Multivariate analysis of refractive data: mathematics and statistics of spherocylinders

Accuracy of Toric Intraocular Lens Calculations Using Estimated Versus Measured Posterior Corneal Astigmatism

PURPOSE

To compare the prediction accuracy of toric intraocular lens calculations using estimated vs measured posterior corneal astigmatism (PCA).

DESIGN

Retrospective case series.

METHODS

A total of 110 eyes of 110 patients with uncomplicated toric intraocular lens implantation were included in this study. Predicted postoperative refractive astigmatism was calculated with the Barrett Toric Calculator using the estimated PCA (E-PCA), the measured IOLMaster 700 PCA (I-PCA), and the measured Pentacam PCA (P-PCA). Refractive astigmatism prediction errors (RA-PEs), including their trimmed (tr-) centroid (mean vector), spread (precision), tr-mean absolute RA-PE (accuracy), and percentage within a certain threshold, were determined using vector analysis and compared between groups.

SETTING

University Eye Clinic, Maastricht University Medical Center+, the Netherlands.

RESULTS

The tr-centroid RA-PEs of the E-PCA (0.02 diopter [D] at 82.2°), the I-PCA (0.08 D at 35.5°), and the P-PCA (0.09 D at 69.1°) were significantly different from each other (P < .01), but not significantly different from zero (P = .75, P = .05, and P = .05, respectively). The E-PCA had the best precision (tr-mean 0.40 D), which was not significantly lower than the I-PCA (0.42 D, P = .53) and P-PCA (0.43 D, P = .06). The E-PCA also had the best accuracy (0.40 D), which was not significantly different from the I-PCA (0.42 D, P = .26) and significantly better than the P-PCA (0.44 D, P < .01). The precision and accuracy of the I-PCA did not significantly differ from those of the P-PCA. There were no statistically significant differences in the percentage of eyes within a certain absolute RA-PE threshold.

CONCLUSIONS

The Barrett Toric Calculator using the E-PCA, I-PCA, or P-PCA showed a comparable prediction of postoperative refractive astigmatism in standard clinical practice.

Subjective refraction using power vectors by updating a conventional phoropter with a Stokes lens for continuous astigmatic power generation

PURPOSE

To implement a pure power vector method for monocular subjective refraction using a regular phoropter with the only modification being the inclusion of a Stokes lens. The proposed methodology was tested with three different Stokes lenses, and the results were compared with conventional clinical refraction procedures.

METHODS

Power vector subjective refraction was performed by attaching a Stokes lens to the Risley prism holder. Stokes lenses allow for pure astigmatic compensation in the form of the J0 , J45 components while the spherical lenses in the phoropter allow determination of the spherical component in the form of M (spherical equivalent). The proposed routine is presented step-by-step using three Stokes lenses having different astigmatic powers.

RESULTS

Monocular subjective refraction was performed on 26 healthy subjects with a mean age of 44 ± 16 years, mean spherical equivalent of -0.56 D (range -5.50 to +2.38 D) and refractive astigmatism ≤1.50 D. No differences were found between the results obtained with the conventional technique versus the vector-based procedure for the spherical equivalent (p = 0.28) or astigmatic components (p = 0.34). In addition, visual acuity (VA) was equivalent through the refractions measured with the conventional and vector procedures (p = 0.12). Repeatability coefficients for J0 and J45 with the new vector methodology were <0.38 D.

CONCLUSIONS

The proposed routine could be helpful for cases where it is difficult to get a valid starting point for conventional refraction (e.g., irregular corneas and media opacities), for testing facilities with limited resources/equipment and/or for motivated clinicians who wish to know about alternative methods of refractive error determination.

Predicting Residual Astigmatism in Cataract Surgery

The purpose of this review is to evaluate the prediction of postoperative residual astigmatism and to determine the best prediction method for astigmatism correction. In recent findings for residual astigmatism in non-toric monofocal intraocular lens (IOL) implanted eyes, vector analysis can be used to correctly evaluate residual astigmatism by decomposing it. In predicting residual astigmatism, the with-the-rule (WTR) and against-the-rule (ATR) astigmatism components can now be almost predicted. This may be due to advances in inspection equipment and surgical technique. However, there are still issues with the oblique astigmatism component. In addition, corneal astigmatism is the most important predictor of postoperative residual astigmatism, and other predictors, such as refractive astigmatism, age, and lens thickness, have also been mentioned. However, all but corneal astigmatism are questionable because of the possibility of confounding variables. Total corneal astigmatism is more accurate in predicting residual astigmatism than anterior corneal astigmatism. Several predictions of residual astigmatism have been reported, but complete prediction has not been possible. Further research is needed, especially in predicting oblique astigmatism. However, I emphasize that the accuracy of predicting WTR and ATR astigmatism has improved considerably and can be predicted using regression equations with total corneal astigmatism.

Astigmatism analysis and reporting of surgically induced astigmatism and prediction error

PURPOSE

To provide a method for determining the vector that, when added to the preoperative astigmatism, results in no prediction error (PE) and to specify statistical methods for evaluating astigmatism and determining the 95% confidence convex polygon.

SETTING

Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California.

DESIGN

Retrospective consecutive case series.

METHODS

An analysis of 3 clinical trials involving toric intraocular lenses was performed. 3 formulas were evaluated (generic vergence formula with zero surgically induced astigmatism, the Barrett toric formula, and the Holladay toric formula). Scalar and vector analyses were performed on each dataset with each formula and the results compared. Since the PE was not a Gaussian distribution, a 95% convex polygon was used to determine the spread of the data.

RESULTS

The mean values for the vector absolute astigmatism PEs were not different for the 3 formulas and 3 datasets. The Barrett and Holladay toric calculators were statistically superior to the zero formula for 3 intervals (0.75, 1.0, and 1.25) in the high astigmatism dataset.

CONCLUSIONS

Residual astigmatism and vector absolute astigmatism PE mean values and SDs are useful but require extremely large datasets to demonstrate a statistical difference, whereas examining percentages in 0.25 diopters (D) steps from 0.25 to 2.0 D reveals differences with far fewer cases using the McNemar test for a P value. Double-angle plots are especially useful to visualize astigmatic vector PEs, and a 95% confidence convex polygon should be used when distributions are not Gaussian.

Dioptric power and refractive behaviour: a review of methods and applications

Myopia is a global healthcare concern and effective analyses of dioptric power are important in evaluating potential treatments involving surgery, orthokeratology, drugs such as low-dose (0.05%) atropine and gene therapy. This paper considers issues of concern when analysing refractive state such as data normality, transformations, outliers and anisometropia. A brief review of methods for analysing and representing dioptric power is included but the emphasis is on the optimal approach to understanding refractive state (and its variation) in addressing pertinent clinical and research questions.

Although there have been significant improvements in the analysis of refractive state, areas for critical consideration remain and the use of power matrices as opposed to power vectors is one such area. Another is effective identification of outliers in refractive data. The type of multivariate distribution present with samples of dioptric power is often not considered. Similarly, transformations of samples (of dioptric power) towards normality and the effects of such transformations are not thoroughly explored. These areas (outliers, normality and transformations) need further investigation for greater efficacy and proper inferences regarding refractive error. Although power vectors are better known, power matrices are accentuated herein due to potential advantages for statistical analyses of dioptric power such as greater simplicity, completeness, and improved facility for quantitative and graphical representation of refractive state.

Long-term changes in the refractive effect of a toric intraocular lens on astigmatism correction

Purpose

To examine the long-term changes in the astigmatism-correcting effect of a toric intraocular lens (IOL) after stabilization of surgically induced astigmatic changes due to cataract surgery.

Methods

Unilateral eyes of 120 patients that received a toric IOL for against-the-rule (ATR) or with-the-rule (WTR) astigmatism were enrolled. Manifest refractive and anterior corneal astigmatism, and ocular residual astigmatism which is mainly derived from internal optics were examined preoperatively, at approximately 2 months postoperatively (baseline) and at 5 ~ 10 years postbaseline. The astigmatism was decomposed to vertical/horizontal (Rx) and oblique components (Ry), which was compared between baseline and 5 ~ 10 years postbaseline.

Results

In the eyes having ATR astigmatism, the mean Rx and Ry of the manifest refractive and corneal astigmatism significantly changed toward ATR astigmatism between the baseline and 5 ~ 10 years postbaseline (p ≤ 0.0304), but those of ocular residual astigmatism did not change significantly between the 2 time points. In the eyes having WTR astigmatism, the Rx and Ry of refractive, corneal, and ocular residual astigmatism did not change significantly between the 2 time points. Double-angle plots revealed an ATR shift in refractive and corneal astigmatism and no marked change in the ocular residual astigmatism in the eyes with ATR astigmatism, and there is no change in this astigmatism in the eyes with WTR astigmatism.

Conclusion

The long-term changes with age in the effect of a toric IOL significantly deteriorated due to an ATR shift of corneal astigmatism in the eyes having ATR astigmatism, while it was maintained in eyes having WTR astigmatism, suggesting that ATR astigmatism should be overcorrected.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00417-021-05406-7.

Surgically induced astigmatism made easy: calculating the surgically induced change in sphere and cylinder for corneal incisional, corneal laser, and intraocular lens-based surgery

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.

V. SD, Nagaraj S, Wittberg DM, Stamper RL, Keenan JD. Accuracy of autorefraction in an adult Indian population

Purpose

Autorefractors allow non-specialists to quickly assess refractive error, and thus could be a useful component of large-scale vision screening programs. In order to better characterize the role of autorefraction for public health outreach programs in resource-limited settings, the diagnostic accuracy of two autorefractors was assessed relative to subjective refraction in an adult Indian population.

Methods

An optometrist refracted a series of patients aged ≥50 years at an eye clinic in Bangalore, India using the Nidek ARK-900 autorefractor first, followed by the 3nethra Royal autorefractor, and then subjective refraction. The diagnostic accuracy of each autorefractor for myopia, hyperopia, and astigmatism was assessed using subjective refraction as the reference standard, and measures of agreement between refractions were calculated.

Results

A total of 197 eyes in 104 individuals (mean age 63 ± 8 years, 52% female) were evaluated. Both autorefractors produced spherical equivalent estimates that were on average more hyperopic than subjective refraction, with a measurement bias of +0.16 D (95%CI +0.09 to +0.23D) for Nidek and +0.42 D (95%CI +0.28 to +0.54D) for 3nethra. When comparing pairs of measurements from autorefraction and subjective refraction, the limits of agreement were approximately ±1D for the Nidek autorefractor and ±1.75D for the 3Nethra autorefractor. The sensitivity and specificity of detecting ≥1 diopter of myopia were 94.6% (95%CI 86.8–100%) and 92.5% (95%CI 88.9–97.5%) for the Nidek, and 89.2% (95%CI 66.7–97.4) and 77.5% (95%CI 71.2–99.4%) for the 3Nethra. The accuracy of each autorefractor increased at greater levels of refractive error.

Conclusions

The sensitivity and specificity of the Nidek autorefractor for diagnosing refractive error among adults ≥50 years in an urban Indian clinic was sufficient for screening for visually significant refractive errors, although the relatively wide limits of agreement suggest that subjective refinement of the eyeglasses prescription would still be necessary.

Polar value analysis of astigmatic change and rotational stability after implantation of V4c toric implantable collamer lens

Background

To evaluate the clinical results and rotational stability of V4c toric implantable collamer lens (TICL, STAAR Surgical Company, Monrovia, CA, USA) in patients with moderate to high myopic astigmatism. Retrospective, interventional case series was performed at Shenzhen Eye Hospital, Shenzhen, Guangdong, China.

Methods

This study enrolled 43 patients (72 eyes) who received TICL implantation to correct myopia and myopic astigmatism. The patients underwent visual and refractive examinations before and 1 month after surgery. Astigmatic changes were estimated using polar value analysis. The difference between the achieved axis and the intended axis at the last follow-up was taken as the rotation of the V4c TICL.

Results

At 1 month postoperatively, the mean safety and efficacy indices were 1.17 and 1.13, respectively. A significant reduction of 8.92±2.58 D was observed in the spherical equivalent refraction (SER), which decreased from −9.29±2.41 D preoperatively to −0.37±0.55 D postoperatively. The astigmatic error of treatment in cylinder format was calculated to 0.50±0.41 @ 15.08° relative to the preoperative stronger meridian at 1 month, postoperatively. At 1 month postoperatively, the mean absolute rotation was 8.30±10.00 degrees (median =5.46 degrees; range, 0.00–58.88 degrees).

Conclusions

TICL could achieve good astigmatic outcomes for correcting moderate to high myopic astigmatism. After TICL implantation, corneal astigmatism remained unchanged. To optimize postoperative astigmatic outcomes in TICL, polar value analysis can be used to build a nomogram.

A Comparison of the Accuracy of 6 Modern Toric Intraocular Lens Formulas

PURPOSE

To compare the accuracy of the Abulafia-Koch, the Barrett, the EVO 2.0, the new Holladay 2 with total surgical-induced astigmatism, the Kane, and the Næser-Savini toric intraocular lens (IOL) power formulas using a large database of toric IOL refractive outcomes.

DESIGN

Retrospective consecutive case series.

PARTICIPANTS

Eight hundred twenty-three eyes of 823 patients who had a toric IOL inserted during surgery.

METHODS

One eligible eye from patients having uncomplicated cataract surgery with insertion of an Alcon SN6AT(2-9) IOL (Alcon Laboratories, Inc, Fort Worth, TX) from 1 surgeon were included in the study. Both preoperative and postoperative biometry were measured using either the IOLMaster 500 or 700 (Carl Zeiss Meditec AG, Jena, Germany). Using vector calculation, the predicted postoperative refractive astigmatism was calculated for each formula. This was compared with the actual postoperative refractive astigmatism to give the prediction error.

MAIN OUTCOME MEASURES

Mean absolute prediction error, standard deviation of the prediction error, and percentage of eyes with a prediction error within ±0.50 diopter (D).

RESULTS

The Kane formula showed the highest proportion of eyes with a prediction error within ±0.50 D with 65.6%, followed by the Barrett formula (59.9%), Abulafia-Koch formula (59.5%), EVO 2.0 formula (58.9%), Næser-Savini formula (56.7%), and Holladay 2 formula (53.9%). The Kane formula showed a statistically significantly lower mean absolute prediction error (P < 0.001) and a significantly lower variance of the prediction error (P < 0.01) compared with all other formulas. No statistically significant difference existed among the mean absolute prediction errors for the Abulafia-Koch, Barrett, and EVO 2.0 toric formulas.

CONCLUSIONS

Use of the Kane toric formula significantly improved the prediction of postoperative astigmatic outcome compared with the other formulas studied.

Astigmatism prediction in small-incision lenticule extraction

PURPOSE

To investigate whether postoperative-induced refractive astigmatism after small-incision lenticule extraction (SMILE) could be predicted by preoperative objective astigmatism measured with autorefraction, keratometry, and Scheimpflug tomography.

SETTING

University eye clinic.

DESIGN

Retrospective case series.

METHODS

Only eyes without preoperative subjective astigmatism treated with SMILE for myopia were included. Postoperative subjective astigmatism was compared with preoperative objective astigmatism. Examinations were performed before SMILE and 3 months postoperatively and included subjective refraction, keratometry, autorefraction, and Scheimpflug tomographer measurements. Astigmatism was analyzed using double-angle plots and multivariate statistics.

RESULTS

A total of 358 eyes of 358 patients were included. The mean preoperative sphere was -7.33 diopter (D) ± 1.46 (SD). The postoperative spherical equivalent was -0.30 ± 0.49 D. Postoperatively, 79.6% and 98.9% of patients had a subjective cylinder ≤0.50 D and ≤1.00 D, respectively. Preoperative objective astigmatism measured with keratometry, autorefraction, and Scheimpflug tomography was significantly different (P < .05) from postoperative subjective refraction when all patients were analyzed; for patients with postoperative refractive astigmatism ≥0.50 D, preoperative astigmatism with keratometry and Scheimpflug tomography was not significantly different from postoperative refractive astigmatism. Preoperative objective astigmatism ≥0.50 D increased the risk ratio of postoperative subjective astigmatism ≥0.50 D by 2.2 (P < .001).

CONCLUSIONS

Preoperative objective astigmatism could not be directly interchanged with postoperative subjective astigmatism, but the presence of preoperative astigmatism ≥0.50 D doubled the risk of inducing a postoperative subjective astigmatism ≥0.50 D. Extra care when performing subjective refraction should be taken in the presence of high objective astigmatism.

Composite-Scattering Plasmonic Nanoprobes for Label-Free, Quantitative Biomolecular Sensing

Biosensing based on localized surface plasmon resonance (LSPR) relies on concentrating light to a nanometeric spot and leads to a highly enhanced electromagnetic field near the metal nanostructure. Here, a design of plasmonic nanostructures based on rationally structured metal-dielectric combinations is presented, called composite scattering probes (CSPs), to generate an integrated multimodal biosensing platform featuring LSPR and surface-enhanced Raman spectroscopy (SERS). Specifically, CSP configurations are proposed, which have several prominent resonance peaks enabling higher tunability and sensitivity for self-referenced multiplexed analyte sensing. Using electron-beam evaporation and thermal dewetting, large-area, uniform, and tunable CSPs are fabricated, which are suitable for label-free LSPR and SERS measurements. The CSP prototypes are used to demonstrate refractive index sensing and molecular analysis using albumin as a model analyte. By using partial least squares on recorded absorption profiles, differentiation of subtle changes in refractive index (as low as 0.001) in the CSP milieu is demonstrated. Additionally, CSPs facilitate complementary untargeted plasmon-enhanced Raman measurements from the sample's compositional contributors. With further refinement, it is envisioned that the method may lead to a sensitive, versatile, and tunable platform for quantitative concentration determination and molecular fingerprinting, particularly where limited a priori information of the sample is available.

Refractive errors in an elderly rural Japanese population: The Kumejima study

The prevalence of refractive errors, which closely relates to visual function difficulties, several ocular disorders, and decreased quality of life, varies among countries and populations. One of the highest prevalence of myopia (spherical equivalent [SE] < -0.5 diopters [D], 41.8%) has been reported in an urban city (Tajimi) in central Japan. Here, we assess refractive conditions in a rural southwestern island (Kumejima) of Japan, where a high prevalence of glaucoma, especially angle-closure glaucoma, has been found. In Kumejima, the prevalence of myopia (SE < -0.5 D), high myopia (SE < -5 D), hyperopia (SE > +0.5 D), refractive astigmatism (cylinder > 0.5 D), and anisometropia (difference in SE between eyes > 1.0 D) were 29.5%, 1.9%, 34.1%, 38.8%, and 15.5%, respectively. Myopia decreased with age up to 70 years old but increased slightly thereafter, whereas hyperopia increased up to 70 years old and was unchanged thereafter. The prevalence of astigmatism and anisometropia was higher in older subjects. The prevalence of myopia and high myopia was higher than most of white, Hispanic, and other Asian populations, while was considerably lower than in the urban city of Japan. The high prevalence of hyperopia should be associated with high prevalence of angle closure glaucoma in this island.

Total Corneal Astigmatism Measurements: Agreement Between 2 Rotating Scheimpflug Cameras

PURPOSE

To investigate agreement between rotating Scheimpflug camera (Pentacam HR, Oculus) and rotating Scheimpflug camera combined with Placido disc corneal topography (Sirius, CSO) in measuring total corneal astigmatism (TCA).

METHODS

In this observational study, all patients undergoing cataract surgery with preoperative measurement of TCA by both devices and a validated corneal topographer (Keratron, Optikon 2000) were retrospectively evaluated. Astigmatism analysis was performed with and without vector analysis separately in eyes with with-the-rule, against-the-rule, and oblique astigmatism. Vector analysis was performed using the Næser polar system.

RESULTS

In 130 eyes of 130 subjects, nonvectorial analysis revealed that the mean TCA values obtained with the Sirius were higher than the corresponding values given by the Pentacam HR in all subgroups, although the difference was statistically significant only in eyes with against-the-rule astigmatism (P = 0.0009). This finding was confirmed by vector analysis. A TCA magnitude difference greater than 0.5 diopters was observed in 20.8% of cases, and a TCA axis difference greater than 10 degrees was observed in 45.4% of cases. Axis differences dropped to 18.5% when only eyes with astigmatism >0.75 diopters were analyzed and 3 measurements were averaged. The mean difference in the meridional and torsional power of TCA was close to zero in all subgroups, but with relatively large standard deviations (approximately 0.5 D).

CONCLUSIONS

Agreement between both devices in measuring TCA is only moderate with respect to both magnitude and axis orientation.

Polar Value Analysis of Low to Moderate Astigmatism with Wavefront-Guided Sub-Bowman Keratomileusis

Purpose

To evaluate the astigmatic outcomes of wavefront-guided sub-Bowman keratomileusis (WFG-SBK) for low to moderate myopic astigmatism.

Methods

This study enrolled 100 right eyes from 100 patients who underwent WFG-SBK for the correction of myopia and astigmatism. The polar value method was performed with anterior and posterior corneal astigmatism measured with Scheimpflug camera combined with Placido corneal topography (Sirius, CSO) and refractive astigmatism preoperatively and 1 month, 3 months, and 6 months postoperatively.

Results

Similar results for surgically induced astigmatism (SIA) and error of the procedure in both anterior corneal astigmatism (ACA) and total ocular astigmatism (TOA). There was a minor undercorrection of the cylinder in both ACA and TOA. Posterior corneal astigmatism (PCA) showed no significant change.

Conclusions

Wavefront-guided SBK could provide good astigmatic outcomes for the correction of low to moderate myopic astigmatism. The surgical effects were largely attributed to the astigmatic correction of the anterior corneal surface. Posterior corneal astigmatism remained unchanged even after WFG-SBK for myopic astigmatism. Polar value analysis can be used to guide adjustments to the treatment cylinder alongside a nomogram designed to optimize postoperative astigmatic outcomes in myopic WFG-SBK.

An alternative clinical routine for subjective refraction based on power vectors with trial frames

PURPOSE

Subjective refraction determines the final point of refractive error assessment in most clinical environments and its foundations have remained unchanged for decades. The purpose of this paper is to compare the results obtained when monocular subjective refraction is assessed in trial frames by a new clinical procedure based on a pure power vector interpretation with conventional clinical refraction procedures.

METHODS

An alternative clinical routine is described that uses power vector interpretation with implementation in trial frames. Refractive error is determined in terms of: (i) the spherical equivalent (M component), and (ii) a pair of Jackson Crossed Cylinder lenses oriented at 0°/90° (J₀ component) and 45°/135° (J₄₅ component) for determination of astigmatism. This vector subjective refraction result (VR) is compared separately for right and left eyes of 25 subjects (mean age, 35 ± 4 years) against conventional sphero-cylindrical subjective refraction (RX) using a phoropter. The VR procedure was applied with both conventional tumbling E optotypes (VR1) and modified optotypes with oblique orientation (VR2).

RESULTS

Bland-Altman plots and intra-class correlation coefficient showed good agreement between VR, and RX (with coefficient values above 0.82) and anova showed no significant differences in any of the power vector components between RX and VR. VR1 and VR2 procedure results were similar (p ≥ 0.77).

CONCLUSIONS

The proposed routine determines the three components of refractive error in power vector notation [M, J₀ , J₄₅ ], with a refraction time similar to the one used in conventional subjective procedures. The proposed routine could be helpful for inexperienced clinicians and for experienced clinicians in those cases where it is difficult to get a valid starting point for conventional RX (irregular corneas, media opacities, etc.) and for refractive situations/places with inadequate refractive facilities/equipment.

Influence of Posterior Corneal Astigmatism on Total Corneal Astigmatism in Eyes With Keratoconus

PURPOSE

To measure posterior corneal astigmatism (PCA) and investigate its influence on total corneal astigmatism (TCA) in eyes with keratoconus.

METHODS

Keratometric astigmatism (KA), PCA, and TCA were investigated by means of a dual Scheimpflug analyzer in patients with keratoconus. Vector analysis was carried out with the Næser polar value method.

RESULTS

We enrolled 119 eyes. PCA magnitude averaged 0.77 ± 0.43 diopters (D) and exceeded 0.50, 1.00, and 2.00 D in 73.9%, 21.8%, and 16.8% of eyes, respectively. PCA averaged 0.95 ± 0.48, 0.55 ± 0.28, and 0.70 ± 0.35 D in eyes with with-the-rule (WTR), against-the-rule (ATR), and oblique astigmatism. The steepest posterior meridian was oriented vertically (between 61 and 119 degrees) in 55.5% of eyes, thus generating ATR astigmatism. The difference between the location of the steepest meridian of KA and that of TCA was >10 degrees in 8.4% of eyes. On average, KA overestimated TCA in eyes with WTR astigmatism by 0.16 D and underestimated TCA in eyes with ATR astigmatism by 0.22 D. The PCA power oriented along the steeper anterior corneal meridian averaged -0.83 ± 0.40, -0.40 ± 0.37, and -0.53 ± 0.43 D for WTR, ATR, and obliquely astigmatic eyes, respectively. Linear regression disclosed a statistically significant correlation (P < 0.0001, r = 0.16) between the meridional powers of TCA and PCA.

CONCLUSIONS

In eyes with keratoconus, PCA displays large, variable values and is correlated to TCA. The influence of PCA on TCA cannot be disregarded when planning astigmatism correction by toric intraocular lenses.

Polar Value Analysis of Corneal Astigmatism in Intrastromal Corneal Ring Segment Implantation

Purpose. To evaluate surgically induced astigmatism (SIA) and the average corneal power change in symmetric intrastromal corneal ring segment (ICRS) implantation. Methods. The study included 34 eyes of 34 keratoconus patients who underwent symmetric Intacs SK ICRS implantation. The corneal pocket incision meridian was the preoperative steep meridian. Corneal power data were obtained before and 3 months after Intacs SK ICRS implantation using scanning-slit topography. Polar value analysis was used to evaluate the SIA. Hotelling's trace test was used to compare intraindividual changes. Results. Three months postoperatively, the combined mean polar value for SIA changed significantly (Hotelling's T² = 0.375; P = 0.006). The SIA was 1.54 D at 99° and the average corneal power decreased significantly by 3.8 D. Conclusion. Intacs SK ICRS placement decreased the average corneal power and corneal astigmatism compared to the preoperative corneal power and astigmatism when the corneal pocket incision was made at the preoperative steep meridian.

Value of posterior keratometry in the assessment of surgically induced astigmatic change in cataract surgery

PURPOSE

To investigate the value of posterior keratometry in the assessment of surgically induced astigmatic change (AC) in cataract surgery, with particular emphasis on the influence of test-retest variability.

METHODS

Seventy-seven eyes of 77 cataract patients scheduled for routine cataract surgery were enrolled. All patients received a 2.2-mm self-sealing scleral incision (n = 24), single-plane clear corneal incision (SPCCI; n = 29) or biplanar clear corneal incision (BPCCI; n = 24). Measurements of anterior and posterior corneal astigmatism were performed with a rotating Scheimpflug camera (Pentacam HR) preoperatively and postoperatively. Two repeated readings were taken preoperatively to assess the role of the test-retest effect. Astigmatic change (AC) was analysed according to the polar value method.

RESULTS

On the anterior corneal surface, SPCCIs and BPCCIs caused a statistically significant mean flattening of the incisional meridian of 0.37 and 0.27 dioptres (D), respectively. Scleral incisions on average did not cause AC, although steepening, flattening or torque beyond the test-retest effect was observed in individual cases. On the posterior surface, mean power changes in the incisional meridian were below 0.1 D for all incisions, and these changes were of the same order of magnitude as the test-retest effect.

CONCLUSION

Surgically induced AC of the posterior corneal surface after cataract surgery is of negligible clinical relevance. Moreover, it is of the same order of magnitude as the test-retest variability of the measurement device and therefore cannot (yet) be reliably assessed.

Comparison between refraction measured by Spot Vision Screening™ and subjective clinical refractometry

OBJECTIVE

The purpose of this study was to evaluate the accuracy of Spot Vision Screening™ as an autorefractor by comparing refraction measurements to subjective clinical refractometry results in children and adult patients.

METHODS

One-hundred and thirty-four eyes of 134 patients were submitted to refractometry by Spot and clinical refractometry under cycloplegia. Patients, students, physicians, staff and children of staff from the Hospital das Clínicas (School of Medicine, University of São Paulo) aged 7-50 years without signs of ocular disease were examined. Only right-eye refraction data were analyzed. The findings were converted in magnitude vectors for analysis.

RESULTS

The difference between Spot Vision Screening™ and subjective clinical refractometry expressed in spherical equivalents was +0.66±0.56 diopters (D), +0.16±0.27 D for the vector projected on the 90 axis and +0.02±0.15 D for the oblique vector.

CONCLUSIONS

Despite the statistical significance of the difference between the two methods, we consider the difference non-relevant in a clinical setting, supporting the use of Spot Vision Screening™ as an ancillary method for estimating refraction.

Long-term outcomes of limbal relaxing incisions during cataract surgery: aberrometric analysis

PURPOSE

To compare the final changes in corneal wavefront aberration by limbal relaxing incisions (LRIs) after cataract surgery.

METHODS

This prospective cumulative interventional nonrandomized case study included cataract and astigmatic patients undergoing LRIs and phaco with intraocular lens implantation. LRIs were planned using Donnenfeld nomogram. The root mean square of corneal wave aberration for total Z(n,i)(1≤n≤8), astigmatism Z(2,±1), coma Z(3-5-7,±1), trefoil Z(3-5-7,±2), spherical Z(4-6-8,0), and higher-order aberration (HOA) Z(3≤n≤8) was examined before and 3 years after surgery (optical path difference-Scan II [OPD-Scan II)]. Uncorrected distance visual acuity and best-corrected distance visual acuity (CDVA) for distance, keratometric cylinder, and variations in average corneal power were also analyzed.

RESULTS

Sixty-four eyes of 48 patients were included in the study. Age ranged from 42 to 92 years (70.6±8.4 years). After LRIs, uncorrected distance visual acuity and best-corrected distance visual acuity improved statistically (P<0.01). The keratometric cylinder value decreased by 40.1%, but analysis of KP90 and KP135 polar values did not show any decrease that could be statistically confirmed (P=0.22 and P=0.24). No significant changes were detected in root mean square of total (P=0.61) and HOAs (P=0.13) aberrations. LRIs did not induce alteration in central corneal power confirming a 1:1 coupling ratio.

CONCLUSION

LRIs determined a nonsignificant alteration of corneal HOA. Therefore, LRIs can be still considered a qualitatively viable mean in those cases where toric intraocular lenses are contraindicated or not available. Yet, the authors raise the question of nonpersonalized nomograms, as in the present study, LRIs did not reach the preset target cylinder.

Assessing the corneal power change after refractive surgery using Scheimpflug imaging

PURPOSE

To investigate whether the Pentacam HR could accurately predict the surgically induced refractive change in patients operated with small-incision lenticule extraction (SMILE) for myopia or femto-second laser in situ keratomileusis (FS-LASIK) for myopia or hyperopic astigmatism.

METHODS

Data from three groups consisting of (1) 410 myopic eyes of 410 patients operated with SMILE, (2) 111 myopic eyes of 111 patients operated with FS-LASIK, and (3) 40 eyes of 40 patients with hyperopic astigmatism operated with FS-LASIK were retrospectively analysed. The change in manifest refraction due to surgery was compared with the objectively measured change in corneal power by the Pentacam HR in three different ways: Sagittal Power (calculated as for placido topographers), True Net Power (calculated by a Gaussian optics formula), and Total Corneal Refractive Power (calculated by ray tracing). Multiple linear regression analysis was performed to investigate which parameters influenced the Pentacam HR's prediction of the change in subjective refraction due to surgery.

RESULTS

The Total Corneal Refractive Power Apex, Zone calculation in a diameter of 4.0 mm effectively predicted the surgically induced refractive change for all three patient groups. The spherical equivalent was predicted with an error of 0.08 ± 0.41 D for the SMILE eyes, 0.05 ± 0.61 D for the myopic eyes operated with FS-LASIK, and -0.15 ± 0.49 D for the hyperopic astigmatic eyes treated with FS-LASIK. Regression showed that preoperative refractive error had a significant impact on the prediction error of the Pentacam HR.

CONCLUSIONS

Ray tracing calculations based on Scheimpflug imaging accurately assessed the change in manifest refraction due to corneal laser surgery.

Correction of myopic astigmatism with small incision lenticule extraction

PURPOSE

To evaluate the outcome after small incision refractive lenticule extraction (SMILE) in patients with myopic astigmatism.

METHODS

Seven hundred seventy-five eyes from 403 patients with myopia treated with SMILE for a cylinder of 0.75 diopters (D) or more were identified from patient records. Six hundred sixty-nine eyes were defined as receiving low (< 2.5 D) and 106 eyes as receiving high (⩾ 2.5 D) astigmatic correction. Patients were examined before and 3 months after surgery. SMILE was performed with a Visumax femtosecond laser (Carl Zeiss Meditec, Jena, Germany). Preoperative and postoperative refractions were converted to polar values. Induced torsion and achieved corrections of sphere and cylinder were determined.

RESULTS

In low astigmatism, the mean preoperative spherical equivalent (SE) was -7.57 ±1.67 D and the cylinder was -1.22 ± 0.49 D. Three months after surgery, SE was -0.19 ± 0.48 D from target, astigmatism was 0.17 ± 0.42 D undercorrected, and a small but significant torsion of the cylinder axis corresponding to 0.05 ± 0.37 D was found. The astigmatic undercorrection measured 13% per diopter of attempted correction. In high astigmatism, preoperative SE was -5.91 ± 2.56 D and cylinder was -3.22 ± 0.67 D. After surgery, the average astigmatic undercorrection was 0.59 ± 0.65 D, equivalent to 16% per diopter of attempted correction. No undercorrection in SE occurred and no torsion was found.

CONCLUSIONS

SMILE in myopic astigmatism offers predictable correction of SE, but a small, significant undercorrection of the astigmatic error. The undercorrection increases with the attempted treatment. Only very little rotation of the cylinder axis was found.

Visual performance of 2 aspheric toric intraocular lenses: comparative study

PURPOSE

To compare the visual and aberrometric outcomes of 2 aspheric toric intraocular lenses (IOLs).

SETTING

Fatebenefratelli e Oftalmico Hospital, Milan, Italy.

DESIGN

Prospective randomized comparative study.

METHODS

Astigmatic patients had cataract surgery with implantation of an Acrysof SN6AT IOL (Group A) or an AT Torbi 709M IOL (Group B). The uncorrected (UDVA) and corrected (CDVA) distance visual acuities, net refractive astigmatism, spherical equivalent (SE), IOL misalignment, and optical quality were evaluated 3 months postoperatively.

RESULTS

The study included 72 eyes. No statistically significant difference was found in UDVA, CDVA, residual refractive astigmatism, intraocular or total higher-order aberrations (Z(n,i) (order of aberrations calculated: 3≤n≤8), coma Z(3,±1), or trefoil Z(3,±2). The UDVA was 0.3 logMAR or better in all eyes and 0.1 logMAR or better in 55.5% of eyes in Group A and in 61.1% of eyes in Group B. Considering polar value analysis, 94.4% of eyes in both groups had a refractive astigmatism value within ±0.50 diopter at KP90 (polar value along 90-degree meridian). The SE was closer to emmetropia in Group A (P=.01). Intraocular lens misalignment of less than 5 degrees was present in 61.1% of cases in Group A (maximum 9 degrees) and in 66.6% in Group B (maximum 11 degrees). Spherical aberration Z(4,0) was significantly lower in Group B.

CONCLUSIONS

Both IOLs had similar clinical effectiveness in term of astigmatism correction, rotational stability, and optical quality. Eyes in Group A appeared significantly nearer to emmetropia, while the IOL in Group B induced significantly less spherical aberration.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

Refractive change after vitrectomy for epiretinal membrane in pseudophakic eyes

PURPOSE

To report the change in refraction in pseudophakic eyes following 23-gauge vitrectomy for epiretinal membrane (ERM), without use of silicone oil, intraocular gas or scleral buckling.

METHODS

Retrospective review of the records of 28 pseudophakic eyes in 28 patients undergoing 23-gauge pars plana vitrectomy for ERM. All 28 eyes had a measured preoperative refraction in their records and were seen minimum 2 months after vitrectomy for measuring their refraction. Fellow eyes (28 eyes) were used as controls.

RESULTS

The mean preoperative refraction was -0.15 ± 0.85 dioptre (D), and the mean postoperative refraction was -0.41 ± 0.93 D. Thus, a myopic shift was observed following vitrectomy with a mean change in refraction of -0.26 ± 0.60 D (range +0.75 to -2.13 D, p = 0.032). The postoperative change in refraction was within ±0.25, ±0.50 and ±1.00 D in 39%, 68% and 96% of the eyes, respectively. The mean absolute refractive error was 0.47 ± 0.44 D. The change in refraction in fellow eyes was +0.01 D (p = 0.82).

CONCLUSION

The change in refraction following 23-gauge pars plana vitrectomy for ERM in pseudophakic eyes was -0.26 D.

Lateral magnification matrix from the dioptric power matrix formalism in the paraxial case

BACKGROUND

Previous studies have highlighted that power matrices fully characterize the concept of dioptric power of any astigmatic surface. Thus, the basic equations in physiological optics can be generalized using the matrix formalism of the dioptric power. Among others, lateral magnification has also been interpreted as a matrix but mainly concerning magnification modification induced by spectacle correction of refractive error.

PURPOSE

To provide a fresh look into a novel paraxial formulation for the assessment of the lateral magnification using power matrices and in presence of astigmatism for thin and thick imaging systems in general.

METHODS

Linear optics provides the frame to generalize into a matrix the lateral magnification concept. Using the power matrix formalism, a lateral magnification matrix is derived in virtue of the dioptric power matrix and the object's reduced axial object distance for the paraxial case. In addition, two different degrees of approximation (thin lens and distant object approximations) are analyzed to further simplify the calculations.

RESULTS

A general formulation of the lateral magnification matrix is obtained and validated by numerical examples showing its applicability to different examples in geometrical and physiological optics. As particular case of interest, the degree of asymmetry of the lateral magnification matrix has been derived from the degree of asymmetry of the dioptric power matrix when dealing with obliquely crossed astigmatic thick lenses.

CONCLUSIONS

The new formulation is applicable under paraxial approximation and is useful for arbitrary thin and thick imaging systems in any media of homogeneous index of refraction (air and others) and including obliquely crossed astigmatic surfaces. The proposed formulation also yields in a novel interpretation of the lateral magnification matrix concept.

Combining refractive and topographic data in corneal refractive surgery for astigmatism: a new method based on polar value analysis and mathematical optimization

PURPOSE

To provide a theoretical approach for combining refractive and topographic data in the planning of corneal laser refractive surgery for astigmatism.

METHODS

Refractive and topographic data for astigmatism were transformed to the corneal plane. Net astigmatisms were converted to polar values. An optimization process was performed with the use of differential calculus.

RESULTS

With this method, the magnitude of the corneal astigmatism is reduced or unaltered, while its orientation is maintained. The method identifies the reduction in corneal astigmatism, which will yield the largest reduction in refractive astigmatic magnitude.

CONCLUSIONS

The advantage of the optimization method described in this article is a consistent reduction in corneal astigmatism towards sphericity. No new corneal astigmatism is carved on the cornea, and probably less tissue is ablated. The optimization method may also be used to combine refractive and topographic data for higher order aberrations with sinusoidal components. However, compared to the traditional purely refractive driven treatment, more refractive astigmatism will remain in the eye in most cases. A controlled clinical trial is necessary for comparing these two treatment modalities.

Analysis of photoastigmatic keratectomy with the cross-cylinder ablation

AIM

The aim was to evaluate the safety and efficacy of the "cross-cylinder" technique in the correction of astigmatism.

SETTING AND DESIGN

A prospective interventional study from a university eye department was conducted.

MATERIAL AND METHODS

The photoastigmatic refractive keratectomy (PARK) using the "cross-cylinder" technique was performed in 102 eyes of 84 patients with at least 0.75 D of astigmatism. The study population was divided into two groups: in the first group the preoperative astigmatic power ranged from -0.75 D to -3.00 D (group 1), in the second group it ranged from -3.25 D to -6.00 D (group 2). Group 1 included 82 eyes of 67 patients (29 males and 38 females) with a mean cylinder power of -1.90 ± 0.63 D, group 2 included 20 eyes of 17 patients (13 males and 4 females) with a mean cylinder power of -4.28 ± 0.76 D. All eyes were targeted for emmetropia. The results were evaluated using Calossi's vector analysis method. Six-month postoperative outcomes are presented.

RESULTS

Six months after PARK the mean sphere for the entire cohort was +0.28 ± 0.75 D (range +2.5 to -2 D), the mean cylindrical power was +0.33 ± 0.51 D (range +2.5 to -1.25 D) and the mean spherical equivalent refraction was +0.73 ± 0.81 D (range +1.75 to -2 D).

CONCLUSIONS

The cross-cylinder technique may be safely used with predictable results for the correction of astigmatism.

Univariate and bivariate polar value analysis of corneal astigmatism measurements obtained with 6 instruments

PURPOSE

To compare the corneal astigmatism measurements from 6 instruments in preoperative assessment for toric intraocular lens (IOL) implantation.

SETTING

Institute of Vision Research, Department of Ophthalmology, Yonsei University College of Medicine, Seoul, South Korea.

DESIGN

Prospective comparative observational study.

METHODS

This study included patients with cataract and more than 1.00 diopter (D) of corneal astigmatism. For preoperative evaluation of toric IOL implantation, the net astigmatism was evaluated using manual keratometry, autokeratometry, partial coherence interferometry (PCI) (IOLMaster), corneal topography/ray-tracing aberrometry (iTrace), scanning-slit topography (Orbscan), and Scheimpflug imaging (Pentacam). All net astigmatisms were converted to polar values. Using the astigmatism measurements from manual keratometry as a standard, Bland-Altman analysis, linear mixed-model, and bivariate graphic analysis were performed.

RESULTS

The study group comprised 257 eyes of 141 patients. Bland-Altman plots showed good agreement between manual keratometry and each instrument for polar values. There was no significant between-instrument difference in KP(90) and KP(135) in the linear mixed model analysis or in bivariate polar values in bivariate confidence ellipses.

CONCLUSION

The corneal astigmatism measurements from autokeratometry, PCI, corneal topography/ray-tracing aberrometry, scanning-slit topography, and Scheimpflug imaging were comparable to those from manual keratometry and can be used interchangeably with manual keratometry to measure corneal astigmatism.

Effects of steep meridian incision on corneal astigmatism in phacoemulsification cataract surgery

PURPOSE

To evaluate surgically induced astigmatism (SIA) when the clear corneal incision is located on the preoperative steep meridian of the corneal astigmatism in phacoemulsification cataract surgery.

SETTING

Seoul St. Mary's Hospital, Seoul, South Korea.

DESIGN

Comparative case series.

METHODS

Patients with preoperative corneal astigmatism greater than 0.50 diopter (D) were evaluated. The corneal incision meridian was chosen by rounding the steep corneal meridian to the closest 10 degrees. All incisions were enlarged to 3.0 mm before intraocular lens implantation. Patients were grouped according to incision location (temporal, superotemporal, superior). Preoperative keratometric data were compared with data collected 2 months postoperatively. Polar value analysis was used to analyze the SIA. The Hotelling trace test was used for comparison of intraindividual changes.

RESULTS

The study evaluated 95 patients (30 eyes temporal incision, 32 eyes superotemporal incision, 33 eyes superior incision). Two months postoperatively, the combined mean polar values for SIA changed significantly in the temporal group (Hotelling T(2) = 0.418; P=.008), superotemporal group (Hotelling T(2) = 1.078; P<.001), and superior incision group (Hotelling T(2) = 1.175; P<.001). The SIA was 0.28 @ 79, 0.40 @ 85, and 0.46 @ 92, respectively.

CONCLUSIONS

Choosing the corneal incision based on the preoperative steep meridian significantly decreased keratometric astigmatism at the temporal, superotemporal, and superior locations. Thus, it is desirable to place the corneal incision on the steep meridian in eyes with corneal astigmatism higher than 0.50 D.

Optimal refraction with monofocal intraocular lenses: no beneficial effect of astigmatism

PURPOSE

This study aimed to determine the optimal spherocylindrical refraction in the monofocal, pseudophakic eye using power vectors in dioptric space.

METHODS

For parallel incident light the defocus of a spherocylinder may be described in dioptric space as: Defocus equivalent for distance fixation = D((SEP,M,x=∞)) = √SEP(2)+(1/2M)(2), where SEP = spherical equivalent power in dioptres (D) and M = astigmatic magnitude in D. In the pseudophakic eye the defocus for any fixation distance x is: Defocus equivalent for the fixation distance x = D((SEP,M,x)) = √(SEP-1/x)(2)+ (1/2M)(2). The cumulative defocus over a fixation interval is the integral of D((SEP,M,x)) . A minimal value for cumulative defocus will indicate a maximal unaided visual acuity (VA) over the chosen fixation interval. We calculated the summated defocus for various spherocylinders for fixation distances ranging from 0.5 m to 6.0 m.

RESULTS

Minimal cumulative defocus was present for pure spheres of -0.25 D to -0.5 D. No beneficial effect of the presence of astigmatism was detected.

CONCLUSIONS

In monofocal pseudophakia the highest possible VAs over the most extended fixation ranges may be achieved with slight myopic refractions without astigmatic components.

In vivo Assessment of Higher-Order Aberrations after Acrysof Toric Intraocular Lens Implantation: A Comparative Study

Purpose

To compare higher-order aberrations (HOAs) and optical quality in eyes implanted with AcrySof SN60TT toric intraocular lens (IOL) or with non-toric AcrySof SN60AT IOL (Alcon Laboratories, Inc., Fort Worth, TX).

Methods

This was a prospective, consecutive, nonrandomized, interventional, comparative study. One hundred eyes with cataract in 56 patients were included (SN60TT group, n=50; SN60AT group, n=50). Patients underwent phacoemulsification through a 2.2-mm temporal corneal incision. Postoperative HOAs, point spread function (PSF) and modulation transfer function (MTF), residual objective refractive astigmatism, and IOL alignment were evaluated using Optical Path Difference (OPD)–Scan II (Nidek, Gamagori, Japan). A novel technique to calculate IOL axis alignment was introduced.

Results

One year postoperatively, no statistical difference in corneal, intraocular, and total HOAs, Strehl ratio, and MTF based on HOAs was found between groups. Toric IOL patients had a net residual refractive astigmatism (M) of 0.44 D±0.47; the difference between expected and obtained astigmatism (M) was 0.043 D (p=0.16). Toric IOL axis misalignment was 2.65±2.39 degrees and no correlation with HOAs was found.

Conclusions

AcrySof SN60TT determines HOAs comparable to the non-toric version providing a good optical quality, and predictably corrects corneal cylinder with a stable postoperative alignment. The OPD-Scan II might be regarded as a fast and reliable method of toric IOL analysis.

Assessment and statistics of surgically induced astigmatism

The aim of the thesis was to develop methods for assessment of surgically induced astigmatism (SIA) in individual eyes, and in groups of eyes. The thesis is based on 12 peer-reviewed publications, published over a period of 16 years. In these publications older and contemporary literature was reviewed(1). A new method (the polar system) for analysis of SIA was developed. Multivariate statistical analysis of refractive data was described(2-4). Clinical validation studies were performed. The description of a cylinder surface with polar values and differential geometry was compared. The main results were: refractive data in the form of sphere, cylinder and axis may define an individual patient or data set, but are unsuited for mathematical and statistical analyses(1). The polar value system converts net astigmatisms to orthonormal components in dioptric space. A polar value is the difference in meridional power between two orthogonal meridians(5,6). Any pair of polar values, separated by an arch of 45 degrees, characterizes a net astigmatism completely(7). The two polar values represent the net curvital and net torsional power over the chosen meridian(8). The spherical component is described by the spherical equivalent power. Several clinical studies demonstrated the efficiency of multivariate statistical analysis of refractive data(4,9-11). Polar values and formal differential geometry describe astigmatic surfaces with similar concepts and mathematical functions(8). Other contemporary methods, such as Long's power matrix, Holladay's and Alpins' methods, Zernike(12) and Fourier analyses(8), are correlated to the polar value system. In conclusion, analysis of SIA should be performed with polar values or other contemporary component systems. The study was supported by Statens Sundhedsvidenskabeligt Forskningsråd, Cykelhandler P. Th. Rasmussen og Hustrus Mindelegat, Hotelejer Carl Larsen og Hustru Nicoline Larsens Mindelegat, Landsforeningen til Vaern om Synet, Forskningsinitiativet for Arhus Amt, Alcon Denmark, and Desirée and Niels Ydes Fond.

Subjective refraction: the mechanism underlying the routine

The routine of subjective refraction is usually understood, explained and taught in terms of the relative positions of line or point foci and the retina. This paper argues that such an approach makes unnecessary and sometimes invalid assumptions about what is actually happening inside the eye. The only assumption necessary in fact is that the subject is able to guide the refractionist to (or close to) the optimum power for refractive compensation. The routine works even in eyes in which the interval of Sturm does not behave as supposed; it would work, in fact, regardless of the structure of the eye. The idealized subjective refraction routine consists of two steps: the first finds the best sphere (the stigmatic component) and the second finds the remaining Jackson cross-cylinder (the antistigmatic component). The model makes use of the concept of symmetric dioptric power space. The second part of the refraction routine can be performed with Jackson cross-cylinders alone. However, it is usually taught and practiced using spheres, cylinders and Jackson cross-cylinders in a procedure that is not easy to understand and learn. Recognizing that this part of the routine is equivalent to one involving Jackson cross-cylinders only allows one to teach and understand the procedure more naturally and easily.

PowerRefractor versus Canon R-50 Autorefraction to assess refractive error in children: a community-based study in ecuador

PURPOSE

To compare the agreement of the PowerRefractor with Canon R-50 autorefraction for measuring refractive error in a community of Ecuadorian children.

METHODS

We examined 1564 children aged 5 to 6 years from two ethnically and geographically similar regions of the Ecuadorian highlands. Results of a refraction obtained without cycloplegia with the PowerRefractor and with the Canon R-50 autorefractor (NCAR) were compared with the gold-standard examination, cycloplegic autorefraction (CAR) with the Canon R-50 autorefractor. Power vectors were used to analyze refractive error. Bland-Altman limits of agreement were obtained.

RESULTS

Although the mean difference in the spherical equivalent refractive error between the PowerRefractor and CAR was small (-0.03 D +/- 0.05 D), the 95% limits of agreement were wide (+/-2.03 D). On the other hand, NCAR showed a greater bias (0.97 D +/- 0.04 D) and smaller limits of agreement (+/-1.49 D). The limits of agreement of the PowerRefractor were also wider than NCAR for measuring astigmatism. When the mean difference was stratified by the subgroups of refractive error vectors, the PowerRefractor was found to have poorer limits of agreement than NCAR for hyperopic defects.

CONCLUSION

The PowerRefractor is accurate, but not as precise for measuring refractive error as compared to the Canon R-50 autorefractor, especially for high hyperopia.