Monochromatic ocular high-order aberrations in children and adolescents.

PURPOSE: To investigate the prevalence and repeatability of high-order aberrations (HOAs) from non-cyclopleged eyes in 1515 children and adolescents 2.5-18 years of age. METHODS: The Leipzig Research Centre for Civilization Diseases (LIFE)-Child study is a population-based, prospective, observational single-centre study that investigates the development of children and adolescents in Germany. Wavefront measurements were repeated three times in each eye of 1515 healthy subjects. Results were described by 36 Zernike coefficients for a 5 mm reference pupil diameter. Short-term repeatability is given for each coefficient. The impact on vision is described by the root mean squared (RMS) value of the HOA Zernike coefficients. RESULTS: High-order aberrations were dominated by five contributions. For 1004 right eyes: spherical aberration (c12 = 0.06 ± 0.07 µm), coma (c7 = 0.03 ± 0.09 µm, c8 = 0.03 ± 0.06 µm) and trefoil (c6 = -0.01 ± 0.07 µm, c9 = 0.008 ± 0.06 µm). The RMS value was 0.18 ± 0.06 µm. Modes higher than fourth order do not contribute clinically to the aberrations. HOAs show no clinically significant dependency with age. Instead, HOA values agree well with previous results on aberrations in adult eyes. Spherical aberration was highly correlated between the two eyes. Repeatability was worst for coma, 0.033 µm, due to variability in the alignment of the pupil centre. The left eye showed, on average, a 0.08 mm larger pupil diameter than the right eye (p < 0.02). CONCLUSIONS: Across the age span from 2.5 to 18 years, we see the same distribution of HOA as for adults. We established that only five Zernike coefficients, spherical aberration, coma and trefoil were of clinical significance in healthy eyes. A high correlation between the two eyes for spherical aberration suggests a common blueprint for each eye in any one subject.

Agreement and Repeatability of Noncycloplegic and Cycloplegic Wavefront-based Autorefraction in Children.

SIGNIFICANCE: Increasing prevalence of refractive error requires assessment of ametropia as a screening tool in children. If cycloplegia is not an option, knowledge about the increase in uncertainty for wavefront-based autorefraction is needed. The cycloplegic agent as the principal variant presents cross-reference and allows for extraction of the influence of accommodation. PURPOSE: The purpose of this study was to determine the repeatability, agreement, and propensity to accommodate of cycloplegic (ARc) and noncycloplegic (ARnc) wavefront-based autorefraction (ZEISS i.Profiler plus; Carl Zeiss Vision, Aalen, Germany) in children aged 2 to 15 years. METHODS: In a clinical setting, three consecutive measurements were feasible for 145 eyes (OD) under both conditions. Data are described by spherical equivalent (M), horizontal or vertical astigmatic component (J0), and oblique astigmatic component (J45). In the case of M, the most positive value of the three measurements was chosen, whereas the mean was applied for astigmatic components. RESULTS: Regarding agreement, differences for ARc minus ARnc were statistically significant: for M, 0.55 (0.55 D; mean [SD]; P < .001), that is, more hyperopic in cycloplegia; for J0, -0.03 (0.11 D; P = .002); and for J45, -0.03 D (SD, 0.09 D; P < .001). Regarding repeatability, astigmatic components showed excellent repeatability: SD < 0.11 D (ARnc) and SD < 0.09 D (ARc). The repeatability of M was SD = 0.57 D with a 95% interval of 1.49 D (ARnc). Under cycloplegia, this decreased to SD = 0.17 D (ARc) with a 95% interval of 0.50 D. The mean propensity to accommodate was 0.44 D from repeated measurements; in cycloplegia, this was reduced to 0.19 D. CONCLUSIONS: Wavefront-based refraction measurement results are highly repeatable and precise for astigmatic components. Noncycloplegic measurements of M show a systematic bias of 0.55 D. Cycloplegia reduces the propensity to accommodate by a factor of 2.4; for noncycloplegic repeated measurements, accommodation is controlled to a total interval of 1.49 D (95%). Without cycloplegia, results improve drastically when measurements are repeated.

Simple approach to the generalized Minkwitz theorem.

The Minkwitz theorem plays an important role in the design of progressive addition lenses. Recently, this theorem has been generalized by Esser et al. [J. Opt. Soc. Am. A34, 441 (2017)10.1364/JOSAA.34.000441JOAOD60740-3232] to non-umbilic lines under the assumption of a symmetric surface. We present a simplified derivation and generalize their findings to arbitrary but sufficiently smooth surfaces.

Transient Ocular Wavefront Data in Type 1 Diabetes Mellitus.

PURPOSE: We report transient ocular wavefront and blood glucose data for one patient with acute type 1 diabetes mellitus after the treatment with insulin has been initiated. CASE REPORT: The wavefront data for both eyes of a 34-year-old male patient were examined by a Hartmann-Shack wavefront sensor. Refraction data and higher-order aberrations were recorded during 130 days for eyes in natural conditions, without cycloplegia. At the beginning, we sampled data every 3 to 4 days and enlarged the intervals, when values settled. In total, we report 20 measurements and 1 baseline entry. Blood glucose levels were recorded at least six times a day during the complete period. For the equivalent sphere, we recorded a bilateral hyperopic shift of 5 D from -2.75 DS to +2.25 DS, followed by a reverse myopic shift of the same amount. The equivalent sphere peaked about 15 to 18 days after the treatment with insulin had begun. Cylinder values kept remarkably stable. Higher-order aberrations are dominated by the spherical aberration. The Zernike coefficient c12 for both eyes changed substantially from OD 0.036 µm and OS 0.062 µm to OD 0.24 µm and OS 0.22 µm (5 mm pupil diameter) following the time pattern of the equivalent sphere. About 60 days after they had reached their peak, all refraction values and higher-order aberrations stabilized at their baseline levels. The baseline was defined by records taken 4 years before the treatment with insulin was commenced. CONCLUSIONS: Wavefront aberrometry gives quantitative insights in the transient alteration and recovering of the eye's optics whilst the therapy of acute type 1 diabetes mellitus is being initiated. The data of this case support the assumption that variations in the crystalline lens, most probably the modification of its refractive gradient index, as a cause for the transient behavior. An explanation is still missing.

Unaided visual acuity and blur: a simple model.

PURPOSE: This article proposes a simple model that describes the quantitative relationship between unaided visual acuity and blur attributed to refractive errors. METHODS: The standard model for describing the relationship between visual acuity and blur, as published by Raasch, is used as a starting point to develop a simpler model based on heuristic arguments. The basis of Raasch's data is augmented by published findings in the range of low-level refractive errors. Sphero-cylindrical refractive errors are transformed into a single blur quantity b, also termed dioptric distance, which serves as an input in both models. The possible influence of the cylinder axis and the pupil size is not included. RESULTS: The quite simple model for the unaided minimum angle of resolution, MAR ∝ 1+ b(2), nicely matches available data and improves the SE of the regression by a factor of 2 in comparison to Raasch's model. CONCLUSIONS: Both models considered in this article describe measurement data equally well. They differ in terms of complexity and functional form. The simple model provides a valid description for low-level refractive errors, where Raasch's model fails. Actual uncertainties in experimental data on unaided visual acuity, especially the frequent lack of information on pupil diameter, prevent meaningful numerical comparison and the refinement of both models. However, theoretical arguments are provided in support of the simple model.

Progressive addition lens measurement by point diffraction interferometry.

PURPOSE: Design a device for accurate measurements of local optical properties of progressive addition lenses (PALs). METHODS: A point diffraction interferometer has been adapted to measure local prescriptions of PALs. RESULTS: The most basic configuration of the interferometer for the measurement of PALs showed in this work presents high dynamic range and accuracy as well as the possibility of choosing the number and position of measurement points. Measurements are taken within a region of interest within a radius of about 0.4 to 1.5 mm. Different PAL designs are measured by the method proposed here and compared with results by a last generation commercial lens mapper. With the point diffraction interferometer we also compared several PAL designs in order to analyze their properties in the progression zone. CONCLUSIONS: The device is compact, robust, and fairly accurate, and the operational principle is very simple. By direct measurements it provides the local dioptric power, i.e., the second order wavefront properties, of the lens for selected regions of interest. The position and area can be chosen by the user. The only mobile part of the setup allows for the selection of the measurement points without any additional prismatic correction or movement of the PAL.

Role of optics in the accuracy of depth-from-defocus systems: comment.

In their paper "Role of optics in the accuracy of depth-from-defocus systems" [J. Opt. Soc. Am. A24, 967 (2007)] the authors Blayvas, Kimmel, and Rivlin discuss the effect of optics on the depth reconstruction accuracy. To this end they applied an approach in Fourier space. An alternative derivation of their result in the spatial domain, based on geometrical optics, is presented and compared with their outcome. A better agreement with experimental data is achieved if some unclarities are refined.

Paraxial optics of astigmatic systems: relations between the wavefront and the ray picture approaches.

PURPOSE: The paraxial propagation of astigmatic wavefronts through astigmatic optical systems can be described by the augmented step-along method (ASAM). Its equivalence to the linear ray optics approach is considered in detail. METHODS: The ASAM is exploited to derive paraxial ray paths through a general coaxial astigmatic system. RESULTS: Starting from the information inherent in the ASAM all 2x2 submatrices rendering the general 4x4 transference of linear optics can be generated. This proves the complete equivalence of both approaches. Additionally, we show that the symplectic relations are automatically obeyed in the ASAM. CONCLUSIONS: The ASAM offers a complete alternative to describe the paraxial optics of astigmatic optical systems. According to the ASAM, an optical system is fully characterized by the back vertex vergence and the angular magnification matrix. Hence, a complete description of the paraxial optics of an eye should not only report the state of refraction but the angular magnification matrix as well, although it is not yet very common. The magnification matrix might be important in cases of anisometropia or the design of progressive addition lenses. Yet, a simple clinical procedure to determine the angular magnification matrix is missing.

An analytical model describing aberrations in the progression corridor of progressive addition lenses.

PURPOSE: In the progression corridor of a typical progressive addition lens (PAL) with an addition of 2.5 D, the power changes by roughly 1/8 D/mm. This renders a power difference of some 0.5 D across a typical pupil diameter of 4 mm. Contrary to this fact, PALs do work well in the progression zone. To explain why, we apply a simple model to derive wavefront characteristics in the progression zone and compare it with recent experimental data. METHODS: We consider a simple analytic function to describe the progression zone of a PAL, which has been introduced by Alvarez and other authors. They considered the power change and astigmatism, which are second-order wavefront aberrations. We include third-order aberrations and compare them with spatially resolved wavefront data from Hartmann-Shack-sensor measurements. RESULTS: The higher-order aberrations coma and trefoil are the dominant aberrations besides astigmatism as given by experimental data. According to our model, the third-order aberrations in the transition zone are strongly coupled to the power change and the cubic power of the pupil radius. Their overall contribution according to experimental data is nicely reproduced by our model. The numeric contribution of higher-order aberrations is small and, for practical purposes, the wavefront can be described locally by the second-order components of sphere and astigmatism only. CONCLUSIONS: We propose a simple analytical model to understand the optics in the progression corridor and nearby zones of a PAL. Our model confirms that for typical pupil sizes, all higher-order aberrations, including the dominant modes of coma and trefoil, are small enough to render an undisturbed vision in the progression zone. Therefore, higher-order aberrations have a minimal impact on the optical performance of these lenses.

Modified point diffraction interferometer for inspection and evaluation of ophthalmic components.

We demonstrate that a modified point diffraction interferometer can be used to measure the power distribution of different kinds of ophthalmic lenses such as spectacles, rigid and soft contact lenses, progressive lenses, etc. The relationship between the shape of the fringes and the power characteristics of the component being tested is simple and makes the design a very convenient and robust tool for inspection or quality control. Some simulations based on the Fresnel approximation are included.

Paraxial propagation of astigmatic wavefronts through noncoaxial astigmatic optical systems.

PURPOSE: The paraxial propagation of astigmatic wavefronts through a noncoaxial system is described. METHODS: The augmented stepalong method (ASAM) for vergences is extended to tilted and decentered elements. RESULTS: Equations for the case of tilted and decentered elements are presented in the framework of vergence calculations. All effects according to the perturbation of a centered system can be derived from the vergences provided by the calculations for the unperturbed system. In particular, the shift in image space rendered by the pertubation is simply the sum of additional decenter and tilt terms to the unperturbed system. CONCLUSIONS: Previous work on the description of the propagation of astigmatic wavefronts has been generalized to noncoaxial systems. This completes the wavefront picture built on the paraxial augmented stepalong method.

Paraxial propagation of astigmatic wavefronts in optical systems by an augmented stepalong method for vergences.

PURPOSE: The propagation of astigmatic wavefronts through astigmatic optical systems is reconsidered in the wavefront perspective. METHODS: The stepalong method for vergences, described by 2x2 matrices, is applied and augmented to produce off-axis information like the magnification. This so-called augmented stepalong method (ASAM) is derived by applying the paraxial propagation of astigmatic wavefronts to tilted wavefronts as well. RESULTS: The features of the ASAM are discussed for a single surface, a thick lens, and a general system. CONCLUSIONS: The ASAM provides all necessary information to describe a centered astigmatic optical system in paraxial approximation.

Tolerating vertex distance changes for spherocylindrical corrections.

Prescriptions depend on the vertex distance. Although weak prescriptions are insensitive to a vertex distance change, stronger ones must be adjusted if the vertex distance is modified by an appreciable amount. The tolerable amount can be specified for pure spherical powers. For spherocylindrical corrections, the concept of dioptric distance is invoked in this article and applied to the propagation of an astigmatic wavefront. This leads to a simple rule that is well suited to decide on the necessity of modifying a prescription.

Oblique central refraction in tilted spherocylindrical lenses.

Spectacle corrections worn in a frame with a faceform tilt should be used with effective spherocylindrical parameters. For the case of oblique central refraction, Keating presented a procedure to determine these parameters in a third-order approximation. The central equation of his approach, the effective dioptric power matrix, is partly the result of an educated guess. Based on the equations of wavefront tracing, an analytical derivation of his equation, slightly modified however, is given in this paper.