Purpose: A recently published manuscript addressed the problem of compensating for aniseikonia between pseudophakic astigmatic eyes using a least-squares calculation scheme. The purpose of this paper is to revisit this topic with the specific aim of providing explicit formulae for the determination of the intra-ocular lens required to produce a specified transverse image size at the plane of the retina and the characteristics of the contact or spectacle lens required to realize some desired refractive outcome.
Methods: The 4 x 4 ray transference is central to the development of all formulae presented in this paper. Specifically, the formula for the determination of the power of the intra-ocular lens required to achieve some transverse image size at the retina is derived directly from the disjugacy of the pseudophakic eye.
Results: The formula is applicable to both stigmatic and astigmatic systems without restriction. A detailed numerical example for an unusual eye is provided.
Conclusion: A formula for the determination of the intra-ocular lens required to produce any given transverse image size at the retina is derived. This approach does not require the application of the Moore-Penrose pseudo-inverse and one is able to work rather with the properties of the optical system directly without further modification.