Biomedical subjects
Publications and source records attributed to S Varadharajan.
Previously we have used a matrix method to do nonlinear calculations and presented exact expressions for the third and fifth order aberration coefficients for a general conic surface as functions of the latus rectum and eccentricity. In this paper we show how the method can be extended to include the case of a general spherocylindrical surface.
A matrix method to do nonlinear calculations is described. This is possible only under the special condition when a transformation maps a zero vector onto a zero vector. Geometrical optics conform to this condition and hence matrix methods can be applied to calculate aberrations. Methods to reduce computational complexities using symmetry arguments are provided. The formalism is applied to study refraction by a conic surface. Aberration coefficients, up to fifth order, are obtained as functions of eccentricity and the latus rectum of the conic surface. The method can be used to model corneal aberrations.
AIM: To illustrate how the concept of ray vector fields can be used to demonstrate the elementary properties of thin lenses. METHODS: Principles of matrix algebra are used. RESULTS: Using simple geometry we give a generalization of Prentice's rule to include thick astigmatic lenses. Starting from the ray vector fields we show the connection between various representations of spherocylindrical lenses (Fourier representation, expansion in terms of the cross-cylinders). We suggest two clinical areas to which these concepts can be applied.
PURPOSE: To introduce the concept of the ray vector field and apply it to a problem in ophthalmic optics. METHODS: Matrix and linear algebra are used to relate ray vector fields and a representation of thin spherocylindrical lenses. RESULTS: Equations were derived relating ray vector fields and a particular coordinate system recommended previously. The method is illustrated with a simple example from ophthalmic optics, namely, addition of spherocylindrical lenses. We also illustrate the method by considering two spherocylinders separated by a distance. CONCLUSIONS: Ray vector fields are intuitively simple and can be used to solve complex ophthalmic optics problems.