In Vitro Strehl Ratios with Spherical, Aberration-Free, Average, and Customized Spherical Aberration-Correcting Intraocular Lenses

Abstract

purpose. To determine in vitro image qualities of artificial eyes achieved with spherical, aberration-free, average spherical aberration-correcting, and customized spherical aberration-correcting IOLs in centered, decentered, and tilted positions.

methods. The in vitro performance of these IOL models was determined by optical bench measurements. The experimental setup included a laser light source controlled by aperture stops that corresponded to 3- and 5-mm pupil apertures, an artificial eye with three alternative corneal models exhibiting low, intermediate, and high spherical aberration (SA), IOLs mounted to an immersed IOL holder that could be moved laterally and tilted, and a charge-coupled device camera and software to determine three-dimensional point spread function (PSF), modulation transfer function, and Strehl ratio.

results. Differences among the various lens models turned out to be low for a 3-mm pupil. For a pupil aperture of 5 mm, customized IOLs showed the best results for perfect lens positioning. With ongoing decentration and tilt, customized IOLs rapidly lost their advantages, particularly in corneas with high SA and IOLs of high diopters. Spherical IOLs were always inferior to aberration-free IOLs.

conclusions. Reasonably well-centered aberration-correcting IOLs may provide considerably better image quality than conventional spherical IOLs. In the presence of significant postoperative decentration and tilt of the IOL, aberration-free IOLs are the safest option among the various intraocular lens designs.

Typically, the cornea of the human eye refracts an incident plane wave into a nonspherical wave. In most instances the peripheral rays are refracted into positions closer to the corneal apex than the paraxial rays. ^{1 2} The wavefront then exhibits positive spherical aberration (SA); this aberration is usually named the corneal SA. Until recently, intraocular lenses (IOLs) with spherical refractive surfaces were used in pseudophakic eyes. Such IOLs exhibited positive SA, adding to the usually positive corneal SA. Therefore, the total SA of pseudophakic eyes is usually high, and the image quality is comparatively low. 

In the past few years, IOLs with varying amounts of negative SA have appeared in the market. Such IOLs are designed to counteract positive corneal SA, ^{3 4} such as the natural lens. ^{5 6} Consequently, the resultant SA of the pseudophakic eye is reduced, and image quality is improved. ^{7 8 9}  

The amount of negative SA differs for the various aspherical IOLs. One (Tecnis; Advanced Medical Optics, Santa Ana, CA) exhibits the largest amount of negative SA and compensates a corneal SA of +0.27 μm. On the low end, two other (Softport AO [Bausch & Lomb, Rochester, NY]; Acritec LC [Carl Zeiss Meditec, Hennigsdorf, Germany]) models are associated with zero SA. A fourth (IQ; Alcon, Alcon Laboratories, Fort Worth, TX) is an example of an IOL with negative SA that lies between these extremes. ¹⁰  

For perfectly positioned IOLs, the most suitable choice of lens from the available SA-correcting models may be based on corneal topography or corneal wavefront error. However, the optimum choice of the IOL model is difficult when lens decentration and tilt are taken into account. IOLs that perform very well in perfectly centered and nontilted positions ^{11 12 13} may provide poor image quality in case of sizable decentration or tilt. In addition, IOLs that provide modest image quality in perfectly centered positions may be comparatively better in positions with considerable decentration or tilt. 

The aim of this study was to develop general guidelines for proper choice of different intraocular lens designs assuming the presence of postoperative lens decentration and lens tilt. 

Methods

Description of the Test Lenses

The principal aim of aspheric lens designs is to achieve minimum amounts of aberration of the pseudophakic eye. Thus, the design of the IOL depends on the parameters of the reference cornea with which it is combined. 

With the exception of toric IOLs and novel coma-reducing IOLs, ¹⁴ commercially available IOLs are designed to compensate corneal SA. Therefore, corneas exhibiting only SA and no other higher order aberrations were considered as reference corneas. Other higher order corneal aberrations were excluded in the reference corneas to study the exclusive influence of corneal SA on ocular image quality with decentered and tilted IOLs. Naturally, the design corneas with spherical SA may produce many other ocular aberrations when combined with decentered or tilted SA-correcting IOLs. In the present experiments, the cumulative influence of all these possible ocular aberrations on image quality was determined by calculation of the associated Strehl ratio. 

For corneas that can be represented by aspheres, corneal SA is a function of corneal refractive power (K value) and corneal topographic asphericity (Q value). For corneas with positive spherical aberration, corneal SA increases with increasing K value and increasing Q value. 

The values 40 diopter (D) and 47 D were chosen as minimum and maximum refractive powers for reference corneas, respectively, to cover a wide clinical range. ^{1 15 16} Accordingly, a minimum Q value of −0.44 and a maximum Q value of −0.03 were used for our reference corneas. ^{1 2 15 16 17 18 19} A cornea with a power of 40 D and a Q value of −0.44 was defined as a low SA cornea. The SA [Z(4,0)] of this cornea was 0.054 μm for a 6-mm aperture. 

The reference cornea with maximum SA exhibited a refractive power of 47 D and a Q value of −0.03 and was termed a high-SA cornea. Its SA [Z(4,0)] was 0.416 μm. 

The third reference cornea exhibited a K value of 43 D and a Q value of −0.26. This reference cornea was named an intermediate SA cornea, and its SA [Z(4,0)] was 0.172 μm. All design corneas exhibited practically no other higher order SA. 

Four different IOL models were combined with the three reference corneas: spherical IOL (SIOL), aberration-free IOL (FIOL), average SA-correcting IOL (AIOL), and customized SA-correcting IOL (CIOL). All IOLs were of biconvex shape. 

The SIOLs were dimensioned for paraxial light rays and exhibited spherical refracting surfaces across the entire lens diameter. The FIOLs were designed such that they did not add any SA to an incoming wave. The refracting surfaces of these lenses were aspheres. 

The AIOLs in our study were optimized to the intermediate SA cornea. Figure 1shows a schematic illustration of a pseudophakic eye consisting of a model cornea and an IOL. The surfaces of the IOL of a given paraxial power were adjusted such that all incident parallel rays were focused by the cornea and the IOL into a single focus on the retina. Consequently, the AIOL was a lens that compensated a corneal SA of 0.172 μm. 

The CIOLs were lenses optimized for any of the particular corneas with which they were combined. For instance, a CIOL combined with the low SA cornea compensated a corneal SA of 0.054 mm, whereas a CIOL combined with the high SA cornea compensated a corneal spherical aberration of 0.416 μm. A CIOL for the intermediate SA cornea compensated a corneal SA of 0.172 μm (i.e., the AIOL and CIOL were identical when combined with the intermediate SA cornea). 

Experimental Setup

A schematic illustration of the experimental setup is shown in Figure 2 . The experimental setup consisted of a laser source (543.5 nm; Uniphase 1654; JDS Uniphase, San Jose, CA), a gray wedge to adjust laser intensity, a collimation system, an aperture stop, an artificial cornea, a wet cell containing the IOL fixed to the lens holder, an imaging system, and a charge-coupled device (CCD) camera. 

The wet cell featured two parallel glass plates of optical quality (BK7; Schott, Southbridge, MA) on the front and rear sides. The wet cell was filled with saline solution. The imaging system, including the CCD, could be moved along the optical axis for different focus positions behind the IOL. 

The design corneas, as described, were simulated in the setup by the artificial cornea (Fig. 2)in combination with the front coverglass of the wet cell. The artificial cornea was an aspheric convex-plano PMMA lens. The aspheric front surface of this artificial cornea was dimensioned as follows: first, a set of light vectors for incident rays from the design cornea to the IOL front surface was determined. This set of light vectors was then used in reverse ray tracing, and the shape of the front surface of the artificial cornea was varied until all rays emerging from this surface were parallel to the optic axis of the setup. This ensured correct light incidence on the IOLs in vitro. As an example, based on the values given in Table 1 , the intermediate SA cornea with a central radius 7.814 mm and an asphericity of −0.26 was simulated by a convex-plano PMMA lens with central front radius of 24.224 mm, an asphericity of −0.198, and a central thickness of 3.138 mm. This PMMA lens represented the artificial cornea. The aperture stop (Fig. 2)had diameters of 10.72 mm for a 5-mm pupil and 6.38 mm for a 3-mm pupil. 

All four IOL models of 10 D, 20 D, and 30 D were combined with the intermediate SA cornea, whereas the low and high SA corneas were combined with the IOLs of 10 D and 20 D and of 20 D and 30 D, respectively. 

The lens holder could be rotated by means of a goniometer (OWIS GO 90) about the y-axis and shifted laterally along the x-axis (Fig. 2) . The goniometer was designed such that the center of rotation coincided with the center of the IOL. Figure 3shows the key elements of the experimental setup. 

For the measurements, an IOL was fixed to the lens holder and immersed in the wet cell. The optical system, consisting essentially of the artificial cornea and the immersed lens, produced a focus (PSF) in the image plane (Fig. 2) . This image was then projected onto a CCD camera. The modulation transfer function (MTF) calculation was based on PSF by Fourier transformation. Given that the MTF was calculated from the intensity distribution of the focus (PSF), the calculated MTF was the noncoherent MTF because phase relations were not conserved in this PSF. All four IOL models were measured for pupil apertures of 3 mm and 5 mm. 

Calculated Optical Key Functions

Analysis software was programmed in LabView (National Instruments, Austin, TX) and featured the following key functions: intensity control (gray wedge), focus search (movable imaging system including the CCD), measurement of PSF, calculation of MTF, and Strehl ratio. 

PSF was measured after adjustment of light intensity and focus position. Then the MTF and the Strehl ratios were calculated. Cutoff frequency was assessed automatically if the optical system was close to perfect. If this assessment failed, such as in the case of strongly degraded MTF functions, the cutoff frequency could be set manually. Figure 4shows examples of the PSF, MTF, and calculated Strehl ratio for one of the measurements. 

Results

Optical bench measurements of artificial eyes were extremely sensitive to any minor deviation of the parameters involved. Consequently, for a pupil diameter of 5 mm, a Strehl ratio of exactly 1 could rarely be achieved for the theoretically diffraction-limited artificial eyes (i.e., for eyes incorporating a customized IOL). According to the Maréchal criterion, ²⁰ a lens or lens system is practically perfect if the root-mean-square wavefront aberration is below 1/14 of the wavelength and if the Strehl ratio exceeds 0.8. In view of this, a measured Strehl ratio of 0.9 was chosen as the minimum acceptable limit of the image quality for measurements with centered CIOLs and 5-mm pupil apertures. With the 3-mm pupil aperture maximum, Strehl ratios in excess of 0.97 could be achieved experimentally. 

Results for the 3-mm Pupil Aperture

IOL Decentration.

Figure 5shows the Strehl ratios as a function of decentration for the four IOL models studied. Differences in performance were small if the pupil was small. In general, Strehl ratios decrease with increasing decentration. This occurred more rapidly with aberration-correcting IOLs than with SIOLs and FIOLs. As is apparent from these results, SIOL and FIOL tended to provide better image quality than the other lens models when decentration was high. 

Worth mentioning is the relatively steep decrease of the Strehl ratio with increasing decentration for the AIOL in combinations of the low SA cornea and the low IOL power of 10 D. 

IOL Tilt.

Figure 6shows the Strehl ratios as a function of lens tilt for the four IOL models investigated. Again, the differences between the various lens models were relatively small, particularly for small amounts of tilt. For average and large IOL powers, the models show similar image qualities at large lens tilt. If the tilt exceeded 4°, the FIOL in combination with the high SA cornea showed better performance. With the exception of combinations of spherical lenses of high power with the high SA cornea, all lens models appeared to provide acceptable image quality even in the presence of lens tilts up to approximately 4°. 

Results for 5-mm Pupil Aperture

IOL Decentration.

Differences in the performance of the various lens models were significant for large pupil aperture (5 mm; Fig. 7 ). The experimental results show the steep decay in image quality with increasing decentration for the CIOL in combination with an intermediate SA cornea or a high SA cornea. By contrast, CIOLs appeared to provide stable and high image quality when implanted into eyes with low SA corneas. With good centration, the AIOL model provided better image quality than the SIOL or FIOL model. With decentration, however, the image quality tended to decrease more rapidly with the AIOL than with the SIOL or FIOL model when combined with the intermediate or high SA cornea. For the intermediate SA cornea, the FIOL appeared to be superior to the other lens models when decentration was 0.15 mm to 0.30 mm. 

IOL Tilt.

Figure 8shows the decrease in image quality for the various lens models with increasing lens tilt. CIOLs provided optimum image quality in all corneal models but performed rapidly poorer with increasing lens tilt. Generally, tilt affected the performance of SIOLs and FIOLs to a lesser extent than AIOLs and CIOLs. For the most likely case of an intermediate SA cornea and an IOL of 20 D, FIOL was better than the other lens designs for tilt angles exceeding 1.5°. The FIOL was superior to the SIOL in all combinations of cornea models and IOL powers. 

Combinations of IOL Decentration and Tilt.

Finally, AIOL exhibiting tilt and decentration was also studied. Figure 9shows the results: the combination of decentration and proper tilt may yield better image quality than tilt or decentration alone. 

Discussion

Given the large diversity of corneal parameters, ^{1 15 16 17 18 19} preoperative determination of the anterior corneal surface and the corneal SA appears to be a prerequisite for proper choice of aspherical IOLs. In this study, the selection of reference corneas with various SA covered a representative range of most likely corneal SA. 

The present in vitro measurements provided information about the deterioration of image quality with increasing decentration and tilt. As a comparative metric for image quality, the Strehl ratio was used that implicitly included the influence of all aberrations induced by the cornea SA and decentered or tilted IOLs. Naturally, the results do not provide information about possibly advantageous postoperative SA ¹⁹ and about possible compensation of SA by neuronal transfer function. ²¹  

SIOLs do provide poorer image quality than all other IOL models in perfectly centered and nontilted positions. However, in the presence of substantial decentration or tilt, SIOLs may provide better image quality than AIOLs and CIOLs (Figs. 5 6 7 8) . 

FIOLs are almost always superior to SIOLs. This is true for perfectly centered and nontilted lens positions and for positions marked by decentration or tilt. 

Ideally positioned AIOLs provide excellent image quality when implanted into eyes with intermediate SA corneas. With the exception of the low SA cornea, they provide better image quality than SIOLs and FIOLs when perfectly positioned. In a low SA cornea, AIOLs appear to exhibit too high negative SA (Fig. 5) . AIOLs are more sensitive to decentration and tilt than FIOLs and SIOLs. The measured higher sensitivity of AIOL to decentration in comparison with FIOL is in agreement with previously reported results. ²²  

CIOLs provide ideal image quality for all types of corneas, but only in perfectly centered and nontilted positions. Particularly in combinations of the high SA cornea and CIOLs of high dioptric power, already minor amounts of decentration or tilt reduce ocular image quality severely. 

Combinations of decentration and tilt may lead to better (Fig. 9)or poorer image quality than decentration or tilt alone. However, favorable combinations of tilt and decentration are accidental and cannot be presumed. 

Mean IOL decentrations reported in the literature range between 0.21 mm and 0.39 mm, with high standard deviations up to 0.25 mm. ^{23 24 25 26} This wide range of postoperative IOL positions was confirmed by phakometric examination in eight eyes with decentration in one axis up to 0.96 mm. ²⁷ Mean values for IOL tilt evaluated in clinical examinations range from 1.4° to 3.11°, with standard deviations up to 1.81°. ^{23 24 25 26 28}  

For individual cases, calculation of the performance of pseudophakic eyes exhibiting corneal aberrations in addition to SA was shown. ²⁹ In addition, the significance of various aberrations and tolerances for misalignment of SA-correcting IOLs for an individual eye was determined. ^{30 31}  

Based on these results we suggest that SIOLs may be safely substituted by FIOLs. For mesopic conditions and large pupil apertures, the CIOLs may be advantageous but only if significant postoperative decentration or tilt can be excluded. 

The AIOL is a valid option for eyes with corneas that exhibit intermediate to high SA in well-aligned positions. For corneas with low SA, the FIOL is preferable because the AIOL may overcompensate corneal SA. 

In conclusion, FIOLs should replace SIOLs. In view of the in vitro results of the present study, the advantages of aberration-correcting IOL designs must be carefully evaluated against FIOLs, particularly when individual corneal data and maximum pupil diameter are not assessed preoperatively. 

 Supported by Grant 11180 from the Jubilaeumsfonds der Oesterreichischen Nationalbank, Vienna, Austria.

 Submitted for publication April 19, 2008; revised August 10, 2008; accepted January 16, 2009.

 Disclosure: S. Pieh, None; W. Fiala, None; A. Malz, None; W. Stork, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

IOL optimization in a pseudophakic eye.

Figure 2.

 

Experimental setup: (a) laser; (b) gray wedge; (c) collimation system; (d) aperture stop; (e) artificial cornea; (f) wet cell with IOL and IOL holder; (g) image plane; (h) imaging system; (i) CCD camera.

Table 1.

 

Positions of the Various Components of the Experimental Setup

Distance between the Essential Optical Components
Plane 1	Distance between Planes (mm)	Plane 2
Laser aperture plane	25.0	Rear side artificial cornea
Rear side artificial cornea	12.9	Front side cover glass
Front side cover glass	5.0	Rear side cover glass
Rear side cover glass	12.4	Lens holder front plane
Lens holder front plane	2.0	Lens holder rear plane
Lens holder rear plane	0.125	Lens center plane
	(half haptic thickness)

Figure 3.

 

Photograph of the main components of the experimental setup: (a) laser; (b) gray wedge; (c) collimation; (d) aperture and artificial cornea; (e) wet cell; (f) goniometer with lens holder; (g) imaging system and CCD).

Figure 4.

 

PSF (left) and corresponding MTF and Strehl ratio (right) of a tilted customized IOL (low SA cornea, 5-mm pupil aperture, CIOL 20 D, 6° tilt).

Figure 5.

 

Measured Strehl ratios for a pupil diameter of 3 mm with decentered IOLs of the four lens designs (SIOL, FIOL, AIOL, CIOL). IOL power from left to right: 10 D, 20 D, and 30 D. Corneal models from top to bottom: low SA cornea (40 D; asphericity, −0.44), intermediate SA cornea (43 D; asphericity, −0.26), and high SA cornea (47 D; asphericity, −0.03).

Figure 6.

 

Measured Strehl ratios for pupil diameters of 3 mm with tilted IOLs of the four lens designs (SIOL, FIOL, AIOL, CIOL). IOL power and corneal models as in Figure 5 .

Figure 7.

 

Measured Strehl ratios for pupil diameters of 5 mm with decentered IOLs of the four lens designs (SIOL, FIOL, AIOL, CIOL). IOL power and corneal models as in Figure 5 .

Figure 8.

 

Measured Strehl ratios for pupil diameters of 5 mm with tilted IOLs of the four lens designs (SIOL, FIOL, AIOL, CIOL). IOL power and corneal models as in Figure 5 .

Figure 9.

 

Example of Strehl ratio of a decentered IOL as a function of tilt.