2.1.

Measurement Limitations

2.1.1.

Resolution, dynamic range, and accuracy

An important consideration in any instrument design is the resolution and dynamic range of the measurement system. For a Shack–Hartmann system, previous work has established the advantages of higher resolution systems.¹² The lenslet Fresnel number is often the limiting factor in dynamic range and accuracy.^13,14 However, the aberrations of the eye are generally smoothly varying. Although the tear film can change on smaller scales,^15–18 the actual wavefront amplitude changes are quite small over the sample area and so smaller samples are more likely to be piecewise planar over the lenslet array.^13–15 This means that for regions of the wavefront with large wavefront variations the spots move together in groups, expanding and contracting the spot spacing. Thus it is possible to exceed the strict limits on dynamic range imposed by previous design approaches if a software algorithm is used to track the spots over these regions.¹⁴ Several such approaches are now practical with advances in computer technology.¹⁹

As the aberrations and even refraction of human eyes are not precisely known and the eye itself is constantly changing, it is difficult to discuss accuracy of the instrument in the direct context of ocular measurements. Repeatability can certainly be determined, but even that may be due to variability in the eye itself, rather than to some feature of the instrument. Generally, we use test objects to determine instrument accuracy and precision of the measurement process. However, measuring a test object is not the same as measuring the eye, which has enormous variability, is constantly in motion, and may have errors induced by the measurement process itself. Ultimately, it may be the efficacy of a correction derived from the measurement that is a measure of the overall accuracy of the instrument in measuring eyes.

The accuracy of the sensor is determined partly by the number of pixels¹³ involved in the centroiding algorithm and partly by the number of spots.¹² In Table 1, we show the parameters for the instrument described herein. Previous instruments designed by the same team have been included for reference. On test optics, typical root-mean-square (RMS) noise level is $<0.02\mu \mathrm{m}$ (full aperture). The system calibration is usually limited by the accuracy of calibration optics but is usually better than 0.008 D over the full range.

Table 1

Instrument specifications comparison to previous instruments.

Instrument	Unit	COAS-HD	iDesign	WaveDyn
Specifications
Input aperture $X$	mm	12.2	10.8	11.5
Input aperture $Y$	mm	8.6	8.6	8.6
Dynamic range of 7 mm pupil	D	3.6	3.9	7.3
Samples in 7 mm pupil		1427	1226	2821
Spatial resolution	mm	0.164	0.177	0.117
Noise floor (RMS WFE)	um	0.031	0.010	0.005
Pixels/lenslet		16	21	21
Pixels/focal spot		33	46	62
WF lenslets $X$		74	61	98
WF lenslets $Y$		53	49	74
Max power (7 mm)	D	3.6	3.4	8.3
Max cylinder	D	7	6.8	16.7
Min sphere (full aperture) IR	D	−12	−16	−12
Max sphere (full aperture) IR	D	6	8	12
Min sphere range (7 mm)	D	−15.6	−19.4	−25
Max sphere range (7 mm)	D	9.6	11.4	12
Iris image FOV $x$	mm	18	18	24
Iris image FOV $y$	mm	13	13	18

Although there is a trade-off between the number of lenslets and the pixels per lenslet,¹⁴ with the extended dynamic range (EDR) algorithm, high-resolution sensor and high speed, $2048\times 1536\text{pixel}$ camera ($\sim 21\times 21\text{pixels}$ per lenslet), it is possible to greatly extend the range of measurable eyes.¹⁷ Thus the dynamic range exceeds $+12$ to $-25\mathrm{D}$ in sphere and 14 D in cylinder. Figure 2 shows an example where the internal wavefront measurement had significant residual error. This caused the focal spots to move out from behind their associated lenslets, which would be beyond the dynamic range using traditional methods. Figures 2(a) and 2(b) shows how this affects the data analysis, adding significant noise and error. In Figs. 2(c) and 2(d), the EDR algorithm was used to progressively analyze the data in annular regions, starting with the central 1.5 mm region. Search areas were identified by extrapolating polynomial fits to identify the next set of focal spots. Then the region was expanded iteratively. In Figs. 2(c) and 2(d), the resulting wavefront shows a smooth transition with no evidence of out-of-range conditions. Note that refraction magnitude is reduced and that the RMS wavefront error is much less in magnitude as the out-of-range errors were mitigated.

Fig. 2

Example wavefront that exceeds the dynamic range limits of classical Shack–Hartmann WFS system. (a) Raw image from the Shack–Hartmann sensor with an overlay showing good spots and (b) zonal reconstruction derived from the measured spot positions, when no EDR is applied. Note in (a) noise in bottom third where spots exceed the dynamic range. (c), (d) The same counterparts as (a) and (b) when EDR is applied. The EDR analysis is implemented where the data were progressively fit in annular regions starting with 1.5-mm radius in 0.5-mm steps. Note that the algorithm successfully tracks the focal spots across the entire pupil.

2.2.

Requirements

The key requirements can be identified by considering the desired applications. The conceived instrument would incorporate a Shack–Hartmann WFS, corneal topographer, eye imaging system, patient fixation system, and patient alignment stage, and of course it will need a computer, chinrest, and optomechanical structure. The instrument is intended to be a stand-alone instrument. As space in most clinics is limited, it is desirable that the instrument size be as small as possible and that it be able to replace one or more existing clinical instruments.

2.3.

Optical System

The optical system consists of multiple, co-aligned optical paths as shown in Fig. 3. These include the eye-image, light injection, WFS, patient fixation, corneal topographer, and rangefinder. These various paths are aligned relative to each other with very tight tolerances ($<0.1\mathrm{mr}$).²⁴ This is possible using the built-in WFS as a reference, as the WFS provides extremely precise alignment information. A fiber-coupled super luminescent diode (SLD) is used as a source for the WFS since this provides a point source of light with low temporal coherence (to minimize speckle).

Fig. 3

Schematic of the aberrometer optical layout. Note: L, lens; M, mirror; QWP, quarter wave plate; BS, beam splitter; PBS, polarized BS; CAM, camera; TSA, telecentric stop aperture; RF, range finder system; SL, Stokes cell lens; VT, video target; FOG, fogging motor; and HHS, Helmholtz source.

2.4.

Eye Imaging System

One key goal of this instrument is the ability to measure position and stability of contact lenses on the eye while simultaneously measuring the wavefront aberrations. Scleral lenses are in common use that have diameters of 18 to 19 mm. Thus the field of view of the eye-image subsystem must be at least 20 mm. It is also desirable to use a telecentric optical system to avoid changes of magnification with defocus, so this requires a quite large main objective. For the new instrument, a 30-mm custom lens was designed, with a $24\times 18\mathrm{mm}$ FOV. The system was also designed with a 6-mm depth of field so the cornea and iris can be imaged simultaneously. This allows imaging small marks (fiducials) on the contact lens while still imaging the pupil. The high-resolution image can also be used to measure the pupil and iris boundaries.

2.5.

Aberrometer

The aberrometer consists of a Badal imaging system to adjust the focus to match the spherical equivalent of the eye. The SLD is prefocused by this same system so that it creates a small focal spot on the retina. The light scattered from the retina is imaged onto a Shack–Hartmann WFS, which is used to control the Badal defocus in a simple control loop.

The WFS is a custom micro-optic, made with photolithography and plasma etching. This process provides an extremely accurate lenslet with very small features. The plasma etching process results in no dead space between lenslets, which minimizes any sources of noise or crosstalk. The resulting sensor has $98\times 74$ samples with more than 7200 measurement points across the sensor. With an appropriate magnification to match the sensor size to typical maximum pupil size, this provides $>2800$ points across a 7-mm pupil. In addition, the pixel density $\sim 21\times 21\text{pixels}/\text{spot}$ provides reasonably good resolution for every point spread function, which can provide more details than just the centroid and hence may be important in light scatter and microaberrations produced by tear film breakup and/or cataracts.

One of the key goals of this new instrument is the ability to measure much more aberrated eyes. The large objective lens facilitates light collection for rays with significant deviation. The lenslets were designed with a modest Fresnel number ($\sim 4$) to facilitate good spot detection accuracy. Normally this would lead to a reduction in the available dynamic range. However, since the samples are so small on the eye (0.116 mm), software is used to track the spots as they move in groups. Although there is still an internal aperture to reduce background light, this is relatively large to allow for measurement of extremely aberrated eyes.

2.6.

Topographer

The topographer resembles a Placido disk system, with a cone that is similar in size to many other topographers. However, instead of rings, a full-gradient topography (or spot-based) system is used. The spots provide a direct measurement of the surface slope in two orthogonal directions, facilitating more direct interpretation of the surfaces. With the large objective lens, there is a large amount of data that is potentially lost right in the center of the optical system. This missing data are filled in by projecting light through a mask to provide a grid of spots on axis. Thus there is no region of the cornea that is unsampled.

2.7.

Rangefinder

With a telecentric optical system that has a large depth of focus, it is more difficult to use imaging of the iris as a means for setting the appropriate distance between the instrument and the eye. A means for accurately measuring the true distance is needed. To this end, a separate “rangefinder” camera was used to view the eye at an angle. The eye-instrument distance can be computed using triangulation.

2.8.

Dynamic Acquisition System

All the cameras and light sources were controlled with custom electronics boards that provide synchronization between the various light sources and cameras. This provides software control of the various acquisition modes, which allows for flexibility to implement various workflows. The system is capable of up to 120 fps for single-channel acquisition, with typically 54 fps in multiplexed cases (wavefront and image or wavefront and topography).

2.9.

Integrated Subjective Digital Refractometer

To obtain accurate measurements of the refractive state of the eye, it is important to include an appropriate fixation target and associated optics.²⁰ Previous instruments (COAS, iDesign) have incorporated the fixation target on the Badal stage to provide appropriate adjustment and fogging but have not compensated the target for astigmatism. For these instruments, it was found that instrument accommodation was prevalent in subjects with high astigmatism. Thus for the new instrument, an astigmatic correction system was developed. This consisted of a Stokes’ cell, which is a pair of cylinder lenses of opposite powers, mounted in cells that can be rotated relative to each other. Combined with an additional motor on the fixation target itself, the fixation target can be controlled for combinations of sphere, cylinder, and axis. Since the target itself is a pixelated programmable display, this essentially incorporates all the features of a subjective digital refractometer.

The subjective refractometer is initialized from the measured wavefront during the autorefract sequence, and the final measurement is presented to the patient as a verification that the refraction measurement provides the best correction. Since the WFS and the fixation channels are separate optical paths with independent calibrations, this verification is an immediate check on the overall quality of any given measurement. The user is provided with manual controls so that he/she can adjust the parameters (sphere, cylinder, or axis) to provide subjective confirmation.

The fixation target is an $800\times 600$ programmable display with $1.6\mathrm{arc}\min /\text{pixel}$ resolution. This can be programmed with letter charts, images, moving images (GIFs), and geometrical targets. The targets can be either static or dynamically presented with user control of the timing and synchronization. The user can also select the brightness as desired. This size target will provide up to $\pm 8\mathrm{deg}$ angular field.

This provides the user with a basic digital phoropter, built into the instrument. The fixation path can be corrected with $\pm 3\mathrm{D}$ of additional sphere (on top of the $\pm 12\mathrm{D}$ Badal system) and up to 6 D of cylinder in 1-deg increments. These can be controlled either automatically or manually by the user. This, in conjunction with the video fixation target, provides for many options in evaluating subjective response in parallel with the objective measurement. Since the target is also viewed through the Badal system, the instrument can be programmed to provide varying apparent axial positions in timed steps. This provides a mechanism for the potential measurement of accommodative range and for psychophysical research. This same sequence can also be programmed by the user to present a sequence of off-axis fixation targets to quickly measure the refraction and aberrations along multiple axes.

2.10.

System

The resulting system specifications are presented in Table 1. The schematic of the system optical layout is presented in Fig. 3 and a photograph of a prototype instrument is shown in Fig. 4. The software has a modular architecture to facilitate the various workflows and parallel processes. The instrument is designed to be operated dynamically with sequences that may last 10 to 30 s. To avoid undue delay in data analysis, the analysis operates in parallel with the acquisition in a separate thread. Thus all the analysis is completed shortly after the acquisition is finished. The data acquisition, data analysis, and data viewer are modular programs that work together to support the different functions. Depending on users’ desire and/or preferences, the data acquisition graphical user interface (GUI) supports customized acquisition with different workflows, controls sequence timing, digital refractometer, and hardware functions (Fig. 5). Due to its wide degree of flexibility, the instrument can serve several different purposes, from clinical measurement and treatment to research. The data viewer provides maps and control of data review for all the various wavefront, refraction, and topography maps (Fig. 6) and can be installed on an external computer as needed. Data can be exported for each image, analyzed frame, and sequence summary in tagged format. Wavefront data can be analyzed to produce all-order and high-order modal (Zernike) and zonal maps, irregularity, raw image, polynomial coefficients, point-spread-function, and simulated images. Corneal topography (CT) analysis includes axial power, mean curvature, refractive power, tangential curvature, sphere elevation, ellipsoid elevation, population ellipsoid elevation, irregularity, corneal aberrations (all and high order), raw image, and eye images.

Fig. 4

Photograph of prototype instrument. The adjustable monitor arm provides operation in many different settings and gives the operator options for working with the patient during the measurement process.

Fig. 5

Data acquisition GUI with (a) live iris (with CT illumination) and (b) raw wavefront and refraction. The highlight rectangular area is WFS camera’s field of view in iris camera.

Fig. 6

Data review screen with (a) eye image, refraction, (b) higher order analysis, (c) CT axis power, (d) WFS raw image, (e) all order analysis, and (f) best fit sphere elevation.

4.1.

Example Measurements

A rigorous verification and validation process was conducted on the first instruments before releasing for human eye measurement. Multiple model eyes with the known and exact diopters and diameters were measured and favorably compared with their specifications. Less than 1% of differences were obtained in each measurement.

Figure 8 shows a wavefront measurement for a 42-year-old male subject with moderate keratoconus. For a fixed analysis pupil of 5.50 mm, his wavefront aberrations were $0.63\mu \text{m}$ RMS, which is above the normal range. In (a), the HOA wavefront measurement for his bare eye is presented, and (b) is the HOA with a scleral lens. His vision was corrected with a scleral lens to reduce his aberrations. However, while the scleral lens reduces his low-order refraction, it did not change the higher orders in this case. In fact, the higher orders are nearly the same magnitude but inverted in sign.

Fig. 8

Higher order wavefront map for a 42-year-old. male patient with moderate keratoconus. (a) Bare eye (no correction) and (b) correction with a scleral lens.

The tear film can be evaluated from both the wavefront and the topography by plotting the residual after subtracting fit polynomials. In Fig. 9, the Zernike polynomials through sixth order were subtracted from the zonal wavefront map. This shows irregularities in the wavefront, which are a good indication of tear film irregularity.²⁹ The irregularity grows in strength until the blink as shown in each successive frames (a)–(f) with time from 0 to 1.435 s with 0.285-s interval. Changes in the irregularity are often the result of tear film variations.

Fig. 9

Example tear film measurement from time (a) $T=0.0\mathrm{s}$, (b) 0.29 s, (c) 0.57 s, (d) 0.86 s, (e) 1.15 s, and (f) 1.44 s.

The spot-based topographer is designed to be able to measure the shape of unusual eyes without assumptions. As each spot provides information about the surface gradient in both $x$ and $y$ directions, the surface reconstruction does not rely on any assumptions other than that the surface is continuous. Thus this provides good information for highly irregular corneas. An example of a keratoconus CT measurement is shown in Fig. 10. The maps have an irregular outline because of the shadows caused the by subject’s nose and eyebrows. It is possible to reduce these shadows by tilting the subjects head slightly temporally. However, since these measurements are made simultaneously with the wavefront measurements, often it is desirable to measure both wavefront and topography in the same orientation as normal patient fixation, that is, straight ahead.

Fig. 10

CT results from a keratoconus subject: (a) eye image with CT illumination, (b) CT axis power, (c) mean curvature, and (d) CT tangential power. The irregular shape of maps from (b) to (d) is the result of shadows from subject’s nose and eyebrows.

Figure 11 shows an example of the dynamic analysis process. Each of the parameters was first filtered using a five-frame running average to identify and eliminate outliers. The image quality metric (fraction of valid focal spots in the measured pupil) is used to identify partial blinks, misalignments, or data with significant corneal reflexes. Pupil size is known to correlate with accommodation response so this is also used as part of the metric. Using Eqs. (1) and (2), the MF is first computed and then the selected exam identified as the maximum value in the sequence. After the completion of a measurement, the sequence of data is analyzed, and the selected exam is displayed to the user. In Fig. 11, the vertical line indicates the location of the maximum MF as defined in Eq. (2).

Fig. 11

(a) Refraction parameters and (b) MF. Data were first filtered to remove outliers. The vertical line indicates the location where the MF is maximized.

Since all of the frames of data are saved during a typical acquisition, the sequence can further be played as a movie to observe fluctuations in the measurements or tear film, or individual frames of data can be extracted.

4.2.

Clinical Study

A small clinical study was used to evaluate the effectiveness of this process. Five subjects, ages 23 to 64 were measured five times each with a 10-s sequence. Figure 12 shows variability of the measurements for both the maximum pupil (MFMPSph) and a fixed analysis pupil of 4 mm (MFAPSph). The variability was not significantly different between the two methods, although it was generally smaller for the maximum pupil method. This may be because the larger pupils generally led to more measurement samples and the smaller pupil measurements are sometimes affected by the corneal reflex. Even so, the repeatability of these methods is generally better than that of subjective methods.³⁰

Fig. 12

Variability: mean (top) and standard deviation (bottom) of the Sphere measurements using the MF approach for (a) max pupil and for an (b) analysis pupil of 4 mm, for subjects age ranging from 23 to 64 years old.

The measured cylinder values show even tighter reproducibility between measurements. The average variability was 0.05 D for the maximum pupil values and 0.06 D for the 4-mm analysis as shown in Fig. 13. The high-resolution WFS provides good data to give accurate astigmatism measurements. Cylinder is generally unaffected by accommodation.

Fig. 13

Variability: mean (top) and standard deviation (bottom) of the cylinder measurements using the MF approach for (a) max pupil and for an (b) analysis pupil of 4 mm, for subjects age ranging from 23 to 64 years old.

For this same dataset, the range of the refraction is presented in Fig. 14. For the maximum pupil analysis, this varied on average by 0.188 and 0.33 D for the 4-mm analysis pupil. Sometimes the range was quite large, especially for the younger subjects. Most of the previous instruments used only a single snapshot acquired after some manual or automatic trigger. Typically, this could be 1 to 6 s after initiation of the measurement process and the timing relative to a blink is usually unknown. Thus the value recorded could be anywhere within the range presented in Fig. 14. The range of measurements during this period thus represents an inherent error in the process for single snapshot measurements. This range provides an internal estimate of the precision of any given measurement.

Fig. 14

Range of sphere values during the 10-s measurement sequence: (a) MP and (b) 4 mm AP.