Normal-eye Zernike coefficients and root-mean-square wavefront errors

Salmon, Thomas; Pol, Corina van de

doi:10.1016/j.jcrs.2006.07.022

Cited by 211 publications

(179 citation statements)

References 28 publications

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“…As indicated by the horizontal zero line, most Zernike polynomials are centered at zero, except for Z 310 (horizontal coma), Z 330 (oblique trefoil) and Z 400 (spherical). The mean of oblique trefoil aberrations is negative and the mean of spherical aberrations is positive, which is consistent with the literature [9,11,23,24]. Furthermore, except for Z 400 , the variations in coma and trefoil aberrations are much higher than in the aberrations at higher levels.…”

Section: Resultssupporting

confidence: 91%

“…Most existing studies control certain factors such as pupil size by categorizing pupil diameters when analyzing HOA in order to avoid confounding effects [11]. However, pupil size is a continuous measure and the arbitrary grouping of pupil size into discreet categories may cause biased inferences and loss of statistical power due to possible misclassification [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…Zernike polynomials in the analyses will be adjusted for pupil sizes. Previous studies adjust for pupil sizes by stratification (dividing patients into different groups according to their pupil sizes) [11,19], such as rescaling pupil sizes into different groups, 6.00 mm, 5.00 mm, etc [8]. Individual pupil sizes are thus not used in the analysis, which potentially result in information loss.…”

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confidence: 99%

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Cluster Analysis of Patients Evaluated in Laser Refractive Surgery

Tong¹

2017

BBIJ

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Purpose: To investigate ocular Higher Order Aberrations (HOA) by examining Zernike polynomials with a novel application of clustering analysis adjusted for age, refractive error and pupil size.Methods: Wavefront aberrations were measured with wavefront aberrometry (ZyWave, Technolas Perfect Vision) on 1509 patients (57.9% females) with a mean age of 43.1 ± 12.0 years (range 18 to 71). We modeled the association of 15 pupil size adjusted (PSA) Zernike polynomials (3 rd to 5 th order) with age and refractive error using linear regression. A statistical method called clustering of linear models (CLM) was used to identify the clusters of Zernike polynomials.Results: Fifteen Zernike polynomials were grouped into four clusters through CLM adjusting for age and refractive error. In the first cluster (Z 311 , Z 310 , Z 331 and Z 330 ), the PSA Zernike polynomials increased with refractive error (regression coefficient, 0.0041; 95% empirical confidence interval [CI]: 0.00015 to 0.0081) but significantly decreased with age (coefficient, -0.0021; 95% CI: -0.0031to-0.0010). In the second cluster (Z 400 ), the PSA Zernike polynomials decreased with refractive error (coefficient, -0.0065; 95% CI: -0.010 to -0.0029) but increased with age (coefficient, 0.004; 95% CI: 0.0031 to 0.0049). No significant associations were detected in the remaining two clusters (secondary astigmatism and secondary coma). Conclusion:Taking advantages of regression model that accounts for pupil size, these results provide a better understanding of HOA in a more population-based perspective. Our clustering approach has the functional capacity to predict the values of Zernike polynomials that are relevant for clinical and commercial use. Keywords IntroductionHigher Order Aberrations (HOA) is distortions in light that result from physical alterations of the optical pathway. The primary ocular factors that contribute to HOA are the tear film, cornea and lens. Wavefront assessment instruments such as the Hartmann-Shack Sensor provide data from which the aberrations of the human's eye are estimated. The understanding of HOA as applied to the visual system and the commercialization of devices that measure HOA has greatly expanded the use of these methods in the clinical setting. Zernike polynomials have been commonly used as the standard method for describing the shape of an aberrated wavefront [1].Zernike polynomials are an orthogonal series of basic functions normalized over a unit circle. They provide a precise mathematical model that has the ability to capture global shape.An important characteristic of Zernike polynomials is that lower order polynomials approximate the overall features of the anatomic shape of the eye very well, while the higher ordered polynomial terms capture local surface features only. A second important property of Zernike polynomials is that they have a direct relationship to optical function. These optical and geometric properties make Zernike polynomials particularly useful for study of the cornea and the optical syste...

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Section: Resultssupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Cluster Analysis of Patients Evaluated in Laser Refractive Surgery

Tong¹

2017

BBIJ

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“…Provided in Equation 1 is the wavefront aberration function for modeling wavefronts. For details on using Zernike Polynomials to model human eyes see [1,18,20,19,9].…”

Section: Simulating Individual Differences In Eyesightmentioning

confidence: 99%

“…This was achieved by measuring and analysing over 2560 wavefronts of healthy human eyes [18]. We use the first fourteen aberrations Equation 1.…”

Section: Simulating Individual Differences In Eyesightmentioning

confidence: 99%

Creating Personalized Digital Human Models of Perception for Visual Analytics

Bennett¹,

Quigley²

2011

User Modeling, Adaption and Personalization

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Abstract. Our bodies shape our experience of the world, and our bodies influence what we design. How important are the physical differences between people? Can we model the physiological differences and use the models to adapt and personalize designs, user interfaces and artifacts? Within many disciplines Digital Human Models and Standard Observer Models are widely used and have proven to be very useful for modeling users and simulating humans. In this paper, we create personalized digital human models of perception (Individual Observer Models), particularly focused on how humans see. Individual Observer Models capture how our bodies shape our perceptions. Individual Observer Models are useful for adapting and personalizing user interfaces and artifacts to suit individual users' bodies and perceptions. We introduce and demonstrate an Individual Observer Model of human eyesight, which we use to simulate 3600 biologically valid human eyes. An evaluation of the simulated eyes finds that they see eye charts the same as humans. Also demonstrated is the Individual Observer Model successfully making predictions about how easy or hard it is to see visual information and visual designs. The ability to predict and adapt visual information to maximize how effective it is is an important problem in visual design and analytics.

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Pupil versus 1st Purkinje capsulotomy centration with femtosecond laser: Long term outcomes with a sinusoidal trifocal lens

Salgado,

Torres,

Marinho

2024

Journal of Biophotonics

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PurposeTo assess the role of femtosecond laser‐assisted capsulotomy centration in the long‐term intraocular positioning of a multifocal intraocular lens.DesignProspective comparative study.MethodsA total of 60 eyes of 30 patients underwent femtosecond laser‐assisted Refractive Lens Exchange (RLE). For every patient, capsulotomy centration was randomly performed according to pupil centre (PC) in one eye and first Purkinje reflex (FPR) in the other. The intraocular lens (IOL) positioning, visual acuities, spherical equivalent, internal aberrometry and quality of vision were assessed and compared at 3 years' follow‐up between groups (PC and FPR).ResultsIntraocular lens positioning showed a statistically significant difference between groups, with a closer centration to the visual axis in the FPR patients (p < 0.001). Internal aberrometry showed higher values in the PC capsulotomy centration group (p < 0.01).ConclusionsFPR centered capsulotomy is associated to a closer centration of the IOL to the visual axis.

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Normal-eye Zernike coefficients and root-mean-square wavefront errors

Abstract: There was a general consensus for the magnitude of HOAs expected in normal adult human eyes. At least 90% of the sample had aberrations less than double the mean values reported here. These values can serve as a set of reference norms.

Cited by 211 publications

References 28 publications

Cluster Analysis of Patients Evaluated in Laser Refractive Surgery

Cluster Analysis of Patients Evaluated in Laser Refractive Surgery

Creating Personalized Digital Human Models of Perception for Visual Analytics

Pupil versus 1st Purkinje capsulotomy centration with femtosecond laser: Long term outcomes with a sinusoidal trifocal lens

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