ABSTRACT
PURPOSE: To present a paraxial method to estimate the influence of variations in ocular biometry on changes in refractive error (S) at a population level and apply this method to literature data. METHODS: Error propagation was applied to two methods of eye modelling, referred to as the simple method and the matrix method. The simple method defines S as the difference between the axial power and the whole-eye power, while the matrix method uses more accurate ray transfer matrices. These methods were applied to literature data, containing the mean ocular biometry data from the SyntEyes model, as well as populations of premature infants with or without retinopathy, full-term infants, school children and healthy and diabetic adults. RESULTS: Applying these equations to 1000 SyntEyes showed that changes in axial length provided the most important contribution to the variations in refractive error (57%-64%), followed by lens power/gradient index power (16%-31%) and the anterior corneal radius of curvature (10%-13%). All other components of the eye contributed <4%. For young children, the largest contributions were made by variations in axial length, lens and corneal power for the simple method (67%, 23% and 8%, respectively) and by variations in axial length, gradient lens power and anterior corneal curvature for the matrix method (55%, 21% and 14%, respectively). During myopisation, the influence of variations in axial length increased from 54.5% to 73.4%, while changes in corneal power decreased from 9.82% to 6.32%. Similarly, for the other data sets, the largest contribution was related to axial length. CONCLUSIONS: This analysis confirms that the changes in ocular refraction were mostly associated with variations in axial length, lens and corneal power. The relative contributions of the latter two varied, depending on the particular population.
Subject(s)
Axial Length, Eye , Biometry , Refraction, Ocular , Refractive Errors , Humans , Refractive Errors/physiopathology , Refractive Errors/diagnosis , Biometry/methods , Refraction, Ocular/physiology , Child , Axial Length, Eye/diagnostic imaging , Cornea/diagnostic imaging , Adult , Infant , Child, Preschool , Infant, Newborn , Male , Female , AdolescentABSTRACT
The intracapsular accommodation mechanism (IAM) may be understood as an increase in the lens equivalent refractive index as the eye accommodates. Our goal was to evaluate the existence of an IAM by analysing observed changes in the inner curvature gradient of the lens. To this end, we fitted a gradient index and curvature lens model to published experimental data on external and nucleus geometry changes during accommodation. For each case analysed, we computed the refractive power and equivalent index for each accommodative state using a ray transfer matrix. All data sets showed an increase in the effective refractive index, indicating a positive IAM, which was stronger for older lenses. These results suggest a strong dependence of the lens equivalent refractive index on the inner curvature gradient.
Subject(s)
Lens, Crystalline , Lenses , Humans , Refraction, Ocular , Accommodation, Ocular , Refractometry/methodsABSTRACT
We present the formulation of a paraxial ray transfer or ABCD matrix for onion-type GRIN lenses. In GRIN lenses, each iso-indicial surface (IIS) can be considered a refracting optical surface. If each IIS is a shell or layer, the ABCD matrix of a GRIN lens is computed by multiplying a typically high number of translation and refraction matrices corresponding to the K layers inside the lens. Using a differential approximation for the layer thickness, this matrix product becomes a sum. The elements A, B, C, and D of the approximated GRIN ray transfer matrix can be calculated by integrating the elements of a single-layer matrix. This ABCD matrix differs from a homogeneous lens matrix in only one integration term in element C, corresponding to the GRIN contribution to the lens power. Thus the total GRIN lens power is the sum of the homogeneous lens power and the GRIN contribution, which offers a compact and simple expression for the ABDC matrix. We then apply this formulation to the crystalline lens and implement both numerical and analytical integration procedures to obtain the GRIN lens power. The analytical approximation provides an accurate solution in terms of Gaussian hypergeometric functions. Last, we compare our numerical and analytical procedures with published ABCD matrix methods in the literature, and analyze the effect of the iso-indicial surface's conic constant (Q) and inner curvature gradient (G) on the lens power for different lens models.
