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1From the Eye Clinic and the 2Department of Electrotechnics, Electronics and Informatics, University of Trieste, Italy; and the 3Department of Medicine and Aging, University of Chieti, Chieti, Italy.
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Abstract |
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METHODS. An optical test bench and suitable software were used to assist in analysis of the optical Fourier transform (OFT) of a test image and to determine the quality of the lens in terms of spatial frequency response. The OFT was automatically converted, by means of an optical–electronic calibration procedure, into a modulation transfer function (MTF) for each lens. The passband value calculated by computer analysis of the MTF is an objective index of the lens quality. Three randomly acquired samples of 24 different models of foldable IOLs were compared. Statistical analysis was performed with two-way and one-way ANOVA for repeated measurements and with the Ryan-Einot-Gabriel-Welsch multiple F test.
RESULTS. The method was demonstrated to be precise and accurate. A large range of passband values was found. Statistically significant differences between the mean passband values for different lenses were found. The lowest passband value (125.60 line pairs [lp]/mm) was measured for the IOL (Lenstec LH3000; Lenstec, Inc., St. Petersburg, FL) and the highest (191.48 lp/mm) for the Acrysof SA30AL (Alcon, Fort Worth, TX).
CONCLUSIONS. Different IOLs can transmit different spectra of spatial frequencies. The best frequency response was provided by acrylic IOLs, particularly those with an asymmetrically biconvex profile. This could be due to a reduction of optical degradation provided by this type of profile. A lens with a higher frequency response should determine a better quality of vision once implanted and the frequency response should therefore be considered when choosing the intraocular lens model.
Many ophthalmologists speculate that it is possible to improve visual acuity using customized corneal ablation1 or adaptive optics.2 The currently used IOL should therefore be optically superior to the natural crystalline lens once implanted in the eye after cataract surgery.
The IOL, together with the total ocular optics, must produce a certain level of image quality at the retina. The IOL, therefore, cannot be the limiting element of vision.
Once an IOL is released by the manufacturer, it is generally assumed to be free of optical defects. Since 1984, the minimum qualification standard for resolving power indicated by the American National Standards Institute (ANSI) has been 100 line pairs per millimeter (lp/mm) for an IOL tested in air using a 3-mm aperture.3 4 Several authors, however, have reported that this requirement may be inadequate for assuring that IOLs are not the limiting factor of vision.5 6 7
Many methods have been used to assess the various aspects of the imaging quality of lenses. The Fourier analysis of the spatial visual stimuli has become common in the past 35 years and the measurement of the modulation transfer function (MTF) of the lens has also been used.8 9 10 This is a measure of the resolving power of the lens and of the definition of the image produced by the lens. MTF measurements have better repeatability and reproducibility than that of the previous industry practice of resolution testing in air with parallel light and the U. S. Air Force three-bar target.9
An optical Fourier transform (OFT) of an image is produced on the back focal plane when an ideally convergent lens is transilluminated by a collimated beam of coherent light placed on the front focal plane.11 The OFT is affected by a scale factor that depends on the focal distance (f) of the lens and on the wavelength (
) of the source. The OFT is the spectrum of the image; in other words, the representation of the image in terms of spatial frequencies transmitted by the lens. When a nonideal lens and an ideal test image that contains an equal amount of all spatial frequencies are used, the OFT is characteristic of that lens. But, to compensate for f and , a precalibration is necessary.11 This can be performed by obtaining a transformation of an image that has a known spatial frequency—for example, a grid. The OFT can be converted into the MTF for each IOL.
The purpose of our study was to evaluate the optical quality of different IOLs using an optical test bench and software to analyze the images obtained and measuring the MTF for the lens tested.
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Methods |
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The optical test bench is made up of several components (Figs. 1 2) . A 632.8-nm helium-neon laser light source is expanded by a telescope system into a coherent, collimated beam of light with a diameter of approximately 50 mm. The expanded laser beam shines on the test image, which contains the broadest possible band of spatial frequencies. Furthermore, it was essential that these frequencies be evenly distributed on the same axis, and a thin slit was therefore chosen as the test image. This type of image comes close to the infinitely fine ideal line, simulating an impulse in one dimension (i.e., the optical translation of a signal used in electronics as an entry to test amplifiers and electronic systems, for example). This ideal-point light source is characterized by a spectrum of spatial frequencies that is very broad, ideally infinite, continuous, and on one axis.
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A relay lens formed by two precision optical collimators with a focal length of 38.1 cm completes the optical test bench and forms the system used to focus the OFT on a CCD video camera. Because the IOL has a focal distance of approximately 1.5 cm, it would have been difficult and imprecise to place the CCD at this position. For this reason the front focal plane of the first collimating lens matches the back focal plane of the IOL and antitransforms the transform, reproducing the image. The second collimating lens once again transforms the image and reproduces the transform on the CCD, which is the entry point of a digital image-processing system.
The OFT produced by the IOL and acquired as described is affected by a scale factor. To obtain the real MTF, independent of the lens power and of the whole optical system, we performed a calibration procedure. This procedure required the acquisition of the OFT of two calibrating images produced by each IOL. As calibrating images we chose two grids of 80 and 100 lines/mm. The OFT of these grids contains repetitions at regular intervals on the transform plane, permitting the calibration of the frequency axis. For example, with an 80-lines/mm grid, repetitive spots centered at frequencies of 0, 80, and 160 lines/mm, and so on, were obtained.
The software used first sought the OFT of the 80-line grid, followed by that of the 100-line grid, and then calculated the number of pixels between one repetition and another to determine the number of pixels corresponding to 1 line/mm. The optical test bench was then ready to analyze the OFT of the image produced by the IOL (Fig. 3) .
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Calculations were performed on the images obtained from the IOLs evaluated to derive the graph of the frequency response, also expressed as the MTF of the intraocular lens. The whole procedure was performed on computer (software developed in a MatLab environment; The MathWorks, Natick, MA).
The graph of the frequency response obtained from the slit response was oscillatory and required interpolating the peaks. The passband (that is, the spatial frequency for which the width of the frequency response is reduced to 70%) was determined from each graph of the frequency response. This is a parameter conventionally used in electronics to measure the maximum frequency at which a system transmits or amplifies a signal. This variable was used to compare the results provided by the different lenses (Fig. 4) .
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Statistical Analysis
Six repeated measurements of passband for three different samples of each IOL model were performed. The mean and standard deviation for each sample lens were calculated. To measure the statistical significance of the differences between the three sample lenses and within the repeated measurements, we used two-way analysis of variance (ANOVA) for repeated measurements. The overall mean of the 18 individual measurements and standard deviation were calculated for each IOL model. We then applied one-way analysis of variance to test for statistically significant differences between the 24 IOL model types. Successively, the Ryan-Einot-Gabriel Welsch multiple F test was applied on the ranked values to compare each value with the value that followed.
All statistical analysis were performed on computer (SPSS ver. 10.0 for Windows; SPSS Sciences, Chicago, IL).
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Results |
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The frequency response curve was obtained from the graph of the slit response by interpolating the peaks of the oscillatory response. The passband (i.e., the spatial frequency for which the width of the frequency response is reduced to 70%) was considered, to compare the results provided by the different lenses (Fig. 4) .
The six repeated measurements of the passband for the three different samples for each IOL model were substantially the same in the means and standard deviations for all the 23 IOL models (Table 1 , 1st, 2nd, and 3rd, lens). Therefore, the two-way ANOVA for repeated measurements resulted not significant for each IOL model, in accordance with the null hypothesis of absence of variability between samples. Variability within measurements for different types of IOLs can consequently be accepted with certainty. These results guarantee this method to be highly precise.
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Discussion |
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Using various new techniques, ophthalmologists today try to reach the potential highest visual acuity for patients. The aim is to improve visual acuity beyond what we consider to be normal, with an improvement of clinical outcomes in terms of visual acuity and contrast sensitivity. The term "supernormal" vision has been introduced to describe this possibility.1 Quantification of optical aberrations to design the ideal refractive corrections has now come into use. These optimal corrections are intended to improve the optical quality of the images at the retinal plane. Results reported after wavefront-guided excimer laser surgery suggest that higher-order aberrations can be decreased.20
Not only during refractive surgery, but also by means of other optical corrections, such as the introduction of an intraocular foldable IOL in the eye after cataract surgery, vision quality can be improved. It has been reported that contrast sensitivity in pseudophakic eyes is higher than in aphakic eyes with spectacle correction, but is lower when compared with normal phakic eyes.21 The cornea has been found to have a positive spherical aberration that increases with age.22 23 The young crystalline lens has a negative spherical aberration that increases with age, becoming positive around the age of 40 years.24 The optical effect of the positive spherical aberration of the cornea could be reduced or eliminated by implanting an IOL with a negative spherical aberration. Aspheric IOLs have then been introduced.25 26 An improvement in quality of vision and in particular in contrast sensitivity has been documented after implantation of Tecnis Z9000 IOLs (Pharmacia).27 To correct the unique astigmatic and spherical requirements for each individual cataract patient, individually crafting IOL has now been supposed.28 When introducing the concept of custom IOL design, the optical quality of an IOL must not be underestimated, with the aim of increasing the contrast and spatial detail of the retinal image once the IOL is implanted within the eye’s optics.
The retina and the spatial distribution of the photoreceptors in the foveola are at the end the decisive limiting factors to visual performance. Foveal cone spacing is assumed to be the cutoff spatial frequency determinant for the eye. Considering the foveal cone diameter to be approximately 2.5 µm, a cutoff frequency of approximately 120 cyc/deg has been postulated.15
Since 1984, the minimum qualifying resolving power of the ANSI standard is 100 lp/mm for an IOL tested in air using a 3-mm aperture. A spatial frequency of 100 mm–1 at the retina corresponds to a visual acuity of approximately 20/20. In angular terms, it is close to 30 cyc/deg.9 Considering the resolution of the retina to be limited by the spacing of light receptors, the human visual system can resolve to approximately 20/5 or 120 cyc/deg.15 This resolution is well above the conventional clinical measures, as it does not compensate for the optics of the eye and postreceptoral neural processing.
In our study we considered the OFT obtained for each lens evaluated, which represents the spatial frequency spectrum transmitted by the IOL optic. The analysis of the extension of this spectrum provides a measure of the optical quality of the lens. The graph of the frequency response has been obtained and expressed as the modulation transfer function of the intraocular lens. The spectrum of spatial frequencies is an intrinsic feature of each image, but of course if an image is an enlargement or a reduced version of another, the spectrum contracts or expands in accordance. Because in the visual process the image is reduced, the spectrum therefore expands. The system we described does not examine the frequency spectrum of a specific image, but the theoretically maximum spectrum that can be produced by an IOL, and therefore it provides a good method to compare the optical quality of different IOLs.
The MTF analysis of an IOL could be examined, for instance, using a 55-nm green wavelength, which corresponds to cone peak efficiency and is the band of visible light spectrum at which many lenses should be optimized.
Our measurements were performed using a standard optical bench for optical procession of the image, supplied with a 632.8-nm He-Ne red laser. Because the OFT is affected by a scale factor depending on the focal distance (f) of the lens and by the wavelength () of the source, using light sources of different wavelengths may give slightly different MTFs. To compensate for f and , a precalibration procedure using grids with a known spatial frequency has been used.11
The method used for this purposes follows the general principles of system theory to evaluate transfer functions and applies them to optics and optometry.11 The specific technique used has been obtained in a general purpose laboratory for optical processing of images.13
The method was precise, as the six repeated measurements of the passband for the three different samples for each IOL model were almost equivalent, in mean values and standard deviations, for all 23 IOL models (Table 1) . Therefore, the results of the two-way ANOVA for repeated measurements were not significant for each IOL model, in accordance with the null hypothesis of absence of variability between samples.
Variability within measurements for different types of IOL can consequently be accepted with certainty. These results guarantee this method to be highly precise.
The frequency response of the different IOLs examined varied according to several factors, including the material and the optic profile of the lens. The best frequency response was provided by acrylic IOLs, particularly those with an asymmetrically biconvex profile. This could be due to a reduction in optical aberrations provided by this type of profile. It would have been of interest to compare the Tecnis Z9000 IOL (Pharmacia) with a modified anterior surface designed to compensate for the positive spherical aberration of the cornea. It was not possible to compare data obtained testing this type of lens, because the OFT obtained had a specific morphology that the software for this system could not process (Fig. 5) .
Given that 20/20 visual acuity corresponds to approximately 100 lp/mm and that the frequencies transmitted by the IOL studied were higher, no tested IOL was found to be a limiting factor for average tested visual acuity.
When trying to achieve the maximum potentiality for the ocular optical system, a higher level of optical quality is essential. An IOL of better optical quality could allow a greater spatial frequency spectrum to be transmitted to the retina. The use of IOLs capable of transmitting a broad spectrum of spatial frequencies would allow them to reach higher values of visual acuity—the ocular optical conditions being equal. Moreover, the implantation of an IOL with a superior optical quality could improve the quality of vision in general and in particularly in terms of contrast sensitivity. For all these reasons, to hold in due consideration the optical quality of the IOLs that implanted every day all over the world during cataract surgery would be beneficial.
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Footnotes |
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Disclosure: D. Tognetto, None; G. Sanguinetti, None; P. Sirotti, None; P. Cecchini, None; L. Marcucci, None; E. Ballone, None; G. Ravalico, 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.
Corresponding author: Daniele Tognetto, Clinica Oculistica, University di Trieste, Ospedale Maggiore, Piazza Ospedale, 1, 34129, Trieste, Italy; tognetto{at}univ.trieste.it.
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  L Mitchell, A C B Molteno, T H Bevin, and G Sanderson Star testing: a novel evaluation of intraocular lens optical quality Br. J. Ophthalmol., May 1, 2006; 90(5): 586 - 592. [Abstract] [Full Text] [PDF]
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