Model of the light sword intraocular lens: in-vitro comparative studies.

This work presents the first models of light sword intraocular lenses (LS IOLs) with angularly modulated optical power. We performed an experimental, comparative study with multifocal and extended depth of focus intraocular lenses, which are available on the market. The measurements conducted in an original optical bench were utilised for an analysis of point spread functions, elongated foci, modulation transfer functions and the areas defined by them. The LS IOL models perform homogeneous imaging in the whole range of designed defocus. The proposed concept of extended depth of focus seems to be promising for the development of presbyopia-correcting intraocular lenses capable of regaining fully functional vision.


Introduction
The implanted intraocular lens (IOL) has a significant effect on vision after cataract surgery. The most popular monofocal IOLs are designed for fine far vision only, and reading glasses are required for near vision. Therefore, an attractive remedy seems to be IOLs enabling additionally functional intermediate and near vision. The most common and clinically tested solutions are multifocal (bifocal or trifocal) intraocular lenses (MIOLs) and accommodating lenses. The above concepts exhibit some limitations. MIOLs split light in different foci, which affects vision quality [1]. Up to now, accommodating IOLs do not provide satisfactory restoration of accommodation [2]. The relatively new and promising elements are extended depth of focus (EDOF) IOLs [3,4]. In contrast to bifocal or trifocal IOLs, EDOF lenses work by focusing light roughly into a stretched light segment, instead of two or three discrete points. The aim of this elongated focus is to improve intermediate and near vision, and to reduce the halo effect. Another solution, offering wider EDOF, are stenopeic IOLs, but a small diameter of their aperture causes low contrast sensitivity [5]. All of the above-mentioned presbyopia-correcting IOLs, although well investigated and optimized, still create some difficulties in intermediate and near vision, especially while performing work on the computer, interpersonal relations and reading. It is necessary to look for an even better solution recovering visual acuity at a whole range of defocus up to 3D or 4D, and providing functional vision with the acceptable contrast. Therefore, we propose a brand-new design of an EDOF IOL profile, based on the concept of the Light Sword Lens (LSL) with an angular modulation of the optical power. Hitherto presented theoretical and numerical studies show that angularly modulated elements provide better imaging uniformity on the whole addition range than multifocal and monofocal lenses [6][7][8]. The LSL applied in a form resembling contact lenses, successfully performs imaging with increased depth of focus. In-vitro studies applying the human eye model [9] and subjective experiments performed in a monocular visual simulator [10], have shown the usefulness of the LSL in correcting presbyopia. According to the recently performed clinical assessment, visual acuity achieved with the LSL correction in a presbyopic eye is comparable to stenopeic, but exhibits no significant loss in contrast sensitivity [11].
This paper presents the first in vitro characterisation of Light Sword Intraocular Lens (LS IOL) models with the angular modulation of optical power, based on the LSL concept. Two models of LS IOLs with different continuous optical power additions were designed and manufactured. Then, we carried out a comparative experimental analysis of the obtained models and commercially available solutions, including bifocal, trifocal, and EDOF IOLs. The measurements were performed in an original optical bench containing a model eye constructed according to the ISO standard and described in section C.3.1 in Ref. [12]. Using the novel part of the bench, we adapted our set-up to the through-focus analysis in object space. For the comparative studies, we used point spread functions (PSFs), modulation transfer function (MTF) values at a spatial frequency of 50 cycles per mm (cpmm), areas under MTF (MTFA) curves from 0 to 50 cpmm and images of the USAF test. The PSFs were captured by a CCD camera as images of a pinhole with a diameter of 5 µm. Then we used these PSFs to calculate MTFs and MTFAs according to the methods described in section 3.

Models of the LS IOL
The LSL is characterized by the angularly variable optical power. It can be seen as a clock face, with a continuously varying optical power increasing as the minutes hand is rotating. As it was proved numerically and experimentally, such asymmetrical geometry provides much better EDOF imaging than elements with symmetry of revolution, such as axicons, axilenses and multifocal lenses [8,13]. In our experiments, we used two models of the LS IOL having the optical powers with continuous additions in ranges from 0 D up to D A , described according to the following formula: where θ denotes the angular coordinate in polar system, D(θ) is the optical power expressed in diopters and D A defines a maximal power addition equal to 3D or 4D in our study . Base power was set at 21D. These models will be termed as LS IOL 3D and LS IOL 4D. The LS IOLs were designed by the ray tracing method for fabrication in poly(methyl methacrylate) (PMMA). Figure 1 shows the geometry of the LS IOL models, with a lateral thickness of 2 mm, an active diameter of 6 mm and variable optical powers defined by Eq. (1). The bottom spherical surface has a curvature radius of 77 mm, while the curvature radius of the upper surface measured in millimetres varies with the angular coordinates according to the following formula: where D(θ) has a numeric value defined by Eq. (1) and n PMMA = 1.490, n SS = 1.336 denotes the refractive indices of PMMA and saline solution used in our optical bench respectively. Along one of semidiameters a characteristic sharp step is visible. Such an edge, of 0.10 mm and 0.18 mm for LS IOL 3D and LS IOL 4D respectively, is a consequence of shape differences corresponding to their minimal and maximal optical power. According to our former objective and subjective tests with the refractive LSLs, such an edge does not induce any diffractive disturbances in the visual field [9][10][11]. On the other hand this discontinuity can generate some problems after implantation of the IOL into a human eye. However, according to the discussion presented in Ref. [9], the step can be substantially smoothed without any noticeable degradation of the images formed. The LS IOL models were fabricated by a molding injection, with nickel moulds manufactured by diamond turning technique using a 5 axis CDT Nanotech 350FG (Moore Nanotechnology Systems, Swanzey, NH). This device is a Ultra Precision Freeform Generator configurable as a 3, 4, or 5 axis machining tool, equipped with a single point diamond turning head. We controlled the optical qualities of the elements interferometrically and found them acceptable within the aperture of a diameter of 3 mm, used in our experiments. Despite their simplified form (lack of haptic and non-bio acceptable material), the fabricated models enabled an analysis of their optical properties in the ISO compliant optical bench designed for characterization of IOLs.

Intraocular lenses
For our comparative studies, we have chosen premium MIOLs of high quality, available currently on the market. They can be classified as bifocal, trifocal or EDOF lenses. Table 1 presents the general manufacturers data, and some additional information is given below. FOCUSforce ReVision (Bausch&Lomb, Rochester, NY) is a diffractive bifocal pupil independent IOL. It is dedicated for distant and near vision, particularly for reading in photopic and mesopic conditions. Some specifications can be found on the manufacturer's website [14].
AT Lisa tri 839MP (Carl Zeiss Meditec AG, Jena, Germany) and AcrySof IQ PanOptix (Alcon, Fort Worth, TX) represent trifocal MIOLs in our analysis. The aim of these lenses is to increase the level of patient satisfaction by making better intermediate vision, being especially important  [22][23][24][25][26][27]. The presence of three foci provided significant intermediate visual results without sacrificing near or distance vision [28][29][30][31][32]. Some photic phenomena, if they were observed, were found to be very mild and not disabling by most of patients [29]. The LSL having an elongated focus is an element especially designed for EDOF imaging. Thus, in our comparative studies, we have included two lenses of this kind: Tecnis Symfony ZXR00 (Tecnis, Abbott Medical Optics, Abbott Park, IL) and Acriva Reviol Tri-ED 611 (VSY Biotechnology, Istanbul, Turkey). The Tecnis Symfony forms an elongated focus and consequently extends the range of vision, which was confirmed by in vitro analysis [33]. Visual results demonstrated very limited disturbing photic phenomena, high levels of spectacle independence as well as postoperative patient satisfaction [34][35][36]. The number of papers describing properties of the Acriva Reviol in peer-reviewed journals is rather limited. Discussion about the diffractive design can be found in Ref. [37]. According to available in vitro and in vivo outcomes, the Acriva Reviol, similarly to the Tecnis Symfony, exhibits EDOF vision, providing visual improvement for far, intermediate, and near distances with a high level of visual quality and patient satisfaction [38,39].

Optical bench and measurements.
We performed our comparative tests in accordance with ISO guidance. The original arrangement, in the form of the optical bench fulfilling requirements of ISO 11979-2 standards [12], was constructed at the Łukasiewicz Research Network -Maksymilian Pluta Institute of Applied Optics in Warsaw, Poland. Figure 2 shows a scheme of this set-up and its picture. A white light LED illuminates the input object, then the modified collimator, the artificial cornea and an IOL. Spectrum and intensity of illumination can be modified by filters. The eye model was constructed according to section C.3.1 of the ISO standard [12]. A spherical aberration free achromat doublet lens Melles Griot LAO 034 (CVI Laser LLC, Albuquerque, NM) stands for the artificial cornea.
The tested IOL in a frame with circular apertures is immersed into a quartz cuvette filled with saline solution. The apertures almost touch the surfaces of the IOL so that the pupil diameter can be precisely defined. A microscope objective Nikon CFI Plan Achromat NA = 25, 10X (Nikon Corporation, Minato, Tokio, Japan) magnifies the output image located behind the cuvette in air. The objective is connected to a digital camera capturing the final image. In order to get high resolution and substantially avoid possible noise, we used 16 bit camera Hamamatsu Orca 4 (Hamamatsu Photonics KK, Hamamatsu, Japan), cooled with liquid. The camera with the microscope objective can be precisely moved along lateral and perpendicular axes by means of a micro-positioning system, controlled by a computer. Our ISO model eye is commonly used for IOLs characteristics [17,[22][23][24][25][26][27]33]. It works correctly only under illumination by a plane wave corresponding to an object located at infinity [40]. Therefore, in the event of the through-focus analysis corresponding to variable defocusing, it is necessary to move a detector. In order to perform the through-focus measurements in a more natural way in object space, we additionally used the modified collimator consisting of a collimator lens and a telescope. This is a novel device, which enables variation of defocus, while maintaining a constant angular magnification in a fixed image plane. In contrast to classical Badal systems, the collimator remains stationary, while only the component of the set-up containing the object plane moves axially, continuously altering the vergence of light illuminating the cornea. The modified collimator can be used in various models of the eye because it allows scaling the distance of the object to control the light vergence in the cornea or in the IOL plane. The required defocus in our system was calculated using Zemax (Zemax, Kirkland, WA) software under the following assumption: the defocus set in the ISO model eye and the perceived defocus in the real eye generate the same incident vergences upon the IOL. In our numerical calculations we approximated the real eye with a physiological model [40]. Further in the paper, we use the rescaled defocus (Fig. 4-7). An axial movement range of about 55 mm gives rise to the defocus range from 0 D to 5 D, corresponding to object distances from infinity to 20 cm in the physiological model eye. A micro-positioning system, controlled numerically, performs the movement very precisely with a resolution of defocus better than 0.01 D. It is worth noticing that contrary to earlier designs of the "artificial eye" setups, the way in which imaging is performed in our device fits well with the human eye, where images stand in a fixed position on the retina.
We mainly based our studies on two-dimensional intensity distributions of images of point-like objects, being non-coherent PSFs. All optical elements of our optical bench were precisely designed and aligned to avoid aberrations. The construction resulted in the diffractive limited arrangement consisting of the modified collimator and the artificial cornea. Thus, to get PSFs, we could use a pinhole with a diameter of 5 µm as the object. In this way we avoided any unwanted diffraction disturbances, because in our limited diffractive system such a small pinhole is equivalent to the point object generating a spherical wave. Following ISO guidance, the pinhole was illuminated by quasi-monochromatic green light with a narrow spectrum, centered at a wavelength of 546 nm. At the beginning of measurements for the selected IOL, we adjusted our optical bench for 0 D (infinity). Then, defocus was changed from 0 D up to 5 D with an increment of 0.05 D. In this way, for every IOL, we captured 101 PSFs using the apertures of 3 mm in diameter. This pupil size was chosen based on the changes in pupil size related to average age of cataract patients under photopic conditions [41,42]. The experiments were carried out in a dark room to avoid light noise.
Then, we processed the obtained intensity distributions to achieve results enabling a reasonable comparison between the LS IOL models and the selected IOLs. Particularly, Through-Focus MTFs (TF MTFs) and Through-Focus MTFAs (TF MTFAs) were utilized for this purpose. All results are presented in the next section. As we proved in earlier publications, the geometry of the LSL enables very uniform imaging within a wide range of defocusing in eye models [6][7][8][9]13]. Thus, experimental characterization of both LS IOL models was repeated with chrome-on-glass, 25 mm diameter 1951 USAF resolution test chart instead of the pinhole. The Through-Focus images of the test are also shown in the next section.  Visualization 8 for LS IOL 3D and Visualization 9 for LS IOL 4D). The movies illustrate also more precisely the dimensions and defocus values of the captured PSFs. Figure 4 shows Through-Focus PSFs (TF PSFs) composed of perpendicular projections of all 101 PSFs, obtained for successive defocus values in the linear light intensity scale. Each projection was created by calculating the cumulated intensities of every cross-section of the PSF along the horizontal axis. The projections for different defocusing values have been combined with some interpolation between them to create a construction representing a side view of an elongated foci scaled in diopters. The intensity distributions shown in Fig. 3,4 and in Supplementary Movies S1-S8 have been normalized separately to the maximum value for each tested IOL.  Figure 5 presents TF MTF curves at a spatial frequency of 50 cpmm corresponding to approximately 15 cycles per degree in the object plane of a real eye [43]. This frequency is suggested by ISO standards, and used in the majority of in vitro evaluations of multifocal or EDOF  IOLs. Moreover, according to the discussion presented in Ref. [44], a frequency of 50 cpmm determines the range of spatial frequencies to identify the Snellen optotypes. We calculated two-dimensional MTFs as absolute values of Fourier transforms of the captured PSFs. Lentis Mplus and LS IOL models are rotationally asymmetric lenses, and even other lenses exhibit slight asymmetry in experimental conditions (Fig. 3). Thus, we obtained unidimensional versions of the MTFs by angularly averaging the radial profiles of the corresponding two-dimensional MTF. Then, these unidimensional MTFs were used to plot the TF MTF curves shown in Fig. 5.

Results
For effective assessment of imaging quality, ISO standards suggest also specifications based on the area under the MTF curve between the two spatial frequencies. Therefore, using the unidimensional MTFs, we calculated MTFAs in a range of spatial frequencies from 0 cpmm up where f denotes a spatial frequency. Recently, the above metrics were found to be highly correlated with clinical results of visual acuity (VA) [39,44]. Figure 6 shows TF MTFAs for all tested IOLs. Finally, we present in Fig. 7 Through-Focus images of the USAF test formed by both characterized LS IOL models.

Discussion
We performed experiments in the artificial eye containing the ISO model eye and the novel modified collimator enabling calibration of our arrangement with the real eye. Controlling movement of the object, we rescaled a real defocus to its value perceived approximately by the IOL implanted in human eye, assuming the same vergence of light incident upon the IOL. The rescaled defocus given in Fig. 4-7 was determined numerically using Zemax software and substituting the real eye with its physiological model [40]. The credibility of this approach is confirmed by the TF MTF curves shown in Fig. 5. They coincide well with those already presented in literature for the same IOLs, e.g. Ref. [17,[22][23][24][25][26][27]33]. Figure 3 and Supplementary Movies S1-S8 show the two-dimensional foci of IOLs, depending on defocusing. Figure 4 illustrates the process of focusing, simulating foci stretched in space behind an IOL illuminated by a plane wave. This way the multifocal character of IOLs can be specified. Bifocal IOLs (ReVision, Lentis Mplus) and trifocal IOLs (AT Lisa, PanOptix) form two or three focal segments respectively. This remark is partly confirmed by Fig. 5, where light focusing is exhibited in the local TF MTF maxima. For Tecnis Symfony and Acriva Reviol, two or three focal segments are combined to provide increased depth of field (Fig. 4). A similar phenomenon, perhaps not so pronounced, occurs in the case of Lentis Mplus, AT Lisa and PanOptix. As a result, they provide satisfactory, homogeneous vision in large ranges of defocus [19,28]. This effect is clearly visible for PanOptix in Fig. 5, where the maxima corresponding to the two focal segments merge with each other. Figure 3 also presents foci on a logarithmic scale to highlight aberrations and noise. They can affect unwanted photic phenomena as e.g. halo.
Rotationally asymmetrical elements such as Lentis MPlus and both LS IOLs form double focal spots in some defocus ranges (Fig. 4). Secondary, a darker spot leads commonly to an off-axis ghost image. It is a natural consequence of multifocality or depth-of-field extension. In the event of rotationally symmetric IOLs, this effect creates halo-like disturbances. In our former subjective experiments with the LSL, ghost images were not perceived by the subjects [10,11].
According to Fig. 4 and Fig. 5, the LS IOL models create elongated continuous foci and TF MTFs with high uniformity in ranges compatible with maximal additions of the elements. In contrary to other IOLs, the LS IOL models form focal spots well visible in a linear scale of intensity during defocusing up to 3 D or 4 D (supplementary Movies S1-S8). For this reason, a sufficiently homogeneous imaging in the optical bench can be expected. This assumption is confirmed by the USAF test imaging shown in Fig. 7. The images are well recognizable in defocusing ranges about 0-3D or 0-4 D for LSL 3D and LSL 4D respectively.
It should be noted that the above imaging, with very high uniformity, was obtained in an objective experiment, performed in an optical bench. Research is underway worldwide to find objective metrics that best match the results of clinical trials on visual acuity (VA) and contrast sensitivity (CS). Substantial progress in this field is presented by the results provided in Ref. [44] and then patented [45]. According to them the MTF values at 50 cpmm and at 100 cpmm do not give satisfactory results. Moreover most TF MTF values at 100 cpmm are small and comparable with experimental errors, which leads to questionable results. Frequently, in the case of MIOLs, clinically measured VA varies slightly with defocus, while TF MTF exhibits high oscillations and reaches small values. The authors justified that the range of spatial frequencies from 0 to 50 cpmm is properly suited to identify 20/20 Snellen letters. Then they proposed the power function connecting predicted VA with MTFA ( [44]) calculated from measurements in the Average Corneal Model eye. Finally, coefficients of the power function were successfully found by the maximal correlation between the predicted and the clinical VA. Reliability of this procedure was lately confirmed in the ISO model eye [39]. Objective in vitro studies were carried out in different eye models, which may be the reason for dissimilarities in the proposed formulae, but still, they illustrate well the high correlation between MTFA-based metrics and clinically measured VA. Figure 6 shows TF MTFA curves based on measurements in our optical bench. According to the published results of clinical trials, Lentis Mplus, AT Lisa and PanOptix allow to get VA better than 0.2 logMAR for defocus up to 3.0-3.5 D [19,20,28,30,32,38]. In the case of the Tecnis Symfony, the same VA values correspond to the smaller defocus up to 2-2.5 D [31,34]. Following the procedure given in Ref. [44] and assuming the unambiguous relationship between clinically measured VA and MTFA values, one can analyze Fig. 6 for the above mentioned IOLs. This analysis suggests that VA better than 0.2 logMAR corresponds to a MTFA value belonging to the range 15-20. Therefore, graphs for LS IOL models presented in Fig. 6, enable the approximate assessment of VA, gained by using a real IOL based on the LSL design. Such reasoning leads to a conclusion for LSL, that VA better than 0.2 logMAR can be expected for continuous defocus range of about 3 D (LSL 3D) or about 4 D (LSL 4D). This finding corresponds well with the results of our previous objective and subjective studies, where the LSL was used in a form resembling a contact lens [9][10][11].
The radially asymmetrical foci created by the LS IOL models have structures similar to those generated by Lentis Mplus (Fig. 3). It can be expected, as the Lentis Mplus is also an angularly modulated IOL with only two optical power values. Therefore LSL can be regarded as its generalization to a continuous range of addition. According to clinical trials, the photic phenomena generated by Lentis Mplus are either unnoticeable or mild [15,16]. This creates a hope for a reduced amount of photic phenomena also using a real IOL based on the LSL design.

Conclusions
The obtained results for the LSL IOL models (Figs. 4,5,6,7) look very encouraging and give hope to construct an intraocular lens enabling fully functional vision. TF PSFs, TF MTFs, TF MTFAs and TF images are characterized by a high degree of homogeneity. Thus, also homogeneous vision similar to the objective imaging in a large range of defocusing (Fig. 7) can be expected. It is important to be aware that this paper is only the beginning of the LS IOL study. Then, we should examine issues such as the influence of lateral focus displacement, observable in Fig. 4, the impact of pupil size on the quality of imaging, or a displacement or a tilt of the element. Chromatic aberrations should also be analyzed, although in our former subjective experiments with the LSL, they were not noticeable [10,11].
According to the results shown in Figs. 4,5,6,7 and our previous outcomes, distant vision may have limited contrast [9][10][11]. Probably, there are two ways in which this problem can be solved. The first is to redesign the element by introducing non-linear angular modulation in to the Eq. (1) or/and windows intended for distant vision, located in fragments of a LS IOL pupil. The second method is connected with some limitation of the depth of focus, through using an undervalued base power of the LS IOL in the human eye. A proper choice of base power can be equivalent to shifting the curves from Fig. 5,6 to the left, to obtain higher MTF and MTFA values for zero defocus.
Despite the above potential inconveniences, the use of continuous angular modulation of optical power for IOLs seems to be very promising.