**3. Corneal spherical aberration**

As mentioned above, the average human cornea induces a significant portion of positive SA, which is typically being described by the Zernike coefficient *Z*<sup>0</sup> 4 (spherical aberration) on a diameter of 6.0 mm at corneal plane. The amount of SA can be calculated from the corneal surface shape by optical ray tracing. A method to do so was described by Norrby et al. providing a reference value for the Liou-Brennan model eye [7, 8]. Calossi provided an overview of SA values for a limited set of variables [3].

Depending on the underlying database, various authors reported different values for the average corneal SA. Holladay et al. reported that the average SA of the human cornea is about +0.27 0.20 μm (value misprinted in the original publication [9] and corrected by Norrby et al. [7]). Similar values were found by Beiko and Haigis (+0.274 0.089 μm) [10]. The widely spread Liou-Brennan model eye provides about +0.258 μm of spherical aberration being close to the reported average clinical values [7, 8]. De Sanctis et al. found higher values in their patients (+0.328 0.132 μm) [11], while Shimozono et al. found lower values (0.203 0.100 μm) [12].

negligible change to the corneal SA. When being analyzed on an optical bench (in a

PhysIOL, Liege, Belgium PODeye 0.11 μm [18] Kowa Pharmaceuticals, Düsseldorf, Germany AvanSee 0.04 [18]

**Manufacturer Product SA correction** Johnson & Johnson Vision, Groningen, The Netherlands TECNIS 0.27 μm [9] HOYA, Nagoya, Japan Vivinex XC1 0.18 μm [17, 18] Carl Zeiss Meditec, Berlin, Germany CT ASPHINA 509MP 0.18 μm [18] Alcon Laboratories, Forth Worth, TX, USA AcrySof IQ SN60WF 0.17 μm [17] Bausch + Lomb, Rochester, NY, USA EyeCee One 0.14 μm [18]

a fixed amount of corneal SA. One of the first aberration-correcting lenses was presented by Holladay et al. providing a correction of 0.27 μm and thus targeting

Today, surgeons may choose from a variety of aspheric IOLs with different amount of compensation for SA (**Table 1**). Theoretically, one could choose the IOL providing the optimum correction for an eye. This would require preoperative examination of corneal topography and analysis of corneal aberrations. Diagnostic instrumentation for the anterior segment such as the Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany) or the CASIA2 (Tomey Corp., Nagoya, Japan) allow direct readout of the SA amount over 6 mm diameter. The SA value calculated from corneal tomographic data could then be used to select an IOL model that provides best correction. Still, since the range of IOLs with different SA corrections is limited, not every eye could be supplied with optimum correction. Clinical results with this "selection method" are controversial but indicate the potential for improvement [14–16]. Piers et al. found that contrast sensitivity peaks with 0 μm of SA [17]. On the contrary, other investigators found that a residual SA of about +0.1 μm may be beneficial for visual performance [18–20]. Manzanera and Artal argued that changes in SA between 0.17 and + 0.2 μm are merely noticeable by patients [21]. This may be an explanation why the differences in visual performance between

Aberration-correcting designs evolved subsequently, providing compensation to

Quatrix Evolutive 0.1 μm [18]

collimated beam), both lenses will show the opposite characteristics [4].

*List of selected intraocular lens models providing correction of spherical aberration.*

aberration-free and aberration-correcting lenses are usually small.

The next logical step is a compensation procedure based on the true individual SA, rather than on average values. Wang et al. found that not only SA should be considered but the full spectrum of corneal aberrations [22–24]. Especially eyes with high amounts of spherical aberration such as eyes after laser refractive surgery or eyes with forme fruste keratoconus could benefit more from customized correction of SA [22, 23, 25] than normal eyes, if centration of the implant can be kept within strict limits. Therefore, an optimum solution could be the customization of intraocular lenses [26, 27]. Several researchers provided theoretical basics and theoretical results showing the potential of customized intraocular lenses [28–31]. The design process of such IOLs requires the implementation of customized model eyes based on biometric data and the use of ray tracing technology [28, 32–36]. The first clinical results with this method have recently been published showing promising

on the average SA found in human eyes [9].

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

**Table 1.**

results [37].

**27**

## **4. Correction of spherical aberration with IOLs**

Aberration correction could be best described as a superposition of wave fronts as outlined in **Figure 3**.

During cataract surgery the corneal SA is typically increased by the likewise positive spherical aberration of a spherical IOL. Therefore, lens designers at first created the "aberration-free" or "aberration-neutral" lens concept, a lens design that was meant to eliminate its intrinsic spherical aberration and thus being neutral to the eye's overall SA [13]. However, the amount of SA is highly depending on the vergence of the incident rays. Therefore, there are differences in the design of "aberrationneutral" lenses: some of them are designed to be neutral to SA in a collimated beam, e.g., a beam as such could be used in measurement instrumentation. Others are designed to be neutral to SA behind some generic model cornea (in a converging beam). Both of them will exhibit a considerable amount of SA when implanted in a real eye; the first will provide a small correction for SA, while the latter may provide

#### **Figure 3.**

*Simplified sketch of the principle of aberration correction: An impinging plane wave front (collimated beam) is refracted by the cornea and affected by spherical aberration (red); the intraocular lens (yellow) compensates for the same amount of spherical aberration (green) resulting in a perfect wave front at the focus plane. Note: The plotted wave fronts do not account for the defocus.*

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


#### **Table 1.**

**3. Corneal spherical aberration**

limited set of variables [3].

*Intraocular Lens*

(0.203 0.100 μm) [12].

as outlined in **Figure 3**.

**Figure 3.**

**26**

*plotted wave fronts do not account for the defocus.*

**4. Correction of spherical aberration with IOLs**

As mentioned above, the average human cornea induces a significant portion of

4

positive SA, which is typically being described by the Zernike coefficient *Z*<sup>0</sup>

(spherical aberration) on a diameter of 6.0 mm at corneal plane. The amount of SA can be calculated from the corneal surface shape by optical ray tracing. A method to do so was described by Norrby et al. providing a reference value for the Liou-Brennan model eye [7, 8]. Calossi provided an overview of SA values for a

Depending on the underlying database, various authors reported different values for the average corneal SA. Holladay et al. reported that the average SA of the human cornea is about +0.27 0.20 μm (value misprinted in the original publication [9] and corrected by Norrby et al. [7]). Similar values were found by Beiko and Haigis (+0.274 0.089 μm) [10]. The widely spread Liou-Brennan model eye provides about +0.258 μm of spherical aberration being close to the reported average clinical values [7, 8]. De Sanctis et al. found higher values in their patients (+0.328 0.132 μm) [11], while Shimozono et al. found lower values

Aberration correction could be best described as a superposition of wave fronts

During cataract surgery the corneal SA is typically increased by the likewise positive spherical aberration of a spherical IOL. Therefore, lens designers at first created the "aberration-free" or "aberration-neutral" lens concept, a lens design that was meant to eliminate its intrinsic spherical aberration and thus being neutral to the eye's overall SA [13]. However, the amount of SA is highly depending on the vergence of the incident rays. Therefore, there are differences in the design of "aberrationneutral" lenses: some of them are designed to be neutral to SA in a collimated beam, e.g., a beam as such could be used in measurement instrumentation. Others are designed to be neutral to SA behind some generic model cornea (in a converging beam). Both of them will exhibit a considerable amount of SA when implanted in a real eye; the first will provide a small correction for SA, while the latter may provide

0 µm + =

*Simplified sketch of the principle of aberration correction: An impinging plane wave front (collimated beam) is refracted by the cornea and affected by spherical aberration (red); the intraocular lens (yellow) compensates for the same amount of spherical aberration (green) resulting in a perfect wave front at the focus plane. Note: The*

+0.27 µm -0.27 µm

*List of selected intraocular lens models providing correction of spherical aberration.*

negligible change to the corneal SA. When being analyzed on an optical bench (in a collimated beam), both lenses will show the opposite characteristics [4].

Aberration-correcting designs evolved subsequently, providing compensation to a fixed amount of corneal SA. One of the first aberration-correcting lenses was presented by Holladay et al. providing a correction of 0.27 μm and thus targeting on the average SA found in human eyes [9].

Today, surgeons may choose from a variety of aspheric IOLs with different amount of compensation for SA (**Table 1**). Theoretically, one could choose the IOL providing the optimum correction for an eye. This would require preoperative examination of corneal topography and analysis of corneal aberrations. Diagnostic instrumentation for the anterior segment such as the Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany) or the CASIA2 (Tomey Corp., Nagoya, Japan) allow direct readout of the SA amount over 6 mm diameter. The SA value calculated from corneal tomographic data could then be used to select an IOL model that provides best correction. Still, since the range of IOLs with different SA corrections is limited, not every eye could be supplied with optimum correction. Clinical results with this "selection method" are controversial but indicate the potential for improvement [14–16]. Piers et al. found that contrast sensitivity peaks with 0 μm of SA [17]. On the contrary, other investigators found that a residual SA of about +0.1 μm may be beneficial for visual performance [18–20]. Manzanera and Artal argued that changes in SA between 0.17 and + 0.2 μm are merely noticeable by patients [21]. This may be an explanation why the differences in visual performance between aberration-free and aberration-correcting lenses are usually small.

The next logical step is a compensation procedure based on the true individual SA, rather than on average values. Wang et al. found that not only SA should be considered but the full spectrum of corneal aberrations [22–24]. Especially eyes with high amounts of spherical aberration such as eyes after laser refractive surgery or eyes with forme fruste keratoconus could benefit more from customized correction of SA [22, 23, 25] than normal eyes, if centration of the implant can be kept within strict limits. Therefore, an optimum solution could be the customization of intraocular lenses [26, 27]. Several researchers provided theoretical basics and theoretical results showing the potential of customized intraocular lenses [28–31]. The design process of such IOLs requires the implementation of customized model eyes based on biometric data and the use of ray tracing technology [28, 32–36]. The first clinical results with this method have recently been published showing promising results [37].

### **5. Limitations of aberration-correcting lenses**

A major limitation for the selection of the appropriate IOL is the accuracy and repeatability of the preoperative corneal topography. The calculation of corneal SA requires highest precision of corneal topography in the periphery, since the difference in elevation between an aspheric corneal surface and a spherical surface is only some microns (**Figure 4**). Schröder et al. investigated the measurement repeatability and precision of several corneal topographers and tomographers and found that the repeatability of these devices is decreasing from the center to the periphery and may not be sufficient to detect small changes in corneal asphericity [38].

aspherics including coefficients a4 and higher (see Eq. 1) and were specifically designed considering some reasonable amount of IOL decentration. The effect of decentration on image performance of some selected IOL designs is shown in **Figures 5** and **6**. The graphs exhibit a drop of the image quality with aspheric lenses below the image quality of a spherical IOL when decentration exceeds 0.4 and

**3.0 mm pupil**

aberration correction approx. -0.18 µm aberration correcting approx. -0.27 µm

spherical aberration neutral

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 decentration [mm]

**4.5 mm pupil**

aberration correction approx. -0.18 µm aberration correcting approx. -0.27 µm

spherical aberration neutral

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 decentration [mm]

*Simulation of modulation transfer function at 30 cycles per degree for four different intraocular lenses and a*

*pupil diameter of 4.5 mm in the Liou-Brennan model eye as a function of decentration [40, 41].*

*Simulation of modulation transfer function at 30 cycles per degree for four different intraocular lenses and a pupil diameter of 3.0 mm in the Liou-Brennan model eye as a function of decentration [40, 41, 57].*

0.3 mm, respectively.

MTF @ 30 cycles/degree

1

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

0

1

0

**Figure 6.**

**29**

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

MTF @ 30 cycles/degree

**Figure 5.**

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Another limitation arises from the concept of aberration correction itself. As outlined in **Figure 3**, the method requires the alignment of the IOL in relation to the cornea to be as perfect as possible. But even if an ideal positioning of the IOL is achieved intraoperatively, the risk of decentration or tilt remains in the postoperative course.

Altmann et al., Eppig et al., and others analyzed the effects of decentration and tilt of spherical and aspherical IOLs on the image quality and found that it is more affected by decentration than by tilt and that the susceptibility of lens misalignment increases with the amount of SA to be corrected [9, 39–46]. Some authors defined that a range of decentration within a SA-correcting IOL would perform better or equal than a standard spherical IOL. This range was reported to be between 0.0 and 0.3–0.8 mm, depending on the design of the lens and simulation conditions [9, 40–42]. In a previous publication, we summarized the data on the IOL decentration from various sources and found that the clinically observed decentration is between 0 and 1 mm but most frequently about 0.3 mm [33, 40, 47–56]. Others showed that there is a tendency for IOLs decentering and tilting into nasal direction with mirror symmetry between both eyes [51].

Gillner et al. showed in a previous publication that IOL designs with a more conservative correction of SA may provide a larger range of tolerance to decentration [41]. Examples thereof are the ZO/ASPHINA design (Carl Zeiss Meditec AG, Berlin, Germany) and the Aspheric Balanced Curve Design (ABCD) (Hoya Corporation, Tokyo, Japan). Both designs are based on higher-order

**Figure 4.**

*Difference in corneal elevation for three surfaces with R = 7.77 mm radius of curvature and several values of Q compared to a sphere.*

aspherics including coefficients a4 and higher (see Eq. 1) and were specifically designed considering some reasonable amount of IOL decentration. The effect of decentration on image performance of some selected IOL designs is shown in **Figures 5** and **6**. The graphs exhibit a drop of the image quality with aspheric lenses below the image quality of a spherical IOL when decentration exceeds 0.4 and 0.3 mm, respectively.

#### **Figure 5.**

**5. Limitations of aberration-correcting lenses**

tive course.

*Intraocular Lens*

**Figure 4.**

**28**

*compared to a sphere.*

A major limitation for the selection of the appropriate IOL is the accuracy and repeatability of the preoperative corneal topography. The calculation of corneal SA requires highest precision of corneal topography in the periphery, since the difference in elevation between an aspheric corneal surface and a spherical surface is only some microns (**Figure 4**). Schröder et al. investigated the measurement repeatability and precision of several corneal topographers and tomographers and found that the repeatability of these devices is decreasing from the center to the periphery and

Another limitation arises from the concept of aberration correction itself. As outlined in **Figure 3**, the method requires the alignment of the IOL in relation to the cornea to be as perfect as possible. But even if an ideal positioning of the IOL is achieved intraoperatively, the risk of decentration or tilt remains in the postopera-

Altmann et al., Eppig et al., and others analyzed the effects of decentration and tilt of spherical and aspherical IOLs on the image quality and found that it is more affected by decentration than by tilt and that the susceptibility of lens misalignment increases with the amount of SA to be corrected [9, 39–46]. Some authors defined that a range of decentration within a SA-correcting IOL would perform better or equal than a standard spherical IOL. This range was reported to be between 0.0 and 0.3–0.8 mm, depending on the design of the lens and simulation conditions [9, 40–42]. In a previous publication, we summarized the data on the IOL

decentration from various sources and found that the clinically observed decentration is between 0 and 1 mm but most frequently about 0.3 mm [33, 40, 47–56]. Others showed that there is a tendency for IOLs decentering and tilting into nasal

Gillner et al. showed in a previous publication that IOL designs with a more

*Difference in corneal elevation for three surfaces with R = 7.77 mm radius of curvature and several values of Q*

conservative correction of SA may provide a larger range of tolerance to decentration [41]. Examples thereof are the ZO/ASPHINA design (Carl Zeiss Meditec AG, Berlin, Germany) and the Aspheric Balanced Curve Design (ABCD) (Hoya Corporation, Tokyo, Japan). Both designs are based on higher-order

direction with mirror symmetry between both eyes [51].

may not be sufficient to detect small changes in corneal asphericity [38].

*Simulation of modulation transfer function at 30 cycles per degree for four different intraocular lenses and a pupil diameter of 3.0 mm in the Liou-Brennan model eye as a function of decentration [40, 41, 57].*

**Figure 6.**

*Simulation of modulation transfer function at 30 cycles per degree for four different intraocular lenses and a pupil diameter of 4.5 mm in the Liou-Brennan model eye as a function of decentration [40, 41].*
