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.

Visual rehabilitation in low-moderate keratoconus : intracorneal ring segment implantation followed by same-day topography-guided photorefractive keratectomy and collagen cross linking

AIM: To present the results of same-day topography-guided photorefractive keratectomy (TG-PRK) and corneal collagen crosslinking (CXL) after previous intrastromal corneal ring segment (ISCR) implantation for keratoconus. METHODS: An experimental clinical study on twenty-one eyes of 19 patients aged, 27.1±6.6 years (range: 19 – 43 years), with low to moderate keratoconus who were selected to undergo customized TG-PRK immediately followed by same-day CXL, 9 months after ISCR implantation in a university ophthalmology clinic. Refraction, uncorrected (UDVA) and corrected distance visual acuities (CDVA), keratometry (K) values, central corneal thickness (CCT) and coma were assessed 3 months after TG/PRK and CXL. RESULTS: After TG-PRK/CXL: the mean UDVA (logMAR) improved significantly from 0.66±0.41 to 0.20±0.25 (P<0.05); K flat value decreased from: 48.44±3.66 D to 43.71±1.95 D; K steep value decreased from 45.61±2.40 D to 41.56±2.05D; K average also decreased from 42.42±2.07 D to 47.00±2.66 D (P<0.05 for all). The mean sphere and cylinder decreased significantly post-surgery from, -3.10±2.99 D to -0.11±0.93 D and from, -3.68±1.53 to -1.11±0.75D respectively, while the CDVA, CCT and coma showed no significant changes. Compared to post-ISCR, significant reductions (P ˂ 0.05 or all) in all K-values, sphere and cylinder were observed after TG-PRK/CXL. CONCLUSION: Same-day combined topography-guided PRK and corneal crosslinking following placement of ICRS is a safe and potentially effective option in treating low-moderate keratoconus. It significantly improved all visual acuity, reduced keratometry, sphere and astigmatism, but caused no change in central corneal thickness and coma.

Effects of pupil center shift on ocular aberrations

Purpose: To investigate effects of pupil shifts, occurring with changes in luminance and accommodation stimuli, on refraction components and higher-order aberrations. Method: Participants were young and older groups (n=20, 22±2 years, age range 18–25 years; n=19, 49±4 years, 45–58 years). Aberrations/refractions at 4 mm and 3 mm diameters were compared between centered and decentered pupils for low (background 0.01cd/m², 0D), and high (6100cd/m², 4D or 6D) stimuli. Decentration was the difference between pupil centers for low and high stimuli. Clinical important changes with decentration were: M ±0.50D or ±0.25D, J180 and J45 ±0.25D or ±0.125D, HORMS ±0.05m, C(3, 1) ±0.05m, C(4, 0) ±0.05m. Results: Because of small pupil shifts in most participants (mean 0.26mm), there were few important changes in most refraction components and higher-order aberration terms. However, M changed by >0.25 D for a third of participants with 4mm pupils. When determining refractions from 2nd-6th order aberration coefficients, the more stringent criteria gave 76/ 534 (14%) possible important changes. Some participants had large pupil shifts with considerable aberration changes. Comparisons at the high stimulus were possible for only 11 participants because of small pupils. When refractions were determined from 2nd order aberration coefficients only, there were only 35 (7%) important changes for the more stringent criteria. Conclusion: Usually pupil shifts with changes in stimulus conditions have little influence on aberrations, but they can with high shifts. The number of aberrations orders that are considered as contributing to refraction influences the proportion of cases that might be considered clinically important.

Visual field coordinates of pupillary circular axis and optical axis

Purpose: We term the visual field position from which the pupil appears most nearly circular as the pupillary circular axis (PCAx). The aim was to determine and compare the horizontal and vertical co-ordinates of the PCAx and optical axis from pupil shape and refraction information for only the horizontal meridian of the visual field. Method: The PCAx was determined from the changes with visual field angle in the ellipticity and orientation of pupil images out to ±90° from fixation along the horizontal meridian for the right eyes of 30 people. This axis was compared with the optical axis determined from the changes in the astigmatic components of the refractions for field angles out to ±35° in the same meridian. Results: The mean estimated horizontal and vertical field coordinates of the PCAx were (‒5.3±1.9°, ‒3.2±1.5°) compared with (‒4.8±5.1°, ‒1.5±3.4°) for the optical axis. The vertical co-ordinates of the two axes were just significantly different (p =0.03) but there was no significant correlation between them. Only the horizontal coordinate of the PCAx was significantly related to the refraction in the group. Conclusion: On average, the PCAx is displaced from the line-of-sight by about the same angle as the optical axis but there is more inter-subject variation in the position of the optical axis. When modelling the optical performance of the eye, it appears reasonable to assume that the pupil is circular when viewed along the line-of-sight.

Landform characterization using geophysics—Recent advances, applications, and emerging tools

This paper presents an overview of the strengths and limitations of existing and emerging geophysical tools for landform studies. The objectives are to discuss recent technical developments and to provide a review of relevant recent literature, with a focus on propagating field methods with terrestrial applications. For various methods in this category, including ground-penetrating radar (GPR), electrical resistivity (ER), seismics, and electromagnetic (EM) induction, the technical backgrounds are introduced, followed by section on novel developments relevant to landform characterization. For several decades, GPR has been popular for characterization of the shallow subsurface and in particular sedimentary systems. Novel developments in GPR include the use of multi-offset systems to improve signal-to-noise ratios and data collection efficiency, amongst others, and the increased use of 3D data. Multi-electrode ER systems have become popular in recent years as they allow for relatively fast and detailed mapping. Novel developments include time-lapse monitoring of dynamic processes as well as the use of capacitively-coupled systems for fast, non-invasive surveys. EM induction methods are especially popular for fast mapping of spatial variation, but can also be used to obtain information on the vertical variation in subsurface electrical conductivity. In recent years several examples of the use of plane wave EM for characterization of landforms have been published. Seismic methods for landform characterization include seismic reflection and refraction techniques and the use of surface waves. A recent development is the use of passive sensing approaches. The use of multiple geophysical methods, which can benefit from the sensitivity to different subsurface parameters, is becoming more common. Strategies for coupled and joint inversion of complementary datasets will, once more widely available, benefit the geophysical study of landforms.Three cases studies are presented on the use of electrical and GPR methods for characterization of landforms in the range of meters to 100. s of meters in dimension. In a study of polygonal patterned ground in the Saginaw Lowlands, Michigan, USA, electrical resistivity tomography was used to characterize differences in subsurface texture and water content associated with polygon-swale topography. Also, a sand-filled thermokarst feature was identified using electrical resistivity data. The second example is on the use of constant spread traversing (CST) for characterization of large-scale glaciotectonic deformation in the Ludington Ridge, Michigan. Multiple CST surveys parallel to an ~. 60. m high cliff, where broad (~. 100. m) synclines and narrow clay-rich anticlines are visible, illustrated that at least one of the narrow structures extended inland. A third case study discusses internal structures of an eolian dune on a coastal spit in New Zealand. Both 35 and 200. MHz GPR data, which clearly identified a paleosol and internal sedimentary structures of the dune, were used to improve understanding of the development of the dune, which may shed light on paleo-wind directions.