A white light source with 2 plus lenses and a pinhole are used to produce a collimated light beam. The artificial eye according to the Gullstrand specifications uses a cornea made of polymethylmethacrylate, an artificial pupil, a mounting for the intraocular lens (IOL), and a retinal plane made of glass. The distance between the IOL and the retinal plane can be adjusted by means of a micrometer screw. The image is magnified with a microscope lens and visualized using a digital camera connected to a personal computer. δ Indicates pinhole diameter; Ω, viewing angle; δ′, diameter of the retinal pinhole image; Δ, diameter of the investigated area on the retina; Δ′, diameter of the investigated area on the chip of the digital camera (CCD-ARRAY); fC, focal length of the collimator lens; fE, focal length of the eye; a, distance between the retina and the microscope objective; and b, distance between the microscope objective and the CCD-ARRAY.
Same set up as Figure 1, but a minus lens is used to obtain a divergent beam. IOL indicates intraocular lens; δ, pinhole diameter; δDL, virtual pinhole diameter created by the dispersing lens; δ′DL, diameter of the virtual pinhole image on the retina; fC, focal length of the collimator lens; fDL, focal length of the dispersing lens; d, distance of the dispersing lens to the nodal point of the eye; a, distance between the retina and the microscope objective; and b, distance between the microscope objective and the chip of the digital camera (CCD-ARRAY).
Point spread function of the monofocal 811C with 20 D (model 811C20; Pharmacia Inc, Columbus, Ohio), the distance focus of the bifocal diffractive 811E (model 811E distance, Pharmacia Inc), the focus of the monofocal SI40NB with 20 D (model SI40NB20; Allergan Optical Inc, Irvine, Calif), and the focus of the SA40N (SA40N distance, Allergan Optical Inc). AU indicates arbitrary units.
Point spread function of the monofocal 811C with 25 D (model 811C25; Pharmacia Inc, Columbus, Ohio), the near focus of the 811E (model 811E near; Pharmacia Inc), the SI40NB with 24 D (model SI40NB24; Allergan Optical Inc, Irvine, Calif), and the near focus of the SA40N (model SA40N near; Allergan Optical Inc). AU indicated arbitrary units.
Modulation transfer function (MTF) of the monofocal 811C with 20 D (model 811C20; Pharmacia Inc, Columbus, Ohio), distance focus of the 811E (model 811E distance; Pharmacia Inc), the monofocal SI40NB with 20 D (model SI40NB20; Allergan Optical Inc, Irvine, Calif) and the distance focus of the SA40N (model SA40N distance; Allergan Optical Inc). Diff indicates diffractive; Diff Limit, MTF of a diffraction-limited lens computed for a pupil opening of 4.5 mm and a light wavelength of 500 nm. The different background shading indicates the clinical relevant area up to 30 cycles/degree.
Modulation transfer function (MTF) of the monofocal 811C with 25 D (model 811C25; Pharmacia Inc, Columbus, Ohio), the near focus of the 811E (model 811E near; Pharmacia Inc), the monofocal SI40NB with 24 D (model SI40NB 24; Allergan Optical Inc, Irvine, Calif), and the near focus of the SA40N (model SA40N near; Allergan Optical Inc). Diff indicates diffractive; Diff Limit, MTF of a diffraction-limited lens computed for a pupil opening of 4.5 mm and a light wavelength of 500 nm. The different background shading indicates the clinical relevant area up to 30 cycles/degree.
Schematic light distribution in bifocal and multifocal intraocular lenses containing a central part only for the distance focus. Intermediate focal points like in the multifocal concept are only indicated.
Pieh S, Marvan P, Lackner B, Hanselmayer G, Schmidinger G, Leitgeb R, Sticker M, Hitzenberger CK, Fercher AF, Skorpik C. Quantitative Performance of Bifocal and Multifocal Intraocular Lenses in a Model EyePoint Spread Function in Multifocal Intraocular Lenses. Arch Ophthalmol. 2002;120(1):23-28. doi:10.1001/archopht.120.1.23
Copyright 2002 American Medical Association. All Rights Reserved. Applicable FARS/DFARS Restrictions Apply to Government Use.2002
To compare the optical properties of bifocal diffractive and multifocal refractive intraocular lenses.
A model eye with a pupil 4.5 mm in diameter was used to determine the point spread function (PSF) of the distance focus and near focus of a diffractive bifocal intraocular lens (IOL) (model 811E; Pharmacia Inc, Columbus, Ohio) and of a refractive multifocal IOL (model SA40N; Allergan Optical Inc, Irvine, Calif) to compare them with PSFs of foci of corresponding monofocal lenses. For interpreting the PSFs the through focus response, the modulation transfer function, and the Strehl ratio were evaluated.
The intensity of the distance focus of the bifocal diffractive lens reached 58.5% and the near focus attained 42.7% of the intensity of a corresponding monofocal lens. The maximal halo intensity surrounding both foci was approximately 4.5%. The distance peak of the refractive multifocal IOL was 73.4% and the near peak 25.1% of a corresponding monofocal lens. The out-of-focus image overlaying the distance focus of the refractive multifocal IOL was approximately 3% of the light intensity of the distance focus, whereas the PSF of the near focus of the multifocal IOL is substantially affected by out-of-focus images. The computed modulation transfer functions show better results for the monofocal lenses, similar results for the tested distance foci, and clear advantages for the bifocal diffractive near focus.
Modulation transfer functions reveal comparable properties for distance vision and a superiority of the bifocal diffractive lens over the refractive multifocal lens for near vision.
IN GENERAL, 2 groups can be distinguished within multifocal intraocular lenses (IOLs), bifocal lenses producing 1 focal point for distance and 1 for near and real multifocal lenses that have focal points for near, distant, and intermediate positions. The development of multifocal lenses in recent years has led to concepts that intensify the distant focus using 1 to 2 mm of the central diameter of the lens mainly for the distance vision. This ensures a good distance visual acuity at a small pupil size under glare conditions, for example, with oncoming traffic at night, if the IOLs are centered.
A commonly used bifocal IOL is the diffractive 811E (Pharmacia Inc, Columbus, Ohio) made of polymethylmethacrylate (PMMA). Diffractive IOLs generate 2 focal points by diffraction of light at the posterior surface of the lens, similar to the physical principle of the Fresnel-phase plate.1- 3 Although 8% of the incident light is lost because of higher orders of diffraction, the relative power distribution of the remaining light is 52% to the distance focus and 48% to the near focus at a pupil diameter of 5 mm according to the manufacturer. This unequal light distribution between the distance and the near focus is caused by the central 1 mm directing light only to the distance focus.
An example of multifocal IOLs is the refractive SA40N (Allergan Optical Inc, Irvine, Calif) with 5 annular aspherical zones incorporated in the anterior surface of the lens to obtain the multifocal function. Each zone has additional refractive power up to 3.5 diopters (D). The central 2 mm is used mainly for the distance focus. The light distribution varies with pupil size. At a pupil diameter of 4 mm, 50% is directed to the distance focus point, 35% to the near focus point, and 15% to intermediate foci.4
The main differences between these 2 lenses are the physical principle used to obtain 1 or more additional focal points and the light distribution between the 2 or more focal points. The perceived image quality is affected by the ability to separate the focused from the unfocused image by retinal and cortical processing. Intraocular lenses dividing the incident light between axially separated images must take care to control the degree of contrast loss by balancing the brightness of the focused and unfocused images. The aim of our investigation was to measure and interpret the point spread functions(PSFs) of 2 lenses of the most recent generation, using a single-pass method in a model eye.
Light from a halogen lamp source (model HLX 64625; OSRAM, Munich, Germany[350-1100 nm, peak at 880 nm]) was transformed to a collimated light beam using 2 plus lenses and a pinhole (Figure 1). An artificial eye was used with a cornea made of PMMA according to the Gullstrand simplified eye model,5 with a diameter of 7.7 mm for the outer curvature and 6.8 mm for the inner. The anterior chamber depth was 5.6 mm and the diameter of the artificial pupil was 4.5 mm. Intraocular lenses could be fixed behind the pupil using the haptics. The retinal plane was made of 0.2-mm-thick glass. The distance between the IOL and the artificial retina was variable and could be adjusted by means of a micrometer screw. In this setup the retinal plane was fixed and the lens plane with the anterior chamber could be moved forward or backward. The artificial eye was filled with water that could communicate between the anterior and posterior chambers through shunts at the top. The image of the pinhole formed at the retinal plane was magnified with a microscope lens before reaching the chip of the digital camera (CCD) (model C4742-95; Hamamatsu Photonics, Tokyo, Japan [1280 × 1024-pixels, spectral response from 350-990 nm, peak at 440 nm]). The camera was connected to a computer and the images obtained on the monitor were measured using specific software. The sensitivity range of the camera could be adapted to the respective task.
The viewing angle Ω was computed in the following way (Figure 1):
where δ′ indicates the diameter of the retinal pinhole image;ƒE, focal length of the eye; δ, pinhole diameter; and ƒC, focal length of the collimator lens.
In the setup used, the δ was 30 µm and the ƒC was 0.08 m.
First, the focus of a 20-D PMMA monofocal lens (model 811C; Pharmacia Inc) was tested using a collimated light beam. This lens is made of the same material and has the same coating as the diffractive bifocal IOL (model 811E; 20 D+4 D, Pharmacia Inc) tested next. The camera sensitivity was set to use the full dynamic range. This setting was retained for the following tests. The distance between the IOL and the retinal plane was adjusted for each focal point using the micrometer screw and recorded. At each focal point the light distribution in a plane perpendicular to the optical axis was recorded. The distance focus of the diffractive bifocal IOL was then investigated. In a similar way, the focus of the monofocal SI40NB with 20 D and the distance focus of the refractive multifocal SA40N (Allergan) with 20 D +3.5 D for near, both made of the same highly refractive silicone, were analyzed.
A second series began of the focus of the 811C with 25 D. The light beam was, therefore, made divergent by placing a lens with −3.25 D 9.5 cm in front of the artificial eye (Figure 2). The dispersing lens generates a virtual image of the pinhole at its focal plane. The height of the retinal image that is needed for computing the viewing angle was determined in this case with the following formula:
where δDL indicates the virtual pinhole diameter created by the dispersing lens; δ, pinhold diameter; DL, focal length of the dispersing lens; and C, focal length of the collimator lens. In the set up used δ was 50 µm, fDLwas −0.308 m, and fC was 0.08 m.
Hence, the viewing angle Ω is as follows:
where δDL indicates the virtual pinhole diameter of the pinhole produced by the dispersing lens; ƒDL, focal length of the dispersing lens; and d, distance of the dispersing lens to the nodal point of the eye.
This setting was retained for the following investigations; the distance between the IOL plane and retinal plane was adjusted using the micrometer screw to find the exact focal point. The near focus of the 811E IOL was then investigated. The monofocal SI40NB with 24 D was evaluated followed by the near focus of the SA40N IOL.
To conclude the investigation of the clinical properties of the lenses, the 2-dimensional PSFs were used to compute the through focus response (TFR),6 the modulation transfer function (MTF)7- 9 using a Fourier transformation, and the Strehl ratio6 in the clinically relevant area from 0 to 30 cycles/degree.
The MTF frequency coordinate has been calibrated using the camera magnification(Figure 1 and Figure 2):
where Δ indicates the diameter of the investigated area on the retina; Δ′, diameter of the investigated area on the CCD-ARRAY; a, distance between the retina and the microscope objective; and b, distance between the microscope objective and the CCD-ARRAY.
where ƒE indicates the focal length of the eye.
In our setup a was 0.016 m and b was 0.224 m.
The height of the investigated area on the retina was used to determine the viewing angle for the used area on the CCD-ARRAY as described earlier. The MTF of the diffraction limited lens was calculated for a pupil opening of 4.5 mm and a wavelength of 500 nm.10
The viewing angle in the first setup was 1.07 minutes of arc. Figure 3 compares the PSF of the monofocal lenses with the distance focus of the bifocal and multifocal lens. The necessary changes of the IOL-retina distance to gain a sharp focal point are listed in Table 1. The PSF of the monofocal 811C exceeds the distance peak of the bifocal IOL. The base of the monofocal cone is comparatively sharply bounded. The light intensity rises uniformly from the focus periphery to the focus center. The bifocal distance peak is characterized by a broad light plateau at the base. The distance peak reached 58.5% of the corresponding monofocal PSF. The halo intensity was determined as the highest point of the halo. The maximum light intensity of the halo is approximately 4.5% that of the distance focus. The cone of the monofocal SI40NB (20-D) IOL nearly coincides with the cone of the monofocal 811C (20-D) IOL. The TFR of the SI40NB IOL reaches 92.6% of the 811C TFR. The distance peak of the SA40N IOL reaches 73.4% of the SI40NB IOL distance peak. The halo surrounding this focus is separated from the central light cone by a shallow trough. The light intensity of the halo is about 3% of the distance peak of the SA40N IOL.
Figure 4 shows PSF in near-focus testing. The viewing angle here was 0.98 minutes of arc. The peak of the 811C with 25 D shows a rather slim shape that is comparatively sharply bounded on the base. The near peak of the diffractive 811E reaches 42.7% of the 811C value. The halo is separated from the main cone by a trough, and reaches up to 4.5% of the near peak. The monofocal SI40NB with 24 D also has the typical shape of a monofocal IOL and reaches 90.6% of the 811C with 25 D. The near peak of the multifocal lens has a different appearance compared with the other bifocal or multifocal PSFs. Starting from a broad base, a nearly uniform increase in light intensity can be seen from the periphery to the center. The TFR reaches 25.1% of the monofocal peak of the SI40NB.
The MTF curves for distance focus testing are shown in Figure 5. Both monofocal MTF graphs are above the tested foci of the bifocal and multifocal lenses. The graphs of the distance foci of the multifocal IOLs show a comparable progression.
The MTFs for the near-focus testing are shown in Figure 6. The monofocal MTF graphs are comparable and are above the near-focus MTFs of the bifocal or multifocal IOLs. The near focus of the diffractive IOL shows a sharp decline at the beginning and then jumps to a modulation level of 0.5 to 0.6 in a flat, falling off progression. The MTF of the near focus of the refractive lens shows a sharp decline at the start and has the worst performance. The Strehl ratio for the area up to 30 cycles/degree for the foci investigated is given in Table 2.
Bifocal or multifocal IOLs produce at least 2 axially separated focal points enabling a pseudoaccommodation.11- 18 This construction focuses objects at infinity and at reading distance on the retina. Under the precondition of an exact preoperative biometry, the patient may gain an independence of glasses after cataract surgery. Apart from sporadic reports about the necessity for explantation of a multifocal IOL,19 excellent clinical results have been reported for these lenses.14,20,21 This seems to be contradictory to intuitive considerations. Because of the reduced TFR in multifocal lenses as a result of the incoming light being divided between more then one focal point, a retinal image of lower quality than in monofocal lenses might be expected. The fact that in multifocal concepts a focused retinal image is overlaid by an out-of-focus image also supports the presumption of impaired image quality. An expression of this superposition of focused and unfocused retinal images is the subjective observation of halos by patients with multifocal implants. Such observations are only perceived when looking at a bright light source against a dark background and do not generally bother the patient.22 It is certainly true that our visual perception is adapted to nonideal retinal images. Thus, refractive irregularities, chromatic aberration, and reduced lens transparency with increasing age23 are compensated by retinal and cortical processing leading to contrast improvement.24 The retinal image is, therefore, only the basis for our visual impression, as is also confirmed by the learning curve observed in patients using intraocular multifocal implants.25 A considerable amount of contrast sensitivity testing has been done to test the image quality gained through multifocal implants. In most cases, only minimal impairment in the middle spatial frequencies—the physiologically most sensitive—has been verified.12,15,16,20,26- 28 An in vivo double-pass test method showed a reduced MTF in patients with intraocular multifocal implants.29,30
Diffractive bifocal lenses were first introduced by 3M Optics, St Paul, Minn, with the model 815LE, a convex-concave IOL. This extraordinary lens shape proved to have the disadvantage of allowing capsular folds, and was replaced by a biconvex diffractive lens, the 3M 825LE. Clinical investigations revealed a too-weak near addition in this lens31 leading to a further change with an intensified near addition with the name 825x+4. Today, Pharmacia Inc produces a diffractive lens model 811E with an accentuation of the distance focus.
The refractive lens investigated is a 5-zone lens with an enforced distance focus and is made of highly refractive silicone. The fact that this lens is foldable is an advantage for the implantation.
The ability to distinguish axially separated images in bifocal or multifocal IOLs is influenced by the light distribution between the focal points as well as the distance of these focal points. If the light division differs over the lens area, light distribution is also a function of the pupil diameter. The distance between the focal points has an effect on the extension of the out-of-focus image and, therefore, on its light intensity. At constant light distribution, a greater distance between the near and distance focal point would increase the contrast between the focused and unfocused images and would facilitate a differentiation of these images. In practice, the distance between a near and a distance focal point is defined by the requirement to focus objects at infinity and at reading distance sharply on the retina. The multifocal lenses investigated differ slightly in the near addition with 4.0 D in model 811E and 3.5 D in model SA40N, according to the manufacturers.
The laboratory setup was intended to simulate the in vivo arrangement as closely as possible. A white light source was selected and an artificial eye with a cornea of PMMA was built according to the Gullstrand parameters. This arrangement includes in the test result the variety of chromatic aberration due to the light-wave band used as well as the spherical aberrations of the cornea —in contrast to a test setup with monochromatic light and solitaire lens testing in a water-filled test container.32 A single-pass method was selected to avoid any disturbance by double passing the refractive media of the artificial eye. The different pinhole sizes were chosen to have comparable viewing angles for distance and near focus testing.
Testing the multifocal IOLs was always performed in comparison to a monofocal lens of the same refractive index and same coating to provide a reference range for accessible light intensity in the focus. A logarithmic scale was used for the PSF to give more prominence to the out-of-focus images of low light intensity.
The transversal light distribution in the focus of the monofocal 811C(Figure 3) shows a regular cone structure, relatively sharply bounded at the bottom, in contrast to the PSF of the distance focus of the 811E that is characterized by a broad base built up by the out-of-focus image. The cone of the monofocal silicone IOL SI40NB in Figure 3 corresponds to the 811C in height and shape. The TFRs of both tested distant foci are comparable, but the shapes differ. While the halo in the distance peak of the diffractive IOL develops more continuously from the focused image, the halo of the refractive distance focus is separated. The explanation is that the central 2 mm in the refractive multifocal IOL is used mainly for the distance focus while in the diffractive concept this central area is only 1 mm. Considering that the halo is produced by the near focus in this arrangement, the greater the central part for distance vision, the more the distance focus is omitted by the near focal light rays (Figure 7).
The different multifocal principles are more apparent from the results for the near-focus testing (Figure 4). The near focus of the bifocal lens shows a defined halo, while the near focus of the multifocal lens shows a rather different shape. The progression of the bifocal near focus, starting from the highest level of the halo, dips before rising steeply to the focus center. In terms of Figure 7, the trough between the halo and the proper cone may be explained by a possible partially overlapping of light intensities generated by the central part of the lens and the out-of-focus image produced by the peripheral part of the lens. The refractive near focus shows a uniform increase in light intensity from the periphery to the focus center. In this case the out-of-focus image, produced by the dominant distance focus and the intermediate foci, cannot be separated from the near focus. This can be explained by a dominant distance and intermediate foci creating in this case a broad conical base. The PSFs for both distance and near focal points show the light distribution with accentuation of the distance focus in both multifocal implants. The necessary changes in the lens retina distance indicate that the near focus of the 811E is more powerful then the declared 4 D and stronger than the near addition of the SA40N. This correlates with our clinical experience when testing the reading distance in both multifocal implants with the best distance correction.18
Modulation transfer functions were computed to approach the clinical relevance of the PSF values. In Figure 5the MTF curves of both monofocal lenses showed the expected results. Both MTF curves of distance foci showed a similar progression. The reduced MTF function of the distance foci of the multifocal lenses compared with monofocal lenses has also been verified in other laboratory testing33 and in clinical contrast sensitivity testing.12,15,16,20,26- 28
The worse performance of the tested near foci compared with the distance foci in relation to the corresponding monofocal lenses is a result of the accentuation of the distance focus in the multifocal lenses tested (Figure 3 and Figure 4). The distinctly worse performance of the near-focus MTF of the refractive IOL at higher spatial frequencies has been confirmed with clinically evaluated defocus curves and near visual acuity testing of both lenses.18,34,35
The results of the Strehl ratio computation express the MTF progression in numbers in a clinically relevant region. The higher Strehl ratio results in the near-focus testing are due to the smaller viewing angle in the second series.
The distance focus of the diffractive lens showed a comparable performance to the distance focus of the refractive lens. In near-focus testing advantages for the diffractive bifocal concept have been demonstrated. This is in accord with clinical results.18,34,35 Although the diffractive IOL has a light loss of 8% of the incident light due to higher orders of diffraction, the refractive concept supplies intermediate foci with approximately 15% of the incident light depending on pupil size. When testing exclusively the distance focus and the near focus, light intensities at intermediate foci are included as out-of-focus images. These out-of-focus images broaden the PSF function, thereby reducing the MTF and influencing the clinical visual outcome. The concept of the refractive lens is to supply the patient with an intermediate vision as well. Defocus testing in both lenses revealed that the intermediate vision in both lenses is about 0.5 Snellen lines, with no advantage for the refractive lens.34 This may be owing to the fact that the light intensities at the intermediate focal points are too weak and too near to the distance and near focal points and are outshone by them to such an extent that the contrast of intermediate images is reduced to an unrecognizable level. Regarding both distance and near vision, intraocular multifocal concepts supplying only 2 focal points with nearly the same light intensity offer better capabilities in balancing brightness and therefore in the contrast of competing images on the retina.
Accepted for publication September 5, 2001.
Corresponding author and reprints: Stefan Pieh, MD, Department of Ophthalmology, University of Vienna Medical School, Währinger Gürtel 18-20, 1090 Vienna, Austria (e-mail: email@example.com).