Reducing ocular aberrations generally improves optical quality, the contrast of images formed on the retina, and thus spatial vision.1–3 In recent years, several approaches have been used to reduce ocular aberrations.2–7
The reduction of ocular longitudinal spherical aberration (LSA) has been achieved successfully with intraocular lenses (IOLs). The Tecnis IOL (Abbott Medical Optics Inc, Santa Ana, California) partially corrects wavefront aberration by compensating for the corneal spherical aberration of an average cataract patient.8 Recent studies show that this lens successfully eliminates spherical aberration in the average pseudophakic eye.7 As a result of the correction of spherical aberration provided by aspheric IOLs, the postoperative contrast vision of patients implanted with this lens has improved, as reported in various studies.7,9
In the pseudophakic eye, the IOL induces chromatic aberration, caused by the dispersion of the lens material. Current IOLs are made of different plastic materials with different dispersive characteristics,10,11 resulting in different magnitudes of pseudophakic ocular chromatic aberration.12 Ocular longitudinal chromatic aberration (LCA) can be compensated by an achromatizing lens in front of the eye, a contact lens, or an IOL.13 When using an IOL as the achromatizing lens, the decentration is limited14 and independent of eye movements, and it ensures that the correction of chromatic aberration occurs close to the eye’s nodal point.15 López-Gil and Montés-Micó13 as well as Siedlecki et al16 analyzed this principle in a schematic eye. In a subsequent study, Artal et al17 tested the principle in real subjects using a vision simulator. They found that the greatest improvement in visual performance was obtained when both LCA and LSA were corrected.17
In this study, we investigated both the potential advantages and disadvantages of a new theoretical design of IOLs, which corrects a fixed amount of LSA and LCA, equal but opposite in sign to the average aphakic eye, leaving the average pseudophakic eye with essentially zero LSA and LCA. A set of 46 eye models was used, which was based on measured corneal topography and axial lengths of 46 individual cataract patients. The average spherical aberration (Z04) of this set of eye models was 0.27±0.16 μm (6-mm corneal aperture), and the axial length was 23.41±1.38 mm.8,18,19 The models have shown the ability to predict improvements in contrast, compared to clinical measurements.20 The models were used to address aspects that were not previously studied: optical performance in a large population of eyes, depth of focus, and tolerance to lens displacement (tilt and decentration).
Materials and Methods
Optical models of 46 human eyes were constructed, using clinical data of 46 cataract patients (see also Piers et al20). Refractive indices and dispersion of ocular media were taken from Legrand.21 The optical calculations (using OSLO Premium [Lambda Research Corp, Littleton, Massachusetts]) were performed for 37 wavelengths (from 385 to 745 nm), representing equal energy white light. The pseudophakic luminosity function was created using the phakic Judd-Voss modified CIE luminosity function, and subsequently subtracting the optical density of the crystalline lens,22,23 then adding the optical density of the IOL (silicone material, refractive index of 1.46 at 545 nm).
For each of the 46 eye models, the IOL power was determined using the SRK/T formula. In general, this does not leave the eye models emmetropic. Therefore, spectacle lenses were placed at 12 mm in front of the anterior corneal surface. The spectacle lenses corrected the spherical and cylindrical power in increments of 0.25 diopters (D). The cylinder axis was determined with a 1° resolution. The best spectacle correction was determined by maximizing the volume under the radial polychromatic modulation transfer function (pMTF) for a 3-mm aperture (photopic pupil size).
Three different IOL designs were evaluated—a traditional spherical IOL (911A, Abbott Medical Optics Inc); an aspheric IOL (Tecnis), correcting the LSA of the average aphakic eye8; and an aspheric refractive/diffractive IOL, correcting for the average LSA and LCA of the aphakic eye. The two IOL designs correcting LSA produced a fixed correction of μm for a 6-mm corneal aperture.8
The LSA and LCA correcting IOL combines a refractive lens with a conventional monofocal diffractive kinoform on the posterior side of the IOL. The diffractive element corrects the chromatic aberration of the eye and the refractive part of the IOL. The refractive part and diffractive part of the lens combined has a fixed amount of correction of chromatic aberration of 0.60 D (between f-line and c-line). This is equal and opposite to the population average of the set of 46 eyes in the aphakic state. Because the refractive part of each IOL power is different, each IOL power has a different ratio between diffractive and refractive optical power. For example, a 20.00-D IOL has a 4.60-D diffractive power and a 15.40-D refractive power, whereas a 25.00-D IOL has a 5.20-D diffractive power and 19.80-D refractive power.
Pseudophakic retinal image quality—average radial pMTF and area under the pMTF curve (AUC) up to 30 cycles per degree (cpd)—and ocular wavefront aberration were calculated in each of the 46 pseudophakic eye models, consecutively containing each of the three lens designs. The eye models incorporated a 5° field angle (visual axis) and a 4-mm apparent pupil size.
The ratio of the AUC for aberration-correcting lenses to the AUC for the spherical control lenses was used to estimate a percent of improvement in predicted optical quality (optical improvement factor). Sensitivity to decentration and tilt was evaluated by introducing various degrees of decentration in the presence of a fixed amount of 3° of temporal tilt.14,24
Figure 1 shows the average radial pMTF for the three IOL designs in the eyes with their best spectacle correction. The pMTF correlates with the aberration correction of the IOL designs: the IOL correcting for both average LSA and LCA shows the highest modulation transfer, followed by the IOL correcting for average LSA only, and the spherical IOL, respectively. The difference in pMTF was statistically significant for all spatial frequencies of 4 cpd and higher (P<.01).
Figure 1. Average modulation transfer function of the 46 eye models, subsequently implanted with the three different intraocular lenses (IOL). Diamonds = IOL correcting longitudinal spherical aberration (LSA) and longitudinal chromatic aberration, squares = IOL correcting LSA only, and triangles = spherical IOL. Error bars denote ±1 standard deviation. cpd = cycles per degree
Figure 2 shows the improvement factors, based on the AUC. Comparing the IOL correcting both average LSA and LCA with the IOL correcting LSA only, the improvement factor is 1.19±0.12. Comparing the IOL correcting both average LSA and LCA with the spherical IOL, the improvement factor is 1.43±0.29. Comparing the IOL correcting average LSA only with the spherical IOL, the improvement factor is 1.21±0.20. All improvements are statistically significant (P<.01).
Figure 2. Average improvement factors of correcting aberrations of the eye as predicted by the radial polychromatic modulation transfer function (pMTF) values. Error bars denote ±1 standard deviation. LSA = longitudinal spherical aberration, LCA = longitudinal chromatic aberration
Figure 3 shows the defocus curves of radial pMTF for a spatial frequency of 8 cpd. The pMTF correlates with the aberration correction of the IOL designs, for a defocus range of at least −0.50 to +0.50 D (P<.01). For the IOL correcting both LSA and LCA, pMTF at 8 cpd is equal or better than the other two designs for the range of −1.00 to +0.50 D. Using the definition of depth of focus of the defocus range over which the MTF is >80% of the peak MTF, the depth of focus was 0.81, 0.74, and 0.71 D for the spherical IOL, the IOL correcting LSA only, and the IOL correcting both LSA and LCA, respectively.
Figure 3. Defocus curves of modulation transfer at 8 cycles per degree (cpd). Diamonds = IOL correcting longitudinal spherical aberration (LSA) and longitudinal chromatic aberration, squares = IOL correcting LSA only, and triangles = spherical IOL. Error bars denote ±1 standard deviation.
Figure 4 shows the radial pMTF when the IOL is decentered in increments of 0.2 mm, and in the presence of 3° of temporal tilt. As shown in Figure 4, the pMTF varies per direction of the decentration. The standard deviation is on average 0.10 (range: 0.06 to 0.14). At a decentration of 0.6 to 0.8 mm, the pMTF levels are similar for all IOL designs. For decentration >0.8 mm, the spherical IOL shows the highest performance.
Figure 4. Radial polychromatic modulation transfer function (pMTF) as a function of intraocular lens (IOL) decentration in the presence of 3° of temporal IOL tilt. The curves show the decentrations in two directions, including their standard deviations. Circles/solid lines represent horizontal decentration, and squares/dashed lines represent vertical decentration. At zero decentration: green line: IOL correcting longitudinal spherical aberration (LSA) and longitudinal chromatic aberration; red line: IOL correcting LSA only; and blue line: spherical IOL.
Chromatic aberration has a detrimental effect on the in-focus retinal image quality. This study shows that correcting both the ocular LSA and LCA increases the optical quality of the pseudophakic eye, and therefore, confirms the studies in symmetrical schematic eye models.13,16 We used a set of eye models that included irregular, higher order aberrations. Furthermore, the eye models were refracted to the nearest 0.25 D with spectacles, thus leaving some residual defocus and cylinder. We believe these factors make these eye models a more realistic representation of pseudophakic eyes. We did not include a Stiles–Crawford effect in our calculations. The Stiles–Crawford effect influences vision and the pMTF; however, for a 4-mm pupil, as we used in our study, the effect is small,15 and consequently, the influence on the trends found is negligible.
The differences among the IOL designs can also be appreciated from the point spread function (PSF). Figure 5 shows the PSF for a typical eye of the set of 46 eye models. The figure shows the larger light intensities achieved when aberrations are being corrected.
Figure 5. Point spread functions resulting from the three intraocular lens designs in a typical eye model of the set of 46 eye models. The colors depict the relative irradiance. The patch size is 5 arc minutes. LCA = longitudinal chromatic aberration, LSA = longitudinal spherical aberration
Current IOLs are made of different plastic materials with different dispersions. But even IOL materials of the same class (eg, acrylic) can have different chromatic characteristics.11 These differences seem clinically significant, as patients implanted with IOLs with high amounts of chromatic aberration have shown reduced contrast sensitivity under certain conditions.25
Longitudinal chromatic aberration of human eyes varies little between individuals.26 As a result, an IOL that corrects a fixed amount of LCA would be beneficial for all or most cataract patients. Although the dispersion of the media was identical in all eye models, the chromatic aberration of the total eye differed for each eye, as a result of differences in eye dimensions. Figure 6 shows the distribution of the LCA of the aphakic eye models, expressed as refractive difference between wavelengths of 486 and 656 nm. The refraction was calculated from the Zernike terms for these two wavelengths.27
Figure 6. Histogram of the longitudinal chromatic aberration (LCA) of the 46 aphakic eye models, expressed as the difference in refraction between wavelengths 486 nm (f-line) and 656 nm (c-line).
A different IOL optical power was chosen for each eye, based on the SRK/T formula. Although IOLs of different optical powers were used, each IOL was designed to correct for the same amount of LCA. Because the LCA for the aphakic eye models showed little variation, correcting a fixed amount of LCA is effective. Yoon and Williams3 showed that the correction of chromatic aberration is especially effective at improving vision if monochromatic aberrations are corrected at the same time. This indicates that for the IOL correcting both LSA and LCA, a customized correction of LSA could result in a further improvement of best focus image quality. Customization of LSA in combination with correction of LCA could have a greater effect than customization of a lens that corrects only LSA.
One of the objectives of this study was to investigate influence of correcting LCA on the depth of field. In general, correcting aberrations may reduce the depth of field. In practice, depth of field depends on the definition or criterion adopted. When the MTF is used for an assessment of depth of field, the 80% criterion often is used, meaning the depth of field range over which the MTF is >80% of the peak MTF. Using the MTF of idealistic on-axis eye models (containing no higher order aberrations other than spherical aberration) and the 80% criterion, depth of field is increased by adding LSA and LCA to the eye model. This effect is attenuated when higher order aberrations are present. In this study, which includes the effects of higher order and asymmetrical aberrations, the difference in depth of field is approximately 0.10 D.
Previous studies have shown that after correcting LSA, IOL decentration is more critical than IOL tilt.24 In this study, the IOL was subsequently decentered in four directions. Our results show that the lenses correcting both LSA and LCA can be decentered, on average, as much as between 0.6 and 0.7 mm before the optical performance is less than that of a spherical control lens, and as much as 1.0 mm before the performance is below that of the Tecnis lens. This suggests that centration of the IOL is important for lenses correcting both LCA and LSA. Several studies have shown that with normal, uneventful cataract surgery, IOL decentration is approximately 0.2–0.3±0.15 mm,14,28 indicating that the combined correction of LCA and LSA can be a viable option in normal, uneventful cataract surgery.
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