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Visual Performance with Lenses Correcting Peripheral Refractive Errors

Atchison, David A.*; Mathur, Ankit; Varnas, Saulius R.

doi: 10.1097/OPX.0000000000000033
Original Articles

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.

Methods 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-min arc 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 >0.5 D 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.

Conclusions 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.




School of Optometry & Vision Science and Institute of Health & Biomedical Innovation (DAA, AM), Queensland University of Technology, Kelvin Grove, Queensland; and Carl Zeiss Vision (SRV), Lonsdale, South Australia, Australia.

David A. Atchison, School of Optometry and Institute of Health & Biomedical Innovation, Queensland University of Technology, 60 Musk Ave, Kelvin Grove, Queensland 4059, Australia e-mail:

The influence of optics on peripheral vision depends on the task. Resolution tasks are limited by the sampling rate of retinal ganglion cells, and hence, they are little influenced by aberrations.1–8 Two examples demonstrate this. Lundström et al.9 found negligible improvement in visual acuity at 20° eccentricity in the nasal visual field despite increasing the degree of peripheral correction in stages from on-axis (foveal) spherocylindrical correction to full correction of peripheral second- and higher-order monochromatic aberrations. Wang et al.5 determined optimal corrections to high-contrast grating targets for three participants at 20° to 40° in the nasal visual field; defocus of ±3 D or more about this correction made little difference to performance.

If the contrast of a peripheral resolution task is decreased sufficiently, the task becomes contrast limited, rather than sampling limited, and is sensitive to optical quality.1,10,11

Peripheral acuity can improve markedly when a detection task replaces the resolution task, such as determining in which of two presentations a grating appears rather than determining whether it is orientated horizontally or vertically. As an example, at optimal correction for 20° nasal visual field, the three participants of Wang et al.5 had grating detection acuities of 15 to 20 cycles per degree compared with resolution acuities of 3 to 5 cycles per degree. However, detection performance deteriorated to be similar to resolution with 3 to 4 D defocus. The main perceptual effect in the range between detection and resolution cutoffs is spatial aliasing, in which grating appearance can be distorted in different ways—this is referred to as “nonveridical” perception. Spatial aliasing has received considerable attention.12–15

Other peripheral visual tasks are affected by optical quality, including motion perception,16 and detection of small spots against a background.17–19

Correcting or manipulating the peripheral optics has been of recent interest, particularly because of the possibility that peripheral refraction might influence the development or otherwise of myopia (see Verkicharla et al.20 for a review). Manipulation may be done with optical interventions such as spectacles,21,22 contact lenses,23,24 and orthokeratology,25–27 usually with the purpose of adding positive power in the periphery to compensate for relative peripheral hyperopia that would otherwise occur in most myopes. For contact lenses, because they move with the eye and because of their close proximity to the eye’s pupil, similar parts are used for each visual field position; the challenge when manipulating the optics of peripheral vision is to not compromise central vision through unwanted higher-order aberrations on-axis. As spectacle lenses do not move with the eye and as eyes cannot be expected to remain stationary behind them, the challenge is now to provide a central region of the lens corrected for the rotating eye and foveal vision, beyond which the design can concentrate on manipulating peripheral refraction. This means accounting for both a pupil rotating about the eye’s center of rotation (∼11 mm behind the pupil) and for a stationary pupil.21,28–30

Swedish groups have investigated whether correcting refraction at a “preferred retinal location” might be of benefit to people with central visual defects such as macular degeneration.31–33 Gustafsson and Unsbo32 compared central and peripheral corrections at the preferred retinal location 15° to 30° away from the fovea in seven participants. Five of seven people showed improvement with the Pelli-Robson contrast sensitivity chart (mean improvement of all people 0.15 ± 0.12 log units) and five of seven showed visual acuity improvement to a high-pass resolution perimetry targets (mean, 0.11 ± 0.07 log units). Lundström et al.31 found improvements in resolution and detection tasks at the preferred retinal location with peripheral correction compared with central correction. Using a low-contrast grating detection task at 25° in the nasal visual field for one participant with juvenile macular degeneration, Baskaran et al.33 were able to make a 0.25-log unit improvement with full adaptive optics correction relative to the central correction.

In this group of studies, the interest was in correcting the optics at a single peripheral location rather than at a range of locations. In terms of correcting the optics at a range of locations, we designed lenses to correct schematic eyes along one meridian of the visual field in a previous work.34 Sankaridurg et al.21 described three designs of spectacle lenses to manipulate peripheral refraction in children with myopia.

The purposes of this work were to design and manufacture spectacle lenses to correct peripheral refraction along the horizontal visual field meridian and to determine whether these resulted in noticeable improvements in visual performance.

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The subject was a 58-year-old man (participant 1), in good general and ocular health, with a right eye subjective refraction of −2.25/−0.50 × 75. His pupil size was approximately 4 mm diameter under the experimental conditions. The left eye was occluded in all procedures. The research followed the tenets of the Declaration of Helsinki and was approved by the Queensland University of Technology human research ethics committee.

The participant was selected as he was particularly well suited to this study. He had appreciable relative peripheral refractive error that was different in the temporal and nasal fields and thus provided a challenge to designing lenses that could appreciably improve vision in the periphery. Furthermore, he was presbyopic and thus cycloplegia was not needed to ensure consistent refraction.

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Measurements were made at 3 m from the stimulus, except for grating detection on-axis for which the resolution of the monitor was insufficient. This measurement was conducted at 10 m.

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Grating Detection Acuity

The targets were 49 cd/m2, 90% center-contrast, Gabor patches, presented on a Sony Triniton Multiscan G520 monitor and under the control of a computer program with a Visual Stimulus Generator VSG 2/5 system (Cambridge Research Instruments). The sizes of the Gabor patches (angles measured from the center of the pattern by which contrast reduced to 60.6% of the central contrast) were 0.5° for fixation and ±5° eccentricities, and 1.0° for other eccentricities. The green gun of the monitor was used to display the stimuli (mean wavelength, 545 nm; full width at half maximum luminance height, 62 nm; CIE chromaticity co-ordinates, x, y = 0.32, 0.57). White boards were placed around the monitor and illuminated by fluorescent light with green cellophane to give a background of similar luminance as the monitor and with chromaticity co-ordinates x, y = 0.37, 0.46. A red LED fixation target was placed at different positions on the boards as appropriate. The participant’s task was to distinguish between two stimuli presented in 0.5-s intervals, one with the Gabor patch and one with an empty field; a control box with two buttons was used for this. A staircase procedure determined the 79% threshold (three consecutive correct responses before increase in spatial frequency; one incorrect response to decrease spatial frequency) with a step size of 0.1 log spatial frequency. The mean of the last six of nine reversals was taken as threshold. Here, log acuity = log (30/SF), where SF is spatial frequency in cycles per degree.

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Contrast Threshold for a Small Circular Spot

The targets were 1.25-min arc white circular spots, presented on a white wall by a Hitachi CP – X880 projector under the control of a computer program with a Visual Stimulus Generator VSG 2/5 system. The experiment was done with some room lighting, and its effect on luminance and contrast was taken into account. The background was 5° horizontally × 4° vertically and 25 cd/m2 luminance. The participant fixated at marked crosses on the wall as appropriate. The participant’s task was to distinguish between two stimuli presented in 0.5-s intervals, one with the spot and one with an empty field; the other procedures were similar to those for the grating acuity experiment, except that contrast rather than spatial frequency was varied. Contrast threshold was ΔL/L where L is the background luminance and ΔL is the threshold increment luminance of the spot.

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Subjective Refraction

Refraction was determined on the basis of the trial lens powers giving the best grating detection acuities in horizontal and vertical meridians of the eye, with a range of trial lenses tested for each visual field position/grating orientation combination (see Fig. 1 for examples). Horizontal gratings were used for refraction along the vertical meridian and vertical gratings were used for refraction along the horizontal meridian. Oblique refraction components were ignored on- and off-axis, as these were considered likely to be too small to have much influence on visual performance.



The order of grating testing was 10° to 30° nasal visual field (N) in 5° steps, followed by 10° to 30° temporal visual field (T) in 5° steps, with omission of 15° T because it coincided with the blind spot. All angles were tested for the horizontal grating, followed by the vertical grating. Testing was then done for the ±5° visual positions, followed by fixation.

Spherical trial lenses were mounted in a trial frame, and centered as well as possible in front of the eye with minimal pantoscopic tilt. Trial lenses were plano-convex or plano-concave in form and were placed with the curved surface facing the eye. The vertex distance was measured as 12 mm and was periodically checked. Sticker annuli, with an inner diameter of 5 mm and an outer diameter of 6 mm, were placed on the back surfaces of the trial lenses and centered on their optical axes. When testing at 5°, the annulus obscured the grating target and the sides of the annuli were removed, leaving approximately 50% of the annulus on the lens.

While performing the experiment, the participant rotated his head so that the fixation target of interest was centered within the blurred-appearing annuli. While this is not an accurate method, it is consistent with the clinical nature of the experiment.

There are a few issues associated with the use of trial lenses in this way. First, the trial lenses provide a degree of spectacle magnification that alters the effective spatial frequency of the gratings. A correction factor for this can be made by multiplying the spatial frequency by (1 – hF v′), the inverse of the approximate spectacle magnification, with F v′ being the lens back vertex power and h being the distance between the lens back vertex and the eye entrance pupil, the latter assumed to be 3 mm inside the eye. The range of correction factors corresponding to best vision was 0.96 to 1.01 (or −0.02 to +0.00 log), and this was considered small enough to be disregarded.

A second issue is that, because of prismatic effects, the angles on the image sides of lenses are different from those on the object side (the image angles are the smaller for negative lens powers and the larger for positive lens powers). A third issue is that the specified on-axis trial lens powers are not the effective powers when the trial lenses are used in the peripheral vision. Because we wanted to specify the results on the image side for the trial lenses to design special lenses, we measured off-axis tangential and sagittal powers and the prism of trial lenses on a Nikon projection vertometer in which they were rotated in 5° steps around a position corresponding to the entrance pupil of the eye.35,36 Prism was measured with the prism compensator. For a given image angle &thetas;′ (the angle of rotation) and prism in prism diopters Δ, the object angle &thetas; was calculated where

In doing these determinations, we rotated lenses to both right and left and took the average of readings to compensate for slight decentrations of the optical centers from the geometric centers of the lenses. Combining the power and prism measurements, and using simple linear and quadratic regressions, we refined the subjective refractions by determining the effective powers at each object angle in 5° steps and the image angles to which these applied.

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Objective Refraction Comparisons

As a comparison with the subjective refractions, we determined refractions with a Wavefront Sciences COAS-HD aberrometer, the use of which for measuring peripheral refraction has been described.37 This was done considering only the second-order terms for a 3-mm-diameter pupil and considering second- to sixth-order Zernike aberration terms for a 3-mm-diameter pupil. The refractions were corrected for 3 m by adding +0.33 D. The oblique components of refraction were small compared with the orthogonal (vertical/horizontal) components.

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Lenses were designed and manufactured by Carl Zeiss Vision based on the subjective refractions. As we wanted refraction corrected for 3 m, a power of +0.23 D was added to the on-axis refraction determined at 10 m. In subsequent on-axis testing of grating acuity with the lenses, a trial lens of power −0.25 D was added to compensate.

The lenses were made of diglycol carbonate (CR39) and provided with anti-reflection coatings. The front surface of each lens had +3.7 D power, the thickness was 2.0 mm, and the back surface had a strip design to give good correction within ±2 mm of the horizontal meridian. Two design approaches were used. One lens was based on raytracing at different points across a 3-mm diameter square aperture to provide a “smoothed” back surface shape (Figs. 2 and 3). The other lens was made on the basis of no smoothing across the aperture—this is the case of classic spectacle lens design in which the pupil aperture is assumed to be limitingly small (Fig. 4). The lenses were designed by specifying a target distribution of ray traced sagittal and tangential power along a horizontal strip of the lens surface with the optimization weight function heavily biased toward the center line of the strip. We refer to the separate lenses as the lens optimized with aperture smoothing and as the lens optimized without aperture smoothing. We refer to them together as special lenses.







Figs. 2 and 4 show the importance of the aperture smoothing to performance. In particular, designing without aperture smoothing will give insufficient hyperopic power changes into the periphery when ray tracing is done across a 3-mm diameter square pupil (Fig. 4).

The bottom part of Fig. 3 shows the root mean square of the vertical and horizontal coma coefficients across a 70° × 15° field (approximately 21 mm × 4 mm), where coma coefficient is given as the refractive power per millimeter across the reference sphere. This shows that the coma is highest at 15° to 20° in both the temporal and nasal fields where the power gradients are the highest. Coma is the most important of the higher-order aberrations in the lenses. However, power variations in these lenses are comparable to progressive lenses, which have been shown to be dominated by second-order aberrations like astigmatism with higher-order aberrations having a minimal impact on optical performance.38,39

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For grating acuity measurements with the lenses, the procedure was as described above for the subjective refraction. Four test sequences were conducted in the following order: 1) the spherical trial lenses that provided the best off-axis correction for each visual field position (already done as the subjective refraction), 2) the spherical trial lens that provided the best on-axis correction, 3) the lens optimized with aperture smoothing, and 4) the lens optimized without aperture smoothing. Three or four measurements were made at each combination of lens condition, visual field position, and grating orientation.

For spot contrast sensitivity determinations, the order of lens testing was as for the grating acuity. For each lens, field testing was done, in order, at fixation, 20° N, 30° N, 25° T, and 30° T. A single spherocylindrical power was required at each position. For trial lens powers, we used a spherical lens and a negative cylindrical lens with a 90° axis. The lens of higher absolute power was put at the position corresponding to the previously measured vertex distance, and the other lens was placed on the object side of this lens. Four determinations were made at each lens condition and position.

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Means and standard deviations of grating detection acuity were determined for each grating orientation (horizontal or vertical), lens condition, and position. Similarly, means and standard deviations of spot contrast threshold were determined for each lens condition and visual field position. Most standard deviations were <0.10 log units. Allowing for the fact that the measurements took some time and there was a delay of over a week between the subjective refraction and the delivery of the lenses, we have assigned practical significance only to lens condition differences ≥0.20 log units.

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Fig. 1 shows through-focus grating detection acuities on-axis and at 20° nasal and 30° temporal visual field positions. On-axis, both horizontal and vertical grating detection are highly sensitive to defocus. Sensitivity is less at the off-axis positions and is less for the vertical grating than for the horizontal grating. Note that the peripheral acuities for horizontal gratings are better than those for vertical gratings by 0.2 to 0.25 log units.

Fig. 5 shows refractions across the visual field for the vertical pupil meridian (top) and for the horizontal pupil meridian (bottom). Note that, for subjective refraction, the meridian of refraction is perpendicular to the grating orientation. This participant shows the typical myopic refraction pattern of relative peripheral hyperopia (averages of the horizontal and vertical refractions relative to the on-axis refractions are positive). Under the scheme of Rempt et al.,40 this is best described as the asymmetric type III pattern. Both meridians on both sides of the visual field have hyperopic shifts into the periphery, but this is much less marked for the horizontal meridian in the nasal field so that the peripheral astigmatism is much greater on the nasal side than on the temporal side. There are discrepancies between the subjective refraction and the objective refractions and between the two objective refractions (second order and up to sixth order): 1) the subjective refraction is about 0.5 D less negative than the sixth-order objective analysis at fixation; 2) for the vertical meridian, the subjective refraction becomes less positive than the objective refractions beyond 20° nasal; 3) for the horizontal meridian, subjective refraction becomes less negative than the objective refractions into the nasal visual field, with the difference between it and the second-order analysis being about 1.25 D at 20° nasal; 4) for the horizontal meridian, subjective refraction is 0.5 D more positive than the second-order objective analysis ≥20° temporal.



Higher-order aberrations, particularly spherical aberration, will influence the subjective refraction as determined by gratings. For example, positive spherical aberration will move refraction in the negative direction and more so for low spatial frequencies than for higher spatial frequencies.41 As this subject has positive spherical aberration at most angles, with the decreasing grating acuity into the periphery, it might be expected that this would give a myopic shift of the subjective refraction relative to the objective refractions, and possibly, this might be occurring in the nasal field beyond 20° (Fig. 5).

Fig. 6 shows the grating detection acuities for the different lens conditions. Considering the best correction results (black circles and solid lines), acuity decreases steadily into the nasal visual field for both grating orientations. The decrease is steep into the temporal field out to 10°, beyond which acuity changes little for either grating orientation. Away from fixation and in accordance with a previous investigation,5 acuity is worse for the vertical grating orientation than for the horizontal grating orientation; the difference is approximately 0.2 log units at most visual positions.



Using the on-axis correction (red squares) causes significant loss of acuity, outside 10° temporal to 5° nasal, at all positions. The largest loss is 0.4 log units for the horizontal grating at 20° to 30° temporal and 25° to 30° nasal.

The lens optimized with aperture smoothing (closed triangles) restores visual acuity at most positions, and there is an indication that it improves vision in the temporal field. Exceptions are the inner visual field positions out to 10°, with a definite decrease of 0.2 log units at 10° temporal for the horizontal grating.

The lens optimized without aperture smoothing (open triangles) is also largely successful in restoring visual acuity at most positions, but it is less successful at doing this than the other lens in the inner (±10°) field, with decreases of 0.2 log units relative to the best correction except at 10° nasal for the vertical grating.

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Spot Contrast Threshold

Fig. 7 shows the spot contrast threshold for the different lens conditions. Considering the best correction results (black circles and solid lines), threshold rises more on the nasal side than on the temporal side, except that the two 20° positions have similar thresholds. Furthermore, threshold is higher at 20° temporal than at 25° and 30° temporal, which might be due to the influence of an extended blind spot (this person has a pronounced temporal myopic crescent). Using the on-axis correction (red squares) causes increases in threshold in the temporal field of 0.4 to 0.5 log units. Both special lenses remove the increase in contrast threshold in the temporal field.



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For the participant in this study, relative to the best correction in the horizontal periphery out to ±30° from fixation, lenses that correct vision on-axis result in losses of grating detection acuity and contrast sensitivity of up to 0.4 log units (2.5 times) and 0.5 log units (3 times), respectively. The special lenses are successful in restoring the majority of this vision. Correction of these lenses is not good within ±10°, which might be due to the rapidly changing gradients at these positions, with the lens optimized with aperture smoothing being more successful than the lens without aperture smoothing. No attempt was made to correct oblique components of refraction as these were small on-axis, and it was assumed that this would be the case off-axis.

While we have been able to design and manufacture lenses that can correct refraction at more than one position in the visual field, we are limited to only one meridian of the visual field and no more than two components of refractive power; extending the design to all meridians is not possible. This type of lens would not be suitable for general vision in which eye movements occur, and hence, any lenses for patients’ use will need a central area that is applicable for vision of the rotating eye. It can be envisaged that the work here is used as a basis to customized peripheral defocus, for example, providing certain levels of relative peripheral myopia. One shortcoming to this is that the subjective method of refraction, which represented about 30 hours of measurements for this participant, is not feasible in a clinical sense, and the clinician would have to rely on objective refraction, which might not always be accurate (Fig. 5).

During this investigation, peripheral correcting lenses were designed for six younger people on the basis of objective refraction. These designs were less of a challenge than the designs reported here because the changes in refractions of the latter were smaller, and the rates of change were less steep across the visual field. The participant used here had a very curved and prolate retinal shape (Figs. 9 and 10 in Verkicharla et al.20), which probably contributed to the high levels of relative peripheral hyperopia. We expect that our participant’s losses in off-axis performance with an on-axis correction would be greater than those of many people because of his high relative peripheral refractive errors, but we do not know if other people with similar relative off-axis refractions would have performed similarly.

David A. Atchison

School of Optometry and Institute of Health & Biomedical Innovation

Queensland University of Technology

60 Musk Ave

Kelvin Grove, Queensland 4059



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This work was supported by ARC Linkage grant LP100199575 and ARC Discovery Grant DP110102018. We thank the Research Division of Carl Zeiss Vision for support and, in particular, Steve Spratt for designing the special lenses.

Received: December 20, 2012; accepted April 21, 2013.

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contrast threshold; grating detection acuity; lens design; peripheral refraction; visual performance

© 2013 American Academy of Optometry