a curved optical path depending on the distribution of refractive index in the cylinder, so that the ray U leaves the cylinder E with a deflection angle .PHI. relative to the z-axis. Thus, the magnitude of the deflection angle .PHI. reflects the refractive index distribution in the cylinder E. The deflection angle .PHI. is expressed as a function of the spacing y of the incidient ray U from the z-axis, namely a deflection function .PHI.(y). The spacing y is indicative of the incident position of the ray U into the cylinder E.
A number of methods have been proposed to measure the refractive index profile of the cylinder E from the deflection function .PHI.(y). Those methods facilitate the non-destructive measurement but have a shortcoming in that the deflection angle can be measured only when the cylinder is placed in a medium whose refractive index is the same as that at the periphery of the cylinder. To this end, the cylinder must be immersed in an index-matching fluid having the same refractive index as that of the cylinder periphery. Besides, the equation representing the optical path in the cylinder, which is necessary for the determination of the refractive index profile of the cylinder based on the reflection function .PHI.(y), has been solved only for the case of the cylinder surrounded by the index-matching fluid.
The conventional methods of measuring the refractive index profile have been used only with preforms which are interim products for making optical fibers. In the preforms and optical fibers, the difference of the refractive index between the core portion and the peripheral portion thereof is small. Thus, the conventional methods have not been intended to measure the refractive index in lenses of distributed refractive index type, in which the refractive index difference between the core portion and the peripheral portion is large.
Four practical methods have been known for determining the refractive index profile of a cylinder by measuring the deflection function .PHI.(y).