Tomographic methods for investigating vector fields with the aid of fibre-optic measuring systems

An investigation is reported of the task of tomographic reconstruction of vector physical fields from sets of contour integrals of the projection of a vector and of the projection of the derivative of a vector along a given direction. It is shown that such reconstruction is possible with the aid of fibre-optic measuring lines. In those cases when the output signal is proportional to the integral of the projection of a given vector, use is made of measuring lines in the form of a narrow loop. The solution of the problem then reduces to the application of integral theorems. However, if the output signal is proportional to the integral of the projection of the derivative of a vector along a direction (representing the problem of a deformable two-dimensional object), it is essential to use measuring lines of stepped form; the potential component of the field is then reconstructed.