Share this article on:

Sustained Convergence, Axial Length, and Corneal Topography

Read, Scott A.*; Collins, Michael J.; Cheong, Shiow-Huoy; Woodman, Emily C.§

doi: 10.1097/OPX.0b013e3181c07923
Original Article

Purpose. To investigate the influence of convergence on axial length and corneal topography in young adult subjects.

Methods. Fifteen emmetropic young adult subjects with normal binocular vision had axial length and corneal topography measured immediately before and after a 15-min period of base out (BO) prismatic spectacle lens wear. Two different magnitude prismatic spectacles were worn in turn (8 Δ BO and 16 Δ BO), and for both tasks, distance fixation was maintained for the duration of lens wear. Eight subjects returned on a separate day for further testing and had axial length measured before, during, and immediately after a 15-min convergence task.

Results. No significant change was found to occur in axial length either during or after the sustained convergence tasks (p > 0.6). Some small but significant changes in corneal topography were found to occur after sustained convergence. The most significant corneal change was observed after the 16 Δ BO prism wear. The corneal refractive power spherocylinder power vector J0 was found to change by a small (mean change of 0.03 D after the 16 Δ BO task) but statistically significant (p = 0.03) amount as a result of the convergence task (indicative of a reduction in with-the-rule corneal astigmatism after convergence). Corneal axial power was found to exhibit a significant flattening in superior regions.

Conclusions. Axial length appears largely unchanged by a period of sustained convergence. However, small but significant changes occur in the topography of the cornea after convergence.





Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Queensland, Australia.

A number of internal and external forces normally act on the eye, including the intraocular pressure, eyelid pressure, and forces from the eye's internal musculature (e.g., ciliary muscle) and extraocular muscles (EOMs). Previous research has shown that changes in some of these forces can lead to alterations in certain ocular optical and biometric parameters. Changes in intraocular pressure can lead to alterations in the eye's axial length.1–3 Changing the position or tension of the eyelids is known to lead to changes in astigmatism and corneal shape.4–6 Ciliary muscle contraction has also been found to be associated with small but significant increases in the eye's axial length.7,8

The forces generated by the eye's EOMs can be substantial,9,10 and as the global portion of the EOMs inserts into the sclera,11,12 with the rectus muscles typically inserting within relatively close proximity to the limbus,13 alterations in EOM forces have the potential to lead to changes in axial length and/or corneal shape. There have been relatively limited studies directly investigating the influence of EOM forces on corneal shape or ocular biometric parameters. Early investigations into the influence of convergence on the cornea using keratometry or photokeratoscopy were not conclusive, with some studies reporting small changes in corneal curvature with convergence14,15 and others finding no corneal change.16 More recently, there have been reports of significant changes in corneal topography after EOM surgical procedures that imply changes in EOM forces may significantly influence corneal shape.17–19

Whether altered EOM forces can lead to changes in ocular biometric parameters, such as eye length, is of particular interest to research into myopia development, given that near work is a known risk factor for the development of myopia,20 and convergence is one of the ocular changes that normally occur when near work is performed. It has been theorized that the mechanical effects of the EOMs during convergence may be an important factor involved in the axial elongation associated with myopia development21; however, there have only been limited studies directly investigating the influence of EOM forces on ocular biometric parameters such as axial length. Bayramlar et al.22 inferred that convergence may underlie increases in axial length associated with near work, as they noted significant axial length elongation to occur in young subjects as a result of near fixation, both with and without cycloplegia.22

Given the relatively limited amount of research directly investigating the influence of EOMs on both corneal shape and eye length, we aimed to investigate the influence of sustained convergence on corneal topography and axial length in a population of young adult subjects.

Back to Top | Article Outline


Fifteen young adult subjects aged from 20 to 31 years (mean age 26 ± 3 years) participated in this study. Subjects were recruited primarily from the students and staff of our university. Seven of the 15 subjects were female, and all subjects exhibited refractions close to emmetropia (mean best sphere refraction −0.1 D ± 0.6 D range + 0.87 to −1.13) normal visual acuity of log minimum angle of resolution 0.00 or better (mean best corrected log minimum angle of resolution visual acuity −0.08 ± 0.09), and no history of strabismus or amblyopia. No subjects had any history of ocular pathology or prior ocular injuries or surgery. Approval from the university human research ethics committee was obtained before commencement of the study. All subjects gave written informed consent to participate and were treated in accordance with the declaration of Helsinki.

As the parameters measured in the study are known to undergo some diurnal variation23,24 and can be influenced by prior visual tasks,5 testing for all subjects was carried out between 10 am and 4 pm at least 2 h after waking, and subjects were advised to refrain from substantial reading before the measurements. All subjects underwent an initial screening examination to determine their refractive status and ensure normal ocular health and binocular vision. A series of clinical binocular vision tests were carried out on each subject including: measures of distance heterophoria (maddox rod technique), near heterophoria (Howell-Dwyer card), stereoacuity (TNO test), near point of convergence, and monocular and binocular amplitude of accommodation (push-up method).

After these initial screening measures, a protocol using base out (BO) prismatic spectacles was carried out to investigate the influence of sustained convergence on axial length and corneal topography. All measurements were carried out on each subject's right eye only. All axial length measures were taken using the Zeiss IOLMaster (Zeiss Meditec, Jena, Germany), a noncontact optical biometer based on the principle of partial coherence interferometry that has previously been shown to provide highly precise measures of axial length.25 At each measurement session, a total of five valid axial length measures were collected (i.e., measures with a signal to noise ratio of >2). Corneal topography measures were carried out using the Medmont E300 videokeratoscope (Medmont Pty, Victoria, Australia). This instrument is based on the placido disc principle and has been shown to be highly accurate and repeatable.26,27 At each of the measurement sessions, four videokeratoscope measures were captured for each subject. The Medmont E300 provides a score for each measure based on the focus, centering, and movement in the image (from 0 to 100), and for this study, only measures exhibiting scores of 95 or greater were saved. The axial length and corneal topography data were always collected in the same order, with the axial length measured first.

Each subject had their axial length and corneal topography measured immediately before and then immediately after they wore 8 Δ BO prismatic spectacles (in conjunction with their best distance spherocylindrical correction) while maintaining distance fixation (i.e., viewing a television at a distance of 5 m) for a period of 15 min, and then immediately before and immediately after they wore 16 Δ BO prismatic spectacles with distance viewing for a period of 15 min. The magnitude of prism used in this study (8 Δ BO and 16 Δ BO) were chosen to represent the approximate angle of convergence for intermediate (i.e., ∼4.5°) and near tasks (∼9°). Previous studies of near work induced corneal and ocular optical changes, typically find the majority of change to have subsided 10 to 15 min after the task.28,29 Therefore, to ensure that prior visual tasks did not influence our results, before the 8 Δ BO prism wear, a period of 15 min of relaxed distance viewing with no prism was carried out, and in between the post 8 Δ BO measures and the pre 16 Δ BO measures, a period of 20 min of distance viewing with no prism correction was undertaken, to allow any residual effects of the 8 Δ BO prism wear to subside. Throughout the duration of prism spectacle wear, subjects were advised to maintain clear single binocular vision and to report any occurrence of diplopia. As distance viewing was maintained for the prism tasks, the eyes were required to converge with accommodation relaxed to maintain clear single vision. Therefore, this prismatic spectacle task allowed the effects of convergence to be investigated without being confounded by substantial concomitant accommodation. To limit crossover effects between the two tasks, the higher magnitude prism correction was always worn last, along with the preceding 20-min distance viewing task without convergence demand.

To further examine the potential influence of convergence on axial length, a subset of eight of the original 15 subjects returned for additional testing on a separate day. On the second day of testing, a high-quality, antireflection-coated prism of power 17.6 Δ (i.e., 10° deviation) (Edmund Optics, Singapore) mounted in a trial frame was used. The use of this prism allowed reliable measurements of axial length to be acquired during the convergence task. Before testing, we confirmed that the presence of the prism in front of the instrument did not influence the accuracy or repeatability of the axial length measures (no significant difference was found in the measured length of the IOLMaster test eye with and without the prism in place). The procedure carried out on this subset of subjects was as follows. Before any measures, each subject observed a 15-min period of relaxed distance viewing (with no prism) after which, baseline (i.e., preconvergence) measures of axial length were carried out. Subjects then wore the trial frame with the prism mounted BO in front of the right eye, and once subjects attained clear single vision, they continued distance viewing for 60 s, and a measurement of axial length was then carried out while the subject viewed the instrument's fixation target through the prism (i.e., the measurement was collected through the prism as the subject continued to converge). The subjects then continued to maintain distance fixation for a further 15 min, wearing the prismatic spectacles. After 15 min, another measure of axial length was carried out through the prism spectacles. After this measurement, subjects removed the prismatic spectacles, and a final (postconvergence) measurement of axial length was carried out with no prism in place. This protocol allowed pre and postconvergence measures, along with measurements of axial length during convergence (after 1 min and after 15 min of convergence) to be carried out. The average standard deviation of change in axial length from the first phase of the study (i.e., the measurements captured immediately after convergence) was ∼13 μm; therefore, a sample of eight subjects has 80% power to detect a 19 μm change in axial length, whereas a sample size of 15 would have an 80% power to detect an 14 μm change in axial length.

Back to Top | Article Outline

Data Analysis

The average prewear and postwear axial length measurements for the 8 Δ and 16 Δ BO prism conditions were calculated for each subject. The raw corneal topography data from each measurement session from before and after the 8 Δ and 16 Δ BO prism conditions were also exported from the videokeratoscope and analyzed using custom written software. Each of the four corneal refractive power, axial curvature, and elevation maps from the pre and post 8 Δ and 16 Δ BO task measurement sessions were analyzed to calculate average maps for each measurement session for each subject.

A range of analyses were carried out on the corneal topography average maps to investigate for significant corneal change associated with the convergence tasks. For each of the average corneal refractive power maps (i.e., the pre and post 8 Δ and 16 Δ BO prism maps), the best fitting corneal spherocylinder was calculated using the method of Maloney et al.30 for each subject's average map from each measurement session. The best fit corneal spherocylinder was then converted into the power vectors M (best sphere), J0 (astigmatism 90/180°), and J45 (astigmatism 45/135°).31

Each average corneal axial curvature maps were first converted into axial power (assuming a corneal refractive index of 1.376), and the axial power maps were analyzed to calculate the average corneal axial power within eight equal sized 45° segments. This analysis allowed the average change in axial power after the 8 Δ and 16 Δ BO tasks, to be calculated for the nasal, superior nasal, superior, superior temporal, temporal, inferior-temporal, inferior, and inferior nasal corneal regions.

To investigate for changes in higher order corneal surface shape, the corneal height data was fit with Zernike polynomials using a least squares fitting method.32 Zernike surface polynomials were fit up to the eighth radial order and expressed in OSA notation.33 We have previously found that the third and fourth order Zernike corneal surface polynomials are typically the coefficients exhibiting the highest magnitude in the normal population; therefore, our analysis of the corneal surface concentrated on these higher order polynomial terms.34

The corneal refractive power, corneal axial power, and corneal height analyses were all carried out for both 4 and 6 mm analysis diameters. Repeated measures analyses of variance (ANOVAs) were used to investigate for significant change in axial length and the corneal topography characteristics as a result of the 8 Δ and 16 Δ BO prismatic spectacle wear. Similarly, with the additional data collected on the second day of testing, repeated measures ANOVA was also used to investigate for change in axial length during and after the 15-min convergence task.

Back to Top | Article Outline


The refractive and binocular vision characteristics of the population are presented in Table 1. All subjects were close to emmetropic and exhibited normal binocular vision. Distance and near heterophoria, near point of convergence, stereoacuity, and amplitudes of accommodation for all subjects were within clinically acceptable normal limits for young adult subjects.35–37



Fig. 1 illustrates the mean axial length before and after the 8 Δ BO and 16 Δ BO prism tasks. Repeated measures ANOVA revealed no significant change in axial length as a result of the prism spectacle wear (p = 0.957). The mean change in axial length after15 min wear of 8 Δ BO prism was 0.003 ± 0.01 mm, and after 16Δ BO prism was −0.003 ± 0.01 mm. The majority of subjects exhibited axial length changes of <10 μm after the sustained convergence task.



Inspection of each subject's corneal axial curvature maps revealed small regions of corneal topographical change for some subjects after the prismatic spectacle wear. The corneal changes typically manifested as horizontal regions of distortion located in the superior and/or inferior peripheral cornea that were usually more prominent after the 16 Δ BO task. Fig. 2 illustrates the changes observed in the axial curvature maps before and after the 16 Δ BO prism task of a representative subject (subject 13), in combination with digital images of the subject's right eye in primary gaze and while wearing the 16 Δ BO prism. Eight of the 15 subjects exhibited similar regions of corneal change.



Analysis of the corneal refractive power spherocylinder revealed some small but statistically significant changes occurring in corneal astigmatism as a result of the prism task. Table 2 displays the mean pre and posttask corneal power vectors and p values from the repeated measures ANOVA. No significant changes were found in the corneal best sphere M or astigmatic power vector J45 as a result of the convergence tasks. However, astigmatic power vector J0 was found to exhibit a significant decrease as a result of the prismatic lens wear (p = 0.03). This is indicative of a small decrease in corneal with the rule astigmatism occurring after the sustained convergence task. Fig. 3 displays the mean change in each of the corneal power vectors for the 6 mm diameter analysis as a result of the convergence tasks. It is evident that the most substantial change occurred in astigmatic power vector J0 after the 16 Δ BO task. The average corneal spherocylinder (6 mm diameter analysis) before the 8 Δ BO task was 49.11/−0.58 × 170 and after the task was 49.09/−0.58 × 170. The average corneal spherocylinder (6 mm diameter analysis) before the 16 BO task was 49.13/−0.60 × 170 and after the task was 49.07 to 0.53 × 170.





The average corneal axial power in a number of the analyzed corneal segments was also found to undergo small but significant change as a result of the convergence tasks. Fig. 4 displays the change observed in corneal axial power within the eight different corneal segments examined, respectively, for the 6 mm analysis diameter. Similar trends were observed for the 4 mm diameter analysis. It is evident from Fig. 4 that the majority of change in axial power occurred after the 16 Δ BO prism task. A small but significant flattening was evident in the superior nasal (mean change −0.07 D after the 16 BO task, p = 0.02), superior temporal (mean change −0.12 D, p = 0.0001), and superior (mean change −0.06 D, p = 0.02) corneal regions after the 16 BO task. The slight steepening observed in the inferior nasal segment after the 16 Δ BO task (mean change +0.05 D, p = 0.1) was not statistically significant at this sample size.



Analysis of the higher order corneal surface Zernike coefficients revealed a small but statistically significant change occurring in the vertical coma term (Z3 −1) as a result of the prismatic spectacle wear (p = 0.004). The changes observed in vertical coma are consistent with the significant change observed in the corneal axial power in the superior corneal regions. The remaining third and fourth-order Zernike coefficients exhibited smaller magnitudes of change that were not statistically significant. Similar trends were observed for both the 4 and 6 mm diameter analyses. Fig. 5 illustrates the mean change in the third and fourth order Zernike coefficients after the 8 Δ BO and 16 Δ BO prism tasks. As with the axial power and corneal spherocylinder data, the largest changes in vertical coma were observed after the 16 Δ BO task. For the 6 mm analysis, the magnitude of change in vertical coma (Z3 −1) after the 16 Δ BO task represents 23% of the mean baseline magnitude of the coefficient.



The results from the smaller sample of eight subjects who returned for the second day of testing for measurements of axial length before, during, and after the 15-min convergence task are presented in Table 3. Repeated measures ANOVA revealed no significant change in axial length as a result of the convergence task (p = 0.65). Pairwise comparisons with Bonferroni correction revealed no significant difference in axial length between the preconvergence measures and any of the “during-” or “post” convergence measurements (p > 0.9).



Back to Top | Article Outline


We have investigated the influence of sustained convergence, brought about through the wearing of prismatic spectacles on the eye's axial length and corneal topography. We found no significant change to occur in the eye's axial length as a result of these sustained convergence tasks. Our findings suggest that the changes in EOM forces brought about by sustained convergence for 15 min are not sufficient to significantly alter eye length. The primary muscles involved in convergence are the horizontal rectus muscles, and the global layer of these muscles are thought to insert into the sclera at a point ∼5.5 mm (for the medial rectus) and ∼7.0 mm (for the lateral rectus) from the limbus.13 The relative anterior location of the scleral muscle insertion may therefore mean that alterations in muscle force of the horizontal rectus muscles have relatively limited influence on posterior eye length.

It has been suggested that EOM forces generated during convergence may be involved in the axial elongation of the globe in myopia.21,38 The lack of change observed both during and immediately after the 15 min of sustained convergence in our current study suggests that the mechanical influence of the EOMs on eye length during convergence is relatively small. However, we cannot discount the possibility that larger magnitudes of convergence or convergence sustained for longer periods of time could potentially lead to changes in eye length. The task involved in our current study involved sustained convergence while subjects maintained distance fixation. During reading, subjects typically converge, accommodate, and also use eye movements. Studies of EOM forces have found that the forces generated by saccadic eye movements are substantially greater than those required to maintain the eye in an off-axis position.9 Therefore, it is probable that the EOM forces generated during a typical reading task will be different to those induced by the sustained convergence task in our experiment, and the influence of reading eye movements on eye length may be an area worthy of further investigation.

Previous studies using similar high-resolution instruments for axial length measurements (i.e., optical biometry based on partial coherence interferometry) have noted small (mean reported axial elongation ranged from 5.2 to 58 μm) but significant increases in the axial length to accompany near viewing in young subjects.7,8 Our findings would suggest that these previously reported changes in axial length with near viewing are primarily due to ciliary muscle contraction as opposed to any concomitant changes in the EOMs associated with near viewing. However, another study using A-scan ultrasonography also investigated changes in axial length associated with near viewing and attributed the measured axial elongation with near viewing (mean elongation reported was 180 μm) to the effects of convergence, as elongation was observed both with and without cycloplegia.22 The changes observed by Bayramlar et al.22 are substantially larger than those found in any subject in our current study during or after sustained convergence activity and are also larger than the changes in axial length recently reported to accompany accommodation.8 As Bayramlar et al.22 assessed a larger amount of convergence, it leaves open the possibility that transient axial length changes may occur with higher levels of convergence.

In contrast to our axial length findings, we did find significant corneal topographical changes to occur after the convergence tasks. The changes that we have observed in the corneal topography appear at least in part due to changes in the position of the eyelids relative to the cornea accompanying the convergence task, as illustrated in Fig. 2. When the eyes converge, the cornea moves relatively nasally with respect to the palpebral fissure, which effectively brings the lids closer to corneal center. Previous investigations have found similar (although typically larger magnitude) corneal topographical changes to occur as a result of the interaction between the eyelids and the cornea in downward gaze.5,39 These previous studies have also noted comparable changes in corneal astigmatism (a shift toward against-the-rule astrigmatism) and vertical coma as a result of eyelid forces in downward gaze to what we have observed in our subjects after sustained convergence. The changes that we have observed in the superior cornea are therefore unlikely to be directly related to EOM forces and are most likely to be due to altered interaction between the eyelids and the cornea associated with convergence. However, the slight steepening found in the nasal cornea that we also observed may be related to changes in the forces from the horizontal rectus muscles associated with convergence.

The corneal changes that we have found with sustained convergence were statistically significant but were generally of a relatively small magnitude. This magnitude of change after a 15-min sustained convergence task is unlikely to substantially influence vision or clinical measures of corneal topography. However, it remains a possibility that larger amounts of convergence sustained for longer periods of time could lead to larger corneal changes than we have observed. Our findings of significant corneal change after sustained convergence may have implications for longer term changes in corneal shape. It has been established that corneal astigmatism typically shifts from a predominance of with-the-rule (i.e., where the steepest corneal meridian is oriented approximately vertically) in young adult subjects, to a predominance of against-the-rule astigmatism (i.e., where the steepest corneal meridian is oriented approximately horizontally) in older adult subjects.40–42 The change that we observed in corneal astigmatism after the convergence task was in the direction of less with-the-rule astigmatism in our population of young adult subjects. This leaves open the possibility that corneal changes due to convergence over a long period of time may contribute to the shift toward against-the-rule corneal astigmatism that typically occurs in older adult subjects.

In conclusion, we have found no significant change in eye length to accompany sustained convergence. However, some small but statistically significant changes were evident in corneal topography after sustained convergence.

Back to Top | Article Outline


Received June 16, 2009; accepted August 31, 2009.

Scott A. Read

Contact Lens and Visual Optics Laboratory

School of Optometry

Queensland University of Technology

Room B556, O Block

Victoria Park Road, Kelvin Grove

Brisbane, Queensland 4059, Australia


Back to Top | Article Outline


1.Cashwell LF, Martin CA. Axial length decrease accompanying successful glaucoma filtration surgery. Ophthalmology 1999;106:2307–11.
2.Leydolt C, Findl O, Drexler W. Effects of change in intraocular pressure on axial eye length and lens position. Eye 2008;22:657–61.
3.Ebneter A, Wagels B, Zinkernagel MS. Non-invasive biometric assessment of ocular rigidity in glaucoma patients and controls. Eye 2009;23:606–11.
4.Grey C, Yap M. Influence of lid position on astigmatism. Am J Optom Physiol Opt 1986;63:966–9.
5.Buehren T, Collins MJ, Carney L. Corneal aberrations and reading. Optom Vis Sci 2003;80:159–66.
6.Collins MJ, Voetz SC, Bretschneider N. The biomechanics of rigid contact lens removal. Cont Lens Anterior Eye 2005;28:121–5.
7.Drexler W, Findl O, Schmetterer L, Hitzenberger CK, Fercher AF. Eye elongation during accommodation in humans: differences between emmetropes and myopes. Invest Ophthalmol Vis Sci 1998;39:2140–7.
8.Mallen EA, Kashyap P, Hampson KM. Transient axial length change during the accommodation response in young adults. Invest Ophthalmol Vis Sci 2006;47:1251–4.
9.Robinson DA. The mechanics of human saccadic eye movement. J Physiol 1964;174:245–64.
10.Collins CC, Carlson MR, Scott AB, Jampolsky A. Extraocular muscle forces in normal human subjects. Invest Ophthalmol Vis Sci 1981;20:652–64.
11.Demer JL, Oh SY, Poukens V. Evidence for active control of rectus extraocular muscle pulleys. Invest Ophthalmol Vis Sci 2000;41:1280–90.
12.Jaggi GP, Laeng HR, Muntener M, Killer HE. The anatomy of the muscle insertion (scleromuscular junction) of the lateral and medial rectus muscle in humans. Invest Ophthalmol Vis Sci 2005;46:2258–63.
13.Porter JD, Baker RS, Ragusa RJ, Brueckner JK. Extraocular muscles: basic and clinical aspects of structure and function. Surv Ophthalmol 1995;39:451–84.
14.Fairmaid JA. The constancy of corneal curvature; an examination of corneal response to changes in accommodation and convergence. Br J Physiol Opt 1959;16:2–23.
15.Lopping B, Weale RA. Changes in corneal curvature following ocular convergence. Vision Res 1965;5:207–15.
16.Mandell RB, Helen RS. Stability of the corneal contour. Am J Optom Arch Am Acad Optom 1968;45:797–806.
17.Kwito S, Sawusch MR, McDonnell PJ, Gritz DC, Moreira H, Evensen D. Effect of extraocular muscle surgery on corneal topography. Arch Ophthalmol 1991;109:873–8.
18.Kwitko S, Feldon S, McDonnell PJ. Corneal topographic changes following strabismus surgery in Grave's disease. Cornea 1992;11:36–40.
19.Nardi M, Rizzo S, Pellegrini G, Lepri A. Effects of strabismus surgery on corneal topography. J Pediatr Ophthalmol Strabismus 1997;34:244–6.
20.Rosenfield M, Gilmartin B. Myopia and nearwork: causation or merely association? In: Rosenfield M, Gilmartin B, eds. Myopia and Nearwork. Boston: Butterworth-Heinemann; 1998:193–206.
21.Greene PR. Mechanical considerations in myopia: relative effects of accommodation, convergence, intraocular pressure, and the extraocular muscles. Am J Optom Physiol Opt 1980;57:902–14.
22.Bayramlar H, Çekiç O, Hepsen IF. Does convergence, not accommodation, cause axial-length elongation at near? A biometric study in teens. Ophthalmic Res 1999;31:304–8.
23.Read SA, Collins MJ, Iskander DR. Diurnal variation of axial length, intraocular pressure, and anterior eye biometrics. Invest Ophthalmol Vis Sci 2008;49:2911–8.
24.Read SA, Collins MJ. Diurnal variation of corneal shape and thickness. Optom Vis Sci 2009;86:170–80.
25.Santodomingo-Rubido J, Mallen EA, Gilmartin B, Wolffsohn JS. A new non-contact optical device for ocular biometry. Br J Ophthalmol 2002;86:458–62.
26.Tang W, Collins MJ, Carney L, Davis B. The accuracy and precision performance of four videokeratoscopes in measuring test surfaces. Optom Vis Sci 2000;77:483–91.
27.Cho P, Lam AK, Mountford J, Ng L. The performance of four different corneal topographers on normal human corneas and its impact on orthokeratology lens fitting. Optom Vis Sci 2002;79:175–83.
28.Collins MJ, Kloevekorn-Norgall K, Buehren T, Voetz SC, Lingelbach B. Regression of lid-induced corneal topography changes after reading. Optom Vis Sci 2005;82:843–9.
29.Ciuffreda KJ, Vasudevan B. Nearwork-induced transient myopia (NITM) and permanent myopia—is there a link? Ophthalmic Physiol Opt 2008;28:103–14.
30.Maloney RK, Bogan SJ, Waring GO III. Determination of corneal image-forming properties from corneal topography. Am J Ophthalmol 1993;115:31–41.
31.Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci 1997;74:367–75.
32.Iskander DR, Collins MJ, Davis B. Optimal modeling of corneal surfaces with Zernike polynomials. IEEE Trans Biomed Eng 2001;48:87–95.
33.Thibos LN, Applegate RA, Schwiegerling JT, Webb R. Standards for reporting the optical aberrations of eyes. J Refract Surg 2002;18:S652–60.
34.Read SA, Collins MJ, Carney LG, Franklin RJ. The topography of the central and peripheral cornea. Invest Ophthalmol Vis Sci 2006;47:1404–15.
35.Freier BE, Pickwell LD. Physiological exophoria. Ophthalmic Physiol Opt 1983;3:267–72.
36.Grosvenor TP. Primary Care Optometry, 4th ed. Boston: Butterworth-Heinemann; 2002.
37.Zaroff CM, Knutelska M, Frumkes TE. Variation in stereoacuity: normative description, fixation disparity, and the roles of aging and gender. Invest Ophthalmol Vis Sci 2003;44:891–900.
38.Bayramlar H. Myopia. Convergence might cause myopia. BMJ 2002;325:1035.
39.Shaw AJ, Collins MJ, Davis BA, Carney LG. Corneal refractive changes due to short-term eyelid pressure in downward gaze. J Cataract Refract Surg 2008;34:1546–53.
40.Anstice J. Astigmatism—its components and their changes with age. Am J Optom Arch Am Acad Optom 1971;48:1001–6.
41.Baldwin WR, Mills D. A longitudinal study of corneal astigmatism and total astigmatism. Am J Optom Physiol Opt 1981;58:206–11.
42.Fledelius HC, Stubgaard M. Changes in refraction and corneal curvature during growth and adult life. A cross-sectional study. Acta Ophthalmol (Copenh) 1986;64:487–91.

corneal topography; axial length; convergence; astigmatism; refractive error

© 2010 American Academy of Optometry