The scanning aberrometer designed and implemented for this study efficiently measured the off-axis wavefront aberrations of human eyes along 37 different lines-of-sight in 8 seconds. Measurements of an induced change in focus of a model eye () indicated the instrument has good precision (≤ 0.03μm, 4mm pupil) and accuracy (≤ 0.02μm, 4mm pupil). These values are equivalent to less than 0.03 diopters of defocus which is neither clinically nor functionally significant. Furthermore, in the evaluation experiment with a human eye, the mean RMSDev of the five repetitive measurements across the non-horizontal LoS is 0.14 µm. This low value suggests that SSHA is a feasible and reliable instrument to be applied in clinical research and diagnosis.
We validated our instrument using a differential-focus experimental-design because it excludes other potential sources of error such as misalignment of the test eye to the instrument. The mean and standard deviation of the differential measurements across multiple LoS can be regarded as the accuracy and precision of the aberrometer itself. Although it was convenient to evaluate the instrument using defocus, the results may be generalized to other aberration modes since wavefront slope is measured with the same accuracy and precision at every point in the pupil. Besides validating the SSHA with the defocus wavefront aberration of the model eye, we also measured the centers of the SH data images from different frames. Since the entrance pupil center of the test eye is conjugated with the rotational center of the scanning mirrors and the SH lenslet plane, the wavefronts emerging at the entrance pupil along different LoS should be sampled at the same location on the lenslet plane as the scanning mirrors (X&Y) scan. Correspondingly, the center of the SH centroid images of different frames should be fixed at the same location on the camera CCD plane. With the well-aligned model eye, we found that this center is very stable as the mirrors scan across the whole designed visual field (±15 degrees, excluding the horizontal LoS): the standard deviation of the center drift of the SH centroid images was 48 microns (horizontal) and 55 microns (vertical) on the CCD plane.
Back scatter of light from the laser probe beam from multiple surfaces (24 surfaces) in the multi-element scanning lenses (DPS 1-4 in ) can enter the SHWS and corrupt measurements. Particularly when the system directs the probe beam along the horizontal LoS, the vertical scanning mirror (X) aims the laser beam along the optical axis of the first scanning relay pair (DPS 3-4). Since the refractive surfaces of these lenses are normal to the incoming laser, their reflectance introduces strong scattering, which contaminates the measurements along the horizontal LoS. We attempted to mitigate this effect by placing aperture A1 at the foci plane between the last relay pair (L5-6). Although this aperture reduces the backward scattering significantly, it also has the undesirable effect of limiting dynamic range of the SHWS. Polarization techniques can be used to reduce backscatter, but we have not yet implemented that idea. A software innovation that iteratively finds the centroids of the SHWS spots based on the compactness, peak and mean brightness of the spots also excludes spots contaminated by backward scattering. The exclusion of a few contaminated spots is tolerable for the modal wavefront reconstruction methods [26
], provided there are enough measured gradients to perform a satisfactory least-squares fit. When measuring the model eye, for example, a reasonable wavefront estimation was possible even for those LoS that suffered from moderate backward scattering. In the presence of strong backward scattering, wavefront reconstruction fails which explains the absence of wavefront measurement along certain LoS ().
Performance of the scanning aberrometer is also limited by scanning speed, the accessible visual field, and pupil size. For example, it takes 8 seconds for the scanning mirrors X&Y to cover the central 30° visual field using the scanning pattern in . This duration is limited by the time required for the mirrors to accelerate, decelerate, and stabilize. High speed scanning is an advantage when measuring subjects with unstable tear films. Some individuals cannot refrain from blinking for 8 seconds, and even for those who can suppress blinking during the scan the tear film changes rapidly between blinks [31
]. One solution is to break the scan into two or more sequences, but faster scanning mirrors would be a better option. The range of visual field locations accessible in one scan is limited by the size of the DPS lenses. As the f-number of these lenses is already small (f/1.8), it may be impractical to expect more than ±15 degrees of scanning angle for a single fixation target. Our approach to extending the accessible visual field is to change the eye’s fixation between scans. By overlapping the scanned areas, internal checks based on repeatability become possible. The dynamic range of the SHWS also limits the range of visual field that can be examined in one scan. The human eye has significant field curvature and oblique astigmatism that threaten to exceed the sensor’s dynamic range. Our design goal of ±15° was guided by theoretical analysis of the variation in aberrations of a wide angle schematic eye [24
], which are within the dynamic range of the current SH lenslet array used in our instrument. Yet another limitation is imposed by the limited size of the beam splitter placed immediately in front of the subject’s eye (BS2 in ). The largest pupil size our instrument can measure is 6 mm for emmetropic subjects.
Although this report focuses mainly on the hardware implementation of a scanning aberrometer, it is worth noting that the development of off-axis wavefront reconstruction over elliptical pupil is also an important aspect of system development. These wavefront reconstruction methods have been summarized elsewhere [26
]. The choice of method for off-axis wavefront reconstruction and representation is application dependent. For example, the Fourier series based methods are generally more efficient computationally than the Zernike polynomial based methods. While for some clinical or scientific applications, the Zernike based method are preferred because the derived Zernike polynomials provide a succinct description of the system in terms that are easily understood, for other applications the best description of the data might be a model eye that reproduces the data [17
]. Two Zernike-based methods are used in our system. For display and reporting, we used Lundstrom’s ‘direct method’ [16
]. It applies classical least-squares fitting of the derivatives of Zernike circle polynomials to gradient data over a circumscribed circular pupil, the radius of which equals the major radius of the elliptical pupil. The absence of gradient data in the region between the ellipse and the circle does not defeat the least-squares method because practical systems are typically over-determined. The obtained wavefront map is preferred for purposes of interpreting a given optical path length (OPL) map as a prescription for a correcting lens. However, for purpose of data management, we found it more convenient to map points in the elliptical entrance pupil to the circular physical pupil, which stretches the OPL map anisotropically as described by Atchison [25
]. The advantage of this stretching is that all the maps have a circular domain with the same diameter, which makes it easy to represent the wavefront with a conventional vector of Zernike aberration coefficients. In this way, data management is simplified, which is important for a system that generates a large amount of data quickly.
Our system incorporates dual scanning mirrors with a fixed SHWS to efficiently measure the off-axis wavefront aberrations of human eyes over a large field of view. In principal, other scanning system designs and sensing techniques could be used instead. For example, replacing our scanning lenses with reflective mirrors might reduce backward scattering and improve performance. Another improvement might be to incorporate other sensing techniques with larger dynamic range. Potential candidates might be laser ray tracing [33
], double pass measurement [34
], and Hartmann Moire wavefront sensor [35
]. These techniques have the potential to grant the instrument much larger dynamic range for wavefront sensing as well as increased range of accessible visual field.