Estimating the astigmatic power of the crystalline lens and eye from ocular biometry

To estimate the astigmatic power of the crystalline lens and the whole eye without phakometry using a set of linear equations and to provide estimates for the astigmatic powers of the crystalline lens surfaces.

Linear optics expresses astigmatic powers in the form of matrices and uses paraxial optics and a 4 × 4 ray transfer matrix to generalise Bennett's method comprehensively to include astigmatic elements. Once this is established, the method is expanded to estimate the contributions of the front and back lens surfaces. The method is illustrated using two examples. The first example is of an astigmatic model eye and compares the calculated results to the original powers. In the second example, the method is applied to the biometry of a real eye with large lenticular astigmatism.

When the calculated powers for the astigmatic model eye were compared to the actual powers, the difference in the power of the eye was \( {\left(0.03\kern0.5em 0.13\kern0.5em 0.04\right)}^{\mathrm{T}}\ \mathrm{D} \) (where T represents the matrix transpose) and for the crystalline lens, the difference was \( {\left(0.08\kern0.5em 0.29\kern0.5em 0.08\right)}^{\mathrm{T}}\ \mathrm{D} \) (power vector format). A second example applies the method to a real eye, obtaining lenticular astigmatism of −5.84 × 175.

The method provides an easy-to-code way of estimating the astigmatic powers of the crystalline lens and the eye.