Optical and visual quality of real intraocular lenses physically projected on the patient's eye.

Visual simulators aim at evaluating vision with ophthalmic corrections prior to prescription or implantation of intraocular lenses (IOLs) in the patient's eye. In the present study, we present the design, implementation, and validation of a new IOL-in-cuvette channel in an Adaptive Optics visual simulator, which provides an alternative channel for pre-operative simulation of vision with IOLs. The IOL is projected on the pupil's plane of the subject by using a Rassow system. A second lens, the Rassow lens, compensates for an IOL of 20 D while other powers can be corrected with a Badal system within a 5 D range. The new channel was evaluated by through-focus (TF) optical quality in an artificial eye on bench, and by TF visual acuity in patients, with various IOL designs (monofocal, diffractive trifocal, and refractive extended depth of focus).


Introduction
Two main physiological changes affect vision as the eye ages: cataracts and presbyopia. A cataract is an opacification of the crystalline lens. The usual treatment for cataract entails the replacement of the natural lens of the eye by an artificial intraocular lens (IOL). In economically developed countries, cataract surgery is performed between 4000 to 11000 times per million population in one year [1]. Another age-related condition, which appears at an earlier stage than cataract, is presbyopia, the loss of accommodation capability in the crystalline lens. While cataract surgery aims at restoring transparency in the lens, it has also become a refractive procedure, as the appropriate IOL power can be selected such that images are projected on the retina, at least for distance. As a result, replacement of the clear crystalline lens with refractive purposes, a procedure known as Refractive Lens Exchange (REL) [2], has become increasingly popular. An alternative to monofocal IOLs in cataract and, even more frequently in REL, are presbyopia-correcting IOLs. The number of multifocal (diffractive or refractive) and extended-depth-of-focus (EDOF) IOLs designs has grown rapidly in the last years [3]. However, it is challenging for surgeons to manage patients' expectations in cataract surgery or REL, as it is difficult to imagine how one will see with the different types of corrections. Visual simulators allow the patients to experience multifocal vision with different IOL designs before surgery.
Many visual simulators are based on adaptive-optics (AO) [4][5][6][7], where the aberrations of the eye are manipulated with an active element conjugated with the pupil plane that can be programmed. In these systems, the lens design is converted into a spatial phase pattern and mapped either with a Deformable Mirror (DM, [8][9][10]), for lenses with smooth varying profiles or with a Spatial Light Modulator (SLM, [6,[11][12][13]), well suited to represent zonal refractive diameter) and its image (entrance pupil diameter) [29]. This difference may be critical in the accuracy of the simulation, as it likely alters the imaging properties of the eye + IOL with respect to the natural (post-operative) case. Another underlying hypothesis is that the wave aberration (representing the IOL) at the entrance pupil and at the iris pupil are equivalent. Solving the effect of magnification and proving the equivalency of both pupil planes will allow us to reproduce the effect of the IOL in the eye, in absolute, and not only relative terms. In fact, except for the presence of the natural crystalline lens, the system that we have implemented in the current study should be set to replicate the absolute performance of the implanted IOL.
In summary, in this study, we describe a new channel that we have implemented in a custombuilt AO visual simulator [13,23,30], that incorporates a Rassow telescope for the projection of a real IOL immersed in a cuvette onto the pupil's plane of the patient. The system corrects for a mismatch in magnification of previous implementations of the Rassow telescope in the literature. We calculated computationally and measured experimentally the optical performance of the system. We measured the through-focus optical performance on bench and the visual performance in patients through three different types of lenses (monofocal, diffractive trifocal, and refractive EDOF). With the incorporation of the new channel in the AO visual simulator, it will be possible, for the first time, to project real IOLs on the patient's eyes and assess the absolute visual performance with IOLs of different powers and designs. This system holds promise to become a reference for validations of visual validations with other simulators.

Methods
We designed and implemented a Rassow system in an Adaptive Optics set-up and tested optical quality on bench and visual quality in patients with monofocal, multifocal, and extended-depthof-focus IOLs. Figure 1 shows the configuration of the implementation. The IOL is immersed in a cuvette composed of metallic support on which the IOL is mounted and filled with distilled water (n=1.33). The Rassow lens (a 60 mm EFL achromatic doublet (Newport PAC16AR.15) that compensates the 20D IOL power) was placed at a distance twice its focal length from the IOL.  1. Schematic diagram of the Rassow telescope implemented in the AO system and the Badal lenses (f' R , focal length of Rassow lens; f' B1 and f' B2 , focal lengths of Badal lenses 1 and 2 respectively; f' Coll , focal length of collimator lens). Distance between Badal lens 1 and 2 is adjusted. PP and RP represent pupil and retinal conjugated planes, respectively.

Rassow system configuration
The capabilities of the Rassow system are complemented with a Badal optometer that allows shifting focus in a ± 4D range around the nominal IOL power (20 D). The Badal system, which was already implemented in the system [30], is composed of two lenses (125 mm, EFL) and two mirrors mounted on a motorized stage that allows the distance between the lenses (and therefore defocus) to be adjusted. The zero-defocus position corresponds to the lens positions such that their separation is equal to the sum of their focal lengths. Higher separations induce positive defocus, and lower separations induce negative defocus.

Optical computer simulations
Computer simulations of the optical performance of the Rassow and Badal Optometer system ( Fig. 1) were performed using Ray Tracing software (Zemax-EE Optical Design Program 2005, Zemax Development Corporation) (Fig. 1), for 4-mm pupil diameter and 555-nm wavelength.
The difference between entrance pupil diameter and iris pupil diameter [29] was theoretically calculated using OpticStudio for corneas of different power. Wavefront maps and the corresponding Modulation Transfer Functions (MTF) of the IOL in the cuvette were obtained on-axis (0 deg) and off-axis at the maximum subtended angle in the AO system (2 deg).

AO-set up (and implementation of the Rassow system in there)
The Rassow IOL projection system was incorporated in a testing channel in the Viobio Lab AOII, described in previous publications [13,23,30]. The system consists of different channels, the following of which are used in the current study: (1) The psychophysical channel contains a Digital Micro Mirrors Device (DMD, DLP Discovery 4100 0.7 XGA, Texas Instruments Incorporated, USA) on a retinal plane. The DMD Channel was monochromatically illuminated with light coming from a supercontinuum laser source (SCLS, Fianium Ltd, United Kingdom) with a selectable wavelength, 555 nm in this study. (2) The AO-Channel was composed of a Hartmann-Shack wavefront sensor (40×32 microlenses and 3.6-mm effective diameter, HASO 32 OEM, Imagine Eyes, France) and an electromagnetic deformable mirror (52 actuators, 15-mm effective diameter, and 50-µm stroke; MIRAO, Imagine Eyes, France), that was used to measure, correct, and induce aberrations. The illumination source was a SuperLuminescent Diode coupled to an optical fiber (Superlum, Ireland) emitting at 827 nm. (3) The natural pupil monitoring system consists of a camera (DCC1545M, High-Resolution USB2.0 CMOS Camera, Thorlabs GmbH, Germany) conjugated with the eye's pupil: (6) A testing channel with a conjugate pupil plane (with ×1 magnification) where phase plates or an optotunable lens working under the principle of temporal multiplexing (SimVis) were projected on the subject's pupil. The Rassow IOL projection system was mounted in a secondary optical breadboard and incorporated in this last channel above the optical set up utilizing two flip-up mirrors so that the IOL in the cuvette was placed in a pupil conjugate plane. Figure 2 shows the schematic diagram of the implementation of the new channel in the Viobio Lab AOII system. The distance between lenses L16 and L17 was modified to control the magnification of the IOL in the Rassow system onto the eye's pupil. The Podeye is a monofocal biconvex, hydrophobic, aspheric monofocal IOL, aiming at correcting a large proportion of the corneal SA (-0.11 µm SA). The FineVision is a diffractive, trifocal, hydrophilic, and aspheric trifocal IOL [31], with three foci, 0.0 D for far-vision, +1.75 D addition for intermediate-vision, and +3.50 D addition for near-vision. The Isofocal is refractive, hydrophobic, with smooth aspheric surfaces (described by the radius of curvature, and 4 conic constants per surface [32]), aiming at providing optimal vision at far and an extended-depth-of-focus into intermediate distances.

Subjects
Three subjects participated in the experiment. Subjects were 26, 27, and 28 years old and nearly emmetropic (Spherical refractive error:+ 0.75, +1.50, and -0.75 D; and cylinder: 0, -0.75, and -0.50 D). All measurements were performed under paralyzed accommodation with Tropicamide (2 drops at the beginning of the session, and 1 drop every hour if required).
All protocols met the tenets of the Declaration of Helsinki and had been previously approved by the Spanish National Research Council (CSIC) Bioethical Committee. All participants were acquainted with the nature of the study and provided written informed consent.

Through-focus on-bench optical quality
An artificial eye consisting of an objective lens (50.8 mm of focal length) and a CCD camera (DCC1240C -High-Sensitivity USB 2.0 CMOS Camera, 1280 × 1024, Global Shutter, Color Sensor; Thorlabs GmbH, Munich, Germany) on the focal plane of the objective was used. Through-focus series of images of an E letter (1.62°angular subtend) displayed in the DMD projector illuminated with green light (555 nm, coherence broken with a holographic diffuser) were taken on the CCD camera (1 Pass), for the three IOLs inserted in the cuvette. The focus was changed in 0.25 D steps using the Badal system. All images were captured with 4.5 mm pupil diameter, with constant laser power (6.90 µW) and similar camera settings, with the DM only correcting the aberrations of the system. The optical quality was assessed as the 2D cross-correlation [33] between each image in the TF series with the image obtained with the monofocal IOL (Podeye) at best focus.

Through focus visual acuity measurements
Visual Acuity (VA) was measured using a tumbling E letter test with an 8-Alternative Forced Choice (8AFC) procedure and a QUEST (Quick Estimation by Sequential Testing) [34,35] algorithm programmed with the Psychtoolbox package of Matlab [36,37] to calculate the size and orientation of the following presented E letter according to the subject's response. The E letter was presented for 0.5 seconds, and subjects were asked to indicate the orientation of the E letter. Each VA measurement consisted of 32 trials and 20 reversals. VA was estimated as the mean of the last 10 reversals and its variability, as the standard deviation of that 10 values. VA was measured in a focus range of +2 to -5 D, with a finer sampling was performed near the experimentally found VA peaks.
VA measurements were performed under cycloplegia using a 4.5 mm pupil. The subject's eye pupil center was aligned with the optical axis of the system with an x-y-z stage and stabilized and a dental impression on a bite bar. Subjects found their best focus with the Badal system while looking at a Maltese cross stimulus prior to performing the VA test for each IOL. The psychophysical stimulus was presented on the DMD, illuminated at 555 nm, and viewed through the real IOL immersed in the cuvette, as well as without the lens. Measurements were performed with the three IOLs in the same session in random order. Subjects rested for 5 min while the corresponding IOL was inserted in the system, with at least 3 breaks. A typical session lasted 120 min.
The multifocal and extended-depth-of-focus IOLs were compared in terms of visual benefit at intermediate (0.60 m) and near (0.40 m). A Visual Benefit metric was calculated as the difference between the logMAR Visual Acuity with a multifocal lens and a monofocal Podeye IOL. Visual Benefit was calculated for both intermediate and near distances [38][39][40]. Visual Imbalance was calculated as the logMAR Visual Acuity standard deviation in a 4.25 D range (from +1 D to -3.25 D).

Results
The following results show the optical simulations of the new channel of the system and the on-bench and in vivo measurements.

Optical simulations
The first simulations aimed at estimating the power of the Rassow lens that compensates for the base power of a 20 D IOL. The Rassow lens was assumed to be a paraxial lens and its specifications were obtained from the closest equivalent lens in Newport's catalog. After selection of the final focal length of the Rassow lens, the distances between L10-L15 and L15-L16 (Fig. 2) were recalculated to compensate for the difference between the theoretical paraxial lens and the real one. The final focal length of the Rassow lens was 60 mn, and distances L10-L15 and L15-L16 were 213 and 210 mm respectively.
The optical quality of the Rassow system was evaluated computationally using the MTF, the spot diagram, and the wave aberrations of the system. Figure 3 shows the estimated MTFs (a) and wave aberrations (b) at 0°and 2°in vertical for a monofocal IOL immersed in the cuvette. Small amounts of spherical aberration were found at 0°(0.02µm), and also of astigmatism (0.05µm) and coma (0.02µm) at 2°. We calculated the magnification factor needed to reproduce the decrease in effective diameter at the IOL plane in the eye by the effect of rays' convergence at the cornea. Calculations were performed assuming different corneal powers (39,43, and 47 D), anterior chamber depths (3.2, 4.5, and 5.5 mm), and entrance pupil diameters (3 and 4.5 mm). The resulting iris pupil diameter and the correspondent magnification are shown in Table 1. A magnification of ×0.87, which corresponds to an eye model with a 43 D cornea and an anterior chamber depth of 3.2 mm was implemented in the system.

Experimental performance of Rassow system
We tested experimentally the magnification of the Rassow system for different positions of the Badal system, the experimental optical performance with monofocal IOLs of different powers, and the spherical aberration of the system. Figure 4 shows the experimental measurements of magnification in the cuvette plane, for different positions in the Badal optometer. The average measured magnification was 0.88. The average standard deviation of measured magnification over repeated measurements was 0.02. The standard deviation of measured magnification across defocus positions in the Badal system was 0.01. The optical performance of the Rassow system was tested using five monofocal IOLs of different powers (Fig. 5), using on bench images of an E-letter, and a cross-correlation optical quality metric (using an E letter image with no lens in the cuvette, with the flip-up mirrors up, as a reference). The Badal optometer allowed spherical compensation for other powers, linearly (R 2 =0.99) in a 5 D range. The measured optical quality metric varied less than 0.02 across IOLs. The spherical aberration induced by the Rassow system was measured with no IOL in the cuvette and defocus corrected with a 20 D trial lens placed in a conjugate pupil plane. In comparison with the spherical aberration measured in the cuvette with monofocal spherical IOLs (-0.07 um and -0.015 um at 4.5-mm pupils, which is consistent with the negative spherical aberrations of these IOLs) measurements of the spherical aberration of the cuvette alone showed very small amounts of positive spherical aberration (<0.02 µm). The experimental results of spherical aberration measurements are in good agreement with predictions from computer simulations of the Rassow system with and without IOLs, as shown in Fig. 6, with the measured values within 75% of the predicted values. RMS for 3 rd order aberrations was lower than 0.04 µm and all values of aberrations of the cuvette with and without IOL were lower than 0.15 µm.  Qualitatively, the higher quality corresponds to the monofocal IOL at Far; however, the image quality decreases rapidly out of focus. The trifocal IOL shows two distinctive broader areas of higher quality at far and intermediate-near distance. The Isofocal IOL shows a wider area of good focus, consistently with its extended depth of focus nature. Figure 7(b) shows the corresponding TF optical quality correlation metric, using the image of the monofocal IOL at best focus as a reference. For IOLs projected on an artificial eye, the optical quality at far does not decrease bellow 0.95 (relative to monofocal at a far distance as a reference) in neither trifocal and Isofocal IOLs, reflecting high optical quality at distance. The Visual Benefit at intermediate (-1.5 D) is 0.03 for the trifocal and 0.07 for the Isofocal, and at near (-3 D) is 0.14 for the trifocal and 0.01 for the Isofocal. The Visual Imbalance was 0.1, 0.04, and 0.07 for the monofocal, trifocal, and Isofocal, respectively. Figure 8 shows the through-focus VA in three patients with the three IOLs projected on the pupil plane with the Rassow-IOL system. The VA with no lens in the cuvette was also measured at a far distance using the former psychophysical channel, with the flip-up mirrors up. The wave aberrations of the eye (along with the corresponding RMS for astigmatism and higher-order aberrations) are shown for each subject. The optical quality of the three subjects measured is shown in terms of RMS wavefront error. The average VA at far with no lens was -0.08 ± 0.07. VA at far with the monofocal IOL and no IOL differed by less than 0 ± 0.03 logMAR on average. Trifocal IOLs increase VA at intermediate, but most predominantly at near, with all subjects showing a peak in VA at around 3.5 D (0.24 ± 0.04 logMAR on average), while the Isofocal IOL provides the highest VA at intermediate distances (0.21 ± 0.02 logMAR on average). The lowest values of VA (both with monofocal and multifocal IOLs) were found in the most aberrated subject (S#2). Figure 9 shows the visual benefit at intermediate (9(a)) and near (9(b)) distances for the trifocal and Isofocal IOLs relative to the monofocal IOL, and the visual imbalance (9(c)) for the three IOLs (for each subject and averaged across subjects). In vivo measurements, in terms of TF VA, replicate, on average, on-bench findings. We found that both curves, correlation metric for TF images and TF VA on subjects, are correlated across subjects, especially for the monofocal IOL (slope = -2.57, r = 0.83; slope = -1.85, r = 0.52; and slope = -1.39, r = 0.43, on average for monofocal, trifocal and Isofocal IOLs respectively).

Discussion
In this study, we introduced a system to project physical IOLs on the pupil's eyes through a Rassow telescope. This represents a new opportunity to validate the experimental simulations of vision with IOLs mapped in an Adaptive Optics element (spatial phase maps) or SimVis simulators (temporal multiplexing), as the physical IOLs can be used as a reference. Previous work used 0 D IOLs in a cuvette [4], which were projected on the eye as if they were phase maps. To our knowledge, this is the first time that a Rassow -IOL projection system has been incorporated into a channel of an Adaptive Optics system, allowing projecting IOLs of standard base power and visual testing.
The use of a Rassow telescope was proposed in the '90s, and to a large extent is the basis for systems that project IOLs on the eye. A recent study compared the Contrast Sensitivity Function through physical IOLs in a laboratory-based Rassow system and the commercial prototype VirtIOL [41]. Measurements were done through three IOLs (monofocal, multifocal, and EDOF) on twenty-one subjects. There was no attempt to assess absolute performance values for each lens, and the study was rather limited to relative comparisons.
Our Adaptive Optics and IOL SimVis visual simulators are based on dynamic elements and therefore fully programmable. This allows a rapid switch between corrections. In contrast, in the Rassow system, the IOLs need to be interchanged to compare vision through different designs allowing only static simulations. However, the incorporation of the Rassow IOL projection system into the channels of an Adaptive Optics system provides a reference for validation of the IOL designs with standard powers mapped in the active elements.
To our knowledge, this study asses for the first time the aberrations of the Rassow system (both computationally and experimentally). Since some of the IOLs (for example monofocal aspheric IOLs or the Isofocal IOL) modulate the spherical aberration of the eye, guaranteeing that the Rassow system does not induce higher-order aberrations is critical. We found that the induced spherical aberration is negligible. In addition, in our system, residual aberrations were compensated using the deformable mirror. Nevertheless, our findings confirm that the Rassow system can be used as a stand-alone simulator for comparing IOLs, which can be built using off-the-shelf optical components without affecting the optics of the IOL to be projected.
To the best of our knowledge, a novelty of this work is the adjustment of the system magnification to compensate the effect of the convergence of the rays by the cornea onto the eye's pupil plane, which effectively decreases the iris pupil diameter that is illuminated [29]. In contrast, the standard 4-focal configuration of the published Rassow systems projects the IOL on the eye assuming that the entrance pupil and the iris pupil diameter are equal. We reduced the effective pupil diameter of the IOL plane by a factor of 0.87 and we calculated that this factor was affected by less than 10% by changes in corneal power, ACD, or entrance pupil diameter using realistic values. While the effect of magnification may be relatively small with certain IOLs that are less dependent on pupil diameter (i.e monofocal or diffractive IOLs), it is expected to play a relevant role with IOLs that modulate higher-order aberrations, the spherical aberration in particular, which are pupil-size dependent.
Optical quality and vision with the projected IOLs match the expectations from these IOLs, as well as prior, defocus curves in patients implanted with these IOLs. We found higher quality at far with the monofocal IOL, followed by Isofocal and Multifocal. The Isofocal IOL outperforms the monofocal and multifocal at intermediate, and the Multifocal IOL outperforms the monofocal and Isofocal at near. Defocus curves with the physically projected IOLs are in good agreement with those obtained by simulating the same IOLs with Spatial Light Modulator or SimVis, in terms of the shape of the curve, with peaks and depth of focus as expected [4]. The combination of these simulation strategies and the Rassow system in the same instrument will allow a direct comparison of adaptive optics and static simulations in phakic patients and therefore direct validations of the visual simulators for different lenses. Simulations (with either physical IOL projected on the eye, or the IOL represented as phase maps or temporal patterns on SLM or SimVis) are generally performed on phakic patients, and therefore all share the assumption that the impact of the native aberrations of the crystalline lens in visual performance is secondary to that of the IOL design. This assumption has proved valid, at least with multifocal IOLs, as shown in patients before and after implantation [23] and in a study that concluded that the influence of the crystalline lens' aberrations is negligible in terms of VA for medium and small pupil diameters [42]. With monofocal IOLs of magnitudes of spherical aberration comparable to those of the ocular components, the presence of spherical aberration from the crystalline lens (negative spherical aberration in young eyes [43] and shifting towards positive in older eyes [44]) likely modulates the spherical aberration in different ways than in the pseudophakic eye. The lack of compensation of spherical aberration of the lens in Rassow-IOL-in cuvette stand-alone system could be a limitation of the system. In our AO system, spherical aberration could be compensated with the deformable mirror, if deemed necessary in certain applications.
In summary, we have presented and validated an optical system for the projection of real IOLs (immersed in a cuvette) on the subject's eye. The system does not induce any large additional aberrations and replicates the effective diameter of the IOL when it is implanted in the eye. We have demonstrated the system on bench (with an artificial eye) and in real subjects (VA) through three different types of lenses (refractive monofocal, diffractive trifocal, and refractive Isofocal) allowing patients to experience vision and evaluate through-focus visual performance without implanting the IOL. The through-focus visual performance with three different IOLs projected on the eye using the Rassow system show differences across individuals (likely arising from differences across patients with natural aberrations) and across lens designs, with presbyopia-correcting IOLs producing a clear visual benefit at intermediate (Isofocal IOL) and near (trifocal IOL). The incorporation of a validated channel for projecting IOLs on the eye adds a reference in Adaptive Optics visual simulators, in which the IOLs are mapped (spatially or temporally) using active elements. Data availability. Data underlying the results presented in this paper are available in Ref. [45].