Peripheral refractometry is the measurement of the refractive error of the eye at selected visual field angles. Over the last few years, researchers from various vision science areas1 have shown an increased interest in this procedure. Given the recently inferred association of peripheral refraction with myopia development,2–4 the relevance and importance of measuring and monitoring peripheral refraction profiles as accurately as possible, has been recognized and has become the topic of many research efforts.
Methodologically, however, the measurement of peripheral refraction encounters substantial technical challenges when using commercially available instruments. Automated refraction instruments are typically designed with the primary purpose of measuring on-axis refraction and not the peripheral optics of the eye. To overcome this limitation, modifications to instrument set-up with respect to the viewing angle (eccentricity) need to be introduced to enable objective measurements of the peripheral optics of the eye. Overall, this requires satisfaction of two alignment criteria with respect to the instrument axis; first, the correct rotational alignment with respect to the participant's eye and hence the peripheral visual field angle, and second, translational alignment (centration) with the entrance pupil.
Alignment with respect to the peripheral visual field angle is commonly achieved by having the participant fixate a target mounted peripherally relative to the instrument axis, for example, by either eye rotation or head turn, or by having the instrument rotate in front of the straight forward-looking eye. Several studies have addressed whether peripheral refraction outcome is affected differently for head or eye-turn measurements.5–8 In three participants, Seidemann et al.7 measured myopic shifts in spherical equivalent of −0.45, −0.95, and −2.30 diopter (D), when the eye was turned by 40°, compared with head turn measurements at the same peripheral angle. Mathur et al.5 measured axial refraction under oblique viewing conditions (30° temporal and 30° nasal) using an auto-refractor, the Shin-Nippon SRW5000 and compared the results to straight-ahead viewing. Although they did not find any significant mean effects for the participant group (n = 53), about 15% of the participants showed significant differences in one of the three refractive vector components. Using the Shin-Nippon SRW5000, Radhakrishnan and Charman6 compared eye and head turn measurements up to 30°. No significant differences between eye and head turn data were found. However, in another investigation, using a Hartmann-Shack aberrometer, the same authors found some evidence of eye turn-induced central refractive error changes of up to 1.00 D in hyperopic direction.8 These changes occurred only in some individuals and after 1 to 2 min viewing at 30° eccentricity. Overall, results from these studies are inconclusive and the possibility remains that large eye rotation may induce some refractive changes based on short-term pressures from extraocular muscles.
Common practice for central autorefraction includes the alignment of the instrument axis with the entrance pupil center as well as longitudinal (axial) adjustment of the instrument in terms of illumination and calibration. The presumption is that both alignment conditions are satisfied as closely as possible when performing peripheral refraction. This, however, is difficult to achieve in practice because of the peripheral observation angle of the eye and the resultant tilt and elliptical shape of the entrance pupil.
Generally, repeatability of auto-refractors for central measurements has been shown to be similar to, or even better than, subjective refraction.9–11 With the introduction of peripheral refractometry, some validation studies of modified peripheral refraction techniques have been conducted. Atchison12 compared peripheral refraction results performed on five participants using two modified auto-refractors, the Shin-Nippon SRW 5000 and the Canon Autoref R-1, and one Hartmann-Shack aberrometer. Considerable intersubject variability was found for most measurements, but overall agreement between instruments was good; the best agreement occurring between the aberrometer and the Shin-Nippon SRW-5000. A larger scale study, of 30 participants, was conducted by Berntsen et al.13 Similarly, peripheral refraction measurements obtained with a modified auto-refractor, the Grand Seiko WR 5100K and an aberrometer, the Complete Ophthalmic Analysis System (COAS) were compared. The COAS measured more minus power than the Grand Seiko WR-5100K for all three directions of gaze (central, 30° temporal and 30° nasal visual field). However, relative peripheral refractive error measurements showed no significant differences between the two instruments. Other instruments such as the PowerRefractor or the double-pass technique were also compared for the use of peripheral refraction and indicated good comparability.7,14
Some investigations using peripheral refraction techniques appear to exhibit higher standard error with increasing eccentricity.5–7,15–19 The source of such variability could be related to physiological differences within the eye's central and peripheral shape and/or a certain level of measurement noise and/or the increasing magnitude of the measurement values.
To our knowledge, no studies have as yet reported on the tolerance of lateral misalignment within the elliptical pupil when measuring peripheral refractive errors. Cheng et al.20,21 investigated the impact of lateral and axial misalignment on aberration data for central measurements using the COAS aberrometer. In consideration of their estimated clinician misalignment range of ±0.5 mm, central aberration values were shown to be stable.
Two additional optical and procedure-related factors affect the reliability of peripheral refraction measurements. As previously shown, with gradual increase in eccentricity, radial astigmatism and coma come into play.22–24 However, commercial autorefraction instruments, at least in their outputs, do not differentiate, between higher order aberrations such as coma and the lower order aberrations (defocus and astigmatism) and do not segregate their optical contributions or effects. Considering that evaluation of peripheral refraction profiles typically require the measurement of numerous eccentricities and/or numerous repeats at select eccentricities, a large number of realignments from the participants and operator's point of view are required for a complete series of valid and reliable readings. As such, any of these modified peripheral refraction techniques has considerable potential for alignment error. Hence, the clinician's normal operation range for peripheral refraction is likely to be larger than when compared with the previously estimated central normal misalignment range of ±0.5 mm when using the COAS instrument.20–21
Based on the current technical intricacies in peripheral refraction measurements, the additional impact of asymmetric aberrations and the tilted and elliptical peripheral entrance pupil, it is reasonable to assume that sensitivity in measurement error for peripheral refraction increases with increasing eccentricity. Hence, from the methodological point of view and with its increasing scientific and clinical relevance, the key objective of this study was to investigate how sensitive the peripheral refraction results are with respect to lateral misaligned pupil centration when compared with the sensitivity of central refraction results.
The study protocol was reviewed and approved by the University of New South Wales Human Research Ethics Advisory Panel and conformed to the tenets of the Declaration of Helsinki. Ten emmetropic (central M ≤0.50 D) and 10 myopic (central M ≤−0.75 D) cooperative adult participants were recruited and successfully enrolled into the study. All participants were screened for good ocular health and had no history of ocular anomalies, such as manifest strabismus, non-orthophoric conditions, or any anterior eye anomalies. Peripheral refraction was measured for the right uncorrected eye in the horizontal meridian. Pupils were not dilated for the measurements.
Central and peripheral refractions were measured with the open-view Shin-Nippon NVision-K5001 (also known as Grand Seiko WR-5100K, Shin-Nippon, Tokyo, Japan). For this study, the auto-refractor was modified (Fig. 1A) to allow for easier peripheral refraction measurements. The primary modification includes the addition of an instrument head, which had been mounted on top of the auto-refractor. The instrument head includes several small red laser diodes that are aligned to project laser fixation targets, one at a time, at various angles onto a 2 to 2.5 m distant wall and hence into the participant's visual field. In this study, the laser fixation targets were presented straight ahead from the center of the auto-refractor and 30° in the nasal and temporal horizontal visual field. The use of bright laser targets on the wall, allows even for uncorrected ametropic participants to be able to recognize and fixate to the target. As there are advantages to aligning the participant's head appropriately, a modified extended chin-rest enables easier off-axis fixation.
Using the method described by Thibos et al.,25 the sphero-cylindrical refraction output S/C × θ was converted to the power vectors, M (spherical equivalent), J180 (with- and against-the-rule astigmatism), and J45 (oblique astigmatism) as followed:
All data handling (e.g., averaging) and subsequent analyses were performed in terms of these power vector components.
Each participant was instructed to turn his/her head toward the presented fixation target while keeping both eyes stationary, relative to head position, in forward gaze (Fig. 1B). The participant's cooperation regarding head alignment and accuracy of fixation was monitored by the operator throughout the measurement procedure. Nevertheless, it should be noted that, in practice, an additional small compensatory eye turn may be difficult to perceive and correct. In three participants, head misalignment was measured (five repeats at 30° nasal and 30° temporal visual field angles), which ranged from −6.85 to +5.15° (mean, −2.13 ± 2.85°). This small compensatory eye turn is unlikely to have a real impact on the data, particularly because the differences related to eye and head turn measurements were, if at all, only found for large peripheral fixation angles.7,8 Fixation targets were viewed with both eyes while maintaining normal blinking. As no participants had manifest strabismus, accurate binocular fixation was maintained for all measurements at all eccentricities.
Entrance Pupil Alignment
At each of the three visual field positions, five readings were recorded at each of five pupil alignment positions, central (0CP), 1 and 2 mm temporal (1TP and 2TP, respectively), and 1 and 2 mm nasal (1NP and 2NP, respectively), while ensuring that the instrument was axially in best focus (Figs. 2 and 3). For subsequent analysis, dealignments are considered positive toward the nasal portion of the pupil and negative toward the temporal portion of the pupil. The data displayed on the Shin-Nippon monitor were linked and retrieved by custom designed software.
It should be noted that when performing peripheral refraction using a Shin-Nippon, oblique head alignment on the chin-rest may result in the instrument incorrectly recognizing the measurement position as that of the opposite eye, especially at large eccentric fixation angles. As such, care needs to be taken that the correct eye measurements are recorded. In this study, this potential error was eliminated by having custom data-acquisition software effect the data transfer, which only allows the data to be collected as dictated by the study protocol.
To achieve a sufficiently large natural diameter of the elliptical minor pupil axis for the performance of de-aligned measurements through all five pupil positions, measurements were performed under low (scotopic) room lighting; between 0.3 and 0.5 lux. The measurement beam as well as the eye illumination for video imaging operate in the infrared and thus do not induce pupil constriction. Pupil dealignment was assisted by a pupil alignment scale attached to the alignment monitor as shown in Fig. 3. The pupil alignment scale is a transparent sheet attached to the monitor with a 10 × 10 grid with 1 mm graduations. Thus each grid-square represents a 1 mm2 area in the plane of the entrance pupil.
Central and Peripheral Refraction—Pupil Alignment
Central and peripheral refraction for different pupil alignment positions was performed in 10 myopic and 10 emmetropic adults (age 19 to 40 years). The mean age (±standard deviation) of the emmetropic group was 30.7 (±5.6 years), and that of the myopic group was 27.2 (±3.8 years). The absolute mean refractive values for M, J180, and J45 measured at the centered entrance pupil position (0CP) are shown in Table 1. The emmetropic group was relatively more myopic in the periphery and the myopic group displayed a small relative hyperopic shift.
With respect to the five pupil alignment positions, key results are presented graphically (Fig. 4) in terms of relative peripheral refractive error from pupil center. For this, refractive power vector components of the centered entrance pupil were subtracted from the corresponding components from the de-aligned pupil measurements. Results of the relative refractive power vectors as a function of lateral pupil alignment were plotted for both participant groups and for both peripheral and the central field angles. The interaction between refractive group and lateral pupil alignment position for each combination of visual field angle and relative refractive vector component was investigated using a repeated-measures analysis of variance.
There was no significant difference between-groups associated with pupil position for the nasal visual field for any of the three refractive vector components (M: F = 0.397, p = 0.536; J180: F = 2.133, p = 0.161; and J45: F = 1.535, p = 0.231). However, there was a difference between refractive groups in the temporal visual field for M and J180 (M: F = 6.74, p = 0.018 and J180: F = 13.20, p = 0.002) but not for J45 (F = 0.014, p = 0.906). Specifically, the curvature as represented by the quadratic term was different between the refractive groups for M and J180 (M: F = 5.641, p = 0.029 and J180: F = 7.899, p = 0.012). This is also indicated by the more quadratic pupil alignment functions in the emmetropic group when compared with the myopic group (Fig. 4). The central visual field measurements also showed a difference between groups for M (F = 5.853, p = 0.026) but not for J180 (F = 2.036, p = 0.171) and J45 (F = 0.027, p = 0.870).
Repeated-measures analysis of variance was performed on the refractive power vectors M, J180, and J45, to compare the centered with the de-aligned entrance pupil positions. For this, a post hoc test for type-I probability with Bonferroni correction was used. Fig. 4 indicates statistically significant differences compared with centered entrance pupil alignment where the critical type-I probability (statistical significance) is set at 0.05.
For central visual field refraction measurements, the relative refractive vector components M and J180 decreased quadratically (r ≥0.98, p < 0.04) with increasing pupil dealignment in both groups. Compared with centered pupil alignment, M and J180 showed significant differences for all temporal and nasal pupil dealignments of 2 mm. The only exceptions where no differences were found were M and J180 for the 2 mm temporal pupil dealignment in the myopic group. A pupil dealignment of 1 mm was only significantly different for J180 in the myopic group, when aligned for the 1 mm nasal pupil position. The maximum M mean difference to centered pupil alignment was −1.03 D found at the 2 mm temporal pupil alignment in the emmetropic group.
For both peripheral visual fields, lateral pupil dealignments of 1 and 2 mm resulted in significant differences for M and J180 when compared with centered pupil alignment (Fig. 4). The only exceptions were the 1 mm temporal M and J180 for myopes measured at the 30° nasal visual field and the 1 mm nasal M and J180 for myopes measured at the 30° temporal visual field. Entrance pupil dealignment at the 30° nasal visual field for the emmetropic group was found to produce the greatest mean difference from centered pupil alignment for both 2 mm temporal (ΔM = −2.77 D, ΔJ180 = −1.57 D) and 2 mm nasal (ΔM = +2.23 D, ΔJ180 = +1.04 D) pupil dealignments. M and J180 showed a significant linear (r ≥0.94, p < 0.02) correlation as dealignment progressed from temporal to nasal for peripheral refraction measurements in both refractive error groups. To assess whether there is an asymmetry between the relative pupil alignment slopes of the nasal and temporal visual fields, the absolute values of the linear slope (D/mm) were determined for M and J180. Overall, the slopes were greater in the nasal visual field (emmetropic group: slope for M = 1.245, J180 = 0.618 and myopic group: slope for M = 0.937, J180 = 0.455) than in the temporal visual field (emmetropic group: slope for M = 0.684, J180 = 0.354 and myopic group: slope for M = 0.769, J180 = 0.452). However, paired t-test analysis showed that this difference in relative pupil alignment slopes between the nasal and temporal visual field was significantly different only in the emmetropic (M: p = 0.00 and J180: p = 0.001) and not in the myopic group (M: p = 0.113 and J180: p = 0.958).
Overall, J45 was least affected by entrance pupil dealignment. Compared with centered pupil alignment, J45 showed only significant differences for central refraction at the 2 mm nasal pupil position in the emmetropic group and for the nasal visual field at the 2 mm temporal pupil position in both groups.
Pupil Misalignment Threshold of Clinical Significance
Regression analysis was used to assess the relationship between refractive error measured for centered and lateral de-aligned pupil measurements, for the two refractive groups and the three visual fields. Data on pupil dealignment vs. visual fields were fitted with equations to determine the pupil misalignment threshold of clinical significance (Table 2). For this analysis, first-order (linear) fits were used for off-axis M and J180, and second-order (quadratic) fits were used for on-axis measurements. A clinically significant difference was defined as ≥0.25 D for M and ≥0.125 D for J180 and J45. Positive x refers to nasal pupil misalignment and negative x refers to temporal pupil misalignment. From this analysis, for central M and J180, the pupil misalignment threshold of clinical significance ranged from +0.79 to −2.33 mm, whereas for peripheral M and J180, the range was as small as ±0.20 to ±0.37 mm.
Peripheral Refraction and Its Tolerance to Lateral Pupil Misalignment
Measuring the peripheral optics of the eye with modified commercial refraction instruments has become increasingly relevant, particularly in the area of myopia research. As no standards exist for calibration and testing of peripheral optics measurements, and given the presence of asymmetric off-axis aberrations, there is no certainty that using auto-refractors (otherwise designed for on-axis refraction) for peripheral refraction provides accurate results, even though the empirical comparison of peripheral refraction data using different instruments showed good agreement12–13 and repeatability was acceptable.26 Furthermore, research is still inconclusive regarding modified peripheral refraction techniques, for example with regards to whether peripheral refraction data obtained by eye or head-turn differ.5–8,27–29
To our knowledge, no report has yet addressed the tolerance of pupil misalignment on peripheral refraction using auto-refractors. In two studies reported, Cheng et al. performed central aberrometer measurements at different lateral pupil alignment positions in human eyes21 and in different aspheric model eyes20 using the COAS aberrometer. Their results showed that the instrument has a high tolerance to the typical lateral misalignment of ±0.5 mm introduced by the operator when measuring central aberrations. In contrast to the findings of Cheng et al., Applegate et al.30–31 demonstrated that fitting of wavefront aberrations to Zernike polynomials can introduce the false appearance of significant artifactual coefficients. These apparently contradictory results may be reconciled if other errors involved in the measurement of wavefront aberrations are taken into consideration. Indeed, Cheng et al. suggested that variability of measurements in the human eyes reflects the changes in the eye's optics, i.e., caused by fixational eye movements or microfluctuations in accommodation, rather than instrument noise. In addition, they showed that asymmetric aberrations occur only to a negligible amount for lateral pupil dealignments when measuring central aberrations.
This study investigated the impact of pupil dealignment on central and peripheral refraction in emmetropic and myopic eyes. Overall, the pupil alignment slopes between the emmetropic and myopic group appeared to be similar for all three visual fields. However, with respect to pupil alignment some differences between both groups were found for the central and 30° temporal visual field measurements as well as with respect to nasal-temporal asymmetry across the visual field. Previous studies have shown that factors such as corneal curvature32 and the shape of the eyeball33 differ between emmetropic and myopic eyes. In addition, the nasal-temporal asymmetry across the visual field has been noted previously and was shown to decrease as myopia increases.34 Thus, it is possible that these ocular differences between refractive groups may have led to some of the differences found with respect to pupil alignment.
With respect to pupil misalignment tolerance, this study has shown that for central autorefraction, the pupil misalignment threshold of clinical significance was ≥0.79 mm. As such, assuming a normal misalignment error of ±0.5 mm in clinical practice, central autorefraction can be considered highly tolerant with respect to lateral pupil dealignment. This is in accordance with previous empirical validation studies of autorefraction instruments for central measurements.9–10 In contrast to the robust results in central refraction, even small pupil dealignments in peripheral refraction led to significant errors. Independent of the refractive error group, our results show that there is a rapid and linear change in the refractive power vectors M and J180, when de-aligning the instrument axis even by only a minimal amount, i.e., 0.2 mm, from the pupil center during the peripheral refraction measurement in the 30° temporal and nasal visual field.
The pupil misalignment threshold for clinical significance in 30° peripheral refraction measurements was found to be much smaller than for central refraction and thus, can have a significant impact on the data. It is reasonable to speculate that this may be a substantial cause of the higher standard errors in peripheral measurement with increasing eccentricities as seen in previous studies.5–7,15–19 In fact, we measured one eye at 0, 20, 30, and 40°, which confirmed that with increasing eccentricity, tolerance to pupil misalignment error decreases even more.
The substantial and significant change in M and J180 for the peripheral refraction measurements at different pupil positions can mainly been attributed to the different entrance angles of the peripheral measurement beam at the curved anterior cornea surface caused by the combination of peripheral measurement beam and changing pupil/cornea position. In addition, it is assumed that the elliptical peripheral entrance pupil and the existence of oblique astigmatism, comatic effects, and other asymmetric higher-order aberrations can have an impact on the measurements of the peripheral optics of the eye with respect to pupil misalignment.
Guirao and Artal35 used a double-pass technique with unequal entrance and exit pupil diameters to demonstrate how odd aberrations, such as coma, influence the point spread function in the peripheral retina. Unlike for the double-pass technique where the point spread images are assessed, the Shin-Nippon NVision-K5001 analyses the detected retinal images of the three arcs that are projected onto the retina. The impact of imaging through the peripheral optics of the eye, including the effect of coma and other asymmetric aberrations, could adversely influence the analysis of the retinal images and render the measurements more sensitive to lateral pupil misalignment.
Factors Contributing to Misalignment Errors during Peripheral Refraction Measurements
In practice, it is difficult for the operator to maintain consistent and accurate centration of the peripheral pupil. This is particularly the case when, unlike in central refraction, the measurement of peripheral refraction profiles requires a large number of realignments and thus, increased participant cooperation as well as operator attentiveness. Misalignment error in peripheral refractometry is augmented by inherent additional tasks, i.e., the need for continuous refixation by the participant, the realignment of the elliptical pupil with respect to the instrument axis, and the retention of a focused peripherally shifted keratometry ring. Furthermore, time constraints and multiple independent measurements can affect the accuracy of these tasks.
There may be additional optical effects that contribute to misalignment errors during peripheral refraction measurements. It has been demonstrated that the observation of the pupil from large peripheral angles distorts the pupil asymmetrically and thus its shape does not precisely resemble an ellipse.36–37 A consequence of this distortion is that the mid-point of the peripheral entrance pupil does not represent the actual center of the pupil. This effect may introduce systematic misalignments in peripheral refraction measurements.
Improving Peripheral Refraction Measurements
Technology is developing at a rapid pace and likewise auto-refractors. The first auto-refractors became commercially available almost four decades ago, at great retail cost.38 Many instruments have been developed since. Especially in terms of affordability, objective refraction instruments are now practical propositions to all practitioners, be they in clinical or research settings. The latest closed-view autorefraction models (i.e., CBD/TOMEY RC-5000, Nidek ARK-530A) have been equipped with automated pupil alignment modes, making the instruments even easier to use and thereby more reliable and time efficient. Despite this advancement, all auto-refractors still face limitations with respect to peripheral refraction, as all are primarily designed for on-axis refraction although off-label use and technical modifications of such instruments potentially compromise some aspects of their performance.
Tabernero and Schaeffel39 recently introduced a new peripheral refraction technique based on photorefraction. This instrument uses a hot mirror to scan across the horizontal meridian of the eye and hence does not require alignments by participant or operator. Although their initial prototype instrument required 22 s to complete a full scan, the application of an optimized linear stage improved the speed significantly. However, it is still likely that during the current measurement duration of 4 s, refraction results may be influenced by fluctuating fixation and accommodation.
Given the results of this study and the foregoing discussions, it would be advantageous to have a fast and convenient instrument, which does not require the additional alignment to the peripheral entrance pupil. Until such an instrument becomes generally available, modifications of current instruments would still be required for peripheral refractometry. It is suggested that more attention be paid to the issue of pupil alignment and to adequately train the instrument operator and preferably assess and validate intraobserver and interobserver variability before the commencement of any clinical study. A pupil scale attached to the alignment monitor may be a helpful tool to facilitate more accurate pupil alignment. Finally, given the increased sensitivity in measurement error, it may also be recommended to increase the number of repeats for peripheral refraction measurements, particularly for larger field angles.
This study has demonstrated that accurate lateral alignment of the entrance pupil with the instrument axis is critical to obtain reliable results when measuring peripheral refraction with auto-refractors. The error sensitivity to misalignment increases linearly toward the periphery. At 30° field angle, lateral pupil misalignment should be kept well below 0.5 mm to ensure clinically relevant accuracy.
We thank Darrin Falk for his assistance with the equipment set-up.
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1. Fedtke C, Ehrmann K, Holden BA. A review of peripheral refraction techniques. Optom Vis Sci 2009;86:429–46.
2. Smith EL, III, Kee CS, Ramamirtham R, Qiao-Grider Y, Hung LF. Peripheral vision can influence eye growth and refractive development in infant monkeys. Invest Ophthalmol Vis Sci 2005;46:3965–72.
3. Smith EL, III, Ramamirtham R, Qiao-Grider Y, Hung LF, Huang J, Kee CS, Coats D, Paysse E. Effects of foveal ablation on emmetropization and form-deprivation myopia. Invest Ophthalmol Vis Sci 2007;48:3914–22.
4. Huang J, Hung LF, Ramamirtham R, Blasdel TL, Humbird TL, Bockhorst KH, Smith EL III. Effects of form deprivation on peripheral refractions and ocular shape in infant rhesus monkeys (Macaca mulatta). Invest Ophthalmol Vis Sci 2009;50:4033–44.
5. Mathur A, Atchison DA, Kasthurirangan S, Dietz NA, Luong S, Chin SP, Lin WL, Hoo SW. The influence of oblique viewing on axial and peripheral refraction for emmetropes and myopes. Ophthalmic Physiol Opt 2009;29:155–61.
6. Radhakrishnan H, Charman WN. Peripheral refraction measurement: does it matter if one turns the eye or the head? Ophthalmic Physiol Opt 2008;28:73–82.
7. Seidemann A, Schaeffel F, Guirao A, Lopez-Gil N, Artal P. Peripheral refractive errors in myopic, emmetropic, and hyperopic young subjects. J Opt Soc Am (A) 2002;19:2363–73.
8. Radhakrishnan H, Charman WN. Refractive changes associated with oblique viewing and reading in myopes and emmetropes. J Vis 2007;7:5.
9. Bullimore MA, Fusaro RE, Adams CW. The repeatability of automated and clinician refraction. Optom Vis Sci 1998;75:617–22.
10. Davies LN, Mallen EA, Wolffsohn JS, Gilmartin B. Clinical evaluation of the Shin-Nippon NVision-K 5001/Grand Seiko WR-5100K autorefractor. Optom Vis Sci 2003;80:320–4.
11. Goss DA, Grosvenor T. Reliability of refraction—a literature review. J Am Optom Assoc 1996;67:619–30.
12. Atchison DA. Comparison of peripheral refractions determined by different instruments. Optom Vis Sci 2003;80:655–60.
13. Berntsen DA, Mutti DO, Zadnik K. Validation of aberrometry-based relative peripheral refraction measurements. Ophthalmic Physiol Opt 2008;28:83–90.
14. Lundström L, Gustafsson J, Svensson I, Unsbo P. Assessment of objective and subjective eccentric refraction. Optom Vis Sci 2005;82:298–306.
15. Calver R, Radhakrishnan H, Osuobeni E, O'Leary D. Peripheral refraction for distance and near vision in emmetropes and myopes. Ophthalmic Physiol Opt 2007;27:584–93.
16. Davies LN, Mallen EA. Influence of accommodation and refractive status on the peripheral refractive profile. Br J Ophthalmol 2009;93:1186–90.
17. Ma L, Atchison DA, Charman WN. Off-axis refraction and aberrations following conventional laser in situ keratomileusis. J Cataract Refract Surg 2005;31:489–98.
18. Whatham A, Zimmermann F, Martinez A, Delgado S, de la Jara PL, Sankaridurg P, Ho A. Influence of accommodation on off-axis refractive errors in myopic eyes. J Vis 2009;9:14.1–13.
19. Gustafsson J, Terenius E, Buchheister J, Unsbo P. Peripheral astigmatism in emmetropic eyes. Ophthalmic Physiol Opt 2001;21:393–400.
20. Cheng X, Himebaugh NL, Kollbaum PS, Thibos LN, Bradley A. Validation of a clinical Shack-Hartmann aberrometer. Optom Vis Sci 2003;80:587–95.
21. Cheng X, Himebaugh NL, Kollbaum PS, Thibos LN, Bradley A. Test-retest reliability of clinical Shack-Hartmann measurements. Invest Ophthalmol Vis Sci 2004;45:351–60.
22. Atchison DA. Higher order aberrations across the horizontal visual field. J Biomed Opt 2006;11:34026.
23. Mathur A, Atchison DA, Scott DH. Ocular aberrations in the peripheral visual field. Opt Lett 2008;33:863–5.
24. Atchison DA, Scott DH. Monochromatic aberrations of human eyes in the horizontal visual field. J Opt Soc Am (A) 2002;19:2180–4.
25. 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.
26. Walker TW, Mutti DO. The effect of accommodation on ocular shape. Optom Vis Sci 2002;79:424–30.
27. Ferree CE, Rand G, Hardy AB. Refraction for the peripheral field of vision. Arch Ophthalmol 1931;5:717–31.
28. Prado P, Arines J, Bara S, Manzanera S, Mira-Agudelo A, Artal P. Changes of ocular aberrations with gaze. Ophthalmic Physiol Opt 2009;29:264–71.
29. Lundström L, Mira-Agudelo A, Artal P. Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes. J Vis 2009;9:17.1–11.
30. Applegate RA, Koenig DE, Marsack DJ, Sarver EJ, Nyugen LC. Pupil center location uncertainty is a major source of instrument noise in WFE measurements. Invest Vis Sci 2009;50:E-abstract 6160.
31. Applegate RA, Thibos LN, Twa MD, Sarver EJ. Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality. J Cataract Refract Surg 2009;35:139–52.
32. Scott R, Grosvenor T. Structural model for emmetropic and myopic eyes. Ophthalmic Physiol Opt 1993;13:41–7.
33. Atchison DA, Jones CE, Schmid KL, Pritchard N, Pope JM, Strugnell WE, Riley RA. Eye shape in emmetropia and myopia. Invest Ophthalmol Vis Sci 2004;45:3380–6.
34. Atchison DA, Pritchard N, Schmid KL. Peripheral refraction along the horizontal and vertical visual fields in myopia. Vision Res 2006;46:1450–8.
35. Guirao A, Artal P. Off-axis monochromatic aberrations estimated from double pass measurements in the human eye. Vision Res 1999;39:207–17.
36. Fedtke C, Manns F, Ho A. The entrance pupil of the human eye: a three-dimensional model as a function of viewing angle. Opt Express 2010;18:22364–76.
37. Jay BS. The effective pupillary area at varying perimetric angles. Vision Res 1962;1:418–24.
38. Guyton DL. Editorial: automated refraction. Invest Ophthalmol 1974;13:814–8.
39. Tabernero J, Schaeffel F. More irregular eye shape in low myopia than in emmetropia. Invest Ophthalmol Vis Sci 2009;50:4516–22.