title: Compensation of aniseikonia in astigmatic pseudophakic eyes.
abstract: OBJECTIVE
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Optometric Science Research Group, Department of Optometry, University of Johannesburg, Auckland Park, Johannesburg 2006, South Africa. gmk@na.rau.ac.za
authors.forename: Graeme E
authors.initials: GE
authors.lastname: MacKenzie
mesh_terms: D000465:Algorithms; D000839:Aniseikonia / Q000628:therapy*; D001251:Astigmatism / Q000628:therapy*; D006801:Humans; D008954:Models, Biological; D009907:Optometry; D019591:Pseudophakia; D012030:Refractive Errors