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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Cataract Refract Surg. Author manuscript; available in PMC 2010 October 11.
Published in final edited form as:
PMCID: PMC2952422
NIHMSID: NIHMS227744

Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality

Abstract

PURPOSE

To examine the impact of the location of the fixation target, pupil center, and reference axis of ophthalmic aberrometers and videokeratographers on the measurement of corneal aberrations relevant to vision.

SETTING

Clinical Research, Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA.

METHODS

The design features of a generic aberrometer and videokeratographer and their interaction with the eye were examined. The results provided a theoretical framework for experimental assessment of pupil translation errors on corneal aberrations relevant to vision and their correction in 129 eyes.

RESULTS

Two key principles emerged. First, the aberrometer’s measurement axis must coincide with the eye’s line-of-sight (LoS). Second, the videokeratographer’s measurement axis (the vertex normal) must be parallel with the eye’s LoS. When these principles are satisfied, the eye will be in the same state of angular rotation and direct comparison of measurements is justified, provided any translation of the pupil from the vertex normal is taken into account. The error incurred by ignoring pupil displacement in videokeratography varies between eyes and depends on the type of aberration and amount of displacement, with the largest residual correction root-mean-square wavefront error being 1.26 μm over a 6.0 mm pupil, which markedly decreases retinal image quality.

CONCLUSION

Translation of the pupil center with respect to the vertex normal in videokeratography should not be ignored in the calculation of the corneal first-surface, internal aberrations of the eye relevant to vision, or the design of refractive corrections based on videokeratography.

Both videokeratography and whole-eye wavefront aberrometry have been used in the design of refractive corrections (eg, corneal refractive surgery, intraocular lenses [IOLs], wavefront-guided contract lenses). Data from videokeratography can be used to calculate corneal first-surface wavefront error (WFE)115 and, in combination with whole-eye WFE measurements, can be used to estimate the internal WFE of the eye.10,1622 Knowledge of the internal aberrations of the eye can in turn be used to design or select the best IOL to implant. Aberrometers and videokeratographers typically use different reference axes for measurement.23 As a result, the pupil center is typically located in 2 different positions with respect to the origin of each instrument’s reference coordinate system.24,2527 It has been argued that calculations of internal WFE using instruments with different alignment criteria can result in errors caused by translation and rotation of the eye.28 For example, if the fixation task of any given instrument causes the eye to angularly rotate and/or to be translated with respect to the reference coordinate system of another instrument, the data from the 2 instruments will measure different aspects of the optical properties of the eye and can introduce errors into whatever calculation is being performed. As a consequence, the design of optical corrections (eg, refractive surgery, IOLs, wavefront-guided contact lenses) can be in error and measurements might not accurately comparable across platforms.

In this study, we systematically examined the impact of the location of the fixation target, pupil center, and reference axis from an instrument-design perspective. We analyzed the measurement of WFE that was relevant to vision for aberrometry and videokeratography independently and then in combination. Finally, we examined the impact of the translation errors in videokeratography on the corneal first-surface WFE relevant to vision.

Alignment of Wavefront Aberrometers

The recommendations of the Optical Society of America (OSA) task force2931 and the resulting American National Standards Institute (ANSI) standard (Z80.28)32 specify that whole-eye WFE be referenced to the center of the pupil using the line of sight (LoS) as the reference axis.2931 The OSA task force and ANSI committee selected referencing to the LoS because the bundle of light that passes through the entrance pupil and leaves the exit pupil defines the quality of the retinal image, which is in turn used by the neural system for visual processing. Thus, the LoS is the most relevant reference axis for defining retinal image quality at the point of fixation.

Our intention was not to model a specific commercial device. Instead, we modeled a generic wavefront aberrometer that met the fixation requirements detailed below and the requirements of the ANSI Z80.28 standard. We further suggest that the ANSI standard be improved to included fixation-target details. Because instrument manufacturers typically do not provide exact details of instrument design due to their proprietary nature, it is beyond the scope of this paper to evaluate which instruments obey these fundamental operating principles and which do not. We encourage each manufacturer to state whether their instrument is compliant with the operating principles detailed in this article and those published in the ANSI Z80.28 standard.

In a generic aberrometer (Figure 1), the fixation target and the probe beam are coaxial, located at optical infinity, and their chief rays pass through the center of the entrance pupil. Two eyes are illustrated: The solid posterior pole represents an emmetropic eye, and the dotted posterior pole represents a myopic eye. Note that the retinal image of the probe beam is centered on the fixation target image regardless of the eye’s state of focus. Thus, even if the eye is defocused due to uncorrected spherical refractive error, light from the narrow probe beam will strike the center of the blur circle formed by the fixation target whose light fills the pupil. Thus, regardless of whether the patient fixates on the fixation target or the probe beam, the eye is looking in the same direction.

Figure 1
Schematic diagram of a generic, ANSI Z80.28-compliant, wavefront aberrometer. The chief ray of the fixation channel and the small probe beam enter the fixating eye along the LoS (dashed line). The posterior poles of an emmetropic eye (solid curve) and ...

Suppose that the wavefront aberrometer is translated in a direction perpendicular to its own axis, as indicated by the bold arrows in Figure 1. This might happen inadvertently or deliberately to avoid corneal reflections from the probe beam. Now the probe beam enters the eye through an eccentric point in the pupil and therefore does not follow the LoS. If the eye is emmetropic, the probe beam will still strike the retina in the middle of the image of the fixation target. However, if the eye is defocused, the eccentric probe beam will not strike the center of the blur circle formed by the fixation target, as shown in Figure 2, A. Thus, the apparent visual direction of the probe beam and the fixation target will be different, which presents the patient with an ambiguous fixation task. The patient must decide whether to fixate on the center of the blurry fixation target or on the probe beam. For wavefront aberrometry, the probe beam’s retinal location is more important than the fixation target’s location because the probe beam provides the light that is reflected out of the eye and measured. In this case, if the patient attends to the center of the blurry fixation target, the probe beam will strike the retina at some eccentric location and therefore aberrations will be measured along an axis that differs from the LoS. The retinal eccentricity of the probe image is dependent on the magnitude of the refractive error and the eccentricity with which the probe beam enters the eye. If the eccentricity with which the probe beam enters the eye is large and the refractive error is large, measurement errors can be significant (Appendix).

Figure 2
Illustration of the consequence of having the narrow probe beam (red line) enter the eye’s pupil eccentric to the LoS (dashed line). A: The narrow probe beam and fixation target are located at optical infinity. Light from the distance fixation ...

One way to avoid the potential measurement errors described above is to shift the fixation target and probe beam axially to make them optically conjugate to the retina, as shown in Figure 2, B. This alternative configuration of the aberrometer ensures that the retinal image of the narrow probe beam will remain centered on the retinal image of the fixation target because both are located at the far point of the eye. By placing the probe and fixation target at the eye’s far point, the requirement for the probe beam to pass through the center of the pupil can be relaxed. Such a configuration minimizes the possibility that the instrument will provide a stimulus to eye rotation if the probe beam enters the pupil at an eccentric location. The potential for eye rotation is not eliminated entirely, however, because the far point of an aberrated eye is not uniquely defined for emmetropic or myopic eyes. Astigmatism and higher-order aberrations (HOAs) can cause the retinal image of the narrow probe beam to be displaced from the center of the retinal image of the fixation target when the probe beam enters the pupil eccentrically. These displacements are typically small in comparison to the displacement due to defocus errors. As a consequence, instruments that make the narrow probe beam and fixation target conjugate to the retina are more tolerant of minor operator misalignment errors with respect to the LoS.

Eye rotation does matter. Tilted optical components have a different aberration structure than components that are not tilted with respect to the reference axis. Thus, eye rotations confound the comparison of data between platforms, the calculations of internal aberrations of the eye, the alignment of a laser platform to the eye for refractive surgery, and the design of any correction to minimize the WFE in the eye. The magnitudes of the errors depend on the amount of the eye rotation. Ideally, system designs should not provide a stimulus for the eye to turn that are different from other instruments in the same class, nor should instruments in different classes (eg, videokeratographers, aberrometers, refractive surgery treatment platforms) provide different stimuli for eye rotation.

Alignment of Videokeratographers

In contrast to the generic wavefront sensor, the generic videokeratographer uses the vertex normal to align the device33 (Figure 3). Here, the operator typically translates the instrument perpendicular to the measurement axis until the first Purkinje image of the fixation target is reflected back along the optical axis of the videokeratographer. When this alignment state is achieved, the instrument is aligned with the vertex normal (or videokeratographer axis [VK axis]) of the cornea. Thus, the eye is in the primary position of gaze, fixating on a distant axial target, when corneal topography is measured.

Figure 3
Alignment of the videokeratographer requires the operator to translate (motion indicated by bold arrows) the videokeratographer until the first Purkinje image of the fixation point lies on the optical axis of the videokeratographer while the eye is tending ...

The location of the pupil center is not considered during alignment, and it is frequently found to be displaced from the reference axis, as shown schematically in Figure 3 or seen in the videokeratography image in Figure 4. The consequences of this pupil displacement are described in a later section. The important point here is that when the videokeratographer is translated laterally by the operator, there is no stimulus to eye rotation. This is because the fixation target is at optical infinity. Translation of the instrument sweeps the incoming beam of light parallel to itself; therefore, the retinal image remains fixed and centered on the fovea. Because the retinal image is fixed, there is no need for ocular rotation to maintain gaze fixation. The only consequence of instrument translation is that different rays are intercepted by the pupil to form the retinal image. Because 1 of these parallel rays passes through the pupil center, the LoS is parallel to, but not necessarily coincident with, the vertex normal.

Figure 4
A typical normal eye captured by a videokeratographer (TMS-1). In this eye, the pupil (outlined in red) is not centered on the vertex normal reference axis (center of all green circles).

If the fixation target is located at a finite optical distance along the measurement axis, the chief ray is not necessarily parallel to the vertex normal, as shown in Figure 5. Thus, if the eye remains in the primary direction of gaze, as shown, the retinal image of the fixation target will fall on the peripheral retina. Therefore, to maintain fixation, the eye must rotate. It seen in Figure 5, light from 3 fixation distances, all on the VK axis, requires the eye to rotate different amounts relative to each other to achieve fixation. Thus, the eye will not be in the standard primary gaze position when corneal topography is measured.

Figure 5
Schematic of an eye aligned to a videokeratometer showing the location of the fixation target at 3 locations along the vertex normal (dashed dot line). The eye is fixating a distant point source, F1. Fixation point sources F2 and F3 are at finite distances. ...

The feature in Figure 5 that shows the presence of eye rotation is the angle between the VK axis and the LoS when the patient is fixating on the target. For the distant fixation target F1, the LoS is parallel to the VK axis, which signifies no ocular rotation. In this case, pupil decentration from the vertex normal is a simple translation error. For finite fixation distance, the LoS is not parallel to the VK axis; thus, pupil decentration from the vertex normal is a combination of translation and rotation errors, as previously noted.28

This is important because if videokeratography is to be used to accurately calculate corneal first-surface aberrations relevant to vision and to correct corneal aberrations to improve foveal vision (eg, design an IOL to improve vision, calculate the internal aberrations of the eye relevant to vision, or design corneal refractive surgery to improve vision), the relevant bundle of rays refracted by the cornea must pass through the eye’s pupil. Other rays blocked by the iris and sclera are not relevant to the formation of the retinal image. Calculating WFE centered on the vertex normal does not accurately represent the bundle of light passing through the pupil unless, by chance, the center of the entrance pupil lies on the vertex normal. As discussed below, it is rare for the vertex normal to coincide with the center of the pupil. As in wavefront sensing, the alignment axis most relevant to foveal vision is the LoS, not the vertex normal.

Videokeratography does not use the LoS as its reference axis because the difference in reference axes for wavefront sensing and videokeratography is historical. Videokeratography instruments were not developed with the intention of calculating corneal aberrations relevant to vision, nor were they developed to use such calculations combined with wavefront measurements to estimate the internal aberrations in the eye or design corrections for the optical errors in the eye to improve vision. As a result, using a reference axis that is centered on the pupil (the LoS) was not a priority. Instead, the priority was to find an easy to implement a clinically viable reference axis. The vertex normal serves this purpose well. Nonetheless, if the LoS were to be used instead, ocular rotation would not depend on the axial location of the fixation target.

In recent years, the increased interest in understanding retinal image quality has led to videokeratography data being used for calculating the WFE of the corneal first surface,115 the design of corneal refractive surgery treatments,34,35 and in combination with wavefront sensing to estimate the internal aberrations of the eye.1622,36 When retinal image quality is the driving force for the calculation, the bundle of rays that passes through the eye’s pupil defines the optically relevant light for vision. As a consequence, proper registration of measurements using different instruments is crucial and fundamentally important in the design of therapy (eg, corneal refractive surgery and IOLs) for correcting the refractive errors in the eye and for calculating corneal first-surface aberrations or internal aberrations relevant to vision.

Relative Alignment of Videokeratographers and Wavefront Sensors

The difference in alignment strategies between the 2 systems is easily seen by combining the systems using a beam splitter. In Figure 6, a generic wavefront sensor and a generic videokeratographer with fixation targets at optical infinity are combined with a beam splitter. When the fixation targets are placed at optical infinity on the respective measurement axes, all rays of light from the fixation targets are parallel to each other and the chief rays are superimposed. As a result, the images of the fixation targets from both instruments will be superimposed, even if the eye has a defocus error, in which case the blur circles will be superimposed. Thus, no eye rotation is required for the eye to move from 1 fixation target to the other. Although not shown, the same would be true if the wavefront sensor (using the LoS as a reference axis) were designed to make the fixation target and probe beams conjugate to the retina. Thus, when 2 systems are designed with their fixation targets at optical infinity and on the instrument optical axis, the displaced pupil viewed by the videokeratographer is a result of a simple translation and not a product of a translation and rotation. Because the ANSI Z80-28 compliant wavefront sensor uses the LoS as a reference axis, it can also make the fixation point conjugate with the retina without initiating an instrument stimulus for eye rotation. However, this is not necessarily true for a corneal topographer aligned to the vertex normal and containing a fixation target on the vertex normal. In the latter case, eye rotation will confound the simple translation of the pupil, as in Figures Figures55 and and77.

Figure 6
A wavefront sensor (WS) and videokeratographer (VK) instrument, each with a fixation target at optical infinity, are aligned to the same eye via a beam splitter. The wavefront sensor is aligned by centering the fixating eye’s entrance pupil on ...
Figure 7
A wavefront sensor (WS) with a probe beam (dashed line) and a videokeratographer (VK) with a fixation target at a finite optical distance along the VK axis, are aligned to the same eye via a beam splitter. The chief ray from the videokeratographer fixation ...

In general, when the fixation target of the videokeratographer is at a finite distance and the fixation target of the wavefront sensor is located at optical infinity or at the eye’s far point, the 2 fixation targets will not appear to be superimposed because their chief rays are not parallel. As shown in Figure 7, eye rotation will be required to switch from 1 fixation target to the other. Thus, the displacement of the pupil with respect to the LoS will be due to translation and rotation, making it more complicated to accurately calculate corneal first-surface aberrations with respect to the LoS. As long as the optical location of the fixation target for the videokeratographer is reasonably close to optical infinity, the eye movement required is insignificantly small. For example, if the fixation target is moved from optical infinity to 4 m in front of the eye, the eye will rotate less than 30 seconds of arc to regain fixation. Given fixational eye movements range up to 5 minutes or arc in ½ minute of time,37 the eye rotations are easily within measurement error for a normal fixating eye. Therefore, it is reasonable to ignore the rotation component as long as the fixation target is near optical infinity and located on the reference axis of each instrument. Fixational eye movements are very small and have little effect on measurement,38 and there is no reason to believe that fixational eye movements will be different between whole-eye WFE measurements and corneal topography wavefront measurements as long as similar fixation targets are used. Thus, the effects of fixational eye movements have essentially no impact on the broader issues discussed in this paper.

A potential penalty of using fixation targets at infinity is loss of fixation accuracy by eyes with large refractive errors. This potential problem can be avoided by adjusting the fixation distance axially along the LoS to place it near the eye’s far point, which is relatively simple in a combined instrument designed with parallel measurement axes and a single fixation target.

In summary, 2 key principles have been identified for alignment of aberrometers and videokeratographers to the eye when the goal is to compare their measurements, use videokeratography to quantify corneal first-surface aberrations relevant to vision, or design refractive corrections. First, the aberrometer’s measurement axis must coincide with the eye’s LoS so that measurements are relevant to foveal vision. Second, the videokeratographer’s measurement axis (the vertex normal) must be parallel to the eye’s LoS to enable the extraction of corneal aberrations that are relevant to foveal vision. When these 2 alignment principles are satisfied, the eye will be in the same state of rotation for both measurements. Direct comparison of measurements is therefore justified, provided any displacement of the pupil from the vertex normal is also taken into account. Satisfying both alignment principles is easiest for a combined instrument that uses a single fixation target; however, it is also possible for some independent instruments carrying separate fixation targets at optical infinity.

In principle, pupil decentration from the VK axis must be taken into account. In practice, errors are committed if decentration is ignored. To estimate the magnitude of these errors in normal eyes, the following section analyzes videokeratography data from the Texas Investigation of Normal and Cataract Optics (TINCO) study. The results illustrate the consequence of pupil translation errors in the calculation of corneal first-surface WFE that is relevant to vision.

SUBJECTS AND METHODS

Experimental Assessment of Pupil Translation Errors

Subjects

This retrospective cross-sectional analysis was of videokeratography data collected from subjects participating in the TINCO study. One eye of 18 to 38 subjects in each decade of life between 20 years and 80 years (total of 177 eyes from 177 subjects) with varying levels of nuclear opalescence as defined by Lens Opacities Classification System III (LOCS III) scores39 were recruited from the clinics, faculty, and staff of the Department of Ophthalmology at the University of Texas Health Science Center in San Antonio and the College of Optometry at the University of Houston. Videokeratography measurements were taken with normal physiological pupils (no dilating drugs). The protocols of the TINCO study were reviewed and approved by institutional review boards of the University of Texas Health Science Center at San Antonio and University of Houston. Subjects were excluded due to poor systemic health, significant cortical cataract, significant posterior subcapsular cataract, and ocular disease other than nuclear cataract. Twenty-nine subjects were removed from the database due to incomplete or bad primary data (primary data included wavefront sensing and LOCS III photographs) or discovery of the existence of retinal disease during testing (typically age-related maculopathy), leaving 148 eyes of 148 qualified subjects (1 eye per subject). Of these 148 eyes, 129 had acceptable videokeratography data. Acceptable data were defined as a readable image and data files that by inspection were not rotated, decentered, or obscured by eyelids or lashes and had no erroneous identified pupil borders. The data from these 129 eyes of 129 subjects are reported here.

Videokeratography Measurements

In the TINCO study, videokeratography was measured using a TMS-1 (Tomey, Inc.) or Keratron (Optikon) videokeratographer. The instruments are similar in that they both use a small Placido cone with a short working distance from the corneal surface, have fixation targets on axis at or near optical infinity, and use the vertex normal as a measurement reference axis. Both targets provide approximately 300 candelas/m2 of illuminance at cornea during measurement.

Pupil Center Location with Respect to the Vertex Normal

Physiological pupil center locations with respect to the vertex normal were extracted from the corresponding data files generated by each videokeratographer. These files were further processed and analyzed using custom routines written in MatLab (version 2007b, The MathWorks). The accuracy of the pupil center location was verified for each subject by visually inspecting the analyzed image (eg, Figure 4). For uniformity of data reporting, the recommendation for ocular WFE reporting29 was followed by converting data of right eyes to look like left eyes respecting the vertical mirror symmetry of humans. As a consequence, positive x values are temporal and positive y values are superior for all eyes whether they are left or right eyes. The pupil center often (but not always) varies for any given eye as a function of luminance.40 These variations when they occur are typically less than 0.2 mm. Here, the optical aberrations of the corneal first surface were calculated over a 6.0 mm pupil assuming the 6.0 mm pupil is centered over the vertex normal or over the center of the displaced pupil.

Calculation of Corneal First-Surface Wavefront Error from Videokeratography Measurements Centered on the Vertex Normal

Corneal first-surface WFE over a 6.0 mm pupil centered on the vertex normal (Figure 8) was calculated using Visual Optics Laboratory (VOL) (version 7.31, Saver and Associates, Inc.). Visual Optics Laboratory calculates the corneal first-surface WFE over the vertex normal by considering the cornea to be a single surface optical model. A selectable Zernike fit (here 6.0 mm) to the corneal examination is performed centered on the vertex, and the chief ray is traced through the center of the Zernike surface. The paraxial focal point is located along this ray downstream from the cornea at a distance equal to the focal distance calculated from the mean apical radius of curvature of the videokeratography examination. The optical path length (OPL) of this chief ray is calculated. For all points on the cornea inside the 6.0 mm pupil, VOL calculates the OPL to the paraxial focus and subtract this from the chief ray OPL to arrive at the optical path difference (OPD). A Zernike fit to the OPD values is performed to yield the corneal first-surface WFE.

Figure 8
Corneal first-surface WFE centered on the vertex normal was calculated over a 6.0 mm pupil. The cross signifies the vertex normal, and the circle is the 6.0 mm pupil diameter over which the WFE was calculated.

Calculation of Corneal First-Surface Wavefront Error from Videokeratography Measurements Centered on the Line of Sight

Corneal first-surface WFE over a 6.0 mm pupil centered on the LoS (Figure 9) was calculated using VOL (version 7.31). Visual Optics Laboratory calculates the corneal first-surface WFE over the LoS using the same procedure as described above for the vertex centered WFE, except the location of the chief ray is shifted to the LoS and the corneal points used to calculate the OPD values are centered at the LoS.

Figure 9
Corneal first-surface WFE centered on the pupil center was calculated over a 6.0 mm pupil. The cross signifies the pupil center, and the circle is the 6.0 mm pupil diameter over which the WFE was calculated.

The WFE of the corneal first surface is identical in Figures Figures88 and and99 and larger than the pupil of interest. The difference in measured WFE in Figures Figures88 and and99 is due to the change in the location of the 6.0 mm pupil center. To visualize the point, picture cutting out each 6.0 mm circle in the actual corneal aberration map and deleting the rest (like using a cookie cutter to cut out a round cookie). The aberration pattern within each 6.0 mm pupil is now different. As a consequence, the WFE over these 2 different 6.0 mm apertures is different.

Simulations of Retinal Image Quality

To visualize the significance of the potential errors that could result from using inappropriate reference axes, imagine measuring the corneal first-surface WFE over the vertex normal and then using these measurements to design a correction for the corneal first-surface WFE centered on the LoS (center of pupil). The resulting residual aberration after correction is the WFE measured with respect to the vertex normal subtracted from the WFE measured referenced to the pupil center. To visualize the resulting loss in retinal image quality, the residual WFE was imported into VOL (version 6.89), and the corresponding point-spread function was convolved with a perfect logMAR visual acuity chart.

RESULTS

Figure 10 shows the location of each subject’s entrance pupil center with respect to the vertex normal. Table 1 shows the mean, standard deviation, minimum and maximum of the horizontal and vertical positions of the entrance pupil center with respect to the vertex normal. The 2 circled data points represent the pupil locations with the greatest vector distance separation (0.92 mm).

Figure 10
The location of the physiological pupil center with respect to the vertex normal in 129 eyes of 129 subjects in the TINCO study. Positive horizontal positions are temporal to the vertex normal. Positive vertical positions are superior to the vertex normal. ...
Table 1
Maximum horizontal and vertical entrance pupil locations with respect to the vertex normal measured by videokeratography. Radial distances for each eye were computed as square root of (Horizontal2 + Vertical2).

Because subjects in the TINCO study were well distributed in age from 20 to 80 years, an analysis was performed to determine whether age significantly affects the location of the physiological pupil center with respect to the vertex normal. Figure 11 shows the horizontal and vertical location of the pupil center with respect to the vertex normal as a function of age. There were weak correlations with age. The pupil center tended to shift nasally and inferiorly ever so slightly with age. The best-fitting linear regression accounted for 2.9% of the variance in the data for the horizontal shift with increasing age and 3.6% of the variance in the vertical shift with increasing age. The small horizontal shift almost reached significance (P = .053). The small vertical shift reached significance (P = .031).

Figure 11Figure 11
Horizontal (A) and vertical (B) entrance pupil location with respect to the vertex normal of videokeratography in millimeters as a function of age in years. Note there the slight tendency for the pupil center to shift temporally and inferiorly with increasing ...

Population data tend to obscure the impact of a shift in the pupil center defining the LoS on the aberration structure of an individual eye. To more clearly show the effect on an individual eye, Table 2 was created. It shows the higher-order root-mean-square (RMS) corneal first-surface WFE, the RMS WFE attributable to astigmatism, and the RMS WFE attributable to coma over a 6.0 mm pupil for the same subject measured with respect to the vertex normal and the pupil center locations representing the 2 circled pupil center locations with the largest separation of Figure 10. Table 2 shows the change in higher-order RMS WFE, astigmatism, and coma. The RMS WFE strips out of the corneal first-surface aberration orientation information and therefore underestimates the importance of pupil location to the calculation of the internal aberrations of the eye and the design of refractive corrections. As seen in Figure 12 for HOAs and Figure 13 for coma, the orientation of the aberration structure changes with the pupil center location. Failure to account for the change in orientation and magnitude of aberration structure will lead to miscalculations of the internal aberrations of the eye and any resulting correction design.

Figure 12
Higher-order corneal first-surface WFE in a normal subject assuming the pupil center is at the vertex normal (A), 0.40 mm nasal and 0.06 mm superior (B), and 0.49 mm temporal and 0.17 mm inferior (C). Note the change magnitude of the HOA and the orientation ...
Figure 13
Coma corneal first-surface WFE in a normal subject assuming the pupil center is at the vertex normal, 0.40 mm nasal and 0.06 mm superior, and 0.49 mm temporal and 0.17 mm inferior. Note the change in magnitude of coma and the change in orientation. The ...
Table 2
Higher-order RMS corneal first-surface wavefront error in micrometers, RMS corneal first surface wavefront error due to astigmatism, and RMS corneal first surface wavefront error due to coma in micrometers for 3 assumed locations of the LoS (pupil center ...

Turning to the population data, regressing each Zernike coefficient value for the corneal first-surface WFE calculated about the pupil center against the same coefficient value of the corneal first-surface WFE calculated about the vertex normal is well described by a linear function with a slope of near 1 (0.897 to 1.029) and an intercept near 0 (−0.026 to 0.077). Figure 14 shows such a regression for horizontal coma. The slope, y-intercept, and coefficient of determination (R2) for a similar regression for each Zernike coefficient through the 4th radial order are shown in Table 3.

Figure 14
Coefficient value for the corneal first-surface vertical coma calculated with respect to the pupil center as a function of the coefficient value for vertical coma for the corneal first surface calculated with respect to the apex normal.
Table 3
Slope, intercept, and coefficient of determination (R2) for the regressions of each Zernike coefficient 2nd through the 4th radial order calculated referenced to the pupil center versus referenced to the apex normal.

The clearest examples of the effect of pupil decentration relative to the vertex normal were found for the Zernike aberration coefficients C(3,+1) (horizontal coma) and C(3,−1) (vertical coma), as shown in Figure 15. As expected from optical first principles, differences between the aberration coefficient C(3,+1) determined for the 2 reference axes increased as the horizontal displacement of the pupil increased. Similarly, the difference between the aberration coefficient C(3,−1) determined for the 2 reference axes increased as the vertical displacement of the pupil increased. These differences are measurement errors produced when data collected along the vertex normal are interpreted as corneal aberrations along the LoS. The rate of change in measurement error for the population was approximately 0.5 μm RMS per millimeter of pupil displacement. The largest error observed was 0.37 μm RMS. Errors of a similar magnitude were also found for astigmatism and defocus coefficients; however, the correlation with pupil displacement was weaker. Errors for coefficient C(4,0) (spherical aberration) were approximately 10-fold smaller than those for coma.

Figure 15Figure 15
Effect of pupil displacement from the vertex normal on corneal aberrations. Ordinate specifies measurement error (in microns), defined as the aberration coefficient measured for a circular patch of cornea concentric to the LoS minus the aberration coefficient ...

Figure 16 shows retinal image simulations of logMAR visual acuity charts spanning the range of analysis outcomes observed in the 129-eye sample. In Figure 16, A, the WFE was collected around a vertex normal that was perfectly centered on the LoS. As a result, the measured corneal first-surface WFE was quantified centered on the pupil. Thus, the design of the correction perfectly compensates the measured WFE centered on the LoS. In Figure 16, B and C, the corneal first-surface WFE was also measured with respect to the vertex normal and used to correct the corneal first-surface WFE with respect to the LoS (pupil center). For both simulations, B and C, the vertex normal was not centered on the LoS. In both B and C, there is a residual error associated with using WFE measured with respect to the vertex normal to correct WFE along the LoS. In Figure 16, B, the resulting residual WFE is representative of the typical (average) residual WFE (0.33 μm RMS WFE over a 6.0 mm pupil) in the 129 test eyes. In Figure 16, C, the resulting residual WFE was the worst in the 129 test eyes, having an RMS WFE of 1.29 μm over a 6.0 mm pupil.

Figure 16Figure 16Figure 16
Retinal image simulations of a logMAR acuity chart resulting from residual error in correction design. A: The vertex normal and LoS are superimposed, resulting in no design errors. B: The vertex normal is not superimposed with the LoS, and the residual ...

DISCUSSION

The focus of this paper is on aberrometer and videokeratographer alignment issues and their consequences on accuracy of WFE measurement relevant to vision and the design of corrections that minimize the WFE in the eye. The considerations presented here focus on the fundamental optical principles of measurement and the resulting impact on the design of corrections that optimize retinal image quality. If the correction is fundamentally designed correctly, the influence of other factors (eg, biomechanical,40 eye tracking,41 decentered ablations42,43) on outcome measures of retinal image quality can be more easily teased out in carefully designed experiments without contamination from the design of the correction itself.

Along these same lines, the retinal simulations of Figure 16 show that high-contrast visual acuity can remain essentially stable despite large, easily visible variations in retinal image quality. This observation emphasizes the point that objective measures of retinal image quality are particularly useful in evaluating the optical performance of a correction independent of actual visual performance, which can underestimate retinal image quality. Furthermore, it is worth noting that the retinal simulations in Figure 16 go a long way toward explaining why some patients with 20/20 or better visual acuity after refractive surgery say, “I do not see as well as I used to.”44

When measuring WFE relevant to vision using topography of the corneal anterior surface, or whole-eye wavefront sensing, it is the bundle of light entering the pupil of a properly fixating eye that forms the retinal image. We have argued that the preferred orientation of the eye for both types of measurement is the primary direction of gaze produced when fixating on a distant target. We have shown that the use of 2 fixation targets in wavefront aberrometers (a conventional target on the LoS and the probe beam) or a conventional fixation target at a finite distance on the VK axis can cause eye rotations that puts the eye in a nonprimary gaze during measurement.

For wavefront aberrometry along the primary LoS, it is essential that the probe beam intersect the retina at the fovea. Therefore, the probe beam is the preferred fixation target. Unfortunately, fixation of the probe beam can cause undesirable eye rotations if the beam does not enter the eye through the pupil center.

For videokeratography, the fixation target is necessarily on the VK axis rather than on the preferred LoS. However, this will not cause the eye to rotate away from the primary position of gaze, provided that the fixation target is located at optical infinity.

It is important for the eye to have the same direction of gaze when comparing measurements from the 2 instruments. This can be easily verified when the 2 instruments are combined with a beam splitter, as shown in Figure 7. When properly aligned, the subject should see the aberrometer’s probe beam lying in the center of the (perhaps blurry) fixation target from the videokeratographer. In this case, any displacement of the eye’s entrance pupil from the VK axis will be due to pure translation, uncontaminated by ocular angular rotation. It is then a simple matter to extract the topography of that portion of the cornea lying over the eye’s entrance pupil for further analysis of corneal aberrations that are relevant to vision.

Our analysis of the TINCO population showed that the translation of the entrance pupil center from the vertex normal in videokeratography varies significantly between individuals. Because it is light passing through the eye’s pupil that defines the retinal image quality, to properly quantify the WFE and the aberration structure relevant to vision, one must take into account the shift of the pupil center from the vertex normal. By analyzing the optical properties of the relevant cornea lying over the entrance pupil, the WFE of the anterior corneal surface that is relevant to vision is defined and registered with the associated whole-eye WFE measurement. Failure to measure the WFE of the eye over the entrance pupil for the eye can lead to corrections that do not optimize retinal image quality, as seen in Figure 16.

Ideally, both measurements (videokeratography and whole-eye wavefront sensing) should be taken simultaneously, centered on the eye’s entrance pupil using the LoS as a reference axis. In the absence of such capability and because corneas cannot be carved to eliminate the aberrations of the eye based on videokeratography data alone, when such data are used to calculate corneal first-surface WFE relevant to vision or to design a refractive correction for the eye, the displacement of the pupil with respect to the vertex normal has to be accounted for to accurately make the calculations. Likewise, when corneal first-surface WFE is combined with whole-eye WFE to calculate the WFE attributable to the internal optics, the displacement of the pupil with respect to the vertex normal should be taken into account. To optimize treatment designed to minimize the optical aberrations in the eye, it is equally important that the treatment platform (eg, in refractive surgery and IOL implantation) not cause a pupil translation or eye rotation different from that of the measurement platform during treatment. In the age of wavefront-guided corrections, attention to where the eye is fixating and the alignment axis of the measurement and treatment platforms is critical to further improving outcomes.

In conclusion, the selection of the vertex normal of a fixating eye to define the videokeratography reference axis does not create a stimulation for the eye to rotate with respect to the whole-eye wavefront measurement as long as the fixation target is at or near optical infinity and placed on the optical axis of the device or the system. The translation errors of the entrance pupil center with respect to the vertex normal in videokeratography measurements vary widely between subjects and have to be accounted for in design of refractive surgery based on videokeratography (eg, corneal refractive, IOLs, wavefront-guided contact lenses) as well as in the calculation of corneal or internal WFE relevant to retinal image quality and vision. Wavefront sensors can also cause the eye to rotate if the subject has significant refractive error, the entry of the probe beam is not centered on the pupil, or the patient fixates on the probe beam as opposed to the center of the fixation target. Alternatively, if the subject fixates on a conventional target on the instrument axis, the probe beam may fall onto peripheral retina, resulting in a peripheral optical measurement. Making the fixation target and probe beam conjugate with the retina minimizes problems of the probe beam being significantly displaced from the center of the fixation target due to improper alignment.

Differences in the stimulus for eye rotation between videokeratography, whole-eye wavefront sensing, and treatment platforms can be minimized by careful attention to instrument design and placement of fixation points. Translation of the pupil center with respect to the vertex normal in videokeratography should not be ignored in the calculation of the internal aberrations of the eye relevant to vision or the design of refractive corrections based on videokeratography designed to improve vision.

Acknowledgments

Supported by National Institutes of Health/National Eye Institute grants R01 EY08520 (Dr. Applegate), R01 EY (Dr. Thibos), K23-16225 (Dr. Twa), and P30 EY 07551 (Core Grant to the College of Optometry, University of Houston); the Visual Optics Institute, and the Borish Endowment to the College of Optometry, Houston, Texas, USA.

Biography

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APPENDIX

Eye Rotations and Corneal Shifts Induced by Fixating the Probe Beam in the Presence of Refractive Error

If the probe beam of the wavefront aberrometer is displaced from the center of the entrance pupil, a stimulus to eye rotation will occur when refractive errors are present and the subject is instructed to fixate on the probe. The magnitude of this stimulus can be determined from the simple optical model in Figure 1, A. The refractive error E of the eye for a target at optical infinity is

E=nfnf+ΔfnΔff2

<flush left>where n’ is the refractive index of the ocular medium. Combining this equation with the similar triangles relationship noted in Figure A1 leads to the conclusion that the angular subtense β of the retinal blur circle, subtended at the nodal point, is β = dE, where d is the pupil diameter.

As the probe beam sweeps across the diameter of the pupil, the retinal intersection of the probe beam sweeps across the diameter of the retinal blur circle created by a conventional fixation point at optical infinity. The retinal eccentricity ε of the probe beam follows the same geometrical optics principles described above, which leads to the conclusion that ε = eE, where e is the displacement of the probe beam from the pupil center. For example, 1.0 mm of displacement of the probe beam in an eye with 5.0 diopters of refractive error causes the probe beam to intersect the retina at eccentricity 5.0 milliradians or 17 arc minutes. To fixate the probe beam, the eye will rotate approximately 1.5 times the retinal eccentricity of the stimulus because the center of rotation of the eye lies posterior to the nodal point.

Figure A1

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A reduced-eye schematic model of the stimulus to ocular rotation induced by the displacement from the pupil center of the probe beam from a wavefront aberrometer. A conventional fixation point at optical infinity (not shown) produces a blur circle on the retina that subtends the angle β at the eye’s nodal point N.

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