POWER SPECTRUM ANALYSIS IN THE STUDY OF OCULAR MECHANISMS

Effect of Accommodation on Peripheral Higher Order Aberrations

Knowledge of the effect of accommodation on image quality of peripheral retina is crucial for better understanding of the visual system, but only a few studies have been carried out in this area. This study was designed to evaluate the effect of accommodation on higher order aberrations from third to sixth Zernike polynomials in central and peripheral retina up to 23° off-axis. We used a Hartmann–Shack aberrometer to measure Zernike coefficients with both accommodated and non-accommodated eyes of 15 healthy subjects. Each Zernike coefficient, total higher order aberrations, spherical aberrations and astigmatism were compared between accommodated and non-accommodated status. Additionally, aberrations in the central retina were compared with the peripheral retina. Accommodation induced significant changes in the Zernike coefficients of vertical pentafoil C5−5 and secondary vertical tetrafoil C6−4 in central retina, secondary vertical astigmatism C4−2 on 23° of temporal retina, secondary vertical tetrafoil C6−4 and tertiary vertical astigmatism C6−2 on 10° of nasal retina, secondary vertical trefoil C5−3 and secondary vertical tetrafoil C6−4 on 23° of nasal retina, and horizontal tetrafoil C44, and secondary horizontal tetrafoil C64 on 23° of inferior retina (p < 0.05). Total higher order aberration was lower in each retinal area examined with accommodation, but it was statistically significant only on 23° temporal retina and 11.5° and 23° of superior retina (p < 0.05). Spherical aberration decreased with accommodation on 23° temporal retina (p = 0.036). Astigmatism was similar in non-accommodated and accommodated eyes. Overall, accommodation affected higher order aberration (HOA) asymmetrically in different peripheral retinal areas.

Characterizing gaze position signals and synthesizing noise during fixations in eye-tracking data

The magnitude of variation in the gaze position signals recorded by an eye tracker, also known as its precision, is an important aspect of an eye tracker’s data quality. However, data quality of eye-tracking signals is still poorly understood. In this paper, we therefore investigate the following: (1) How do the various available measures characterizing eye-tracking data during fixation relate to each other? (2) How are they influenced by signal type? (3) What type of noise should be used to augment eye-tracking data when evaluating eye-movement analysis methods? To support our analysis, this paper presents new measures to characterize signal type and signal magnitude based on RMS-S2S and STD, two established measures of precision. Simulations are performed to investigate how each of these measures depends on the number of gaze position samples over which they are calculated, and to reveal how RMS-S2S and STD relate to each other and to measures characterizing the temporal spectrum composition of the recorded gaze position signal. Further empirical investigations were performed using gaze position data recorded with five eye trackers from human and artificial eyes. We found that although the examined eye trackers produce gaze position signals with different characteristics, the relations between precision measures derived from simulations are borne out by the data. We furthermore conclude that data with a range of signal type values should be used to assess the robustness of eye-movement analysis methods. We present a method for generating artificial eye-tracker noise of any signal type and magnitude.

Is 25Hz enough to accurately measure a dynamic change in the ocular accommodation?

BACKGROUND

Accommodation is often recorded at a low sampling rate using devices such as autorefractors that are designed to measure the static refractive error. It is therefore important to determine if that resolution is sufficient to accurately measure the dynamic properties of accommodation. The current study provides both theoretical and empirical evidence on the ideal sampling rate necessary to measure a dynamic response.

METHODS

Accommodative and disaccommodative step stimuli ranging from 1-3D (1D steps) were presented using a Badal optical system. Responses from 12 children (8-13 years) and 6 adults (20-35 years) were recorded using a dynamic photorefractor (DPR). Fast Fourier transformation was applied to the unsmoothed dynamic responses including position, velocity and acceleration. Also, velocity and acceleration main sequence (MS) characteristics were compared between three photorefractor conditions on 3 subjects.

RESULTS

The Nyquist sampling limit necessary to accurately estimate position, velocity and acceleration was at least 5, 10 and 70Hz, respectively. Peak velocity and acceleration were significantly underestimated at a lower rate (p<0.5). However, the slope of MS remained invariant with sampling rate (p>0.5).

CONCLUSION

Contrary to the previous findings, a dynamic accommodative response exhibited frequencies larger than 10Hz. Stimulus direction and amplitude had no influence on the frequencies present in the dynamic response. Peak velocity and acceleration can be significantly underestimated when sampled at a lower rate. Taken as a whole, low sampling rate instruments can accurately estimate static accommodation, however, caution needs to be exercised when using them for dynamic accommodation.

Phase dependencies between longitudinal corneal apex displacement and cardiovascular signals: is the ocular pulse influenced by the electrical activity of the heart?

BACKGROUND

The aim was to establish phase relationships between the principal harmonic, related to the heart rate, of synchronically registered longitudinal corneal apex displacement (LCAD), blood pulsation (BP) and electrical heart activity signals in a group of healthy subjects.

METHODS

Longitudinal corneal apex displacement was non-invasively measured using an ultrasonic distance sensor. Synchronously, electrocardiographic (ECG) and blood pulsation signals were acquired. As all considered signals are non-stationary (that is, their spectral characteristics vary in time), a reliable and repeatable phase estimation method was sought. For this, a range of phase estimators were tested in the windowed regime of simulated non-stationary signals. Two robust estimators that showed minimum mean square error performance, were selected for further analysis of real signals registered for seven subjects participating in the study.

RESULTS

The windowed cross-correlation and the windowed minimum sum of squared error method achieved the best results among the estimators considered and their outputs were averaged to arrive at a robust phase estimator. Across the subjects, it was found that an increase in the time delay between the principal harmonic of BP and ECG signals, θ(BP,ECG), corresponds to a slight time delay increase between the corresponding harmonics of longitudinal corneal apex displacement and blood pulsation signals, θ(LCAD,BP) and a decrease in the time delay between those of longitudinal corneal apex displacement and ECG signals, θ(LCAD,ECG). Significant correlation (paired t-test, p < 0.05) were found between θ(BP,ECG) and θ(LCAD,BP) as well as between θ(BP,ECG) and θ(LCAD,ECG). There was no significant correlation found between θ(LCAD,BP) and θ(LCAD,ECG).

CONCLUSION

The results indicate that longitudinal corneal apex displacement and correspondingly the ocular pulse phenomenon have not only a vascular origin but could also be influenced by the electrical activity of the heart.

Ultrasonic in vivo measurement of ocular surface expansion

Our aim was to ascertain whether the ultrasonic measurement of longitudinal corneal apex displacements carried out in a proper headrest is a credible method of ocular pulse (OP) detection. To distinguish between longitudinal movements of the eye globe treated as a rigid body and ocular surface expansion caused by the variations of the eye-globe volume, two ultrasound distance sensors were applied to noninvasively measure displacements of cornea and sclera. The same sensors were used to examine the influence of the anterio-posterior movements of a fixed head on the registration of corneal apex pulsation. In both experiments, ECG signals were synchronically recorded. Time, spectral, and coherence analyses obtained for four healthy subjects showed that the ocular surface expansion due to pulsatile ocular blood flow (POBF) is the main component of longitudinal corneal displacement. Ocular surface pulsation is always affected by the head movement. However, there exist some unique properties of signals, which help to distinguish between head and eye movements. A rigid headrest and a bite bar are required to stabilize the head during OP measurement. Ultrasonic technique enables noninvasive and accurate in vivo measurement of corneal pulsation, which could be of interest for indirectly estimating intraocular pressure propagation and POBF component.

Comparison of high-speed videokeratoscopy and ultrasound distance sensing for measuring the longitudinal corneal apex movements

Two different methods to measure binocular longitudinal corneal apex movements were synchronously applied. High-speed videokeratoscopy at a sampling frequency of 15 Hz and a custom-designed ultrasound distance sensor at 100 Hz were used for the left and the right eye, respectively. Four healthy subjects participated in the study. Simultaneously, cardiac electric cycle (ECG) was registered for each subject at 100 Hz. Each measurement took 20 s. Subjects were asked to suppress blinking during the measurements. A rigid headrest and a bite-bar were used to minimize undesirable head movements. Time, frequency and time-frequency representations of the acquired signals were obtained to establish their temporal and spectral contents. Coherence analysis was used to estimate the correlation between the measured signals. The results showed close correlation between both corneal apex movements and the cardiopulmonary system. Unraveling these relationships could lead to better understanding of interactions between ocular biomechanics and vision. The advantages and disadvantages of the two methods in the context of measuring longitudinal movements of the corneal apex are outlined.

Accommodative fluctuations, lens tension, and ciliary body thickness in children

PURPOSE

To investigate the relationship among microfluctuations in accommodation, resting tension on the crystalline lens, ciliary body thickness, and refractive error in children.

METHODS

Subjects were 49 children, aged 8 to 15 years. Subjects wore habitual correction over their left eye and an infrared filter over the right eye during accommodative measurements. Monocular accommodation was measured continuously for two, 30-second periods using a PowerRef I at a sampling rate of 25 Hz while subjects viewed a high-contrast target at 0.25 m. The high (1.0 to 2.3 Hz) and low- (0 to 0.6 Hz) frequency components of the power spectrum from a fast Fourier transform of the accommodative response were used in analysis. Resting tension on the crystalline lens was assessed by measuring the amplitude of the oscillations of the crystalline lens after a rightward 20 degrees saccadic eye movement. Ciliary body thickness was measured 2 mm posterior to the scleral spur from images obtained with a Zeiss Visante optical coherence tomography (OCT). Cycloplegic spherical equivalent refractive error was obtained with the Grand Seiko autorefractor.

RESULTS

The mean +/- SD spherical equivalent refractive error was -1.00 D +/- 2.25 (range, -6.00 D to +3.44 D). Greater power in the log of the high-frequency component of accommodative microfluctuations was associated with thinner ciliary bodies (p = 0.03) and lower ages (p = 0.0004). More hyperopic refractive errors with greater power in the high-frequency component (p = 0.0005) and the low-frequency component (p = 0.02). No statistically significant relationship was found for the low-frequency component or root mean square of accommodative microfluctuations and refractive error.

CONCLUSIONS

High-frequency microfluctuations of accommodation appear to be suppressed with thicker ciliary bodies. These variations in accommodation need to be observed in a longitudinal study to better assess the functional significance of their relationship to ciliary body size and refractive error.

Binocular correlation of ocular aberration dynamics

Fluctuations in accommodation have been shown to be correlated in the two eyes of the same subject. However, the dynamic correlation of higher-order aberrations in the frequency domain has not been studied previously. A binocular Shack-Hartmann wavefront sensor is used to measure the ocular wavefront aberrations concurrently in both eyes of six subjects at a sampling rate of 20.5 Hz. Coherence function analysis shows that the inter-ocular correlation between aberrations depends on subject, Zernike mode and frequency. For each subject, the coherence values are generally low across the resolvable frequency range (mean 0.11), indicating poor dynamic correlation between the aberrations of the two eyes. Further analysis showed that phase consistency dominates the coherence values. Monocular and binocular viewing conditions showed similar power spectral density functions.

Adaptive optics system for investigation of the effect of the aberration dynamics of the human eye on steady-state accommodation control

It is now known that defocus is not the only aberration in the eye that exhibits dynamic behavior during fixation. It is currently unknown what effects, if any, the dynamics of these other aberrations have on steady-state accommodation control. We constructed an adaptive optics system to serve as a tool for future investigations in this area. The system has several design features of interest, including automated precompensation of defocus and astigmatism and a method to bypass a scanner used to reduce speckle. It also has the facility to measure the eye's aberrations independent of the aberration manipulation device-a 37-actuator membrane deformable mirror. Coherence function analysis was used to assess the deformable mirror performance in terms of coupling between Zernike modes. Modes beyond third radial order showed severe coupling. Pilot data were collected on one subject to demonstrate the utility of this system in steady-state accommodation studies. The value of the system for future work in this area is discussed.

Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system

It is fairly well established that the higher-order aberrations of the eye fluctuate over relatively short time periods, but as yet there is no conclusive evidence regarding the origin of these fluctuations. We measured the aberrations and the pulse pressure wave simultaneously for five subjects. The aberrations were measured by using a Shack-Hartmann sensor sampling at 21.2 Hz. We decomposed the aberration data into Zernike coefficients up to and including fifth order and also calculated the rms wave-front error. From the pulse data the heart rate variability signal was also derived. Coherence function analysis showed that for all subjects there was a weak correlation between many of the aberrations and the pulse and the derived heart rate variability. The pulse and the heart rate variability can account for only 11% +/- 2% and 20% +/- 2%, respectively, of the aberration dynamics.

The effect of monocular and binocular viewing on the accommodation response to real targets in emmetropia and myopia

PURPOSE

Decreased blur-sensitivity found in myopia has been linked with reduced accommodation responses and myopigenesis. Although the mechanism for myopia progression remains unclear, it is commonly known that myopic patients rarely report near visual symptoms and are generally very sensitive to small changes in their distance prescription. This experiment investigated the effect of monocular and binocular viewing on static and dynamic accommodation in emmetropes and myopes for real targets to monitor whether inaccuracies in the myopic accommodation response are maintained when a full set of visual cues, including size and disparity, is available.

METHODS

Monocular and binocular steady-state accommodation responses were measured with a Canon R1 autorefractor for target vergences ranging from 0-5 D in emmetropes (EMM), late-onset myopes (LOM), and early-onset myopes (EOM). Dynamic closed-loop accommodation responses for a stationary target at 0.25 m and step stimuli of two different magnitudes were recorded for both monocular and binocular viewing.

RESULTS

All refractive groups showed similar accommodation stimulus response curves consistent with previously published data. Viewing a stationary near target monocularly, LOMs demonstrated slightly larger accommodation microfluctuations compared with EMMs and EOMs; however, this difference was absent under binocular viewing conditions. Dynamic accommodation step responses revealed significantly (p < 0.05) longer response times for the myopic subject groups for a number of step stimuli. No significant difference in either reaction time or the number of correct responses for a given number of step-vergence changes was found between the myopic groups and EMMs.

CONCLUSION

When viewing real targets with size and disparity cues available, no significant differences in the accuracy of static and dynamic accommodation responses were found among EMM, EOM, and LOM. The results suggest that corrected myopes do not experience dioptric blur levels that are substantially different from emmetropes when they view free space targets.

The influence of tinted lenses upon ocular accommodation

We determined the effect upon accommodative responses of tinted lenses prescribed for the relief of visual discomfort in a group of five long term lens wearers. Static and dynamic responses were measured under four viewing conditions (1) prescribed tinted lens (2) neutral density filter (3) tinted lens of complementary colour and (4) no absorptive lens. While similarity and normality of the mean stimulus-response functions between the four viewing conditions were evident, the low frequency component of the accommodation microfluctuations was significantly greater while viewing the target in the 'no lens' viewing condition. These increases in the low frequency components (LFC) of the accommodation may be a subtle indicator of visual stress in these patients. Colour specificity is not supported by this finding.

The effect of abnormal fixational eye movements upon visual acuity in congenital nystagmus

PURPOSE

The purpose of this study was to investigate the role that abnormal eye movements play in the degradation of visual acuity.

METHODS

Visual acuity was measured monocularly in 10 normal subjects (26.7+/-4.3 years) and 5 subjects with congenital nystagmus (34.9+/-8.8 years), using Regan Repeat Letter charts (RRL) and a logMAR based test (LogMAR Crowded Acuity Test (CAT)) while eye movements were continuously recorded using a commercially available infrared limbal eye tracker (Type 54, Optoelectronic Developments, UK). The eye tracker was controlled via a virtual oscilloscope (Viewdac, Keighly Instruments, UK) on an IBM PC clone (Opus Technology 486).

RESULTS

The mean visual acuity obtained with RRL was significantly higher than that obtained by CAT in the subjects with congenital nystagmus. A significant correlation was found between the root mean square value of the nystagmus waveform and the angular extent of CAT. Linear regression analysis revealed a correlation between the duration of the foveation periods and the linear acuity of the subjects with congential nystagmus. The nystagmus waveforms also demonstrated increased amounts of high frequency components (HFC: >3.0 Hz) when compared to the normal eyes.

CONCLUSIONS

The results of this study reveal 1) RRL charts provide a measure of a subjects resolution limit which is less dependent on eye movements; 2) the duration of foveation periods has a significant effect on visual acuity measurements obtained using a linear test chart format; 3) the predominance of high frequency components in the congenital nystagmus waveforms lead to short foveation periods adding to the degree of fixation instability.

Effect of an intervening screen on accommodation to a distant object

Background: An intervening screen has been suggested to induce an inward shift of accommodation when viewing a distant object. This is an example of the Mandelbaum effect. However, there have been no objective measures of the magnitude of this effect in this particular situation. Methods: Accommodation was recorded with an infra-red optometer, while subjects (n = 16) viewed a distant letter target with or without an intervening screen. Screens were placed near the individual dark focus distance or at 50 cm. In a second experiment the contrast of the distant target was varied and subjects (n = 5) viewed the target directly or through a screen placed near the individual dark focus distance. Results: In the main experiment, the Mandelbaum effect was not significantly different from zero and was less than 0.5 D in every subject. In addition, accommodation was not more variable when viewing through the screen. However, it may be that some subjects do demonstrate a Mandelbaum effect while others do not. The individual dark focus level did not predict susceptibility to the Mandelbaum effect for a screen at the dark focus. Subjects reported their perceptions of the tasks and some noted changes in the perceived distances of objects when viewing through a screen. In the second experiment, the Mandelbaum effect (< 0.6 D) did not vary with distant target contrast. Conclusions: When viewing a distant object through a screen there is a small (< 0.6 D) or negligible inward shift of accommodation.

Accommodative microfluctuations and pupil diameter

The nominally steady-state accommodation response exhibits temporal variations which can be characterized by two dominant regions of activity; a low frequency component (LFC < 0.6 Hz) and a high frequency component (1.0 < or = HFC < or = 2.1 Hz). There is no consensus as to the relative contribution made by each of the frequency components of the microfluctuations to the control of steady-state accommodation. We investigate the effect of variations in artificial pupil diameter (0.5, 1, 2, 3, 4 and 5 mm pupils) on the microfluctuations of accommodation, while three young emmetropic subjects view, monocularly, a photopic high contrast Maltese cross target placed at a dioptric distance equal to their open-loop accommodation level. Average power spectra were calculated for five accommodation signals, each of 10 sec duration, collected for each viewing condition at a sampling rate of 102.4 Hz using a continuously recording infrared objective optometer. For artificial pupil diameters < or = 2 mm the power of the LFC was found to increase as a function of reducing pupil diameter, while for artificial pupil diameters > 2 mm the LFC was found to be relatively constant. No systematic change in the HFC with varying artificial pupil diameter was observed. Changes in the root-mean-square (r.m.s.) value of the fluctuations with varying pupil diameter were significant (one-way ANOVA, F = 8.507, P = 0.0001, d.f. = 89) and showed a similar form to the changes in the LFC.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of target luminance on microfluctuations of accommodation

It is feasible that small temporal variations in steady-state accommodation may provide feedback to the accommodation control system through changes in retinal image contrast and that this feedback may be used to maintain an optimal accommodation response. The complex waveform of microfluctuations is dominated by two distinct regions of activity; a low frequency component (LFC < 0.6 Hz) and a high frequency component (1.0 < or = HFC < or = 2.3 Hz). Whereas the HFCs appear to be correlated with some intraocular manifestation of arterial pulse the contribution of the LFCs to the control of steady-state accommodation is unclear. The present study investigates the effect of target luminance on the waveform of accommodative microfluctuations. Three young emmetropic observers viewed monocularly a high contrast (90%) Maltese cross target placed at a vergence equal to their dark-focus level of accommodation in a Badal stimulus system. The luminance of the target was varied from 0.002 to 11.63 cd m-2 in nine equal logarithmic steps. Five continuous accommodation signals were collected for each viewing condition at a sampling rate of 102.4 Hz, and average power spectra subsequently calculated with a frequency resolution of 0.1 Hz. One-way ANOVA revealed a significant variation in the root-mean-square (r.m.s.) value of the microfluctuations (F = 19.795, d.f. 124, P = 0.0001) which could be attributed mainly to increases in the r.m.s. value for the two lowest luminances (0.002 and 0.004 cd m-2). Power spectrum analysis revealed that these changes in the microfluctuations could be attributed to increases of power in the LFC.(ABSTRACT TRUNCATED AT 250 WORDS)

Calibration of the Canon Autoref R-1 for continuous measurement of accommodation

The Canon Autoref R-1 is an infrared optometer which allows free-space viewing. Pugh and Winn described hardware modifications necessary to convert the Autoref R-1 from an instrument capable of taking single static measurements of the eye's accommodative (refractive) status to an instrument capable of continuous measurement of the accommodative status of the eye. We describe two methods of calibrating the Autoref R-1 for continuous measurement of accommodation for any individual eye. The assumptions and sources of error underlying these calibration techniques are discussed. We also describe further hardware modifications to simplify signal acquisition from the Autoref R-1.

Arterial pulse modulates steady-state ocular accommodation

Rapid and continuous fluctuations in ocular focus are known to occur when the eye views a stationary target. The advent of high-speed infra-red optometers has established that these microfluctuations of ocular accommodation have two dominant components: low frequency of less than 0.6 Hz and high frequency between 1.0-2.3Hz. Although the retinal image blur associated with microfluctuations has the potential to guide and maintain optimum accommodation levels, there is no consensus with regard to the respective contribution of each of the dominant frequency components. Using a newly-designed measurement and recording system we show that, when viewing a stationary target located at 25cm, individuals exhibit little variation in the frequency of low frequency components but significant variation in high frequency components. Simultaneous measurements of ocular accommodation and systemic arterial pulse demonstrate that the variation in high frequency component is significantly correlated with arterial pulse frequency. Since control experiments indicate that the microfluctuations are derived from activity of the crystalline lens our observations could provide the basis for a non-invasive method of assessing the effects of arterial pulse on ciliary body/choroidal vasculature, the vitreous/lens interface and intraocular pressure. Further, it is feasible that under certain conditions an abnormal increase in the magnitude of arterial pulse may affect the aggregate nature of accommodative microfluctuations to an extent that disrupts the normal control processes maintaining optimum retinal contrast during sustained near vision.

The frequency characteristics of accommodative microfluctuations for central and peripheral zones of the human crystalline lens

Temporal variations in the nominally steady-state accommodation response can be characterized approximately by two principal regions of dominant activity: a low frequency region (LFR less than 0.6 Hz) and a high frequency region (HFR greater than 1.0 Hz). The observed changes of activity in the LFR induced by varying stimulus conditions has led to the proposal that this region may be utilized as an error detector in the accommodation feed-back loop. The role of fluctuations in the HFR is, however, equivocal particularly as several reports have shown their magnitude to be positively correlated with pupil size. The implication is that HFRs are a consequence of the mechanical and elastic properties of peripheral rather than central zones of the crystalline lens and hence do not contribute to the accommodation control process. The aim of the study was to compare the incidence and magnitude of microfluctuations in LFRs and HFRs for central and peripheral lens zones when viewing a near target. Accommodation was measured continuously with a modified Canon Autoref R1 infra-red optometer on five young emmetropic subjects. We show that although the total power of the microfluctuations is reduced in the periphery, the form of the power spectra is similar for central and peripheral zones. Thus rather than being spurious effects caused by the periphery of the lens HFRs are present for both central and peripheral lens zones.