Generalized ray tracing method for the calculation of the peripheral refraction induced by an ophthalmic lens

A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence point of interest. Afterwards, generalized ray tracing provides the principal curvatures of the local wavefront at that point, and its orientation after being refracted by the lens. The curvature values of the local wavefront are interpreted as the sagital and tangential powers of the lens at the point of interest. The proposed approach is validated using a double-check of the calculated lens performance in the spherical lens case: while finite ray tracing is validated using a commercial ray tracing software, generalized ray tracing is validated using a software application for ophthalmic lens design based on the classical version of Coddington equations. Equations of the complete tracing process are developed in detail for the case of generic astigmatic ophthalmic lenses as an example. Three-dimensional representation of the sagital and tangential powers of the ophthalmic lens at all directions of gaze then becomes possible, and results are presented for lenses with different geometries.

A Novel MRI-Based Approach to Peripheral Refraction and Prediction of Myopia Progression.

Ocular Development, Peripheral Refraction and Custom Optical Design: the New Wave in Optometry and Visual Science Research

Previous studies suggest that the refractive status of the peripheral retina can influence the development and progression of myopia. Our aim was to compare peripheral refractions in the same cohort of human eyes corrected with spectacle lenses vs soft contact lenses. Ten young adults with moderate to high myopia (-5.00 D to -8.00 D) were investigated. Open-field autorefraction was used to measure on- and off-axis refractions with the eyes in primary gaze, when uncorrected, and when corrected with spectacles and contact lenses. Measures were made every 5° out to 30° horizontally in nasal and temporal retina and analysed as power vectors (M, J(0) , and J(45)). Partial coherence interferometry measures of eye size were also made on-axis and off-axis at 10º and 20º in nasal and temporal retina. Subjects (mean age 24; range 19-29 years) had an average on-axis mean-sphere refraction of -6.33 ± 0.31 D (mean ± 1 S.E.) and an average axial eye length of 25.99 ± 0.20 mm. The average relative peripheral refraction (RPR) for all subjects across all eccentricities was hyperopic when uncorrected (+0.90 ± 0.14 D) and also when corrected with spectacles (+1.01 ± 0.13 D) but changed to a myopic RPR when corrected with contact lenses (-1.84 ± 0.61 D). There was a highly significant effect of correction on peripheral refraction (p < 0.0001). Peripheral J(0) astigmatism also became significantly more negative (less with-the-rule) on correction with contact lenses (p = 0.015), whereas J(45) astigmatism remained unchanged. On- and off- axis eye length measures indicated a relatively prolate eye shape. Correcting the on-axis refractive error in moderate to high myopia with conventional spherical spectacle lenses results in hyperopic defocus in the peripheral retina. Correcting the same eyes with conventional spherical soft contact lenses results in significant myopic defocus in the peripheral retina. These results corroborate the general findings of earlier studies and the predictions of optical modelling by others. If the refractive status of the peripheral retina does influence myopia progression, then these results suggest that myopia progression should be slower with conventional contact lens wear than with conventional spectacle wear. However, previous studies comparing myopia progression with conventional spectacles and conventional contact lenses have reported no such difference.

Myopia: its prevalence, origins and control

To report the results of 12-month wear of three novel spectacle lens designs intended to reduce peripheral hyperopic defocus and one standard design control lens and their effect on the progression of myopia in Chinese children aged 6 to 16 years. Chinese children (n = 210) with myopia (-0.75 D to -3.50 D sphere, cylinder <or=-1.50 D) were randomized to one of four groups wearing either one of three novel spectacle lens designs (types I, II, or III) or conventional, single-vision spectacle lenses. Data were collected at 6 and 12 months. Primary and secondary outcome measures were the changes in central cycloplegic auto-refraction and eye axial length, respectively. Peripheral refraction along the horizontal meridian (nasal and temporal) was taken at baseline with and without spectacle lenses. Multivariate linear regression was used to adjust analyses for important covariates. Progression in eyes wearing control spectacle lenses at 6 and 12 months was -0.55 D +/- 0.35 D and -0.78 +/- 0.50 D, respectively. For the entire group, no statistically significant differences were observed in the rates of progression with the novel designs in comparison to control spectacle lenses. However, in younger children (6 to 12 years) with parental history of myopia (n = 100), there was significantly less progression (-0.68 D +/- 0.47 D vs. -0.97 D +/- 0.48 D) with lens type III compared with control spectacles (mean difference, 0.29 D, std error, 0.11, p = 0.038). There were no statistically significant differences in the rate of progression of myopia between the control and novel lens wearing eyes for the age group 6 to 16 years. The finding of reduced progression of myopia with type III lens design in younger children with parental myopia needs to be validated in a more targeted study.

Progressive myopia is a leading problem in modern optometry and ophthalmology in general. In recent years, refractive therapy with orthokeratology lenses has gained popularity among methods to control myopia progression. The aim: To study peripheral refraction in children with myopia with the use of orthokeratology lenses (OKL) of combined design. Methods. We followed up 60 children (117 eyes) diagnosed with uncomplicated mild to moderate myopia. All children underwent a complete ophthalmological examination as well as corneal keratotopography and peripheral refraction determination. Statistical analysis of correlations between peripheral corneal refraction under the influence of OKL, peripheral defocus, and axial length growth gradient was performed. Results. An inverse correlation relationship of -0.2 (p=0.03) was obtained between corneal differential power in the return 6 mm zone and peripheral refraction in its corresponding peripheral refraction of 23° on the temporal side. A positive correlation with a correlation coefficient of 0.21 (p=0.026) was obtained between the defocus in the temporal part and the gradient of myopia progression over one year, while the same result was obtained in the nasal part with a correlation coefficient of 0.2 (p=0.036). Concluсions. Difference corneal power at the periphery may be prognostic in relation to the course of myopia in OКL users. With an aboveaverage pupil diameter, combined design orthokeratology lenses are more effective in controlling myopia due to the greater influence of the formed corneal refractive ring on peripheral refraction.

The aim of this study is to investigate if baseline relative peripheral refraction (RPR) influences the myopia control effects in Chinese myopic children wearing Defocus Incorporated Multiple Segments (DIMS) lenses. Peripheral refraction at 10°, 20°, and 30° nasal (10 N, 20 N, 30 N) and temporal (10 T, 20 T, 30 T) retina were measured at six-month intervals for children who participated in a 2-year randomized controlled trial. The relationship between the baseline peripheral refractions and myopia progression and axial length changes were analysed. A total of 79 children and 81 children in the DIMS and single vision (SV) group were investigated, respectively. In the DIMS group, more baseline myopic RPR spherical equivalent (SE) was associated with more myopic progression (10 N: r = 0.36, p = 0.001; 20 N: r = 0.35, p = 0.001) and greater axial elongation (10 N: r = −0.34, p = 0.001; 20 N: r = −0.29, p = 0.006) after adjusting for co-factors. In the SV group, baseline RPR had association with only myopia progression (10 N: r = 0.37, p = 0.001; 20 N: r = 0.36, p = 0.001; 30 N: r = 0.35, p = 0.002) but not with axial elongation after Bonferroni correction (p > 0.008). No statistically significant relationship was found between temporal retina and myopia progression or axial elongation in both groups. Children with baseline myopic RPR had statistically significant more myopia progression (mean difference around −0.40 D) and more axial elongation (mean difference 0.15 mm) when compared with the children having baseline hyperopic RPR in the DIMS group but not in the SV group. In conclusion, the baseline RPR profile may not influence future myopia progression or axial elongation for the SV lens wearers. However, DIMS lenses slowed down myopia progression and was better in myopia control for the children with baseline hyperopic RPR than the children with myopic RPR. This may partially explain why myopia control effects vary among myopic children. Customised myopic defocus for individuals may optimise myopia control effects, and further research to determine the optimal dosage, with consideration of peripheral retinal profile, is warranted.

Over the past few decades, the prevalence of myopia has significantly increased, especially in East and Southeast Asian countries, where the prevalence of myopia in school leavers is now around 80%. The risk of myopia related complications such as myopic macular degeneration, retinal detachment, cataract, glaucoma, visual impairment and blindness, all increase with increased severity of myopia without any safe threshold of myopia for any of its known ocular complications.Various specially designed contact lenses and spectacle lenses has been developed to prevent myopic progression. The Orto‐K treatment contact lenses are worn during the night to decrease the corneal refractive power so that during the day you can see far without optical correction. Peripheral hyperopic refraction is assumed to increase the progression of myopia. To correct the relative peripheral hyperopic refraction various contact lenses and glasses have been developed so that the central myopic refractive error is fully corrected and the peripheral refraction corrected to the direction of hyperopia in relation to the central correction.The main aims this presentation is to highlight the chalenges, related to conducting and reporting these studies, and with a few examples show differences between statistically significant and in practice significant treatment benefits.There is a large individual variation in the progression of myopia. Progression of myopia in two same aged myopics with the same myopia can significantly differ from each other. Myopia progresses generally more in the early stages. The most significant factors causing variation in myopia progression are parental myopia, time and intensity spent on near work, time spent outdoors, age of myopia onset, and change in refraction prior to the myopia examination point. Especially the wide range range in baseline refraction and age at the beginning of the research intervention makes reliable randomization challenging. Comparability would be improved if the randomisation to the treatment and control group could be carried out for example half or one year before beginning the treatment intervention. In this way, the potential effects of the natural progression of myopia in study groups could be taken into account.The the difference between treatment and control groups are often reported as percentage benefit, which actually does mean much. For example 50% benefit of treatment can be received from refraction canges 0.1 D vs 0.2 D, which is practicaly nothing or 1.0 D vs. 2.0. It is also important to report in what period of time the benefit of treatment occurs and when the treatment is no longer beneficial, instead of reporting about sustained benefit, when the changes between the groups do not change.Before new therapies are generally introduced, several independent studies on the benefits and potential harms and complications of treatments shuld be conducted with sufficiently large datasets.The presentation discusses, with some practical examples, in more detail about these and other factors potentially affecting on the reliability of clinical studies about myopia treatment.

PurposeTo compare changes in relative peripheral refraction (RPR) associated with myopia progression in myopic children wearing Defocus Incorporated Multiple Segments (DIMS) lenses and single vision (SV) spectacle lenses over 2 years.MethodsA 2-year double-blind, randomized controlled trial was conducted on 183 myopic children. Subjects were allocated to either wearing DIMS (n = 93) or SV spectacle lenses (n = 90). Peripheral refraction at 10°, 20°, and 30° of the nasal (10N, 20N, 30N) and temporal (10T, 20T, 30T) retinal eccentricities, central refraction, and axial length after cycloplegia were monitored every 6 months.ResultsDIMS group showed symmetrical peripheral myopic shifts between the nasal and temporal retina (comparing myopic shifts between the nasal and temporal retina, the difference between the corresponding eccentricities were nonclinically significance). SV group showed asymmetrical peripheral myopic shifts between the nasal and temporal retina, with more myopic shifts (all P ≤ 0.001) at 10T (−0.32 ± 0.62 diopters [D]), at 20T (−0.69 ± 0.95 D), and 30T (−0.85 ± 1.52 D). No significant changes in RPR spherical equivalent (M) were noted in the DIMS group, whereas significant increases (all P < 0.0001) in hyperopic RPR M were observed at 10N (0.27 ± 0.45 D), 20N (0.75 ± 0.72 D), and 30N (0.98 ± 0.76 D) in the SV group.ConclusionsWearing DIMS lenses resulted in a significantly different peripheral refraction profile and RPR changes, as well as significant myopia control effects when compared with SV lenses. Myopia control adopting myopic defocus in the midperiphery influenced peripheral refraction and slowed central myopia progression, most likely through alteration of overall retinal shape.

To compare the patterns of relative peripheral astigmatic refraction (tangential and sagittal power errors) and eccentric eye length between progressing and stable young-adult myopes. Sixty-two right eyes of 62 white patients participated in the study, of which 30 were nonprogressing myopes (NP group) for the last 2 years and 32 were progressing myopes (P group). Groups were matched for mean spherical refraction, axial length, and age. Peripheral refraction and eye length were measured along the horizontal meridian up to 35 and 30 degrees of eccentricity, respectively. There were statistically significant differences between groups (p < 0.001) in the nasal retina for the astigmatic components of peripheral refraction. The P group presented a hyperopic relative sagittal focus at 35 degrees in the nasal retina of +1.00 ± 0.83 diopters, as per comparison with a myopic relative sagittal focus of -0.10 ± 0.98 diopters observed in the NP group (p < 0.001). Retinal contour in the P group had a steeper shape in the nasal region than that in the NP group (t test, p = 0.001). An inverse correlation was found (r = -0.775; p < 0.001) between retinal contour and peripheral refraction. Thus, steeper retinas presented a more hyperopic trend in the periphery. Stable and progressing myopes of matched age, axial length, and central refraction showed significantly different characteristics in their peripheral retinal shape and astigmatic components of tangential and sagittal power errors. The present findings may help explain the mechanisms that regulate ocular growth in humans.

Current methods to slow myopia progression based on the theory of peripheral defocus have shown their efficacy when used as spectacle, contact, and orthokeratology lenses. Spectacle lenses with highly aspherical microlenslets (Stellest®) were introduced into clinical practice in 2020, and their efficacy was rated highly in different studies. AIM: To investigate peripheral defocus imposed by Stellest® spectacle lenses in myopic children. MATERIAL AND METHODS: Peripheral refraction (PR) was evaluated in 42 children (84 eyes) with low-to-moderate myopia. Patients of Group 1 (42 eyes) were examined under cycloplegic conditions, without correction and with HAL spectacle lenses, in the primary position and different directions of gaze, 15° and 30° temporally (T) and nasally (N) from the fovea. Patients of Group 2 (42 eyes) were examined under mydriatic conditions, without correction and with HAL spectacle lenses, 5°, 10°, 15° nasally and temporally from the fovea, in the different directions of gaze. PR was measured using the Grand Seiko WAM-5500 open-field binocular autorefractor. To calculate peripheral defocus, central (axial) refraction was subtracted from the peripheral spherical equivalent taking into account the +/− sign. RESULTS: HAL spectacle lenses reduced hyperopic defocus and imposed a myopic one in all tested areas of the near retinal periphery; the differences at N5 and N10 points were statistically significant (р 0.05). At N15 point ocular movements imposed myopic defocus of −0.26 D (р 0.05). There is also a trend towards a decrease in hyperopic defocus at T15 and N30 points. CONCLUSION: The first study of peripheral refraction with HAL spectacle lenses (Stellest®) helped demonstrate that the lenses imposed myopic defocus on the retinal periphery, with the greatest defocus on the near nasal periphery.

To evaluate the changes in peripheral refraction profiles associated with myopia progression and treatment modalities used in the Cambridge Anti-Myopia Study. one hundred and seventy-seven myopes in the age range of 14 to 22 years were enrolled in the study. The mean spherical equivalent refractive error was 3.12 1.87 diopters (D) and the refractive error of each participant was corrected with contact lenses. The participants were randomly assigned to one of four treatment groups, which included: altered spherical aberration and vision training, altered spherical aberration only, vision training only, and control. Peripheral refractive error was measured using an open field autorefractor in the central 60° of the retina in 10° steps. The refractive error was measured using cycloplegic autorefraction. Two-year refractive progression data and initial peripheral refraction measurements were available in 113 participants. Measurements of peripheral refraction and cycloplegic refraction were obtained at three visits over 2 years in 12-month intervals for 92 participants. All subjects showed a relative peripheral hyperopia, especially in the nasal retina. A limited magnitude of myopia progression of -0.34 ± 0.36 D over 2 years was found in each of the four groups on average. There were no significant differences in the rate of progression between any of the treatment groups (P > 0.05). Initial peripheral J45 astigmatic refractive error at 20° and 30° in the nasal retina was weakly correlated with progression of myopia over 2 years (r = -0.27, P = 0.004 and r = -0.20, P = 0.040, respectively; n = 113). The change in spherical equivalent peripheral refractive error at 30° nasal retina over time was also significantly correlated with progression of myopia especially at 24 months (r = -0.24, P = 0.017, n = 92). Relative peripheral hyperopia is associated with myopia. Myopia progression may be weakly linked to changes in the peripheral refraction profiles in the nasal retina. However, a causative link between peripheral refractive error and myopia progression could not be established.

To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite raytracing. The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes that are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, appears impossible in the majority of cases. The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.

To compare peripheral refraction along both the horizontal and vertical retinal meridians before and after orthokeratology (OK) lens wear. Nineteen young adult myopic subjects (mean age, 28 ± 7 years) were fitted with OK lenses in both eyes. Central and peripheral refraction and corneal topography measurements were taken before and after 14 nights of OK. All measurements were taken with no correction or OK lens in place. At baseline before OK, peripheral spherical equivalent refraction (M) across the horizontal meridian did not vary significantly from center. M across the vertical meridian was more myopic than the center (p < 0.05). After OK, there was a significant hyperopic shift in M (p < 0.001); both meridians now experienced myopic peripheral refraction. At baseline, J180 across the horizontal meridian was more negative than the center, and along the vertical meridian, it was more positive than the center (all p < 0.05). At baseline, J45 was more positive than center with increased eccentricity in the temporal and inferior retina and more negative than center with increased eccentricity in the nasal and superior retina. Orthokeratology caused greater rate of change of peripheral J180 across both retinal meridians (p < 0.001). Furthermore, compared with baseline, J45 became more positive in the nasal and superior retina and more negative in the temporal and inferior retina (all p < 0.05). Orthokeratology lenses induced significant changes in peripheral refraction along the horizontal and vertical meridians. As peripheral myopia was measured at baseline along the vertical meridian, the results of our study suggest that inducing greater degrees of myopic defocus on to the peripheral retina, more than habitually experienced, may be required for effective myopia control. Further investigation into the critical threshold of retinal area receiving myopic defocus and the impact of duration of exposure is necessary to improve the efficacy of current myopia control treatments.