[Calculation of pseudophakic and phakic toric lenses for correction of corneal astigmatism--theory and clinical aspects].
BACKGROUND
In the last decades the implantation of pseudophakic and phakic toric lenses has become wide-spread for the correction of corneal astigmatism in cases of classical cataract surgery with implantation of a posterior chamber lens or in cases of refractive surgery with implantation of a piggyback lens. The purpose of this review article is to present an en bloc mathematical strategy for calculating pseudophakic and phakic toric lenses and for deriving the spectacle refraction after implantation of an arbitrary lens.


METHODS
We restrict ourselves to a centred coaxial optical system containing spherocylindrical surfaces and interspaces with a homogeneous optical medium. All calculations are done in the paraxial space according to linear Gaussian optics. We define an optical model for the pseudophakic and phakic eye and characterise all known refractive surfaces and interspaces between the surfaces with 4 x 4 refraction and translation matrices, respectively. The entire optical system is described with a 4 x 4 system matrix, which relates the impinging beam (slope angle and height, both in x and y directions) with the exiting beam (slope angle and height, both in x and y directions) and extract the required parameters from the matrix representation.


RESULTS
In example 1, we describe step-by-step how to derive a pseudophakic toric lens implant from the biometric parameters and in example 2 we estimate the residual refraction at spectacle plane after implantation of a pseudophakic lens. In example 3, we describe step-by-step how to derive a phakic toric lens implant from the initial refraction and biometric measurements and in example 4 we estimate the residual refraction at spectacle plane after implantation of a phakic lens.


CONCLUSIONS
The calculation scheme presents a strategy for calculating toric lenses and residual refractions based on a thin lens model of the spectacle correction, the cornea and the lens implant. This model can be generalised easily to a thick lens model, if the appropriate geometric parameters of both lens surfaces are known. The phakic lens calculation can directly be transferred to the case of pseudophakic piggyback lenses.
Langenbucher
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A
Medizinische Optik am Institut für Medizinische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen. achim.langenbucher@imp.uni-erlangen.de
Viestenz
A
A
Szentmáry
N
N
Seitz
B
B
Viestenz
A
A
D001251:Astigmatism / Q000601:surgery*; D006801:Humans; D007910:Lenses, Intraocular; D016014:Linear Models; D008433:Mathematics; D016011:Normal Distribution; D055095:Optics and Photonics; D012029:Refraction, Ocular