Symbolic algebra approach to the calculation of intraocular lens power following cataract surgery

We present a symbolic approach based on matrix methods that allows for the analysis and computation of intraocular lens power following cataract surgery. We extend the basic matrix approach corresponding to paraxial optics to include astigmatism and other aberrations. The symbolic approach allows for a refined analysis of the potential sources of errors ("refractive surprises"). We demonstrate the computation of lens powers including toric lenses that correct for both defocus (myopia, hyperopia) and astigmatism. A specific implementation in Mathematica allows an elegant and powerful method for the design and analysis of these intraocular lenses.