Journal of Refractive Surgery

Original Article 

Matrix-optical Representation of Currently Used Intraocular Lens Power Formulas

Wolfgang Haigis, MS, PhD

Abstract

PURPOSE

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.

METHODS

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).

RESULTS

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.

CONCLUSIONS

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. [J Refract Surg. 2009;25:229-234.]

AUTHOR

From University Eye Hospital, Wuerzburg, Germany.

The author has no financial or proprietary interest in the materials presented herein.

Correspondence: Wolfgang Haigis, MS, PhD, University Eye Hospital, 11, Josef-Schneider-Str, D-97080 Wuerzburg, Germany. Tel: 49 931 201 20640; Fax: 49 931 201 20454; E-mail: w.haigis@augenklinik.uni-wuerzburg.de

Received: September 19, 2007

Accepted: January 11, 2008

Posted online: May 15, 2008

Click here to read the Letter to the Editor.

Abstract

PURPOSE

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.

METHODS

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).

RESULTS

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.

CONCLUSIONS

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. [J Refract Surg. 2009;25:229-234.]

AUTHOR

From University Eye Hospital, Wuerzburg, Germany.

The author has no financial or proprietary interest in the materials presented herein.

Correspondence: Wolfgang Haigis, MS, PhD, University Eye Hospital, 11, Josef-Schneider-Str, D-97080 Wuerzburg, Germany. Tel: 49 931 201 20640; Fax: 49 931 201 20454; E-mail: w.haigis@augenklinik.uni-wuerzburg.de

Received: September 19, 2007

Accepted: January 11, 2008

Posted online: May 15, 2008

Click here to read the Letter to the Editor.

Authors

10.3928/1081597X-20090201-09

Sign up to receive

Journal E-contents