Uniformity of accommodation across the visual field

Abstract

We asked the question: Does accommodation change the eye's focusing power equally over the central visual field in emmetropic and myopic adult eyes? To answer this question we modified our laboratory scanning wavefront aberrometer to rapidly measure ocular refractive state over the central 30° diameter of visual field as a function of foveal accommodative demand. On average, ocular refractive state changed uniformly over the central visual field as the eye accommodated up to 6 D. Visual field maps of accommodative error (relative to a spherical target surface of constant vergence) reveal subtle patterns of deviation on the order of ±0.5 D that are unique to the individual and relatively invariant to changes in accommodative state. Population mean maps for accommodative error are remarkably uniform across the central visual field, indicating the retina of the hypothetical “average eye” is conjugate to a sphere of constant target vergence for all states of accommodation, even though individual eyes might deviate from the mean due to random variations. No systematic difference between emmetropic and myopic eyes was evident. Since accuracy of accommodation across the central visual field is similar to that measured in the fovea, loss of image quality due to accommodative errors, which potentially drives myopia and may affect many aspects of visual function, will be similar across the central retina.

Introduction

When the viewing distance to an object of regard changes, the eye compensates by changing the shape of its internal crystalline lens in order to maintain a clearly focused retinal image. This process of accommodation alters the eye's focusing power not only for the portion of the retinal image corresponding to the object of regard, but also for the remaining retinal image of the rest of the visual field. This global effect of accommodation occurs because the crystalline lens is in close contact with the iris and completely covers the pupil. Thus, except for pathological cases, light must pass through the crystalline lens in order to form the retinal image. 

In this study we asked the question: Does accommodation change the eye's focusing power equally over the central visual field? The central 30° diameter of visual field is an area of considerable interest because within this region many visual functions change rapidly, such as light sensitivity, acuity, spatial and temporal summation, and pupillary light reflex (Aulhorn & Harms, 1972). This central area includes the fovea, parafovea, perifovea, and macula, and therefore is of prime clinical importance as documented routinely by fundus photography and perimetric testing (Donahue, 1999). In order to interpret possible changes in visual function across the central visual field that might occur during accommodation, it would be helpful to know how uniformly the eye's refracting power changes as the eye accommodates. 

Our central question can be stated more precisely using the optical concept of refractive state, which is defined as the inverse of the distance from the eye's first principal plane to the axial location for positioning an object so the retinal image of that object is optimally focused on the retina. That optimum object location is said to be optically conjugate to the retina, and thus the locus of all points in object space that are optically conjugate to the retina is called the retinal conjugate surface. Using this terminology we can restate the question of interest in two equivalent ways. Does refractive state change uniformly over the visual field when the eye accommodates? Does the geometrical shape of the retinal conjugate surface change when the eye accommodates? 

Previous investigations of the effect of accommodation on peripheral refractive state typically report data relative to the fovea, which is a useful indicator of the changing balance between the eye's refracting power and dioptric length of the eye. Early work by Smith and colleagues reported uniform change in refractive power and astigmatism with accommodation for eccentricities up to 30° along the horizontal meridian, which was consistent with theoretical analysis of the Le Grand schematic eye model (Smith, Millodot, & McBrien, 1988). Later, Walker and Mutti (2002) reported that accommodation caused the eye's refractive state along a peripheral line of sight (30° into the nasal visual field) to become relatively more hyperopic (i.e., underpowered) compared to the foveal line of sight. From this evidence they concluded the retinal shape became more prolate, a conclusion resting on the implicit assumption that refractive power of the eye changed uniformly across the visual field. Experimental support for that assumption reported by Calver, Radhakrishnan, Osuobeni, and O'Leary (2007) indicated the local change in refractive power produced by 2.5 D of accommodative demand is independent of target eccentricity along the horizontal meridian. However, their main finding contradicted Walker and Mutti (2002) in that accommodation caused emmetropic eyes to become relatively myopic at peripheral eccentricities, with little change in myopic eyes. To the contrary, Davies and Mallen (2009) reported peripheral relative refractive errors are unaffected by accommodation in emmetropic or myopic eyes. The distinction between myopic and emmetropic eyes was further challenged by Whatham et al. (2009) who reported accommodation in myopic eyes causes peripheral relative refractive state to become progressively more myopic (i.e., overpowered). More importantly, these latter authors cast doubt upon the functional significance of peripheral relative refractive errors. They argued that such measurements give potentially misleading impression of retinal blur, and its possible impact on eye growth and myopia development, since accommodation is often insufficient to optimally focus the foveal retinal image. This lag of accommodative was found experimentally to be sufficient in magnitude as to reverse the sign of peripheral relative myopia, becoming peripheral absolute hyperopia instead. 

The work summarized here used clinical autorefractors to measure refractive state over the central portion of the pupil, thereby ignoring the contribution of higher-order aberrations to refractive state measurements. This methodological limitation is overcome by the use of wavefront aberrometers to measure the eye's refractive properties (Thibos & Hong, 1999). For example, Lundstrom, Mira-Agudelo, and Artal (2009) measured aberrations out to 40° eccentricity horizontally and 20° vertically and computed refractive state using the Zernike coefficient C₂⁰ for defocus. Like Calver et al. (2007), they reported accommodation had no consistent change in peripheral relative defocus for myopic eyes but emmetropic eyes became relatively more myopic in the periphery. Mathur, Atchison, and Charman (2009) investigated the central visual field of young adult emmetropes more thoroughly by measuring wavefront aberrations at 38 field positions along numerous meridians for two states of accommodation (0.3 and 4 D). They found no consistent, statistically significant change in peripheral relative refractive error when accommodation increased. A similar conclusion was reached by Tabernero and Schaeffel (2009) using a custom photoretinoscope. 

In summary, prior research into the effects of accommodation across the visual field has emphasized the difference between peripheral and foveal refractive states, which is evidently small and inconsistent. However, such investigations tell us little about the three-dimensional shape of the retinal conjugate surface and how it changes during accommodation. To fill this gap of knowledge we used custom apparatus (Wei & L. Thibos, 2010) for measuring ocular wavefront aberrations over the central 30° of visual field (i.e., 15° eccentricity along any meridian), modified to enable studies of accommodation. An important feature of our scanning wavefront aberrometer is rapid sampling of the visual field for an eye with fixed direction of gaze, thereby reducing the possibility of artifacts caused by lengthy experiments or changes in gaze direction. Given the possible importance of peripheral optical defocus for eye growth and myopia development (Smith, 2011), we compare results for adult populations of emmetropic and myopic eyes. 

Methods

We recruited 16 young, adult (mean age: 25 years, age range: 19–36 years), functionally-emmetropic volunteers, none of whom use corrective lenses habitually and all of whom achieved uncorrected visual acuity of 20/20 or better. Subsequent aberrometry measurements confirmed the emmetropic status (mean of spherical equivalent refraction = 0.2 D, standard deviation = 0.3 D) of this population. We also recruited 18 myopic volunteers (mean age: 26 years, age range: 20–32 years) for whom spherical equivalent ranged from −1D to −7D (mean = −3.6 D and SD = 1). Left eyes were measured while right eyes were occluded. Subjects were screened for ocular pathology. All subjects had normal visual acuities (20/20 or better with spectacle correction) and < 0.75 D of central astigmatism. Informed consent was obtained from all participants after verbal and written explanation of the procedures involved in the study. The experiment adhered to the tenets of the Declaration of Helsinki and conformed to a protocol approved by the institutional research board at Indiana University. 

Measurements were obtained with a custom-built instrument (Indiana Scanning Aberrometer for Wavefronts, I SAW, shown schematically in Figure 1) designed to measure ocular aberrations at 850 nm over a 30° diameter field of view centered on the foveal line-of-sight. The instrument measures aberrations associated with a particular location in the visual field by focusing a spot of light (the “retinal beacon”) on the retinal surface at the corresponding retinal location. Light reflected out of the eye from the retinal beacon is captured by a wavefront sensor for analysis. Due to variations in head size and shape, the full 30° field could not be accessed in all subjects without vignetting of the Shack-Hartmann sensor (Adaptive Optics Associates, Inc., Cambridge, MA) in some visual field locations. By reducing the maximum tested eccentricity to 13.5° it became possible to measure the central 27° diameter field completely in all subjects. Although wavefront aberrations have been reported for eccentricities beyond 13.5° (Jaeken & Artal, 2012; Lundstrom et al., 2009; Mathur et al., 2009), in our experience accurate measurements are limited to about 30° of eccentricity if the aberrometer relies on the Shack-Hartmann wavefront sensor for pupillometry (Shen, Clark, Soni, & Thibos, 2010). Defocus measurements were corrected to 552 nm (the centroid of the luminance spectrum of the accommodation target) using the Indiana Eye model of ocular chromatic aberration (Coe, Bradley, & Thibos, 2014; Nam, Rubinstein, & Thibos, 2010; Thibos, Ye, Zhang, & Bradley, 1992). Design principles, technical specifications, and validation results for the basic instrument are available elsewhere (Wei & L. Thibos, 2010). For the current study the instrument's dynamic range was expanded by introducing a pair of relay lenses in a Badal configuration (Goncharov, Nowakowski, Sheehan, & Dainty, 2008) to enable the measurement of eyes over a wide range of refractive states (+8 D to −10 D). The instrument's data acquisition rate (2 visual field locations per second) was sufficient to sample the central visual field in a randomized sequence of 37 locations [eccentricities 0°, 5°, 10°, 13.5° along 12 visual meridians 0° to 360° in 30° steps] in approximately 16 s. Normal blinking was permitted, with subsequent rejection of corrupted data images by quality control procedures. Wavefronts reflected from the eye were descanned by the scanning mirrors and directed into a conventional Shack-Hartmann wavefront sensor, which reported wavefront aberrations in the form of Zernike polynomial coefficients (American National Standards Institute, 2004). 

Figure 1

 

Simplified schematic diagram of the Indiana Scanning Aberrometer for Wavefronts, I SAW. Tip and tilt of a pair of mirrors conjugate to the eye's pupil control the angle of incidence of a probe beam, which in turn sets the location of a retinal beacon. Reflected light from the retinal beacon is descanned by the same mirrors before entering the Shack-Hartmann wavefront sensor. Accommodation is induced by a target viewed foveally through a Badal lens but not through the scanning mirrors.

Since the I SAW instrument's scanning mirrors create a virtual image of the wavefront sensor positioned at various locations of the visual field, one might ask whether the virtual image of the sensor rotated about the instrument's measurement axis in the process. This is important for interpreting the measured axes of astigmatism and higher-order aberrations. We verified that the eye's vertical midline remained vertical when viewed by the wavefront sensor through the scanning mirrors. Therefore, no adjustment in the measured axes of astigmatism or other aberrations was necessary. System aberrations measured along all peripheral lines-of-sight relative to the central line-of-sight were less than wavelength/4, which indicates diffraction-limited performance (Rayleigh criterion) over the measured visual field. Manual and automatic quality control procedures checked for a variety of potential problems, including pupil vignetting by the lids, rotational eye movements due to loss of fixation, translational eye movements due to inadequate head restraint, or poor quality data images due to back scatter, or dim, blurred, or missing spots associated with tear film breakup. 

The pupil was monitored continuously with a CCD camera to aid alignment of the center of rotation of the incoming scanning beam with the pupil center. Since the pupil camera did not look through the scanning mirrors, it was not useful for off-axis pupillometry. Instead, we used the wavefront sensor as a pupilometer for wavefront aberrometry. Morphological filters applied to the Shack-Hartmann data image yielded a binary image of the eye's entrance pupil, from which the pupil boundary was detected and fit with an ellipse by the method of least squares to determine pupil center and diameter. Wavefront slope data were then fit with Zernike polynomials over the circumscribed circular domain of the fitted ellipse (Wei & L. N. Thibos, 2010). 

The natural pupil size determined from the Shack-Hartmann data image was used to compute dioptric refractive state from the measured Zernike coefficient for defocus (C₂⁰). Although pupil constriction was observed as the eye accommodated, the amount of constriction varied significantly between individuals in both study populations. The population mean for pupil diameter decreased from 7.1 mm (standard deviation = 1.1 mm, relaxed eye) to 6.4 mm (SD = 1.2 mm, accommodating eye) for emmetropic eyes. The corresponding decrease for the myopic population was from 6.9 mm (SD = 0.9) to 5.6 mm (SD = 1.1). These small variations in pupil size would be expected to have a minor impact on computed refractive state (Martin, Vasudevan, Himebaugh, Bradley, & Thibos, 2011). 

The eye's far-point, defined as the optical conjugate of the fovea when accommodation is fully relaxed, is an important reference for interpreting refractive state measurements. Prior to data collection, an initial estimate of the subject's far-point was determined by asking the subject to adjust target vergence to the most positive value (i.e., the most distant location) that permitted clear vision of 20/50 letters or a Maltese cross subtending about 1.9°. This target location, called the nominal far point in this report, was used to program a series of target locations that would present all subjects with the same randomized sequence of nominal accommodative demands. This use of a common sequence, consisting of eight levels of nominal demand from 1 D beyond the nominal far-point to 6 D in front of the far-point, in 1 D steps, permitted averaging of results across subjects. 

An example dataset obtained for one individual (YL, nominal far-point vergence = +0.6 D) is shown in Figure 2, with negative target vergence marked on the lower abscissa and accommodative demand relative to the nominal far-point marked on the upper abscissa. The left-hand ordinate of Figure 2 indicates the eye's refractive state as measured by the aberrometer for all 37 test locations and all eight levels of accommodative demand. The dashed line in this figure shows the ideal case of perfect accommodation, for which refractive state = target vergence for all levels of demand and therefore the target is always conjugate to the retina. For each subject, we inspected this type of graph to identify the lowest red circle. The ordinate value of this lowest point (labeled “R” in the graph) indicates the negative vergence of the foveal conjugate point when the eye was in its least accommodated state during the experiment. In other words, the numerical value of R is a refined measure of the foveal far-point. We then computed accommodative response by referencing refractive state to this refined far-point, as shown by the right-hand ordinate in Figure 2. 

Figure 2

 

Example dataset collected for one individual, showing how accommodative demand and response was determined. Symbols show how refractive state (indicated on left-hand ordinate) varies with target vergence (bottom abscissa) along the fovea line-of-sight (red circles) and along peripheral lines-of-sight (blue squares). From these coordinates we determined nominal accommodative demand (upper abscissa, defined as target vergence relative to the nominal far-point vergence N) used during the experiments. Accommodative response (right-hand ordinate) is defined as refractive state relative to the refined measure R of the far-point vergence. Dashed black line is the prediction for perfect accommodation.

Accommodation was induced with single, high-contrast letters displayed on a micro (12 mm × 9 mm, 15 μm square pixels) computer monitor (Liteye Systems, Inc., Centennial, CO) in a Badal configuration. This accommodation stimulus also served as the fixation target. Subjects performed a tumbling-E acuity task during the visual field scan to promote accurate fixation and accommodation throughout the data collection period. Visual field scans of ocular wavefront aberrations were obtained for the eight levels of nominal accommodation demand described above, for a total of 37 × 8 = 296 test conditions in each eye. For each test condition, the visual field was scanned five times to estimate measurement variability, yielding approximately 1,500 wavefront measurements per subject in less than 1 hr. This significant increase in data acquisition rate compared to nonscanning methods (Mathur, Atchison, & Scott, 2008) enabled measurement of many states of accommodation before inducing observer fatigue. A detailed diagram of the complete I SAW system is given in the Appendix. 

In this study the I SAW instrument was used to reveal the shape of the retinal conjugate surface as shown schematically by Map A in Figure 3. The aberrometer tells us where in object space light reflected from the retinal beacon comes to focus, as determined by the Zernike coefficient for defocus C₂⁰. This focus point is imperfect due to the presence of oblique astigmatism and higher-order aberrations but Zernike analysis takes account of these optical imperfections by computing the best-fitting paraboloid (method of least-squares) to the reflected wavefront (Thibos, Hong, Bradley, & Applegate, 2004). This paraboloid is an approximation to a best-fitting spherical wavefront centered on a focus point given by Zernike coefficient C₂⁰. Each focus point is therefore conjugate to the retinal surface according to the minimum RMS metric and the vergence of these retinal conjugate points is interpreted as the eye's refractive state along each of the 37 measured lines-of-sight. Before drawing comparisons between subjects or computing population averages we subtracted the measured refractive state from the refined measurement of foveal far-point vergence so that each subject's accommodative response would be relative to their own far-point. We adopted the usual sign convention for which positive values of accommodative response indicate the eye has greater refracting power and therefore the retinal conjugate surface is closer to the subject. 

Figure 3

 

Definition of four types of visual field map reported in Results. See Methods for detailed descriptions of map types.

Measurements of refractive state across the visual field are presented graphically in visual field coordinates as seen by the observer when using the left eye. Four different conventions for displaying visual field maps were used to achieve different goals. 

•  
  Map #A: Refractive state or accommodative response: Basic measurements of refractive state for each retinal location of the probe beam (and corresponding visual field location) are used to create visual field maps of the vergence of the retinal conjugate surface for individual eyes. By convention, real conjugate points at a finite distance have negative vergence. To facilitate comparison of eyes with different far-points, refractive state is referenced to the refined measure of the foveal far-point to derive maps of accommodative response. Accommodative response maps are thus the vergence difference between the retinal conjugate surface and a reference sphere centered on the eye's first principal point and passing through the foveal far-point P.
•  
  Map #B: Local accommodation: change in absolute refractive state at each retinal locus. For each retinal location, the relaxed value is subtracted from the accommodated value to give positive values of accommodation. This map tells us the difference in vergence between the retinal conjugate surface of the accommodating eye and the conjugate surface of the relaxed eye (as specified by the least accommodated state recorded during the experiment).
•  
  Map #C: Peripheral relative defocus: refractive state of peripheral retina relative to the fovea. Positive values indicate the peripheral line of sight has more power than the foveal line of sight, hence producing “peripheral relative accommodative lead/myopia.” This map tells us the vergence difference between the retinal conjugate surface of the accommodating eye and a reference sphere centered on the eye's first principal point and passing through the foveal retinal conjugate point in the accommodated state.
•  
  Map #D: Accommodation error: refractive state relative to target vergence. Absolute refractive state at each retinal location is subtracted from foveal target vergence. Positive error indicates an over-powered eye (i.e., accommodative lead). This map tells us the vergence difference between the retinal conjugate surface of the accommodating eye and a reference target sphere centered on the eye's first principal point and passing through the foveal target.

Results

Our main finding is that ocular refractive state is nearly constant over the central visual field for all states of accommodation in individual eyes as well as for population means, which confirms and extends previous results of Smith et al. (1988). The upper panel of Figure 4 shows type-A visual field maps of refractive state for eight levels of accommodative demand for an individual eye (emmetropic observer CM). This eye was selected for presentation because it displayed the largest variation in refractive state across the visual field, yet even for this most deviant eye the RMS variation across the map was small (0.44 D). Before computing the population mean maps shown in the middle and bottom panels of Figure 4, individual maps of refractive state were referenced to a refined estimate of the eye's far-point to construct accommodative response maps. Each panel of Figure 4 presents a sequence of maps (corresponding to an ascending sequence of accommodative demands) in an ascending sequence of colors, which indicates the eye's accommodation increased as the demand presented by the visual target increased. More important is the uniformity of color in each map, which indicates variation of refractive state across the central visual field is small compared to range of accommodation investigated. Uniformity of refractive state, in turn, indicates the retinal conjugate surface is spherical for all states of accommodation. Uniformity of accommodative response is evident also for the population average of emmetropic eyes (middle panel of Figure 4) and for the population of myopic eyes (bottom panel of Figure 4). This main finding is summarized in Figure 5, which shows mean accommodative response (averaged over all meridians and subjects) varies little with visual field eccentricity for both populations of subjects. 

Figure 4

 

Type A maps of the central visual field for eight levels of accommodative demand. Upper panel shows measured refractive state for the individual with the most nonuniform maps. Middle panel shows mean accommodative response for the emmetropic population and bottom panel shows mean response for the myopic population. Each map shows how refractive state or accommodative response varies across the central visual field (temporal visual field on the left, superior visual field on top). All maps of the visual field span 30° in diameter (i.e., maximum eccentricity = 15°). Black circles show the sample locations, which are interpolated to make a continuous map with scale shown by the color bar on the far right. Number in upper right corner of each map is nominal accommodative demand, equal to nominal far point vergence—target vergence. Number in the lower left corner is the mean ±1 standard deviation of the 37 measurements displayed in the visual field map. For graphs of population means, accommodative response is relative to the refined estimate of the foveal far-point of each individual eye. Maps for the individual eye show absolute measurements before subtracting the far-point vergence. Tabulated numerical values for the 37 sample points in every population graph are available as supplementary material.

Figure 5

 

Effect of visual field eccentricity on mean accommodative response. Symbols indicate mean response averaged over eight meridians and all subjects in each population. Error bars represent ±1 standard deviation of those responses. Standard errors of the means (not shown) are smaller than the symbol radius. Abscissa values are staggered for clarity. Numbers near each curve indicate nominal accommodative demand.

In the upper and middle panels of Figure 4 the spatial average of the map for −1 D demand is slightly positive compared to the map for 0 D demand. This indicates the eye typically accommodated slightly when the Badal visual target moved 1 D beyond the foveal far-point. According to Figure 5, this inappropriate accommodation was about 0.5 D on average in emmetropic eyes but nearly zero for myopic eyes. This “lead” of accommodation may be a case of “instrument myopia” in which the eye returns to a resting state of accommodation when the blurred (i.e., “fogged”) target is inadequate for maintaining the fully relaxed state.(Hennessy, 1975) For targets closer than the far-point, accommodative response is less than demand (i.e., accommodative “lag”), which is not unexpected for monocular stimulation of accommodation with a Badal system. Although these errors of accommodation are of interest, they did not defeat our primary mission of stimulating accommodation sufficiently to enable a determination of the uniformity of refractive power changes over the visual field. Provided most subjects accommodated by approximately the same amount to a given demand, thereby keeping between-subject variance low, absolute accommodative accuracy was not required to achieve our main goal. 

Accommodation is defined as a change in refractive state, which can be measured independently for each point in the visual field. In principle, this local amount of accommodation could vary with visual field location but, as shown by the type-B maps in Figure 6, we found that local accommodation is nearly uniform for individual eyes as well as for population mean of emmetropic and myopic eyes. This is not surprising, given the results of Figure 4, since local accommodation is the difference between visual field maps for distant and near targets. Subtracting one uniform map from another yields a uniform map of local accommodation. In practice, this means that the amount of accommodation measured foveally occurs also at other locations in the central field. We emphasize that our results say nothing about accommodative response to a peripheral stimulus. In our experiments accommodation was stimulated by a foveal target, so results in Figure 6 imply that if the eye accommodates foveally by some amount to a foveal stimulus, then the eye also accommodates locally by the same amount across the central visual field. 

Figure 6

 

Type B visual field maps of local accommodation for eight levels of accommodative demand. Color bar scale shows the local change in refractive state produced by accommodation at each point in the visual field. All maps of the visual field span 30° in diameter (i.e., maximum eccentricity = 15°). Graphical conventions are the same as in Figure 4. Tabulated numerical values for the 37 sample points in every population graph are available as supplementary material.

Approximate uniformity of visual field maps in Figure 4 and Figure 6 is accentuated by a relatively coarse dioptric scale appropriate for a 6 D range of accommodative demand. Uniformity of refractive state implies a spherical shape of the retinal conjugate surface. To better reveal small deviations from the perfect sphere, we next subtracted the foveal refractive state from all measurements to produce a type-C map. Graphically, this is equivalent to constructing a reference sphere centered on the eye's first principal point and passing through the foveal point on the retinal conjugate surface. This type-C map, called peripheral relative defocus in the literature, tells us how close the retinal conjugate surface is to a perfect sphere for each accommodative state. Deviations are measured on a dioptric scale since peripheral relative defocus is computed as the vergence difference between the retinal conjugate surface and a reference sphere containing the foveal retinal conjugate point. 

Deviation of the retinal conjugate surface from a perfect sphere was similar for all accommodation levels in individual eyes and also for the population means of emmetropic and myopic eyes (Figure 7). Although we observed considerable intersubject variability, the hypothetical average emmetropic adult eye in our subject pool exhibited a central-peripheral gradient in refractive power with more peripheral retinal loci being myopic relative to the fovea. The center of symmetry was slightly displaced towards nasal retina. This nasal displacement was so extreme in the individual CM that it gives the appearance of a nasal-temporal gradient. In this eye, nasal retina experiences “peripheral relative myopia,” whereas temporal retina experiences “peripheral relative hyperopia” for all states of accommodation. A variety of patterns unique to each individual were observed, with accommodation producing little change in the pattern. When averaged, the idiosyncrasies of individual eyes tended to cancel, revealing an average pattern that was nearly symmetrical about the fovea. 

Figure 7

 

Type C visual field maps of peripheral relative defocus for eight levels of accommodative demand. Color bar scale shows the difference between foveal refractive state and the refractive state at each point in the visual field. All maps of the visual field span 30° in diameter (i.e., maximum eccentricity = 15°). Graphical conventions are the same as in Figure 4. Numerical values for the 37 sample points in every population graph are available as supplementary material.

To help interpret the functional significance of peripheral relative defocus reported in Figure 7 we examined accommodative error, which is defined as the difference between the refractive state map of the eye and the target vergence map of the visual world. As emphasized by Flitcroft (2012), target vergence maps vary widely in the natural world, and this was undefined in our laboratory experiment because the visual stimulus was confined to a small area near the fixation point. In the absence of an explicit target vergence map, we assumed the target is a surface of constant vergence (for example, a spherical perimetry bowl centered on the eye and passing through the fixation point). Thus for present purposes we computed accommodative error as the vergence difference between the retinal conjugate surface and a reference sphere centered on the eye's first principal point and passing through the fixation target. 

Accommodative error maps of type-D displayed in Figure 8 reveal a general trend: When the fovea lags, the central field lags with it. The subtle patterns of peripheral relative defocus revealed in Figure 7 now appear as more or less accommodative lag. This result is particularly striking for subject CM who demonstrated relatively large amounts of peripheral relative myopia in nasal retina but peripheral relative hyperopia in temporal retina (Figure 7). Despite these variations, the eye showed accommodative lag throughout the visual field for moderate levels of accommodation (Figure 8). The apparent lead of accommodation evident for 0 D and for −1 D demand is greater than was evident in Figure 4, which is probably an artifact produced by errors in locating the nominal far-point. As illustrated in Figure 2, if the nominal far-point (N) lies beyond the refined far-point (R) then accommodative lead relative to the nominal far-point (red horizontal line in the graph) will appear to be greater than for lead relative to the refined far-point (green horizontal line in the graph). Since target vergences were programmed at the beginning of the experiment based on nominal far-point estimates, the extra lead evident in Figure 8 indicates that when the target was placed at the nominal far-point during the experiment, the target was actually beyond the refined estimate of the eye's far-point as determined by data analysis at the end of the experiment. Therefore, lead relative to the zero-demand target is greater than lead relative to the far-point. 

Figure 8

 

Type D visual field maps of accommodation error for eight levels of accommodative demand. Color bar scale shows the difference between foveal target vergence and the refractive state at each point in the visual field. All maps of the visual field span 30° in diameter (i.e., maximum eccentricity = 15°). Graphical conventions are the same as in Figure 4. Tabulated numerical values for the 37 sample points in every population graph are available as supplementary material.

Discussion

In this study we asked the same question two ways. Does refractive state change uniformly over the central visual field when the eye accommodates? Does the geometrical shape of the retinal conjugate surface change when the eye accommodates? Our experimental evidence indicates that refractive state does indeed change uniformly over the central visual field when the eye accommodates, as reported previously in the literature on human eyes (see Introduction) and also in rhesus monkey (He, Wendt, & Glasser, 2012). Moreover, since the shape of the retinal conjugate surface is nearly spherical in the relaxed eye, the shape remains nearly spherical as the eye accommodates to targets at various distances. This result holds not only for individual eyes, but also for population means of emmetropic and myopic eyes. Thus we conclude the central portion of the retinal conjugate surface of the hypothetical “average eye” is nearly spherical over a 6 D range of accommodative demand. Slight deviations from the spherical form in individual eyes may therefore simply represent random variations about the central tendency of the population. 

Previous work by Smith and colleagues (1988) reported that accommodation changes ocular refractive power uniformly for eccentricities up to 30° along the horizontal meridian, which was predicted by theoretical optical analysis of the Le Grand schematic eye model (Smith et al., 1988). Our experiments, using wavefront technology that takes higher order aberrations into account, confirm those measurements and theoretical predictions along eight visual meridians and eight levels of accommodation for two populations of eyes (emmetropic and myopic). In addition, we report the magnitude of individual variation that occurs within the population for a variety of ways of interpreting measurements of refractive state across the visual field. 

The spatial pattern of peripheral relative defocus, which has been widely studied in the past, was found in our experiments to be unaffected by accommodation, suggesting the pattern is likely due to factors other than the crystalline lens (e.g., cornea or retinal profile). However, as emphasized by Whatham et al. (2009), peripheral relative defocus is only one factor determining retinal blur. Local accommodative error, which takes target vergence into account, is more likely to be relevant to myopia development. A simple way to envision accommodative error responsible for retinal blur emerges from our finding that the retinal conjugate surface is typically spherical. If the central portion of the visual world lies on a sphere of constant vergence, like a perimeter bowl, then accommodative error will be the same everywhere in the central field. Deviations from a spherical world will therefore be the primary factor responsible for variation in blur across the retinal surface at any state of accommodation. 

Previous researchers have built a strong case for the influence of peripheral refractive errors on eye growth by studying the mid- and far-periphery (for a review, see Smith, 2011). Placing that work in context requires knowledge of any refractive errors in the central visual field. For example, Smith, Hung, and Huang (2009) raised experimental animals in a manner that allowed unrestricted central vision while optically blurring peripheral vision. To interpret the results of that experiment requires knowledge of how much defocus the central area of unrestricted vision likely experienced during rearing when accommodation was unrestricted. The implicit assumption was that refractive error was constant over the central region and, moreover, remained constant during accommodation. Our study provides support for that assumption by demonstrating uniformity of refractive state across the central visual field for a range of accommodative states. 

Assumptions and potential sources of error

Our study used a wavefront aberrometer to determine the location in object space of the retinal conjugate surface. That method makes two implicit assumptions: (a) that the fundus is a thin reflector, and (b) that the plane of reflection of the probe beam is located axially near the photoreceptors. In fact, the fundus is a thick reflector that can be dissected with micron precision using optical coherence tomography (Gao, Cense, Zhang, Jonnal, & Miller, 2008). Optical simulations of the Shack-Hartmann measurement of bilayer fundus reflections have demonstrated that conventional centroid-based algorithms report defocus values for the radiance-weighted sum of defocus values for each reflecting layer (Liu, Thibos, Marin, & Hernandez, 2014). The implication for our study is that the retinal conjugate locations we report refer to the radiance-weighted mean of the multiple reflections produced by the thick human funds. Prior work suggests the mean axial location of fundus reflection is slightly posterior to the cone entrance apertures (Teel, Jacobs, Copland, Neal, & Thibos, 2014), which cause the eye's refractive state to appear slightly biased in the myopic direction (i.e., the measured retinal conjugate is closer to the eye than expected for the photoreceptors). If this bias is independent of retinal eccentricity, then it would have no effect on the shape of the retinal conjugate surface, only its absolute axial location. 

Crossed polarizers placed in the illumination and imaging channels of the I SAW instrument were used to avoid contamination of data images from the horizontal visual field caused by back scattering from scanning lenses (Wei & L. Thibos, 2010). However, this improved design has implications for the accuracy of wavefront measurements. Ignoring the birefringence of cornea, lens, and retina (Marcos, Diaz-Santana, Llorente, & Dainty, 2002; Prieto, Vargas-Martin, McLellan, & Burns, 2002), polarized light reflected from cone outer segments and depolarized light reflected from posterior layers (retinal pigment epithelium and choroid) will enter the aberrometer. Both sources of light are transmitted if a quarter-wave plate is inserted to convert linear polarization to circular, but only depolarized light will be transmitted without the quarter-wave plate. A smaller myopic bias in measured refractive states would be expected when a quarter wave plate is present (Burns, Wu, Delori, & Elsner, 1995), which is the configuration used for the majority of results we report here. We evaluated these possibilities in a pilot experiment by measuring refractive state with and without the quarter-wave plate. No statistically significant difference was obtained, which suggests that most of the light captured by the aberrometer was depolarized. Assuming this depolarized light was reflected by the retinal pigment epithelium or choroid, a slight myopic bias would be expected as discussed above (Teel et al., 2014). 

Ocular refractive state was specified in our study by the Zernike coefficient C₂⁰, which corresponds to the curvature of the spherical wavefront that is a least-squares fit to the aberrated wavefront reflected from a subject's eye. However, many alternative metrics are available for computing refractive state from a wavefront aberration function (L. N. Thibos et al., 2004) so the question arises whether a different choice of metric may have significantly altered our results and conclusions. To explore this possibility we compared Zernike refractive states with those computed by two other metrics: paraxial refractive state (i.e., the Seidel metric, which depends only on the local curvature of the eye's wavefront at the pupil center), and visual Strehl ratio computed from Modulation Transfer Function (VSMTF), which has been shown to be an unbiased measure of foveal refractive state for small letters (Martin et al., 2011). These comparisons are displayed for the population mean of emmetropic eyes in Figure 9. These visual field maps confirm that refractive state is uniform across the visual field regardless of metric. When accommodation is relaxed (bottom row of Figure 9), maps for all three metrics are nearly identical. As the eye accommodates, the maps remain uniform but begin to diverge in absolute value, with the Zernike metric indicating less accommodation than was computed by the Seidel metric, and VSMTF maps intermediate between these two extremes. This ordering of refractive states is likely due to spherical aberration, which typically changes from positive to negative as the eye accommodates (Thibos, Bradley, & Lopez-Gil, 2013). 

Figure 9

 

Type A visual field maps of accommodative response for emmetropic population derived using different metrics for determining refractive state from wavefront aberrations. Left column shows accommodative response derived with the minimum RMS metric, the middle column shows accommodative response obtained by optimizing visual quality metric VSMTF, and right column shows accommodative response determined by the paraxial (Seidel) wavefront curvature. Graphical conventions are the same as in Figure 4 except the color calibration bar is on top.

Conclusion

Ocular refractive state changes uniformly over the central visual field as the eye accommodates. Blur due to accommodative errors across the central field for a target of constant vergence is similar to that measured in the fovea. Thus loss of image quality due to accommodative errors, which potentially drives myopia and may affect many aspects of visual function, will be similar across the central retina. 

Acknowledgments

Commercial relationships: Vistakon, Inc. Jacksonville, FL, supplied funding (F); Indiana University has licensed patents to Vistakon, Inc. for which TL is listed as a co-inventor (I); LNT consults for Vistakon, Inc. (C); Indiana University has licensed patents to Vistakon, Inc. for which LNT is listed as a co-inventor (P). 

Corresponding author: Tao Liu. 

Appendix

Figure A1

 

Detailed optical layout of the scanning Shack-Hartman aberrometer (Wei & L. Thibos, 2010) as modified for accommodation experiments. LD- laser diode; BE- beam expander; HSWS-Hartman Shack wavefront sensor; L1-Badal focusing lens; L2-Badal offset lens; L3, L4- telescope relaying pupil plane to pupil camera and fixation path; L5, L6-telescope relaying pupil plane to X scanner; L7, L8-telescope relaying pupil plane to Y scanner; L9, L10-telescope relaying pupil plane to lenslet array; L11- focusing wavefront on retina camera; BS-pellicle beamsplitter; HWP-half-wave plate; LP1, LP2-crossed linear polarizer; QWP-quarter-wave plate. All polarization optics are working at wavelength λ = 850 nm.