In the determination of the angular rotational position of an axial asymmetry, such as of optically inhomogeneous regions, in an optically transparent body, e.g. stress concentration zones of optical PM-fibers, where the body is located in arbitrary angular start positions, the body is illuminated during rotations thereof to different angular positions around its longitudinal axis. For different angular positions the difference is then determined between light, which has passed through the fiber end and in its position corresponds to the central part of the fiber, and light, which has passed through the fiber end and in its position corresponds to the region of the fiber located immediately outside the central part. These differences, considered as a function of the rotation angle, constitute a curve having a shape typical of the considered body. This curve is compared to a reference curve, for different translational positions of the reference curve, and that translation position is found, where a maximum agreement is obtained of the curves. The translation value of this translational position gives the angular offset of the body from a reference position. By this method a correct alignment can be made of for example two optical PM-fibers of different types and also the basic type of an unknown PM-fiber can be determined.