Aberration Correction with Aspheric Intraocular Lenses

*Timo Eppig, Jens Schrecker, Arthur Messner and Achim Langenbucher*

#### **Abstract**

The shape of the normal human cornea induces positive spherical aberration (SA) which causes image blur. In the young phakic eye, the crystalline lens compensates for a certain amount of this corneal aberration. However, the compensation slowly decreases with the aging lens and is fully lost after cataract extraction and implantation of a standard intraocular lens (IOL). Conventional spherical IOLs add their intrinsic positive SA to the positive SA of the cornea increasing the image blur. As a useful side effect, this also increases the depth of focus—often referred to as pseudo-accommodation. Aspheric intraocular lenses have been introduced to be either neutral to SA or to compensate for a certain amount of corneal SA. A customized correction for the individual eye seems to be the most promising solution for tailored correction of SA. In this chapter we will provide detailed information on the various concepts of aspheric intraocular lenses to elucidate that the term "aspheric intraocular lens" is being used for a large amount of different lens designs.

**Keywords:** spherical aberration, aspheric surface, customized intraocular lens, decentration, tilt

#### **1. Introduction**

The disease pattern of cataract comprises pathologic conditions of the human eye resulting from an opacification of the crystalline lens. The most frequent causes for the development of cataract are age-related transformation processes. Although research on pharmacologic treatment of cataract has been in focus for many years, the surgical extraction of the cloudy crystalline lens and implantation of an artificial intraocular lens (IOL)—referred to as cataract surgery—represent the only available treatment. Cataract surgery is one of the most frequently performed surgical procedures with several million surgeries being performed worldwide each year.

First IOL developments were primarily targeted on biocompatible materials and new fixation techniques rather than on correction of ocular aberrations other than defocus and astigmatism. First lens implants were made from polymethyl methacrylate, therefore being rigid and requiring large incisions for implantation. Furthermore, the optimum site of implantation (anterior chamber, iris, ciliary sulcus, or capsular bag) still had to be found, and adequate haptics for proper fixation had to be developed. Surgical results were therefore less predictable [1, 2].

In the early 1980s, foldable silicone materials and later acrylic materials allowed implantation through smaller ports and therefore caused less damage to the corneal structure allowing a faster rehabilitation. This finally facilitated ambulant cataract

surgery. In the following years, the capsular bag was identified as the optimum position for an IOLs, and the development of new lens power calculation formulas dramatically increased the predictability of the refractive outcome [1].

where z is the height of the surface from the apex (= 0 mm), r is the radius of curvature, and ρ is the radial coordinate from the center to the periphery. Q is called "asphericity" [3], and a2n are higher-order aspheric coefficients. X is a placeholder for additional polynomials, such as Zernike polynomials, which can be used to define additional surface shapes. From this equation numerous aspheric surface profiles can be generated (**Figure 2**), and most of current aspheric intraocular lens designs are based on the formula above. Equation (1) can be expanded to represent toric and biconic surfaces as well. The asphericity Q is identical to the conic constant κ (often used in optical design software) and can be transformed from other shape definitions for the aspheric surface such as the eccentricity e or

*Q* ¼ �*e*

The second type of aspherical surfaces, called "zonal asphere," is constructed from a set of annular rings with varying radius of curvature and asphericity. For a

By modulating radius of curvature, asphericity, and aspheric coefficients, the SA induced by the surface can be customized. Additional polynomials can be added on top to create non-rotationally symmetric aspheric surfaces to compensate for higher-order errors such as coma or trefoil. For example, one alternate way to compensate for spherical aberration would be to modulate the aspherical surface with a linear combination of Zernike polynomials representing various orders of

<sup>4</sup> <sup>þ</sup> *<sup>C</sup>*<sup>22</sup> � *<sup>Z</sup>*<sup>0</sup>

<sup>6</sup> <sup>þ</sup> *<sup>C</sup>*<sup>37</sup> � *<sup>Z</sup>*<sup>0</sup>

Q-asphere with 4th and 6th order coefficients non-Q-asphere with 2nd to 6th order coefficients Q-asphere with up to 14th order coefficients


*Variation of optical surface section with increasing number of coefficients. z is the elevation relative to the surface apex. All curves are derived from intraocular lens designs for an average power (20 to 22 D) lens.*

detailed description of these surfaces, please refer to the literature [5, 6].

*<sup>X</sup>* <sup>¼</sup> *<sup>C</sup>*<sup>11</sup> � *<sup>Z</sup>*<sup>0</sup>

sphere Q-asphere <sup>2</sup> (2)

<sup>8</sup> þ ⋯ (3)

the index of eccentricity e<sup>2</sup> [3]:

*Aberration Correction with Aspheric Intraocular Lenses DOI: http://dx.doi.org/10.5772/intechopen.89361*

spherical aberration:


**Figure 2.**

**25**

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

z / mm
