A refraction correction technique which includes nonsymmetric index of refraction

The problem of predicting refraction errors in a nonsymmetric, inhomogeneous atmospheric refractive index distribution is examined, utilizing the basic (vector) differential equation of a ray path. The simplifications made in the basic equation are based on known atmospheric refraction characteristics in conjunction with the limitations inherent in obtaining distributions over a wide region which are valid for a given time. The assumptions made are 1) , 2) total bending is small, and 3) the gradient of along the ray path is approximately the same as the gradient of along the straight line in the launch direction. A fourth assumption, not mathematically necessary but useful in analyzing actual situations, is that the gradient of may be described by regions of constant gradient. The first three assumptions allow the general three-dimensional ray path to be computed in terms of its two plane-ray projections; the fourth assumption yields a mathematically simple solution for each path.