Wavefront Aberration Analysis Research Articles

Aberrometry in the diagnosis and treatment of keratoconus

Keratoconus (KC) is a bilateral progressive disease that often begins in young adulthood. Advanced KC significantly impairs patients' quality of life, making early detection of the condition a critical goal for specialists. Early identification of KC greatly influences both the treatment strategy and the outcomes. This review focuses on the ocular wavefront in KC, which is of interest from the perspective of early diagnosis. The article outlines the nature of optical aberrations in the eye, particularly in KC, and the principles of wavefront aberration analysis. An increase in higher-order aberrations is one of the earliest signs of incipient KC and a key contributor to reduced visual quality. Some of the widely used KC treatment methods, such as corneal cross-linking and the implantation of intracorneal segments, has been established to positively impact many aspects of KC pathogenesis, including reduction in higher-order aberrations, which in turn improves visual quality. Monitoring of the outcomes of treatment or optical correction in KC using higher-order aberrations is a delicate approach, as vision improvements following treatment are often unexplained by routine eye examination methods. However, the choice of the optimal method of visual rehabilitation for KC patients remains unresolved. Efforts to find new treatment methods, primarily through combinations and modifications of existing techniques, are ongoing. The article discusses this promising approach of using wavefront as an additional criterion for assessing the performance of the optical system in the diagnosis, treatment, and optical correction of KC.

Современные подходы к хирургии катаракты на основании анализа волнового фронта

Relevance. Cataract is the leading cause of visual impairment worldwide. Even in the early stages of cataract development, when the maximum visual acuity often remains high, patients complain of a decrease in image quality (light scattering, diplopia), which is expressed in the difficulty of performing daily and professional activities. The cause of this condition in most cases is internal aberrations of a higher order. One of the topical issues of modern ophthalmology is the definition of indications for surgery of primary cataracts with high visual acuity. Purpose. The purpose of this literature review was to describe the current state of the problem of wavefront changes in patients with various types of initial lens opacity. Material and methods. A systematic analysis of scientific publications of domestic and foreign authors on the resources PubMed, Medline from 2000 to 2022, devoted to the currently existing methods for assessing the quality of vision of patients with initial opacification of the lens, was carried out. Results. Our literature review showed the great importance of assessing wavefront aberrations in patients with initial cataracts and high visual acuity. With the advent of modern diagnostic systems – aberrometers with the possibility of an isolated assessment of internal aberrations, doctors have the opportunity to interpret data on the effect of lens changes on the quality of vision. Conclusion. Visual acuity in patients with initial cataract is not a unique evaluation criterion for determining the timing of surgical intervention. Analysis of wavefront aberrations to a greater extent describe visual impairments and can be used as objective criteria for prescribing surgical treatment. The study of aberrations of the human eye makes it possible to give an objective and quantitative assessment of the optical functions of the eye, which expands the possibilities for diagnosis and for the formation of surgical approaches for initial lens opacities in patients with high visual acuity. Key words: higher-order wavefront aberrations, cataract

Finite Element Analysis of Wave-Front Aberrations of Medium and High Myopia with Different CCT after Small Incision Lenticule Extraction (SMILE)

In this study, the wave-front aberrations of medium and high myopia with different CCT after SMILE were studied by the finite element method. Then, the various trend of wave-front aberrations with clinical significance was obtained. When CCT was the same, the wave-front aberrations of myopia with different diopters were different. When CCT increased, the variations of wave-front aberrations of myopia with different diopters were different. However, regardless of the degree of myopia, the variations of defocus and primary spherical aberration were the most obvious. The larger the CCT, the smaller the absolute values of defocus and primary spherical aberration.

Derivation of Ambiguity in Wavefront Aberration and Quantitative Analysis in AO System

Adaptive optics (AO) can effectively correct wavefront aberration, with many works qualitatively utilizing the defocus preconditioner to improve the aberration correction accuracy, but no work has yet quantitatively optimized the defocus distance to obtain higher accuracy. Spurred by the theoretical gap, this paper provides the derivation revealing the mechanism of the above phenomenon and proposes a theoretical method for determining the optimal defocus distance (OPDD) according to AO system parameters instead of numerous tests. Given that the complex conjugate amplitude can generate the same point spread function (PSF), we define the dual wavefront and present the Zernike coefficients expression with additional aberration due to the PSF variation. Then we derive the probability of the dual wavefront (PDWF) with the relevant conclusions of label noise. We suppose that the defocus preconditioner reduces the PDWF, thus effectively improving the accuracy, which is verified through the quantitative analysis where a deep neural network is utilized to correct aberration. Furthermore, the correction accuracy at the theoretical OPDD is no less than 98% of the highest accuracy in experiments, which quantitatively demonstrates the effectiveness of the method. Overall, this work significantly improves the efficiency of the AO system setup.

Analysis of Corneal Scheimpflug Densitometry and Ocular Wavefront Aberrations Post Descemet Stripping Automated Endothelial Keratoplasty.

To assess the role of corneal densitometry and wavefront aberrations post Descemet stripping automated endothelial keratoplasty (DSAEK) and their correlation with visual acuity. Twenty-seven eyes of 25 patients with nonresolving corneal edema for more than 3 months as a result of Fuchs endothelial corneal dystrophy, pseudophakic bullous keratopathy, or secondary endothelial dysfunction were enrolled in a prospective interventional study and underwent DSAEK. Postoperative evaluation for corneal aberrations, including Higher order aberrations (HOAs) and corneal densitometry (CD), was performed using anterior-segment optical coherence tomography (Avanti RTvue XR; Optovue) and Scheimpflug imaging (Pentacam, Oculus Optikgeräte GmbH, Wetzlar, Germany) at 6 months. A correlation analysis of corneal aberrations, including HOAs and CD, with postoperative best-corrected visual acuity at 6 months was performed. Mean best-corrected visual acuity (BCVA) improved from 1.67±0.53 log of minimum angle of resolution (logMAR) to 0.2±0.22 logMAR post DSAEK at 6 months (P≤0.0001). At 6 months, mean root-mean-square (RMS) total corneal aberrations (includes HOA and low-order aberration [LOA]), RMS total HOA, and RMS LOA of the central 6-mm zone were 4.99±2.64, 1.80±0.9, and 4.55±2.64, respectively. The mean corneal densitometry from anterior, central, and posterior zones were 39.12±12.77, 23.9±7.2, and 13.54±2.04 gray scale units, respectively. Total anterior aberrations (r=0.051; P=0.006), anterior LOA (r=0.049; P=0.009), total corneal aberrations (r=0.051; P=0.001), total HOAs (r=0.095; P=0.057) and LOAs (r=0.050; P=0.002), and total CD from 0 to 2 mm (r=0.010; P=0.038) and 2 to 6 mm (r=0.014; P=0.018) showed a significant inverse correlation with postoperative BCVA. There was an inverse relationship between post DSAEK BCVA and total corneal HOAs and full-thickness densitometry at 6 months. Scheimpflug imaging with added tools for corneal aberration and densitometry analysis gives further insight into the suboptimal vision achieved despite transparent corneas post DSAEK.

Shape of the anterior surface of the cornea after extended wear of silicone hydrogel soft contact lenses.

To measure geometrical changes in the anterior surface of the cornea after wearing silicon hydrogel (SiH) soft contact lenses continuously for 1week. Forty-three eyes with 3.0D of myopia and 22 eyes with 3.0D of hyperopia were enrolled in the prospective, interventional study. All subjects underwent a general eye examination, corneal tomography with wavefront aberration analysis, corneal thickness measurements and epithelial thickness mapping before and after wearing SiH lenses (Acuvue Oasys) for 7days. No significant changes in average keratometry were observed in either refractive group. In the myopic group, keratometry findings for the flat meridian (K1) and central corneal thickness decreased significantly. After +3.0 D lens wear in the hyperopic group, a significant decrease in epithelial thickness up to 3.19µm was observed in the central and paracentral cornea, (p<0.001). In both refractive groups, the largest epithelial thickness increase was seen in the periphery. A decrease in spherical aberration was noted in myopic eyes, while an increase of both higher order corneal aberrations and coma was found in hyperopic subjects. Extended wear of SiH lenses results in a significant change in epithelial thickness leading to alteration in the geometry of the anterior surface of the cornea, particularly in hyperopic patients. These epithelial thickness variations lead to changes in the higher order aberrations of the cornea.

Theoretical Analysis of Wave-Front Aberrations Induced from Conventional Laser Refractive Surgery in a Biomechanical Finite Element Model.

PurposeTo examine the biomechanical effects-induced wave-front aberrations after conventional laser refractive surgery.MethodsA finite element model of the human eye was established to simulate conventional laser refractive surgery with corrected refraction from –1 to –15 diopters (D). The deformation of the anterior and posterior corneal surfaces was obtained under the intraocular pressure (IOP). Then, the surface displacement was converted to wave-front aberrations.ResultsFollowing conventional refractive surgery, significant deformation of the anterior and posterior corneal surfaces occurred because of the corneal biomechanical effects, resulting in increased residual wave-front aberrations. Deformation of the anterior surface resulted in a hyperopic shift, which was significantly increased with the increasing refractive correction. The residual high-order aberrations consisted of spherical aberration, vertical coma, and y-trefoil. Spherical aberration was significantly positively correlated to enhanced refraction correction. The effect of posterior corneal surface on induced wave-front aberration was less than the anterior corneal surface. The IOP slightly affects the postoperative defocus, coma, and spherical aberration. When treatment decentration occurred during the procedure, the hyperopic shift decreased as the eccentricity increased. Treatment decentration had a significant impact on the spherical aberration and the coma. In addition, the ocular tissue elasticity played a key role in hyperopic shift, whereas it had little effect on the other aberrations.ConclusionsAmong the many factors that affect high-order aberrations after conventional laser refractive surgery, the alterations in corneal morphology caused by biomechanical effects must be considered, as they can lead to an increase in postoperative residual wave-front aberrations.

Correlation analysis of wavefront aberrations and accommodations in myopia and hyperopia

ABSTRAKTWstęp: Celem badania było przeprowadzenie analizy porównawczej dotyczącej akomodacji, pseudoakomodacji (PA) i aberracji wyższego rzędu (higher order optical aberrations – HOA) u dzieci oraz młodzieży z krótkowzrocznością i nadwzrocznością.Materiały i metody: W badaniu wzięło udział 88 pacjentów w wieku 5–24 lat (średnia 12,5 ±0,7). Zbadano 123 oczu z krótkowzrocznością (średnia −5,27 ±1,6 D) i 53 oczu z nadwzrocznością (średnia +3,1 ±1,15 D). Dokonano pomiaru obiektywnej odpowiedzi akomodacyjnej i względnej rezerwy akomodacyjnej. Wartość amplitudy pseudoakomodacyjnej (pseudoaccomodation amplitude – PA) oszacowano na podstawie różnicy między obliczoną mocą dodatkowej soczewki +3.0 D a najmniejszą mocą soczewki dodatniej umożliwiającą czytanie po wywołaniu cykloplegii (1% chlorowodorku cyklopentolanu × 2) z odległości 33 cm. Obliczono również wartości aberracji wyższego rzędu (średni kwadrat reszt, root mean square – RMS), pionowego i poziomego trefoil, pionowej i poziomej coma (coma7, coma8), oraz aberracji sferycznej (spherical aberration – SA).Wyniki: Obiektywne i subiektywne parametry akomodacji były znacząco niższe w krótkowzroczności niż w dalekowzroczności, natomiast wartości aberracji fali (RMS HOA, pionowy trefoil, coma7) oraz PA były znacząco wyższe. Stwierdzono różnice w zależnościach między parametrami aberracji i akomodacji w krótkowzroczności i nadwzroczności. W przypadku krótkowzroczności wykazano dodatnią korelację między RMS oraz pionową coma i akomodacją, natomiast pionowy trefoil oraz SA były dodatnio skorelowane z PA. W nadwzroczności stwierdzono dodatnią korelację między wartością pionowego trefoil a akomodacją oraz PA, odwrotną korelację między pionową coma a PA, oraz odwrotną korelację między poziomym trefoil i SA a akomodacją.Porównanie pacjentów krótkowzrocznych i nadwzrocznych wykazało odmienne zależności między aberracją sferyczną mierzoną po wywołaniu cycloplegii a akomodacją. Nie stwierdzono zależności między krótkowzrocznością a obiektywną odpowiedzią akomodacyjną, natomiast zaobserwowano dodatnią korelację z wartością PA. Nadwzroczność była ujemnie skorelowana z obiektywną odpowiedzią akomodacyjną, jednak nie stwierdzono zależności z wartością PА. U osób krótkowzrocznych zaobserwowano istotnie wyższe wartości SA oraz szerszą amplitudę PA. Natomiast w nadwzroczności wartość SA malała istotnie w kierunku wartości ujemnych przy wyższej amplitudzie PA.Wnioski: W krótkowzroczności stwierdzono obniżenie parametrów akomodacji oraz podwyższenie wartości HOA i PA. Porównanie oczu krótkowzrocznych i nadwzrocznych wykazało zróżnicowane powiązania między parametrami akomodacji oraz fali. Stwierdzone cechy należy uwzględnić przy opracowywaniu metod korekcji ukierunkowanych na refraktogenezę.

Effective wavefront aberration measurement of spectacle lenses in as-worn status

An effective wavefront aberration analysis method for measuring spectacle lenses in as-worn status was proposed and verified using an experimental apparatus based on an eye rotation model. Two strategies were employed to improve the accuracy of measurement of the effective wavefront aberrations on the corneal sphere. The influences of three as-worn parameters, the vertex distance, pantoscopic angle, and face form angle, together with the eye rotation and corresponding incident beams, were objectively and quantitatively obtained. The experimental measurements of spherical single vision and freeform progressive addition lenses demonstrate the accuracy and validity of the proposed method and experimental apparatus, which provide a potential means of achieving supernormal vision correction with customization and personalization in optimizing the as-worn status-based design of spectacle lenses and evaluating their manufacturing and imaging qualities.

Informative feature selection based on the Zernike polynomial coefficients for various pathologies of the human eye cornea

The study was devoted to the analysis of wavefront aberrations under changes of the cornea surface curvature in the human eye. The analysis was based on the representation of aberrations of the front and rear corneal surfaces as superposition of Zernike functions. Weight coefficients of the Zernike polynomials were the object of this study. The data under analysis were obtained in a number of clinical trials in the Branchevski’s eуе clinic. The most informative weight coefficients were analyzed from the point of view of classification of patients by particular diagnosis. A comparison of the classification results was carried out using thirty front and rear corneal features, as well as the most informative features. The features were ranked by the informativity criterion for solving a specific classification task. While doing analysis, the informativity was evaluated on the basis of values of a separability criterion. An additional estimation of informativeness was carried out by calculating the classification error by a K-means method. As a result of the analysis, basic Zernike functions that are most informative for particular eye pathologies were identified.

Measurement of spectacle lenses using wavefront aberration in real view condition.

A wavefront aberration analysis method for measuring spectacle lenses in real-view condition is proposed and verified using experimental apparatus based on the eye-rotation model. Two strategies-feedback positioning and posture adjustment of incident beams and Hartmann-Shack wavefront-aberration sensor calibration at each measurement subarea-are applied to improve measurement accuracy. By simulating the real-view condition, wavefront aberration and user power on the vertex sphere can be obtained. Comparison experiments demonstrate the validity and accuracy of the proposed method and experimental apparatus. Freeform progressive addition lenses are also measured and the results analyzed. The findings provide a possible approach for optimizing the design of spectacle lenses and evaluating their manufacturing and imaging quality.

Image system analysis of human eye wave-front aberration on the basis of HSS

Hartmann–Shack sensor (HSS) has been used in objective measurement of human eye wave-front aberration, but the research on the effects of sampling point size on the accuracy of the result has not been reported. In this paper, point spread function (PSF) of the whole system mathematical model was obtained via measuring the optical imaging system structure of human eye wave-front aberration measurement. The impact of Airy spot size on the accuracy of system was analyzed. Statistics study show that the geometry of Airy spot size of the ideal light source sent from eye retina formed on the surface of HSS is far smaller than the size of the HSS sample point image used in the experiment. Therefore, the effect of Airy spot on the precision of the system can be ignored. This study theoretically and experimentally justifies the reliability and accuracy of human eye wave-front aberration measurement based on HSS.

Wavefront aberration analysis in misalignment passive positive-branch unstable laser resonators

Eigenmode of resonators with asymmetric circular mirrors based on misalignment passive positive-branch unstable resonator is investigated in the paper. To do so, we use iterative algorithm to simulate the effect of intracavity phase perturbation on eigenmode structure properties of the passive confocal unstable resonator. On this basis, further experiment of output beam properties on a misaligned passive unstable laser resonator has been performed by adopting Hartmann–Shack (H–S) method and Zernike modal wavefront reconstruction. Wavefront distribution and the first 35-order Zernike coefficient included in the wavefront are obtained. The results show that intracavity tilt perturbation notablely affects outcoupled beam intensity distribution, and will also increase some high-order aberrations of beam phase properties. However, low-order Zernike tilt aberration is the main component with phase-tilted perturbation is introduced into resonator cavity. Defocus, low-order astigmatism and coma aberration will all be brought with the augument of phase tilt aberration, which will obviously degrade output beam quality. When intracavity compensating elements are adopted for optical aberration correction, the correction of tilt aberration should be considered first.

Spatial–temporal-covariance-based modeling, analysis, and simulation of aero-optics wavefront aberrations

We introduce a framework for modeling, analysis, and simulation of aero-optics wavefront aberrations that is based on spatial-temporal covariance matrices extracted from wavefront sensor measurements. Within this framework, we present a quasi-homogeneous structure function to analyze nonhomogeneous, mildly anisotropic spatial random processes, and we use this structure function to show that phase aberrations arising in aero-optics are, for an important range of operating parameters, locally Kolmogorov. This strongly suggests that the d5/3 power law for adaptive optics (AO) deformable mirror fitting error, where d denotes actuator separation, holds for certain important aero-optics scenarios. This framework also allows us to compute bounds on AO servo lag error and predictive control error. In addition, it provides us with the means to accurately simulate AO systems for the mitigation of aero-effects, and it may provide insight into underlying physical processes associated with turbulent flow. The techniques introduced here are demonstrated using data obtained from the Airborne Aero-Optics Laboratory.

Analysis of wavefront aberration induced by turbulent flow field in liquid-convection-cooled disk laser

The wavefront aberration induced by turbulent flow field in liquid-convection-cooled disk laser is numerically analyzed. By using the large-eddy-simulation model, the structure of time-random turbulent eddies are described and the effects of turbulent eddies on wavefront aberration are illustrated, indicating that the wavefront aberration varies primarily with the temperature field. By integrating the thermal-induced variations of the refractive index along the laser beam path within the flowing liquid, the two-dimensional wavefront aberration is obtained, showing that the wavefront aberration occurs mainly at the thermal boundary layer, where the temperature gradient is large.

Theoretical analysis of wavefront aberration caused by treatment decentration and transition zone after custom myopic laser refractive surgery

To analyze the induced wavefront aberrations caused by treatment decentration and transition zone after custom myopic laser refractive surgery. Refractive Surgery Center, Tianjin Eye Hospital & Eye Institute, Tianjin Medical University, Tianjin, China. Cohort study. Wavefront aberration data from potential refractive surgery candidates were used. Based on the preoperative wavefront aberrations, the custom ablation profile was computed. Then, the influence of treatment decentration and especially that of the transition zone on induced wavefront aberrations was studied. The impact of angle mismatch on induced aberrations was analyzed. Data from 117 eyes (77 patients) were analyzed. The transition zone played a significant role in the influence of decentration on the induced aberrations in refractive surgery. Induced coma and spherical aberration increased rapidly as the lateral translation increased, and coma was significantly larger than other Zernike aberration terms. The induced aberrations from decentration with oblique incidence in the laser ablation profile were less than in the actual laser ablation process for slight subclinical decentration. The induced aberrations were not closely related to the subclinical unmatched angle from eye cyclotorsion. The induced aberrations from lateral translation were correlated with the position vector. The transition zone was designed to smooth the transition from the optical zone to the untreated cornea, and it mainly dominated induced coma and spherical aberration. To achieve the best postoperative visual performance, the effect of the transition zone in refractive surgery should be taken into account, especially for scotopic pupils.

Wavefront aberration and pattern visual evoked potential analysis before and after the cataract sur gery

Objective To analyze the wavefront aberration and pattern visual evoked potential in the patients with age-related cataract before and after the surgery.Methods Twenty-two patients with agerelated cataract (30 eyes) undergoing phacoemulsification and intraocular lens implantation were collected.The patients aged from 46 to 84 years with the best corrected visual acuity from 0.5 to 0.8 before the surgery.Wavefront aberration and pattern visual evoked potential test were measured before and after the surgery.The data were analyzed by statistical SPSS 13.0 software.Results Wavefront aberration analysis showed that the values of root-mean-square total high order aberration (RMSh) and root-mean-square fourth-order aberration (RMS4) were significantly reduced after the surgery ( P ＜ 0.01 ).The latent period of P100 in pattern visual evoked potential test (60' and 15' check) was shortened after the surgery (P ＜ 0.05 ).Conclusion Wavefront aberration measurement and pattern visual evoked potential test are effective assessments of visual function in the patients with age-related cataract at immature stage. Key words: Cataract; Wavefront aberration; Pattern visual evoked potential; surgery

全息曝光系统轴向调节误差对光栅衍射波像差的影响

全息曝光系统轴向调节误差对光栅衍射波像差的影响

The influence of the sampling dots on the analysis of the wave front aberration by using the covariance matrix method

The covariance matrix method is a simple method for solving the Zernike polynomial with the higher fitting precision. In this paper, it was used to analyze the several optical wave fronts of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We had found that the PV (peak-to-valley) and rms (root-mean-square) values of the wave front aberration changes with changing the Zernike term and the expressions for the several optical wave fronts with the different sampling dots were wrong. By analyzing the relations among the condition number of the coefficients matrix, the Zernike term, and the number of the sampling dots, it was indicated that the number of the sampling dots had only reduced the fluctuation the PV and the rms value while the Zernike term increases, but did not change the case that the expressions for the wave front aberration were wrong when the Zernike term is larger than 14, especially when the number of the sampling dots is less. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis by using the covariance matrix method in optical testing.

Stability of Zernike coefficients solved by the covariance matrix method in the analysis of the wave front aberration

The deduction of Zernike coefficients is usually influenced by the finite number of sampling dots on interferogram and their inherited measurement errors. In this paper, a simplified Gram–Schmidt method for solving the Zernike polynomial with the higher fitting precision is presented and used to analyze the wave front aberrations for the circle interference fringe of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We find the stability of the Zernike coefficients changes with changing the Zernike term, which has lead to the wrong expression for the wave front aberration. By analyzing the condition number of the coefficients matrix and the fitting precision of the method, it is indicated that the instability can be avoided when the Zernike term is lower than 14. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis in optical testing.