Calculation and least-squares estimation of surface curvature and dioptric power from meridional measurements

The calculation or estimation of dioptric power or surface curvature from meridional measurements is an important problem with applications in a number of areas. By phrasing the problem in terms of matrices and applying new results in the mathematics of matrices one is able to reformulate the problem into a standard form that is well known in mathematics and statistics. As a result the solution can be written down directly. The method copes with any number of measurements along any number of meridians, including repeated measurements along the same meridian, and is more general than methods previously proposed. It gives least-squares and best estimates of the true surface curvature or dioptric power. Being phrased in standard statistical terms the method lends itself readily to extension to related types of problems such as least-squares estimation under certain types of constraints. Matrix methods employed in this paper are likely to find wider application in optometry and the vision sciences.