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Net cylinder and spherocylinder formats characterize individual keratometries and prescriptions but must be converted to dioptric vectors to allow for calculations and statistical analyses. Næser's polar value system was specifically developed for the analysis of the surgically induced refractive change along the surgical meridian. This study provides a short description together with a practical manual and a computer program for the use of this dioptric vector method. Measurement techniques, vector equations, statistical methods, and terminology are reviewed. The analysis is identical for corneal and refractive measurements and for corneal incisional, corneal laser, and intraocular lens-based surgery. The choice of appropriate surgical reference meridians for standard surgical procedures is demonstrated. The Excel file may be used by the reader for future studies., (Copyright © 2020 Published by Wolters Kluwer on behalf of ASCRS and ESCRS.)

Purpose: To compare the accuracy of a thick-lens intraocular lens (IOL) power formula using the manufacturer's cutting-card information (the Næser 1 formula) and calculated data from open sources (the Næser 2 formula) for IOL architecture; and to compare these results with the achievements of the Barrett Universal II, Haigis, Hoffer Q, Holladay 1, and SRK/T formulas., Setting: IRCCS GB Bietti Foundation, Rome, Italy., Design: Retrospective case series., Methods: For each IOL power formula, the prediction error in refraction was retrospectively calculated in eyes after phacoemulsification with implantation of the SN60WF posterior chamber IOL. The predictions made using the different formulas were optimized in retrospect by adjusting the respective constants. The mean arithmetic error (ME), the variance, and the median absolute error (MedAE) were calculated, as well as the dependency of the arithmetic error on the axial length., Results: The study comprised 151 eyes. The Næser 1 and Næser 2 formulas were identical clinically and statistically. The ME (P = .278 with a one-way analysis of variance) and the variances for arithmetic errors (P = .248 with Levene's homogeneity test) were similar for all 7 formulas. A combined metric of ME, variance, MedAE, and arithmetic error on the axial length suggested the Næser 2 formula as the most accurate, followed by the Næser 1, Barrett Universal II, Haigis, SRK/T, Hoffer Q, and Holladay 1 formulas., Conclusions: The Næser thick-lens IOL power equations based on calculated and manufacturer's IOL data provided similar accuracies and performed approximately as the best thin-lens formulas. Cutting-card information is not necessary in current IOL power calculation., (Copyright © 2019 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.)

Purpose: To compare keratometric astigmatism (KA) and different modalities of measuring total corneal astigmatism (TCA) for toric intraocular lens (IOL) calculation and optimize corneal measurements to eliminate the residual refractive astigmatism., Setting: G.B. Bietti Foundation IRCCS, Rome, Italy., Design: Prospective case series., Methods: Patients who had a toric IOL were enrolled. Preoperatively, a Scheimpflug camera (Pentacam HR) was used to measure TCA through ray tracing. Different combinations of measurements at a 3.0 mm diameter, centered on the pupil or the corneal vertex and performed along a ring or within it, were compared. Keratometric astigmatism was measured using the same Scheimpflug camera and a corneal topographer (Keratron). Astigmatism was analyzed with Næser's polar value method. The optimized preoperative corneal astigmatism was back-calculated from the postoperative refractive astigmatism., Results: The study comprised 62 patients (64 eyes). With both devices, KA produced an overcorrection of with-the-rule (WTR) astigmatism by 0.6 diopter (D) and an undercorrection of against-the-rule (ATR) astigmatism by 0.3 D. The lowest meridional error in refractive astigmatism was achieved by the TCA pupil/zone measurement in WTR eyes (0.27 D overcorrection) and the TCA apex/zone measurement in ATR eyes (0.07 D undercorrection). In the whole sample, no measurement allowed more than 43.75% of eyes to yield an absolute error in astigmatism magnitude lower than 0.5 D. Optimized astigmatism values increased the percentage of eyes with this error up to 57.81%, with no difference compared with the Barrett calculator and the Abulafia-Koch calculator., Conclusion: Compared with KA, TCA improved calculations for toric IOLs; however, optimization of corneal astigmatism measurements led to more accurate results., (Copyright © 2017 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.)

Purpose: To evaluate the influence of posterior corneal astigmatism on total corneal astigmatism in patients with 1.00 diopter (D) or more of corneal astigmatism., Setting: Private practice, Bologna, Italy., Design: Prospective case series., Methods: Corneal astigmatism was measured using a Scheimpflug camera combined with a corneal topographer (Sirius). Keratometric astigmatism, anterior corneal astigmatism, posterior corneal astigmatism, and total corneal astigmatism were evaluated. Vector analysis was performed according to the Næser method., Results: One hundred fifty-seven eyes were enrolled. Keratometric astigmatism was with the rule (WTR), against the rule (ATR), and oblique in 84.0%, 11.5%, and 4.5% of eyes, respectively. Posterior corneal astigmatism exceeded 0.50 D and 1.00 D in 55.4% of eyes and 5.7% of eyes, respectively. The mean posterior corneal astigmatism was 0.54 D, inclined 91 degrees in relation to the steeper anterior corneal meridian. The steepest meridian was vertically aligned in 93.0% of cases. Compared with total corneal astigmatism, keratometric astigmatism overestimated WTR astigmatism by a mean of 0.22 D ± 0.32 (SD), underestimated ATR astigmatism by 0.21 ± 0.26 D, and overestimated oblique astigmatism by 0.13 ± 0.37 D. In the whole sample, a difference in astigmatism magnitude of 0.50 D or more was detected between keratometric astigmatism and total corneal astigmatism in 16.6% of cases and the difference in the location of the steep meridian was greater than 10 degrees in 3.8% of cases., Conclusion: In patients who are candidates for surgical correction of astigmatism, measuring only the anterior corneal curvature can lead to inaccurate evaluation of the total corneal astigmatism., Financial Disclosure: Mr. Versaci and Mr. Vestri are employees of Costruzione Strumenti Oftalmici Srl. No author has a financial or proprietary interest in any material or method mentioned., (Copyright © 2014 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.)

Purpose: To evaluate outcomes after laser in situ keratomileusis (LASIK) in highly astigmatic myopic and hyperopic eyes., Setting: University eye clinic., Design: Retrospective case series., Methods: Eyes with more than 2.0 diopters (D) of astigmatism were identified from patient records. The mean preoperative cylinder was -3.92 D ± 0.82 (SD) in myopic eyes and -4.42 ± 1.10 D in hyperopic eyes. Patients were examined preoperatively and 3 months postoperatively. Laser in situ keratomileusis was performed with a Visumax femtosecond laser and a MEL-80 excimer laser. Preoperative and postoperative refractions were converted to polar values. Induced torsion and achieved correction of sphere and cylinder were determined., Results: After 3 months, the mean sphere was 0.48 ± 0.68 D in myopic eyes and the mean cylinder -0.97 ± 0.52 D. Spherical equivalent (SE) correction was 0.05 ± 0.42 D from target. Astigmatism was 0.77 ± 0.62 D undercorrected (P<.01), and the mean induced torsion was -0.18 ± 0.51 D (P=.02). Astigmatic undercorrection was 21% of the intended correction. In hyperopia, the mean 3-month refraction was 0.79 ± 0.83 D in sphere and -1.38 ± 0.90 D in cylinder. The SE refraction was -0.01 ± 0.71 D from target. Astigmatism was 1.17 ± 0.81 D undercorrected (P<.01), with no significant torsion. Intended and achieved astigmatic corrections were correlated, with astigmatism being 28% undercorrected., Conclusions: Laser in situ keratomileusis in highly astigmatic eyes precisely corrected SE refraction but led to astigmatic undercorrection, particularly in hyperopia. Little to no torsion of the cylinder axis was induced., (Copyright © 2012 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.)