The Gaussian formula and spherical aberration of the static and moving curved mirrors from Fermat's principle

The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in the information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations.Comment: 15 pages, 7 figures, uses iopart. Major revisions on the physical interpretations of the results. Accepted for publication in J. Op

Intraocular Lens Power Calculation—Comparing Big Data Approaches to Established Formulas

Purpose To evaluate the predictive performance of traditional intraocular lens (IOL) power calculation formulas (e.g., SRK/T, Haigis, Hoffer Q, and Holladay I) compared to advanced regression models, including classical linear models, regression splines, and random forest regression, in predicting postoperative refraction following cataract surgery. Design Retrospective, comparative analysis of IOL power calculations. Subjects The study included 886 eyes from 631 patients who underwent cataract surgery with monofocal aspherical IOL implantation. Methods Biometric measurements were obtained using optical biometry (IOLMaster 700), and postoperative refraction was assessed at least 4 weeks after surgery. Formula constants for 5 IOL formulas (SRK/T, Haigis, Hoffer Q, Holladay I and Castrop V1) were optimized using root mean squared error (RMSE). Regression models (classical linear model, regression splines, and random forest regression) were trained on 4 datasets categorized by axial length (AL); normal, short, long, and random. Model performance was assessed using mean absolute error (MAE), RMSE, and prediction error variance, for both in-sample and out-of-sample predictions. Main Outcome Measures The primary parameters measured were MAE, RMSE, and prediction error variance. Results Regression models outperformed traditional IOL formulas in in-sample prediction error. Overall, linear regression models performed similarly to traditional formulas with respect to out-of-sample prediction error. The lowest out-of-sample prediction error (MAE = 0.279, RMSE = 0.359) was achieved with a model where effects of some covariates (R2, AL, CCT) were modelled as nonlinear via regression splines. This model outperformed all traditional formulas, and the Castrop formula, which had the lowest errors among the formulas (MAE = 0.284, RMSE = 0.359). Random forest regression showed strong in-sample performance but poor out-of-sample generalizability due to overfitting. Conclusions Regression models which allow for nonlinear effects, e.g. based on regression splines, provide a promising alternative to traditional IOL formulas for predicting postoperative refraction. Linear regression and random forest regression models can reduce in-sample error, however, their clinical utility is currently limited by out-of-sample performance. Future work should focus on improving generalizability and integrating machine learning models into clinical practice to enhance refractive outcomes, especially for eyes with atypical anatomy

Measuring benefits and patients' satisfaction when glasses are not needed after cataract and presbyopia surgery: scoring and psychometric validation of the Freedom from Glasses Value Scale (FGVS©)

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to reduce the number of items, create a scoring method and assess the psychometric properties of the Freedom from Glasses Value Scale (FGVS), which measures benefits of freedom from glasses perceived by cataract and presbyopic patients after multifocal intraocular lens (IOL) surgery.</p> <p>Methods</p> <p>The 21-item FGVS, developed simultaneously in French and Spanish, was administered by phone during an observational study to 152 French and 152 Spanish patients who had undergone cataract or presbyopia surgery at least 1 year before the study. Reduction of items and creation of the scoring method employed statistical methods (principal component analysis, multitrait analysis) and content analysis. Psychometric properties (validation of the structure, internal consistency reliability, and known-group validity) of the resulting version were assessed in the pooled population and per country.</p> <p>Results</p> <p>One item was deleted and 3 were kept but not aggregated in a dimension. The other 17 items were grouped into 2 dimensions ('global evaluation', 9 items; 'advantages', 8 items) and divided into 5 sub-dimensions, with higher scores indicating higher benefit of surgery. The structure was validated (good item convergent and discriminant validity). Internal consistency reliability was good for all dimensions and sub-dimensions (Cronbach's alphas above 0.70). The FGVS was able to discriminate between patients wearing glasses or not after surgery (higher scores for patients not wearing glasses). FGVS scores were significantly higher in Spain than France; however, the measure had similar psychometric performances in both countries.</p> <p>Conclusions</p> <p>The FGVS is a valid and reliable instrument measuring benefits of freedom from glasses perceived by cataract and presbyopic patients after multifocal IOL surgery.</p