Manipulation of the eye’s aberrations using adaptive optics (AO) has shown that optical imperfections can affect the dynamic accommodation response. A limitation of current system designs used for such studies is an inability to make direct measurements of the eye’s aberrations during the experiment. We present an AO system which has a dual wavefront sensing channel. The corrective device is a 37-actuator piezoelectric deformable mirror. The measurements used to control the mirror, and direct measurements of the eye’s aberrations, are captured on a single Shack-Hartmann sensor. Other features of the system include stroke amplification of the deformable mirror and a rotating diffuser to reduce speckle. We demonstrate the utility of the system by investigating the impact of aberration dynamics on the control of steady-state accommodation on four subjects.
©2009 Optical Society of America
The human eye suffers from a number of image degrading monochromatic aberrations which fluctuate over time . AO is a powerful technique that can dynamically manipulate these aberrations. The technique was originally developed to increase image quality in ground-based telescopes by compensating for atmospheric turbulence . Less than a decade ago, the first systems capable of real-time correction of the eye’s aberrations were demonstrated [3, 4]. AO has now become an invaluable tool for investigating the effect of the eye’s aberrations on visual acuity and to obtain high resolution in-vivo images of the retina. For a review see .
A comparatively new application of AO for the eye is in the study of the effect of the monochromatic aberrations on accommodation. The accommodation system is responsible for altering the power of the eye’s lens to bring an object of interest into focus. It is well known that this system responds to a variety of cues such as binocular disparity, chromatic aberration and size, see for example . These cues provide the system with the necessary information to guide the accommodation response in the correct direction. Several investigators, such as Walsh and Charman, have proposed that monochromatic aberrations can also provide such a cue . Even-order aberrations in particular, such as spherical aberration, result in the point spread function (PSF) being different depending upon whether the image is focussed in front of or behind the retina. Wilson and colleagues have demonstrated that subjects can perceive such differences . With the advent of AO it is possible to manipulate these aberrations during the dynamic accommodation response. Correcting them has been shown to adversely affect the dynamic response in some subjects [9, 10].
Aberrations have also been found to affect the steady-state (or static) level of accommodation [11, 12]. Even when the eye is focussed on a stationary target the accommodation level is never truly static however. The eye exhibits small fluctuations in focus about a mean level with an amplitude of around a few tenths of a diopter. For a review of the properties of these so-called microfluctuations in accommodation see . Several investigators such as Winn have proposed that the low frequency component (LFC) of these fluctuations (<0.6 Hz) aids steady-state accommodation control . This is based on evidence that the LFC increases in magnitude under conditions where the stimulus is degraded and the depth of focus of the eye is increased [15–19]. Gambra et al. for example have found the accommodative fluctuations increase significantly when static amounts of spherical aberration are induced .
All AO systems for the eye are operated in closed-loop, and so the eye’s aberrated wavefront passes onto the aberration manipulation device before reaching the sensor. Hence it is not possible to obtain a direct independent measure of the eye’s aberrations and consequently the accommodation response. When studying the dynamic accommodation response, for example, it is necessary to differentiate between the defocus step introduced by the system and the eye’s response. To overcome this Chen and colleagues stored the voltages of the deformable mirror during the experiment . They then used a collimated beam in place of the eye and played back the voltages to determine the contribution to the measured aberrations during the experiment from the mirror. However, this is a time consuming process especially given that often many trials are used in accommodation studies. In another study by Hampson and colleagues a hot mirror was used to bypass the deformable mirror to obtain direct measurements of the eye’s aberrations during each experimental run . However, measurements of the eye and mirror channel could not be obtained simultaneously, and so only preprogrammed mirror movements could be used for the experiments.
In this paper we present an AO system in which the sensing branch contains an extra channel to independently measure the eye’s aberrations using the same sensor as that used to control the deformable mirror. We used the system to measure the effect of dynamically correcting various aberrations on the steady-state accommodation control of four subjects. The advantages of the system design for future accommodation studies is discussed.
2. Adaptive optics system
A schematic of the AO system is shown in Fig. 1. All components are mounted on a 600×900 mm research-grade breadboard (Newport Ltd, UK).
2.1. Illumination path
The eye is illuminated by a 830 nm fibre-coupled laser diode (Access Pacific, UK). Light is collected from the fibre tip and collimated using a molded glass aspheric lens with a focal length of 4.51 mm. The beam is focused by L 2 onto a rotating diffuser to reduce speckle . Unlike the scanning method proposed by Hofer et al. , the diffuser can be placed outside the wavefront sensing path. This reduces the amount of optics required in this path as the scanner needs to be conjugated to the eye’s pupil and also bypassed for the visible stimulus . An example of the Shack-Hartmann spots with and without the diffuser is shown in Fig. 2.
After passing through the diffuser the light is re-collimated by L 3. Upon entering the system via pellicle beamsplitter PBS, the beam passes through a Badal optometer arrangement consisting of two plane mirrors, PM 2 and PM 3, mounted on a motorized stage. This is used to change the accommodation level at which experiments are carried out. The beam enters lenses L 4 and L 5, and the eye, slightly off-axis so back-reflections can be blocked by aperture A 2. The diameter of the beam at the eye is 1 mm. The power is 120 µm, which is less than one fifth of the maximum permissable exposure at the cornea for eight hours continuous viewing of this wavelength .
2.2. Wavefront sensing paths
The aberrations are measured using a Shack-Hartmann wavefront sensor consisting of a CCD camera (Retiga EXi, QImaging, Canada) and a lenslet array with a focal length of 7 mm and pitch of 200 µm. Owing to magnification changes through the system, the pupil is sampled at 0.5 mm intervals. The wavefront is sampled at 20 Hz. The wavefront sensing branch consists of two channels. One channel obtains direct measurements of the eye’s aberrations. The other obtains measurements of the aberrations after passing via the deformable mirror and so is used to control the aberration manipulation. Both measurements are captured by the same Shack-Hartmann sensor which reduces system cost and complexity.
2.2.1. Direct eye aberration measurement path
The wavefront sensing light returning from the eye is separated into two paths via cube beamsplitter CBS. Fifty percent of the wavefront sensing light is reflected at CBS and is directed towards the Shack-Hartmann sensor as shown in Fig. 3(a). A neutral density (ND) filter is placed in this channel to balance the brightness of the two measurement paths. As this light has not passed via the deformable mirror a direct measurement of the aberrations of the eye is obtained.
2.2.2. Aberration manipulation path
The path of the light in the aberration manipulation channel is shown in Fig. 3(b). The light transmitted by CBS passes onto a 37-actuator piezoelectric deformable mirror (Flexible Optical BV, The Netherlands). The light strikes the deformable mirror twice to effectively double its stroke . The principle of this so-called stroke amplification is illustrated in Fig. 4. Stroke amplification is a cost effective way of doubling the stroke of a corrective device as it can be readily achieved using only two lenses L 8 and L 9, and a plane mirror PM 6. The magnification through the system is such that the full surface of the mirror (30 mm) is covered by a 6.25 mm pupil. Upon returning from the deformable mirror the light is reflected by CBS and is then directed towards the sensor by PM 7 and PM 8.
To assess the ability of the deformable mirror to generate individual Zernike polynomials each Zernike mode up to and including the fifth radial order (excluding piston, tip and tilt) was gradually induced in either direction relative to the mid point. This was carried out using an artificial eye consisting of a 20 mm focal length lens with a 6 mm pupil and a piece of card as the retina. The Zernike convention used was that specified by the Optical Society of America Taskforce . Fig. 5 plots the measured Zernike coefficients against the programmed values. Black dashed lines indicate the targeted values. For all Zernike modes, the targeted Zernike coefficient value closely matches the ideal response. Mode coupling tends to increase towards the borders of the permitted range. Certain Zernike modes, Z-1 5 and Z5 5 for example, demonstrate significant coupling with Z0 2, particularly at the limit of the range, with a value close to 30% of the actual intended mode. For the majority of the modes tested there is minimal coupling. The range of the generation of Zernike polynomials was limited by the dynamic range of the Shack-Hartmann wavefront sensor, which was found to be roughly the same for positive and negative values.
2.2.3. Equivalence of both measurement paths
Although the measurements from both channels are captured by a single sensor, the wavefront travels through different paths and so it is important to verify that both channels are equivalent. To demonstrate the equivalence of both channels, spherical trial lenses (-0.75 to +0.75 D) and cylindrical trial lenses (-0.75 to +0.75 D, at axes 20± to 180±) were placed in front of an artificial eye and the average of 20 measurement frames were recorded. The resultant change in the measurements registered by both channels was noted. For cylindrical lenses, the resultant sphero-cylindrical changes were compared with the ideal values calculated using power vector analysis in terms of M (mean sphere), J 0 (orthogonal astigmatism) and J 45 (oblique astigmatism) . The equivalence of the channels was assessed by the correlation coefficient values, r, and by using a Bland and Altman (or Tukey mean-difference) plot . A high correlation coefficient indicates that the two values are linearly related, but this does not indicate whether they agree in value . A Bland and Altman plot consists of a plot of the difference between two measured values versus their mean and provides a good indicator of bias.
Fig. 6(a)–(d) plots the measurements obtained by the two channels against the powers of the trial lenses for sphere, M, J 0 and J 45 respectively. All r values were greater than 0.98 and p was less than 0.01. The corresponding Bland and Altman plots are shown in Fig. 6(e)–(h). The means of the differences between both channels are found to be close to 0 D for all four components (range -0.024 to 0.016 D), indicating negligible systematic bias.
2.3. Stimulus path
The stimulus consists of a Maltese cross on a black background. It is illuminated by a white light source with a 550 nm filter and subtends one degree at the retina. The luminance is 6.7 cd/m2. This stimulus light enters the system at PBS. We found that the light transmitted by PBS from the ingoing laser source formed a spot on the dark part of the stimulus. Light from this could be seen by the CCD camera and so introduced noise in the sensing measurements. To remove this the infrared light transmitted by PBS is directed away from the stimulus using a hot mirror at 45± which reflects infrared and passes visible light. The path of the visible light through CBS to and from the deformable mirror results in two unwanted visible beams directed towards the Shack-Hartmann sensor. These are blocked using an infrared (IR) filter.
3. Accommodation experiment
It has been found that several aberrations show some degree of correlation with microfluctuations in focus, see for example [27, 28]. As the microfluctuations in focus aid the maintenance of steady-state accommodation, the purpose of this experiment was to investigate whether aberration dynamics affect steady-state accommodation control. This was assessed by monitoring changes in the LFC of accommodation fluctuations in response to dynamically correcting various aberrations. In order to isolate the effect of the dynamic component of the aberrations, the influence of their static level (i.e. DC level) were removed. This was achieved by running the AO system in closed loop for 5 seconds before each experimental run to remove the average level of each aberration.
Four subjects (30±4 yrs) with no known ocular pathology took part in this study. Two subjects were emmetropic and two were myopic. The prescription of the right eye of subject EM was -6.00/-0.50×90, and -1.75/-0.50×90 for KH. Both subjects wore their spectacles during the experiment. The measurement and correction of ocular wavefront aberrations were performed on the right eye over a 5 mm pupil diameter. Since all subjects had natural pupil diameters greater than 5 mm, dilation could be avoided. Subjects were stabilized with a bite bar and told to maintain fixation on the stimulus which was placed at a 2 D accommodation level. They were allowed to blink naturally during each measurement run. Each run lasted 20 s and the wavefront was sampled at 20 Hz. There were ten experimental conditions in total and each was repeated ten times. These were as follows:
1. Aberration fluctuations without any correction, i.e. baseline (B).
2. All aberrations corrected except defocus (CA).
3. All even-order aberrations corrected except defocus (CE).
4. All odd-order aberrations corrected (CO).
5. Defocus corrected (CZ0 2).
6. Astigmatism axis 0°, 90° corrected (CZ2 2).
7. Vertical coma corrected (CZ-1 3).
8. Trefoil corrected (CZ3 3).
9. Secondary astigmatism axis ±45° corrected (CZ-2 4).
10. Spherical aberration corrected (CZ0 4).
The experimental runs were presented in a randomized order. When several Zernike terms were corrected, aberrations up to and including eighth radial order were included. In order to compare across conditions the influence of static aberrations were also removed in the baseline condition.
4. Data analysis
For each Shack-Hartmann measurement for each run measured by the eye only channel, Zernike tip Z-1 1 and defocus Z0 2 coefficients were calculated. The locations of blinks were found by identifying sharp spikes in the Zernike tip coefficient . Assuming a blink duration of 250 ms , five data points were deleted and a cubic spline function was used to interpolate between points before and after a blink. The accommodation fluctuations in Diopters were calculated using
where the Zernike coefficients C 0 2, C 0 4 and C 0 6 are specified in micrometers and R is the pupil radius in millimeters . C 0 2 is the coefficient for Zernike defocus and C 0 4 is that of spherical aberration. For each measurement run the power spectral density function (PSD) was calculated. Owing to the 20 s measurement time and 20 Hz sampling rate, information on the magnitude of frequencies in the range 0.05–10 Hz could be obtained. Prior to calculating the PSD the linear trend was removed from the time signals to avoid contributions to the PSD from frequencies with a period greater than the 20 s measurement time, which is a source of noise . The time course signals were multiplied by a Hanning window to reduce spectral leakage . The area under each PSD in the range 0.05–0.6 Hz (i.e. LFC) was calculated. For each subject a one way analysis of variance (ANOVA) was performed to determine significant difference amongst conditions.
As detrending effectively removes drifts in the accommodation level which could be an indication of the accommodation system receiving reduced clues, the standard deviation (SD) of each time record was also calculated. Again ANOVA was performed on each subject.
Fig. 7 shows typical time-course records of the accommodation fluctuations for the baseline condition for each subject. The magnitude of the fluctuations are similar to previous studies . The average area under the PSDs across subjects for each condition is shown in Fig. 8. ANOVA revealed no significant differences for each subject (p>0.05). In the case of the SD, there were no significant differences except for subject KH. For this subject, the SD when correcting defocus (Z 0 2) was significantly greater than the baseline condition and when correcting astigmatism (Z 2 2) (p<0.05). On inspection of the time-course records, this proved to be due to noticeable drifts in the records when correcting defocus.
6.1. Instrument design
We have presented a closed-loop AO system that allows simultaneous measurement of the eye’s aberrations directly. The measurements of both the direct eye’s aberrations and those used to control the deformable mirror are captured by a single Shack-Hartmann sensor. This reduces the cost and complexity of the system. In this investigation we have used the channel that directly measures the eye’s aberrations primarily to determine the fluctuations in accommodation. Hence one could argue that for accommodation studies using AO there is no need to use a Shack-Hartmann sensor as a more simple optometer which only measures accommodation could be used, such as a dynamic retinoscope. However having a system capable of measuring all aberrations in the eye directly, allows more complex investigations to be carried out. The extra channel is essential when carrying out experiments in which the aberrations are dynamically inverted during the accommodation response for example. The common control algorithm used to control an AO system and the one used in this system is
where v is the vector of voltages sent to the deformable mirror, g is the gain (typically set to 0.3), C is the control matrix, Z meas is the vector of the measured Zernike coefficients via the deformable mirror and Z req are the required Zernike coefficients. From Equation 2 it can be seen that it is not possible to dynamically invert aberrations as Z meas is not a continuous direct measure of the eye’s aberrations. With the AO system presented here dynamic inversion of the aberrations can readily be achieved using a modified control algorithm:
where Z eye are the Zernike coefficients as measured in the eye-only channel. As there will inevitably be a minor difference in the baseline aberration measurement in the two channels, the final algorithm would be given by
where Z bias is a vector containing the differences in the baseline measurements of the Zernike coefficients between the two channels. This algorithm has been successfully implemented in another study .
Another advantage of having a two-channel system is that it is more convenient to determine the bandwidth of the system. This is determined from the ratio of the eye’s aberrations with and without the correction device operating and so can be readily found from the ratio of the output from both channels.
Additional advantageous features that are employed in this system include a rotating diffuser to reduce laser speckle. This can be placed outside the wavefront sensing path and so is more convenient than other methods such as scanning. The light strikes the deformable mirror twice to produce a cost effective way of doubling the stroke of the device, which only requires two lenses and a plane mirror. We found that upon doing this the dynamic range of the sensor was slightly less than the capabilities of the mirror. Although this has not been an issue in this study, in future work increased dynamic range of the wavefront sensor may be necessary in order to cope with larger levels of aberration inversion for example. Future experiments may also benefit from the inclusion of a more flexible target that can be varied in terms of luminance, spectral composition, contrast, and spatial frequency.
As previously mentioned, all AO systems for the eye are in a closed-loop configuration. One reason is that open-loop systems require very accurate calibration, which is difficult owing to hysteresis and non-linearity of the correction device. With the development of liquid crystal on silicon devices (LCOS), open-loop systems have been realized in the field of Astronomy. See for example . The application of open-loop systems to the eye in the future would simplify the system presented here as two wavefront sensing paths would not be required.
6.2. Aberration dynamics and steady-state accommodation
For three out of our four subjects used in this study, we did not find a significant effect of aberration correction on the magnitude of the accommodative microfluctuations both in terms of the power of the LFC and the SD of the fluctuations in accommodation. For one subject we found that only the SD for the correction of defocus (Z 0 2) was significantly greater than the baseline condition and when correcting astigmatism (Z 2 2). Upon inspection of the time traces this was found to be due to considerable drifts when correcting defocus. Several investigators have proposed that the eye may use accommodative microfluctuations, in particular the LFC, to maintain the required steady-state accommodation level. This is based on observed increases in the magnitude of the LFC with increasing depth of focus, see for example . As we found an effect in only one subject for a limited amount of conditions, our results may at first sight appear counter to the current literature. However in our investigation, prior to each experimental run, including when the baseline fluctuations were measured, the static aberration levels were corrected. Hence the depth of focus was minimized prior to each run and so we would not expect the subsequent correction of the aberration microfluctuations to significantly impact the depth of focus.
A limited number of studies have directly assessed the effect of aberrations on the LFC of accommodation microfluctuations. In these studies static levels of aberrations have been induced. Stark and colleagues found that inducing astigmatism could cause the fluctuations in accommodation to increase in magnitude in two out of their seven subjects . Collins et al. found no increase in the LFC when inducing spherical aberration in their two subjects . To the authors’ knowledge, this is the first study to investigate the effect of aberration dynamics on steady-state accommodation control. Using AO, Gambra et al. found that the fluctuations were generally smallest when the subject had their natural aberrations present and when all aberrations were corrected as compared to when inducing spherical aberration . However in the corrected state, they operated the mirror in closed-loop then stopped it before the measurements. Hence no dynamic correction was performed during the measurements.
Currently, we do not know why only one subject was affected by the correction of aberrations and others were not. The effect of aberration dynamics on the dynamic accommodation response has also been proven to be subject dependent . The closed-loop bandwidth of our system is limited to around 1 Hz. As aberration fluctuations extend well beyond this, it is not possible to completely remove these fluctuations. It may be that for three of the subjects, their remaining aberration fluctuations were sufficient to keep the eye in good focus.
This paper has described an AO system for the study of the role of ocular aberration dynamics in steady-state accommodation control. A key feature of this system is its ability to apply closed-loop aberration modifications while simultaneously acquiring an independent measure of aberration dynamics and accommodation accuracy. The utility of this system for the study of accommodation function has been demonstrated in a small cohort of human subjects.
The authors are grateful to the Engineering and Physical Sciences Research Council for funding under grant EP/D036550/1.
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