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Purpose: To determine the optimal number of data points required for optimization of formulae for classical lens power calculation.\ud \ud Methods: A large dataset of preoperative biometric values was used to assess the convergence of formula constants in a number of established intraocular lens power calculation formulae.\ud \ud Results: In formulae with a single constant, 80 to 100 clinical data points are sufficient to obtain convergence. The Haigis formula (3 constants), requires 200 to 300 data points although refractive error converges more rapidly.\ud \ud Conclusions: In all formulae 80 to 100 clinical data points are sufficient to achieve a stable mean refractive error.

Background: Spherical and astigmatic powers for phakic intraocular lenses are frequently calculated using fixed ratios of phakic lens refractive power to refractive spherical equivalent, and of phakic lens astigmatism to refractive cylinder. In this study, a Monte-Carlo simulation based on biometric data was used to investigate how variations in biometrics affect these ratios, in order to improve the calculation of implantable lens parameters.\ud Methods: A data set of over sixteen thousand biometric measurements including axial length, phakic anterior chamber depth, and corneal equivalent and astigmatic power was used to construct a multidimensional probability density distribution. From this, we determined the axial position of the implanted lens and estimated the refractive spherical equivalent and refractive cylinder. A generic data model resampled the density distributions and interactions between variables, and the implantable lens power was determined using vergence propagation.\ud Results: 50 000 artificial data sets were used to calculate the phakic lens spherical equivalent and astigmatism required for emmetropization, and to determine the corresponding ratios for these two values. The spherical ratio ranged from 1.0640 to 1.3723 and the astigmatic ratio from 1.0501 to 1.4340. Both ratios are unaffected by the corneal spherical / astigmatic powers, or the refractive cylinder, but show strong correlation with the refractive spherical equivalent, mild correlation with the lens axial position, and moderate negative correlation with axial length. As a simplification, these ratios could be modelled using a bi-variable linear regression based on the first two of these factors.\ud Conclusion: Fixed spherical and astigmatic ratios should not be used when selecting high refractive power phakic IOLs as their variation can result in refractive errors of up to ±0.3 D for a 8 D lens. Both ratios can be estimated with clinically acceptable precision using a linear regression based on the refractive spherical equivalent and the axial position.

Toric intraocular lenses (IOL) provide a reliable and predictable option for permanent correction of corneal astigmatism. In order to determine the lens strength necessary for achieving the desired correction, the operator can either use the calculation mode implemented in the biometry device or the calculation service offered by the lens manufacturer; however, in many cases a classical lens calculation from biometric data is not carried out but only a simplified estimation, which translates the corneal astigmatism into the torus of the toric IOL. This translational ratio, which is mostly used as an average standard value, can however show a substantial range of variation, so that in a worst case scenario an undercorrection of the refractive cylinder of up to 12.5 % or an overcorrection of up to 17 % can result. The purpose of this study was to elaborate the biometric effect sizes which determine the relationship between the corneal astigmatism to be corrected and the torus necessary for a full correction of an IOL.A total of 16,744 datasets were extracted from the IOLCon web platform and initially the axial position of the IOL implant was derived independent of a formula, based on the preoperative biometric values and the postoperative spherical equivalent. Subsequently, based on a ray propagation strategy for spherocylindrical vergences, the corresponding refractive value of a full correcting toric IOL was calculated. The translational relationship as a ratio between lens toricity and corneal astigmatism was analyzed for potential biometric effect sizes with a Monte Carlo simulation.The Monte Carlo simulation showed that the ratio of lens toricity to corneal astigmatism cannot be assumed as being constant. The analyzed data revealed an average translational ratio of 1.3938 ± 0.0595 (median 1.3921) with a range from 1.2131 to 1.5974. The axial position of the IOL was found to have the greatest influence, whereby the more posterior the lens position the higher the ratio. Due to the correlation of axial eye length and axial lens position, the eye length can be assumed to be an indirect effect size. The corneal equivalent refractive strength and the corneal astigmatism have no noteworthy effect on the translational ratio.Many calculation tools on the market simplify toric IOL power calculation by assuming a constant ratio of lens toricity to corneal astigmatism; however, the present simulation study showed that such a simplification can lead to clearly incorrect results. Accordingly, an individual calculation of IOL toricity based on biometric parameters (e.g. based on vergence propagation matrices or full aperture ray tracing) is recommended.HINTERGRUND UND ZIELSETZUNG: Torische Kapselsacklinsen bieten heutzutage eine zuverlässige Option der permanenten Korrektur eines Hornhautastigmatismus. Zur Ermittlung der für den gewünschten Ausgleich erforderlichen Linsenstärke kann der Operateur entweder auf die in seinem Biometriegerät implementierten Berechnungsmodi oder auf den vom Linsenhersteller angebotenen Kalkulationsservice zurückgreifen. In vielen Fällen wird dabei allerdings keine klassische Linsenberechnung aus biometrischen Daten durchgeführt, sondern nur mit einer vereinfachten Abschätzung gearbeitet, die den Hornhautastigmatismus in den Torus der tIOL übersetzt. Dieses dann zumeist als durchschnittlicher Standardwert genutzte Übersetzungsverhältnis kann jedoch eine erhebliche Schwankungsbreite aufweisen, sodass im ungünstigsten Fall eine Unterkorrektur des refraktiven Zylinders um bis zu 12,5 % oder eine Überkorrektur um bis zu 17 % resultieren kann. Ziel dieser Studie war es aufzuzeigen, welche biometrischen Einflussgrößen das Verhältnis zwischen dem zu korrigierenden Hornhautastigmatismus und dem für dessen Vollkorrektur notwendigen Torus einer Kapselsacklinse bestimmen.Aus der WEB-Plattform IOLCon wurden 16.744 Datensätze extrahiert, und anhand der präoperativen biometrischen Größen und dem postoperativen sphärischen Äquivalent wurde zunächst die axiale Position der Kapselsacklinse formelunabhängig abgeleitet. Anschließend wurde, basierend auf der Propagation sphärozylindrischer Vergenzen, der entsprechende Brechwert einer emmetropisierenden Kapselsacklinse ermittelt. Das Übersetzungsverhältnis als Quotient aus dem Torus der Linse und dem Hornhautastigmatismus wurde mit einer Monte-Carlo-Simulation auf seine potenziellen Einflussgrößen hin untersucht.Die Monte-Carlo-Simulation zeigt, dass nicht von einem konstanten Übersetzungsverhältnis ausgegangen werden kann. Für die hier zugrunde gelegten klinischen Fälle ergibt sich ein mittleres Übersetzungsverhältnis von 1,3938 ± 0,0595 (Median 1,3921) mit einer Spannweite von 1,2131 bis 1,5974. Den größten Einfluss hat hierbei die axiale Position der Kapselsacklinse – je weiter posterior sich diese befindet, desto höher ist das Übersetzungsverhältnis. Aufgrund der Korrelation der axialen Linsenposition mit der Augenlänge kann die Augenlänge als indirekte Einflussgröße gewertet werden. Der Äquivalentbrechwert sowie der Astigmatismus der Hornhaut besitzen keinen nennenswerten Effekt auf das Übersetzungsverhältnis.In einer ganzen Reihe von Berechnungsmodulen wird die Kalkulation des Torus der Kapselsacklinse dahingehend vereinfacht, dass dieser mittels eines einfachen konstanten Umrechnungsfaktors aus dem gemessenen Hornhautastigmatismus abgeleitet wird. Die vorliegende Studie zeigt jedoch, dass diese Vereinfachung zu deutlich fehlerhaften Ergebnissen führen kann. Dementsprechend wird eine individuelle Berechnung des Torus der IOL aus gemessenen biometrischen Größen (z. B. mittels Vergenzpropagation, Matrizen oder mittels Full-aperture-Raytracing) empfohlen.

PURPOSE: To compare the visual performance of an individually customized intraocular lens (IOL) versus a standard spherical aberration-correcting IOL. METHODS: In this prospective comparative study, 74 eyes of 60 patients scheduled for cataract surgery were randomized in a 2:1 ratio to receive either an individually customized IOL (; HumanOptics AG, Erlangen, Germany; customized group) or an aspheric IOL with a standard correction of spherical aberration (SA) (Tecnis ZCB00; Johnson & Johnson Vision Surgical, Inc., Santa Ana, CA; standardized group). In the customized group, IOL calculation was based on a minimum of a merit function that contained terms representing residual refraction, residual SA, and modulation transfer function. In the standardized group, the IOL was calculated with a routine procedure using the Holladay formula and had a standard SA correction of −0.27 µm. Refraction, visual acuity (far, intermediate, near), photopic and mesopic contrast sensitivity, defocus curve, corneal and ocular spherical aberration, and pupil size were measured 4 weeks and 3 months postoperatively. RESULTS: The customized group comprised 48 eyes of 37 patients and the standardized group 26 eyes of 23 patients. At 3 months, mean total ocular SA (5 mm) was 0.04 ± 0.06 µm in the customized group and −0.01 ± 0.05 µm in the standardized group. Uncorrected distance visual acuity and distance-corrected near visual acuity were statistically significantly better in the customized group. Contrast sensitivity testing yielded significantly better results in the customized group under photopic and mesopic conditions for almost all spatial frequencies. Compared to the standardized group, the defocus curve of the customized group showed a wider plateau surrounding the distance focal point. CONCLUSIONS: With the implantation of an individually optimized aspheric IOL visual performance, especially contrast sensitivity, can be significantly improved compared to a standard aberration-correcting IOL. [ J Refract Surg. 2019;35(9):565–574.]

The classical Javal's rule allows estimation of refractive cylinder from keratometric astigmatism using scaling for vergence transformation, with an additional half dioptre of cylinder against-the-rule. With increasing popularity of toric intraocular lenses it has been shown that keratometric astigmatism does not fully reflect the entire astigmatism of the phakic or pseudophakic eye.\ud \ud Researchers mostly argue that this mismatch is primarily due to astigmatism of the corneal back surface, and some papers propose correction strategies to consider this mismatch with the keratometric values. In this Technical Note we address this issue using a vector analysis and show the consequences of this correction on the front and back surface as well as total astigmatism of the cornea. As examples we focus on the correction strategies proposed by Abulafia and by Savini, frequently used in clinical practice.\ud \ud The main conclusion is that, since corneal tomographers do not systematically show zero total astigmatism in situations where keratometry measures astigmatism against-the-rule of around 3 dioptres, there may be reasons other than the corneal back surface for this mismatch between keratometry and total astigmatism. A number of possible sources of this mismatch are proposed.

Significance There is a high variation of chromatic dispersion with contemporary intraocular lens (IOL) materials. It is well known that chromatic aberration limits the optical performance especially with high-power lenses. Lens manufacturers, however, rarely provide data on the chromatic dispersion of their materials, limiting the comparability of available materials. Purpose This study aimed to analyze chromatic dispersion of hydrophobic and hydrophilic IOLs without prior knowledge of the IOLs' geometries. Methods We adapted Bessel's method for measuring focal length by placing the IOL in a wet cell. The chromatic dispersion of several hydrophobic and hydrophilic IOLs was characterized by measuring their focal lengths at multiple wavelengths. From the measured focal lengths, the refractive indices and the Abbe numbers were obtained. We measured four hydrophobic and two hydrophilic IOL models with a nominal power of 21 to 29.5 D. Results The hydrophobic IOLs had lower Abbe numbers (Abbe numbers 50). Most Abbe numbers were in agreement with the values provided by the IOL manufacturers, and the measurements were independent from IOL power. The repeatability for the Abbe number was better than ±3.5% for all lenses and better than ±2% for lenses between 21 and 26.5 D. The dispersion could be described by a Conrady model (R > 0.997). Conclusions The hydrophobic materials showed larger dispersion than did the hydrophilic IOL materials resulting in increased chromatic aberration. The method allowed for an estimation of the IOL's Abbe number without prior knowledge of IOL geometry.

Reverse genetics has been an indispensable tool revolutionising our insights into viral pathogenesis and vaccine development. Large RNA virus genomes, such as from Coronaviruses, are cumbersome to clone and to manipulate in E. coli hosts due to size and occasional instability1-3. Therefore, an alternative rapid and robust reverse genetics platform for RNA viruses would benefit the research community. Here we show the full functionality of a yeast-based synthetic genomics platform for the genetic reconstruction of diverse RNA viruses, including members of the Coronaviridae, Flaviviridae and Paramyxoviridae families. Viral subgenomic fragments were generated using viral isolates, cloned viral DNA, clinical samples, or synthetic DNA, and reassembled in one step in Saccharomyces cerevisiae using transformation associated recombination (TAR) cloning to maintain the genome as a yeast artificial chromosome (YAC). T7-RNA polymerase has been used to generate infectious RNA, which was then used to rescue viable virus. Based on this platform we have been able to engineer and resurrect chemically-synthetized clones of the recent epidemic SARS-CoV-24 in only a week after receipt of the synthetic DNA fragments. The technical advance we describe here allows to rapidly responding to emerging viruses as it enables the generation and functional characterization of evolving RNA virus variants - in real-time - during an outbreak.

Purpose: To provide additional information on normal values of static pupil diameter measurements for binocular infrared pupillometry with PupilX, a commercial pupillometer, and assess the reproducibility of this device’s measurements. Methods: The pupil diameters from 91 study participants with normal eyes with an average age of 39.7 years (SD 16.4 years) were measured with PupilX under scotopic (0 lx), mesopic (1 lx), and photopic (16 lx) illumination. To assess the repeatability of the device, each measurement was repeated 5 times. Results: The mean pupil diameters were 6.5 mm (SD 1.3 mm), 5.5 mm (SD 1.2 mm), and 4.03 mm (SD 0.9 mm) under scotopic, mesopic, and photopic illumination. Left and right eyes showed no difference in mean pupil diameters. The mean unsigned anisocoria was 0.26 mm (SD 0.32 mm) under scotopic, 0.26 mm (SD 0.27 mm) under mesopic, and 0.19 mm (SD 0.19 mm) under photopic illumination. The decrease in pupil diameter with age was largest for scotopic (≈0.057 mm/y) and smallest for photopic illumination (≈0.025 mm/y). The repeatability of the pupillometer was better than 0.2 mm. Conclusions: This study provides reference values for age- and light-related pupil diameters measured with the PupilX digital pupillometer in normal subjects.

To compare corneal tomography and its statistical uncertainty for measurements obtained by three clinically used corneal tomographers: A Scheimpflug camera (Pentacam HR), a swept source optical coherence tomography system (CASIA SS-1000), and Placido ring imaging (TMS-5).Repeated measurements with all three devices on 34 normal eyes were used to estimate the repeatability, precision, and mean values of corneal elevation and pachymetry within 8 mm diameter. The repeatability (standard deviation) was calculated for each data point of the corneal elevation data-maps of anterior and posterior cornea as well as for the pachymetry data-maps. Uncertainty on the position of the eye at each measurement might contribute to the differences between elevation data-maps. To take this into account, we defined the precision as the standard deviation for the elevation data-maps of anterior and posterior cornea after correction of misalignment-effects (rotation, translation). The mean elevation and pachymetry data-maps were fitted with Zernike polynomials for interdevice-comparison.Pentacam HR offered the best repeatability and precision for the anterior corneal elevation (3 and1.6 μm, respectively). CASIA SS-1000 offered good repeatability and precision with high resolution for posterior corneal elevation, and the best repeatability for pachymetry (3 μm). TMS-5 measured anterior elevation with similar repeatability to CASIA SS-1000 (6 μm). The data-maps of the three tomographers could not be used interchangeably. The largest differences were observed for pachymetry and posterior corneal elevation data-maps.Misalignment limited the repeatability of TMS-5 and Pentacam HR, but had little influence on the repeatability of CASIA SS-1000.

We investigated whether eyes with keratoconic corneal tomography pattern could benefit more from aberration correction with custom intraocular lenses (IOLs) than normal cataractous eyes despite the effect of misalignment on the correction of aberrations. Custom IOLs (cIOLs) were calculated for twelve normal and twelve keratoconic eyes using personalized numerical ray tracing models. The Stiles-Crawford weighted root-mean-square spot-size (wRMS) at the virtual fovea was evaluated for cIOLs and aberration-neutral IOLs (nIOLs) in a simulated clinical study with 500 virtual IOL implantations per eye and per IOL. IOL misalignment (decentration, tilt, rotation) and pupillary ectopia (4.5 mm iris aperture) were varied upon each virtual implantation. The nIOLs achieved average wRMS of 16.4 ± 4.3 μm for normal, and 92.7 ± 34.4 μm for keratoconic eyes (mean ± standard deviation). The cIOLs reduced the average wRMS to 10.3 ± 5.8 μm for normal, and 28.5 ± 18.6 μm for keratoconic eyes. The cIOLs produced smaller wRMS than nIOLs in most virtual implantations (86.7% for normal and 99.4% for keratoconic eyes). IOL misalignment resulted in larger wRMS variations in the keratoconus group than in the normal group. Custom freeform IOL-optics-design may become a promising option for the correction of advanced aberrations in eyes with non-progressive keratoconic corneal tomography pattern.

To investigate the impact of intraocular lens (IOL) decentration ≤±1 mm and IOL tilt ≤±10° on the fixation axis and spherical equivalent refraction (SE), 50 pseudo-phakic eyes were simulated using numerical ray-tracing. We computed the position of the object point whose image ends up at the virtual fovea for each scenario and estimated the corresponding change of fixation axis and SE. The eye turned opposite to the direction of IOL decentration or tilt to compensate for the associated prismatic effect (angle

Purpose To discuss the impact of intraocular lens-(IOL)-power, IOL-thickness, IOL-shape, corneal power and effective lens position (ELP) on the distance between the anterior IOL vertex (ALP) of a thick IOL and the ELP of its thin lens equivalent. Methods We calculated the ALP of a thick IOL in a model eye, which results in the same focal plane as a thin IOL placed at the ELP using paraxial approximation. The model eye included IOL-power (P), ELP, IOL-thickness (Th), IOL-shape-factor (X), and corneal power (DC). The initial values were P = 10 D (diopter: 1 D = 1 m-1), 20 D, 30 D, Th = 0.9 mm, ELP = 5 mm, X = 0, DC = 43 D. The difference between ALP and the ELP was illustrated as a function of each of the model parameters. Results The ALP of a thick lens has to be placed in front of the ELP for P>0 IOLs to achieve the same optical effect as the thin lens equivalent. The difference ALP-ELP for the initial values is -0.57 mm. Minus power IOLs (ALP-ELP = -0.07 mm, for IOL-power = -5 D) and convex-concave IOLs (ALP-ELP = -0.16 mm, for X = 1) have to be placed further posterior. The corneal power and ELP have less influence, but corneal power cannot be neglected. Conclusion The distance between ELP and ALP primarily depends on IOL-power, IOL-thickness, and shape-factor.

Purpose To implement a setup which allows simultaneous visualization of the far and near distance light field of multifocal intraocular lenses (MIOL) with two different wavelengths. Methods We used two different laser systems (532 nm and 405 nm) in junction with Powell lenses to create vertical laser lines. One laser line was collimated to simulate far distance imaging while the second laser line was diverging simulating near distance imaging at approximately 0.3 m distance. The MIOL was placed in a glass cuvette filled with balanced saline solution which was doped with two different fluorophores. The fluorophores were chosen to have a large Stokes shift and good separation between their excitation and emission bands. Image acquisition was performed with a slit lamp bio microscope and a digital single reflex camera. We investigated three different IOL types: a bifocal MIOL, a trifocal MIOL and an extended depth of focus IOL. Results We found that Propidium iodide and Fluorescein were appropriate fluorophores. Propidium iodide was excited at 532 nm and showed a red fluorescence while Fluorescein was excited at 405 nm showing the green fluorescence. Both lasers required a high power of approximately 30 mW in order to create a visible fluorescent reaction in the cuvette. All three MIOL types provided a good separation between far and near distance light. The regions of overlapping light fields were visible as yellow fluorescence. Conclusions In contrast to the previously published setups using a single wavelength with collimated excitation light and axially separated far and near distance foci the current setup allows superposition of the far and near distance foci which is more realistic compared to the situation in the eye. The dual wavelength approach enables an easy optical separation of far and near distance light.

Background So-called aberration-free intraocular lenses (IOLs) are well established in modern cataract surgery. Usually, they are designed to perfectly refract a collimated light beam onto the focal point. Methods We show how much aberration can be expected with such an IOL in a convergent light beam such as that found anterior to the human cornea. Additionally, the aberration in a collimated beam is estimated for an IOL that has no aberrations in the convergent beam. The convergent beam is modelled as the pencil of rays corresponding to the spherical wavefront resulting from a typical corneal power of 43 m −1 . The IOLs are modelled as infinitely thin phase plates with 20 m −1 optical power placed 5 mm behind the cornea. Their aberrations are reported in terms of optical path length difference and longitudinal spherical aberration (LSA) of the marginal rays, as well as nominal spherical aberration (SA) calculated based on a Zernike representation of the wavefront-error at the corneal plane within a 6 mm aperture. Results The IOL designed to have no aberrations in a collimated light beam has an optical path length difference of −1.8 μm, and LSA of 0.15 m −1 in the convergent beam of a typical eye. The corresponding nominal SA is 0.065 μm. The IOL designed to have no aberrations in a convergent light beam has an optical path length difference of 1.8 μm, and LSA of −0.15 m −1 in the collimated beam. Conclusions An IOL designed to have no aberrations in a collimated light beam will increase the SA of a patient's eye after implantation.

The capabilities of a weighted least squares approach for the optimization of the intraocular lens (IOL) constants for the Haigis formula are studied in comparison to an ordinary least squares approach. The weights are set to the inverse variances of the effective optical anterior chamber depth. The effect of random measurement noise is simulated 100000 times using data from N = 69 cataract patients and the measurement uncertainty of two different biometers. A second, independent data set (N = 33) is used to show the differences that can be expected between both methods. The weighted least squares formalism reduces the effect of measurement error on the final constants. In more than 64% it will result in a better approximation, if the measurement errors are estimated correctly. The IOL constants can be calculated with higher precision using the weighted least squares method.

We propose a framework for the analysis of the repeatability and precision of corneal elevation and the repeatability of corneal thickness data measured by clinically used topographers and tomographers. The repeatability is given by the standard deviation of different measurements of the same eye for each data point. The differences between measurements can partially be explained by different positions of the eye at each measurement. The precision is given by the standard deviation of the data after correction for displacements (decentration, tilts, rotations). The applicability is demonstrated using measurements of the Pentacam HR [1] (Oculus Optikgerate GmbH, Wetzlar, Germany) Scheimpflug tomographer. It provides anterior corneal elevation data with a precision that was almost limited by the axial resolution of 1μm in the central 6mm zone. This is approximately five times better than the precision of the posterior elevation. The results can be applied to surface approximation of the exported corneal elevation data and give a measure for the goodness of the fit.