Polynomial decomposition method for ocular wavefront analysis

Prediction of manifest refraction using machine learning ensemble models on wavefront aberrometry data

PURPOSE

To assess the performance of machine learning (ML) ensemble models for predicting patient subjective refraction (SR) using demographic factors, wavefront aberrometry data, and measurement quality related metrics taken with a low-cost portable autorefractor.

METHODS

Four ensemble models were evaluated for predicting individual power vectors (M, J₀, and J₄₅) corresponding to the eyeglass prescription of each patient. Those models were random forest regressor (RF), gradient boosting regressor (GB), extreme gradient boosting regressor (XGB), and a custom assembly model (ASB) that averages the first three models. Algorithms were trained on a dataset of 1244 samples and the predictive power was evaluated with 518 unseen samples. Variables used for the prediction were age, gender, Zernike coefficients up to 5th order, and pupil related metrics provided by the autorefractor. Agreement with SR was measured using Bland-Altman analysis, overall prediction error, and percentage of agreement between the ML predictions and subjective refractions for different thresholds (0.25 D, 0.5 D).

RESULTS

All models considerably outperformed the predictions from the autorefractor, while ASB obtained the best results. The accuracy of the predictions for each individual power vector component was substantially improved resulting in a ± 0.63 D, ±0.14D, and ±0.08 D reduction in the 95% limits of agreement of the error distribution for M, J₀, and J₄₅, respectively. The wavefront-aberrometry related variables had the biggest impact on the prediction, while demographic and measurement quality-related features showed a heterogeneous but consistent predictive value.

CONCLUSIONS

These results suggest that ML is effective for improving precision in predicting patient's SR from objective measurements taken with a low-cost portable device.

Digital ocular swept source optical coherence aberrometry

Ocular aberrometry is an essential technique in vision science and ophthalmology. We demonstrate how a phase-sensitive single mode fiber-based swept source optical coherence tomography (SS-OCT) setup can be employed for quantitative ocular aberrometry with digital adaptive optics (DAO). The system records the volumetric point spread function at the retina in a de-scanning geometry using a guide star pencil beam. Succeeding test-retest repeatability assessment with defocus and astigmatism analysis on a model eye within ± 3 D dynamic range, the feasibility of technique is demonstrated in-vivo at a B-scan rate of >1 kHz in comparison with a commercially available aberrometer.

Comparison of Low Degree/High Degree and Zernike Expansions for Evaluating Simulation Outcomes After Customized Aspheric Laser Corrections

Purpose

The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations.

Methods

Initial anterior corneal surface profiles were modeled as conic sections with pre-operative apical curvature, R0, and asphericity, Q0. Postoperative apical curvature, R1, was computed from intended defocus correction, D, diameter zone, S, and target postoperative asphericity, Q1. Coefficients of both Zernike and LD/HD polynomial expansions of the rotationally symmetrical corneal profile were computed using scalar products. We modeled different values of D, R0, Q0, S, and ΔQ = Q1 to Q0. The corresponding postoperative changes in defocus (Δz20 vs. Δg20), fourth order (Δz40 vs. Δg40) and sixth order (Δz60 vs. Δg60) Zernike and LD/HD spherical aberrations (SAs) were compared. In addition, retrospective clinical data and wavefront measurements were obtained from two examples of two patient eyes before and after corneal laser photoablation.

Results

The z20, varied with both R0 and Q0, whereas the LD/HD defocus coefficient, g20, was relatively robust to changes in asphericity. Variations of apical curvature better correlated with defocus and ΔQ with SA coefficients in the LD/HD classification. The impact of ΔQ was null on g20 but induced significant linear variations in z20 and fourth order SA coefficients. LD/HD coefficients provided a good correlation with the visual performances of the operated eyes.

Conclusions

Simulated variations in postoperative corneal profile and wavefront expansion using the LD/HD approach showed good correlations between defocus and asphericity variations with variations in corneal curvature and SA coefficients, respectively.

Translational Relevance

The relevance of this study was to provide a clinically relevant alternative to Zernike polynomials for the interpretation of wavefront changes after customized aspheric corrections.

Coma Influence on Manifest Astigmatism in Coma-Dominant Irregular Corneal Optics

PURPOSE

To evaluate the influence of coma on manifest refractive cylinder (MRC) in eyes with coma-dominated corneal optics and suggest alternative guidelines for surgical planning of astigmatism correction in topography-guided ablation and toric intraocular lens (IOL) exchange surgery.

METHODS

Twelve eyes with coma-dominant corneal optics and low lenticular astigmatism were selected. The astigmatism remaining after subtraction of total corneal astigmatism (TCA) and lenticular astigmatism from MRC, termed discrepant astigmatism, was calculated and correlated to corneal coma at the anterior surface. Refractive and topography data were then used to simulate topography-guided refractive surgery (topography-guided group) in 7 eyes and lenticular exchange surgery with toric intraocular lens (IOL) implantation (toric IOL group) in 5 eyes. The estimated postoperative MRC after correction of TCA or MRC for each group was compared.

RESULTS

The axis and amplitude of discrepant astigmatism correlated strongly with the axis and amplitude of coma. In the topography-guided group, where topography-guided ablation eliminated corneal higher order aberrations (HOAs), TCA-based correction led to less estimated postoperative manifest astigmatism than MRC-based correction. In the toric IOL group, where removal of the crystalline lens did not affect corneal HOAs, MRC-based correction via toric IOL implantation led to less estimated postoperative astigmatism than TCA-based correction.

CONCLUSIONS

Discrepant astigmatism in eyes with coma-dominant corneal optics correlates with coma. In such eyes, treating TCA, along with corneal HOAs, instead of MRC, seems appropriate in topography-guided treatments, whereas treating MRC may be a better choice in lenticular exchange surgery with toric IOL implantation, where corneal HOAs are not treated. [J Refract Surg. 2021;37(4):274-282.].

An Alternative Wavefront Reconstruction Method for Human Eyes

PURPOSE

To expand upon and clinically demonstrate the results of a new polynomial decomposition method.

METHODS

To discuss the theoretical considerations comparing the qualitative and quantitative information produced by the Zernike coefficients and a new polynomial decomposition basis, in a comparative series of theoretical and clinical case studies.

RESULTS

These comparative studies validate the novel polynomial basis that decomposes the wavefront, with clear segregation of the higher and lower aberrations. There is no artifactual reduction of some of the higher order aberration coefficients, providing a more clinically relevant retinal image quality prediction.

CONCLUSIONS

Some of the inherent limitations of the Zernike polynomials in clinical ophthalmic applications can be solved by a novel set of polynomials forming an alternative higher order basis. The new basis provides a clear separation between modes containing lower order terms versus higher order terms and offers clinicians a more clinically realistic wavefront analysis. [J Refract Surg. 2020;36(2):74-81.].

Zernike monomials in wide field of view optical designs

Zernike polynomials are universal in optical modeling and testing of wavefronts; however, their polynomial behavior can cause a misinterpretation of individual aberrations. Wavefront profiles described by Zernike polynomials contain multiple terms with different orders of pupil radius (ρ). Zernike polynomials are a sum of high and low orders of ρ to minimize the RMS wavefront error and to preserve orthogonality. Since the low-order polynomials are still contained in the net Zernike sum, there is redundancy in individual monomials. Monomial aberrations, also known as Seidel or primary aberrations, are useful in studying an optical design's complexity, alignment, and field behavior. Zernike polynomial aberrations reported by optical design software are not indicative of individual (monomial) aberrations in wide field of view designs since the low-order polynomials are contaminated by higher order terms. An aberration node is the field location where an individual (monomial) aberration is zero. In this paper, a matrix method is shown to calculate the individual monomial aberrations given the set of Zernike polynomials. Monomial aberrations plotted as a function of field angle (H) indicate the field order (Hⁿ) and the location of true aberration nodes. Contrarily, Zernike polynomial versus field (ZvF) plots can indicate false aberration nodes, due to the polynomial mixing of high- and low-order terms. Accurate knowledge of the monomial aberration nodes, converted from Zernike polynomials, provides the link between a ray-trace model or lab wavefront measurement and nodal aberration theory (NAT). This method is applied to two different optical designs: (1) 120° circular FOV fish-eye lens and (2) 120^∘×4^∘ rectangular FOV, off-axis, freeform four-mirror design.

Refractive surgery beyond 2020

Refractive surgery refers to any procedure that corrects or minimizes refractive errors. Today, refractive surgery has evolved beyond the traditional laser refractive surgery, embodied by the popular laser in situ keratomileusis or 'LASIK'. New keratorefractive techniques such as small incision lenticule extraction (SMILE) avoids corneal flap creation and uses a single laser device, while advances in surface ablation techniques have seen a resurgence in its popularity. Presbyopic treatment options have also expanded to include new ablation profiles, intracorneal implants, and phakic intraocular implants. With the improved safety and efficacy of refractive lens exchange, a wider variety of intraocular lens implants with advanced optics provide more options for refractive correction in carefully selected patients. In this review, we also discuss possible developments in refractive surgery beyond 2020, such as preoperative evaluation of refractive patients using machine learning and artificial intelligence, potential use of stromal lenticules harvested from SMILE for presbyopic treatments, and various advances in intraocular lens implants that may provide a closer to 'physiological correction' of refractive errors.

Using Artificial Intelligence and Novel Polynomials to Predict Subjective Refraction

This work aimed to use artificial intelligence to predict subjective refraction from wavefront aberrometry data processed with a novel polynomial decomposition basis. Subjective refraction was converted to power vectors (M, J0, J45). Three gradient boosted trees (XGBoost) algorithms were trained to predict each power vector using data from 3729 eyes. The model was validated by predicting subjective refraction power vectors of 350 other eyes, unknown to the model. The machine learning models were significantly better than the paraxial matching method for producing a spectacle correction, resulting in a mean absolute error of 0.301 ± 0.252 Diopters (D) for the M vector, 0.120 ± 0.094 D for the J0 vector and 0.094 ± 0.084 D for the J45 vector. Our results suggest that subjective refraction can be accurately and precisely predicted from novel polynomial wavefront data using machine learning algorithms. We anticipate that the combination of machine learning and aberrometry based on this novel wavefront decomposition basis will aid the development of refined algorithms which could become a new gold standard to predict refraction objectively.

Wavefront sensing, novel lower degree/higher degree polynomial decomposition and its recent clinical applications: A review

We are in the midst of a shift towards using novel polynomials to decompose wavefront aberrations in a more ophthalmologically relevant way. Zernike polynomials have useful mathematical properties but fail to provide clinically relevant wavefront interpretation and predictions. We compared the distribution of the eye's aberrations and demonstrate some clinical applications of this using case studies comparing the results produced by the Zernike decomposition and evaluating them against the lower degree/higher degree (LD/HD) polynomial decomposition basis which clearly dissociates the higher and lower aberrations. In addition, innovative applications validate the LD/HD polynomial basis. Absence of artificial reduction of some higher order aberrations coefficients lead to a more realistic analysis. Here we summarize how wavefront analysis has evolved and demonstrate some of its new clinical applications.

Customised aberration-controlling corrections for keratoconic patients using contact lenses

Technological advancements in the design of soft and scleral contact lenses have led to the development of customised, aberration-controlling corrections for patients with keratoconus. As the number of contact lens manufacturers producing wavefront-guided corrections continues to expand, clinical interest in this customisable technology is also increasing among both patients and practitioners. This review outlines key issues surrounding the measurement of ocular aberrations for patients with keratoconus, with a particular focus on the possible factors affecting the repeatability of Hartmann-Shack aberrometry measurements. This review also discusses and compares the relative successes of studies investigating the design and fitting of soft and scleral customised contact lenses for patients with keratoconus. A series of key limitations that should be considered before designing customised contact lens corrections is also described. Despite the challenges of producing and fitting customised lenses, improvements in visual performance and comfortable wearing times, as provided by these lenses, could help to reduce the rate of keratoplasty in keratoconic patients, thereby significantly reducing clinical issues related to corneal graft surgery. Furthermore, enhancements in optical correction, provided by customised lenses, could lead to increased independence, particularly among young adult keratoconic patients, therefore leading to improvements in quality of life.