Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Higher-order aberrations and anisometropia

Purpose/aim Myopia incidence is increasing around the world. Myopisation is considered to be caused by a variety of factors. One consideration is whether higher-order aberrations (HOA) influence myopisation. More knowledge of optics in anisometropic eyes might give further insight into the development of refractive error. Materials and methods To analyse the possible influence of HOA on refractive error development, we compared HOA between anisometropes and isometropes. We analysed HOA up to the 4th order for both eyes of 20 anisometropes (mean age: 43 ± 17 years) and 20 isometropes (mean age: 33 ±17 years). HOA were measured with the Shack-Hartman i.Profiler (Carl Zeiss, Germany) and were recalculated for a 4 mm pupil. Mean spherical equivalent (MSE) was based on the subjective refraction. Anisometropia was defined as ≥1D interocular difference in MSE. The mean absolute differences between right and left eyes in spherical equivalent were 0.28 ± 0.21 D in the isometropic group and 2.81 ± 2.04 D in the anisometropic group. Interocular differences in HOA were compared with the interocular difference in MSE using correlations. Results For isometropes oblique trefoil, vertical coma, horizontal coma and spherical aberration showed significant correlations between the two eyes. In anisometropes all analysed higher-order aberrations correlated significantly between the two eyes except oblique secondary astigmatism and secondary astigmatism. When analysing anisometropes and isometropes separately, no significant correlations were found between interocular differences of higher-order aberrations and MSE. For isometropes and anisometropes combined, tetrafoil correlated significantly with MSE in left eyes. Conclusions The present study could not show that interocular differences of higher-order aberrations increase with increasing interocular difference in MSE.

Visual performance with lenses correcting peripheral refractive errors

Purpose To design and manufacture lenses to correct peripheral refraction along the horizontal meridian and to determine whether these resulted in noticeable improvements in visual performance. Method Subjective refraction of a low myope was determined on the basis of best peripheral detection acuity along the horizontal visual field out to ±30° for both horizontal and vertical gratings. Subjective refraction was compared to objective refractions using a COAS-HD aberrometer. Special lenses were made to correct peripheral refraction, based on designs optimized with and without smoothing across a 3 mm diameter square aperture. Grating detection was retested with these lenses. Contrast thresholds of 1.25’ spots were determined across the field for the conditions of best correction, on-axis correction, and the special lenses. Results The participant had high relative peripheral hyperopia, particularly in the temporal visual field (maximum 2.9 D). There were differences > 0.5D between subjective and objective refractions at a few field angles. On-axis correction reduced peripheral detection acuity and increased peripheral contrast threshold in the peripheral visual field, relative to the best correction, by up to 0.4 and 0.5 log units, respectively. The special lenses restored most of the peripheral vision, although not all at angles to ±10°, and with the lens optimized with aperture-smoothing possibly giving better vision than the lens optimized without aperture-smoothing at some angles. Conclusion It is possible to design and manufacture lenses to give near optimum peripheral visual performance to at least ±30° along one visual field meridian. The benefit of such lenses is likely to be manifest only if a subject has a considerable relative peripheral refraction, for example of the order of 2 D.

Children’s accommodation during reading of Chinese and English texts

Purpose: Inaccurate accommodation during nearwork and subsequent accommodative hysteresis may influence myopia development. Myopia is highly prevalent in Singapore; an untested theory is that Chinese children are prone to these accommodation characteristics. We measured the accuracy of accommodation responses during and nearwork-induced transient myopia (NITM) after periods spent reading Chinese and English texts. Methods: Refractions of 40 emmetropic and 43 myopic children were measured with a free-space autorefractor for four reading tasks of 10-minute durations: Chinese (SimSun, 10.5 points) and English (Times New Roman, 12 points) texts at 25 cm and 33 cm. Accuracy was obtained by subtracting accommodation response from accommodation demand. Nearwork-induced transient myopia was obtained by subtracting pretask distance refraction from posttask refraction, and regression was determined as the time for the posttask refraction to return to pretask levels. Results: There were significant, but small, effects of text type (Chinese, 0.97 ± 0.32 diopters [D] vs. English, 1.00 ± 0.37 D; F1,1230 = 7.24, p = 0.007) and reading distance (33 cm, 1.01 ± 0.30 D vs. 25 cm, 0.97 ± 0.39 D; F1,1230 = 7.74, p = 0.005) on accommodation accuracy across all participants. Accuracy was similar for emmetropic and myopic children across all reading tasks. Neither text type nor reading distance had significant effects on NITM or its regression. Myopes had greater NITM (by 0.07 D) (F1,81 = 5.05, p = 0.03) that took longer (by 50s) (F1,81 = 31.08, p < 0.01) to dissipate. Conclusions: Reading Chinese text caused smaller accommodative lags than reading English text, but the small differences were not clinically significant. Myopic children had significantly greater NITM and longer regression than emmetropic children for both texts. Whether differences in NITM are a cause or consequence of myopia cannot be answered from this study.

Letter to the editor

We read with interest the article entitled ‘Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality’ by Amanda C Kingston and Ian G Cox (2013). The authors provided higher order aberrations data for a sample of 1124 eyes and performed correlation analyses to compare higher order aberrations with refraction and biometry data, such as spherical equivalent power and corneal curvature. Special attention was drawn to spherical aberration...

Age-dependence of the average and equivalent refractive indices of the crystalline lens

Lens average and equivalent refractive indices are required for purposes such as lens thickness estimation and optical modeling. We modeled the refractive index gradient as a power function of the normalized distance from lens center. Average index along the lens axis was estimated by integration. Equivalent index was estimated by raytracing through a model eye to establish ocular refraction, and then backward raytracing to determine the constant refractive index yielding the same refraction. Assuming center and edge indices remained constant with age, at 1.415 and 1.37 respectively, average axial refractive index increased (1.408 to 1.411) and equivalent index decreased (1.425 to 1.420) with age increase from 20 to 70 years. These values agree well with experimental estimates based on different techniques, although the latter show considerable scatter. The simple model of index gradient gives reasonable estimates of average and equivalent lens indices, although refinements in modeling and measurements are required.

Pupil shape as viewed along the horizontal visual field

Purpose: Changes in pupil size and shape are relevant for peripheral imagery by affecting aberrations and how much light enters and/or exits the eye. The purpose of this study is to model the pattern of pupil shape across the complete horizontal visual field and to show how the pattern is influenced by refractive error. Methods: Right eyes of thirty participants were dilated with 1% cyclopentolate and images were captured using a modified COAS-HD aberrometer alignment camera along the horizontal visual field to ±90°. A two lens relay system enabled fixation at targets mounted on the wall 3m from the eye. Participants placed their heads on a rotatable chin rest and eye rotations were kept to less than 30°. Best-fit elliptical dimensions of pupils were determined. Ratios of minimum to maximum axis diameters were plotted against visual field angle. Results: Participants’ data were well fitted by cosine functions, with maxima at (–)1° to (–)9° in the temporal visual field and widths 9% to 15% greater than predicted by the cosine of the field angle . Mean functions were 0.99cos[( + 5.3)/1.121], R2 0.99 for the whole group and 0.99cos[( + 6.2)/1.126], R2 0.99 for the 13 emmetropes. The function peak became less temporal, and the width became smaller, with increase in myopia. Conclusion: Off-axis pupil shape changes are well described by a cosine function which is both decentered by a few degrees and flatter by about 12% than the cosine of the viewing angle, with minor influences of refraction.

Diurnal variations in ocular aberrations of human eyes

Purpose: To investigate the diurnal variations in ocular wavefront aberrations over two consecutive days in young adult subjects. Materials and methods: Measurements of both lower-order (sphero-cylindrical refractive powers) and higher-order (3rd and 4th order aberration terms) ocular aberrations were collected for 30 young adult subjects at ten different times over two consecutive days using a Hartmann-Shack aberrometer. Fifteen subjects were myopic and 15 were emmetropic. Five sets of measurements were collected each day at approximately 3 hourly intervals, with the first measurement taken at ~9 am and the final measurement at ~9 pm. Results: Spherical equivalent refraction (p = 0.029) and spherical aberration (p = 0.043) were both found to undergo significant diurnal variation over the two measurement days. The spherical equivalent was typically found to be at a maximum (i.e. most hyperopic) at the morning measurement, with a small myopic shift of 0.37 ± 0.15 D observed over the course of the day. The mean spherical aberration of all subjects (0.038 ± 0.048 μm) was found to be positive during the day and gradually became more negative into the evening, with a mean amplitude of change of 0.036 ± 0.02 μm. None of the other considered sphero-cylindrical refractive power components or higher-order aberrations exhibited significant diurnal variation over the two days of the experiment (p>0.05). Except for the lower-order astigmatism at 90/180 deg (p = 0.040), there were no significant differences between myopes and emmetropes in the magnitude and timing of the observed diurnal variations (p>0.05). Conclusions: Significant diurnal variations in spherical equivalent and spherical aberration were consistently observed over two consecutive days of measurement. Research and clinical applications requiring precise refractive error and wavefront measurements should take these diurnal changes into account when interpreting wavefront data.

Cataract surgery in eyes with low corneal astigmatism : implantation of the AcrySof IQ Toric SN6AT2 intraocular lens

Purpose The aim of this study is to assess the refractive and visual outcomes following cataract surgery and implantation of the AcrySof IQ Toric SN6AT2 intraolcular lens (IOL) (Alcon Laboratories, Inc) in patients with low corneal astigmatism. Materials and Methods A retrospective, consecutive, single surgeon series of ninety-eight eyes of 88 patients following cataract surgery and implantation of the AcrySof IQ Toric SN6AT2 IOL in eyes with low preoperative corneal astigmatism. Postoperative measurements were obtained at one month post surgery. Main outcome measures were monocular distance visual acuity and residual refractive astigmatism. Results The mean preoperative corneal astigmatic power vector (APV) was 0.38 ± 0.09 D. Following surgery and implantation of the toric IOL, mean postoperative refractive APV was 0.13 ± 0.10 D. Mean postoperative distance uncorrected visual acuity (UCVA) was 0.08 ± 0.09 logMAR. Postoperative spherical equivalent refraction (SER) resulted in a mean of - 0.23 ± 0.22 D, with 96% of eyes falling within 0.50 D of the target SER. Conclusions The AcrySof IQ Toric SN6AT2 IOL is a safe and effective option for eyes undergoing cataract surgery with low amounts of preoperative corneal astigmatism.

Using pulse transit delay in Z-scan to discriminate between excited-state absorption and other nonlinear processes in ZnO nanocones

We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.

Myopic anisometropia : ocular characteristics and aetiological considerations

Anisometropia represents a unique example of ocular development, where the two eyes of an individual, with an identical genetic background and seemingly subject to identical environmental influences, can grow asymmetrically to produce significantly different refractive errors. This review provides an overview of the research examining myopic anisometropia, the ocular characteristics underlying the condition and the potential aetiological factors involved. Various mechanical factors are discussed, including corneal structure, intraocular pressure and forces generated during near work that may contribute to development of anisomyopia. Potential visually guided mechanisms of unequal ocular growth are also explored, including the influence of astigmatism, accommodation, higher-order aberrations and the choroidal response to altered visual experience. The association between binocular vision, ocular dominance and asymmetric refraction is also considered, along with a review of the genetic contribution to the aetiology of myopic anisometropia. Despite a significant amount of research into the biomechanical, structural and optical characteristics of anisometropic eyes, there is still no unifying theory, which adequately explains how two eyes within the same visual system grow to different endpoints.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Inhibition of form-deprivation myopia by a GABAAOr receptor antagonist, (1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA), in guinea pigs

Purpose To investigate the effects of the relatively selective GABAAOr receptor antagonist (1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA) on form-deprivation myopia (FDM) in guinea pigs. Methods A diffuser was applied monocularly to 30 guinea pigs from day 10 to 21. The animals were randomized to one of five treatment groups. The deprived eye received daily sub-conjunctival injections of 100 μl TPMPA at a concentration of (i) 0.03 %, ( ii) 0.3 %, or (iii) 1 %, a fourth group (iv) received saline injections, and another (v) no injections. The fellow eye was left untreated. An additional group received no treatment to either eye. Prior to and at the end of the treatment period, refraction and ocular biometry were performed. Results Visual deprivation produced relative myopia in all groups (treated versus untreated eyes, P < 0.05). The amount of myopia was significantly affected by the drug treatment (one-way ANOVA, P < 0.0001); myopia was less in deprived eyes receiving either 0.3 % or 1 % TPMPA (saline = −4.38 ± 0.57D, 0.3 % TPMPA = −3.00 ± 0.48D, P < 0.01; 1 % TPMPA = −0.88 ± 0.51D, P < 0.001). The degree of axial elongation was correspondingly less (saline = 0.13 ± 0.02 mm, 0.3 % TPMPA = 0.09 ± 0.01 mm, P < 0.01, 1 % TPMPA = 0.02 ± 0.01 mm, P < 0.001) as was the VC elongation (saline = 0.08 ± 0.01 mm, 0.3 % TPMPA = 0.05 ± 0.01 mm, P < 0.01, 1 % TPMPA = 0.01 ± 0.01 mm; P < 0.001). ACD and LT were not affected (one-way ANOVA, P > 0.05). One percent TPMPA was more effective at inhibiting myopia than 0.3 % (P < 0.01), and 0.03 % did not appreciably inhibit the myopia (0.03 % TPMPA versus saline, P > 0.05). Conclusions Sub-conjunctival injections of TPMPA inhibit FDM in guinea pig models in a dose-dependent manner.

Cone Ratios in Myopia and Emmetropia: A Pilot Study

Purpose There is a suggestion that the long wavelength-sensitive (LWS)-to-middle wavelength-sensitive (MWS) cone ratio in the retina is associated with myopia. The aim was to measure the LWS/MWS amplitude modulation ratio, an estimate of the LWS/MWS cone ratio, in young adult emmetropes and myopes. Methods Multifocal visual evoked potentials were measured when the LWS and MWS cone systems were excited separately using the method of silent substitution. The 30 young adult participants (22 to 33 years) included 10 emmetropes (mean [±SD] refraction, +0.3 [±0.4] diopters [D]) and 20 myopes (mean [±SD] refraction, -3.4 [±1.7] D). Results The LWS/MWS amplitude modulation ratios ranged from 0.56 to 1.80 in the central 3- to 13-degree diameter ring and from 0.94 to 1.91 in the peripheral 13- to 30-degree diameter ring. Within the central ring, the mean (±SD) ratios were 1.20 (±0.26) and 1.20 (±0.33) for the emmetropic and the myopic groups, respectively. For the peripheral ring, the mean (±SD) ratios were 1.48 (±0.27) and 1.30 (±0.27), respectively. There were no significant differences in the ratios between the emmetropic and myopic groups for either the central (p = 0.99) or peripheral (p = 0.08) rings. For the latter, more myopic refractive error was associated with lower LWS/MWS amplitude modulation ratio; the refraction explained 16% (p = 0.02) of variation in ratio. Conclusions The relationship between the LWS/MWS amplitude modulation ratios and refraction at 13 to 30 degrees indicates that a large longitudinal study of changes in refraction in persons with known cone ratio is required to determine if a low LWS/MWS cone ratio is associated with myopia development.