Matrix-optical representation of currently used intraocular lens power formulas

The formulas presently used to calculate the power of intraocular lenses (IOLs) are the SRK II, SRK/T, Holladay I, Hoffer Q, and Haigis. Apart from the empirical SRK II, these formulas are based on paraxial optics. With different notations and different algebraic forms, a comparison between formulas is difficult. Matrix techniques, on the other hand, have been successfully used in paraxial optics for many years, offering an elegant, simple, and straightforward way to characterize complex optical systems. The aim of this study, therefore, was to represent the current theoretical IOL formulas in matrix notation.

The SRK/T, Holladay I, Hoffer Q, and Haigis formulas were analyzed, algebraically transformed, and expressed in matrix-optical notation in the form of translation and refraction matrices and the system matrix. An example calculation was carried out and compared to results from two commercial biometry instruments (Zeiss IOLMaster and Tomey AL-2000).

Although all formulas examined are based on thin lens optics in paraxial approximation, considerable differences exist in the interpretation and calculation of corneal power, axial length, and effective lens position as well as the manner in which individual IOLs are represented ("IOL constants"). All relations necessary for matrix-optical representation are given.

The matrix-optical representation of the currently used IOL power formulas offers new insights into the calculation of IOLs and allows a deeper understanding of the advantages and drawbacks of each formula.