**2. Aspheric lenses**

With the improvement in IOL power calculation, the goal of cataract surgery became predictable; the focus of cataract surgery shifted from "restoration of vision" to "refractive surgery." Manufacturers started optimizing the IOL optic from an equiconvex spherical lens design to different aspheric surface profiles and finally multifocal and free-form surface designs. The buzzword of those days was "spherical aberration" (SA) which should be eliminated to improve contrast sensitivity and visual acuity. Spherical aberration is one of the monochromatic aberrations that is caused by the difference in focal length (or optical power) for varying aperture diameter of a lens. For positive spherical aberration, the optical power increases from the lens center to the periphery, and rays far from the optical axis will intersect the optical axis in front of the paraxial focus (**Figure 1**).

Any spherical optical surface causes SA. To achieve an equal distribution of optical power across the lens diameter, the optical surfaces have to be tailored accordingly. SA can only be reduced by varying the spherical radii of curvature of anterior and posterior surface yielding a so called best-form lens, but it cannot be eliminated. This can be achieved by implementing aspheric surfaces. There are basically two types of aspheric surfaces that have been described in the literature, the first one is referred to as "continuous asphere" and can be described by the formula

$$z = \frac{\frac{1}{r} \cdot \rho^2}{1 + \sqrt{1 - (1 - Q) \cdot \frac{1}{r^2} \rho^2}} + \sum\_{n=1}^{n=8} a\_{2n} \cdot \rho^{2n} + X \tag{1}$$

#### **Figure 1.**

*Rays focused by a lens with positive spherical aberration (top) compared to a lens without spherical aberration (bottom) [4]*.

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

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

With the improvement in IOL power calculation, the goal of cataract surgery became predictable; the focus of cataract surgery shifted from "restoration of vision" to "refractive surgery." Manufacturers started optimizing the IOL optic from an equiconvex spherical lens design to different aspheric surface profiles and finally multifocal and free-form surface designs. The buzzword of those days was "spherical aberration" (SA) which should be eliminated to improve contrast sensitivity and visual acuity. Spherical aberration is one of the monochromatic aberrations that is caused by the difference in focal length (or optical power) for varying aperture diameter of a lens. For positive spherical aberration, the optical power increases from the lens center to the periphery, and rays far from the optical axis

dramatically increased the predictability of the refractive outcome [1].

will intersect the optical axis in front of the paraxial focus (**Figure 1**).

1 *<sup>r</sup>* � *<sup>ρ</sup>*<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � ð Þ� <sup>1</sup> � *<sup>Q</sup>* <sup>1</sup>

<sup>q</sup> <sup>þ</sup>X*<sup>n</sup>*¼<sup>8</sup>

*<sup>r</sup>*<sup>2</sup> *ρ*<sup>2</sup>

*Rays focused by a lens with positive spherical aberration (top) compared to a lens without spherical aberration*

*n*¼1

*<sup>a</sup>*2*<sup>n</sup>* � *<sup>ρ</sup>*<sup>2</sup>*<sup>n</sup>* <sup>þ</sup> *<sup>X</sup>* (1)

*z* ¼

**Figure 1.**

**24**

*(bottom) [4]*.

1 þ

Any spherical optical surface causes SA. To achieve an equal distribution of optical power across the lens diameter, the optical surfaces have to be tailored accordingly. SA can only be reduced by varying the spherical radii of curvature of anterior and posterior surface yielding a so called best-form lens, but it cannot be eliminated. This can be achieved by implementing aspheric surfaces. There are basically two types of aspheric surfaces that have been described in the literature, the first one is referred to as "continuous asphere" and can be described by the formula

**2. Aspheric lenses**

*Intraocular Lens*

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

$$Q = -e^2 \tag{2}$$

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

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 spherical aberration:

$$X = \mathbf{C\_{11}} \cdot Z\_4^0 + \mathbf{C\_{22}} \cdot Z\_6^0 + \mathbf{C\_{37}} \cdot Z\_8^0 + \cdots \tag{3}$$

**Figure 2.**

*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.*
