November 1999
Volume 40, Issue 12
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Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   November 1999
Accommodation Responses and Ageing
Author Affiliations
  • Gordon Heron
    From the Department of Vision Sciences, Glasgow Caledonian University, Scotland; and the
  • W. Neil Charman
    Department of Optometry and Vision Sciences, University of Manchester Institute of Science and Technology, Manchester, United Kingdom.
  • Lyle S. Gray
    From the Department of Vision Sciences, Glasgow Caledonian University, Scotland; and the
Investigative Ophthalmology & Visual Science November 1999, Vol.40, 2872-2883. doi:https://doi.org/
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      Gordon Heron, W. Neil Charman, Lyle S. Gray; Accommodation Responses and Ageing. Invest. Ophthalmol. Vis. Sci. 1999;40(12):2872-2883. doi: https://doi.org/.

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Abstract

purpose. To study the impact of age on accommodation dynamics.

methods. Monocular accommodation responses were measured continuously using a modified Canon Auto Ref R1 infrared optometer. The stimulus was a single letter oscillating sinusoidally between 2.38 and 1.33 D providing a stimulus amplitude of 0.52 D, about a mean level of 1.86 D. Response characteristics were used to quantify gain and phase. Step responses were also recorded between these stimulus vergence levels for calibration purposes and to measure reaction and response times. Nineteen visually normal subjects 18 to 49 years of age participated, and 11 frequencies were used in the range 0.05 to 1.0 Hz. A key feature of the experimental design was to use a stimulus vergence range that lay within the amplitude of accommodation of all the observers.

results. Accommodation gain reduced and phase lag increased with age, particularly at the higher frequencies used. No strongly significant change with age was found for reaction and response times or accommodation velocity, and results were similar for both far-to-near and near-to-far responses. Response amplitude for the step change in target vergence declined with age, and substantial differences were found between the measured and predicted (from reaction time) phase lags at 1.0 Hz as a function of age. Young observers showed a phase lag that was shorter than predicted, whereas older observers’ measured phase lags were considerably larger than predicted.

conclusions. Results show that for a target oscillating sinusoidally in a predictable manner at a modest amplitude, the main ageing effects occur in phase lag, which is appreciably longer than predicted from reaction times in the older observers. The effects of ageing on gain were not as marked. Although responses to small step changes do reduce with age, there is no evidence of increased response times with ageing. In general, accommodation function in the middle-aged eye is quite robust despite a dwindling amplitude of accommodation. These results provide evidence of accommodative vigor in youth and a slowing of accommodation with ageing.

The decline of the amplitude of accommodation with age is well known, and the need to use glasses for reading and close work is a readily recognized feature of middle age. Although knowledge of the physiological processes of presbyopia is incomplete 1 it is widely accepted that changes in the elastic components of the accommodation mechanism with age play a significant part in this process. 2 3 4 The role of the ciliary muscle in the process of presbyopia is less well established, but it is possible that its effect on the accommodation mechanism is reduced with age due to changes in its morphology and its relation to components of the zonule, 5 6 even though its contractive power is reported to remain undiminished with age. 7 8  
The reduced facility to accommodate for near vision, the hallmark of presbyopia, could be expected to influence the dynamic characteristics of accommodation. There have been a number of reports that show that accommodation velocity reduces with ageing. An early finding was provided by Allen, 9 who used a reaction timer to measure the time interval of accommodation responses in subjects 7 to 49 years of age and found response times were slower for the older subjects. More recently, studies using an infrared optometer 10 11 12 or photoretinoscopy techniques 13 have shown a slowing of accommodation with ageing, whereas a similar conclusion has been reported by Beers and van der Heijde 14 who continuously recorded lens axial thickness during accommodation. 
A limitation of many of these previous studies is that relatively large changes in accommodation stimuli were used. In some cases 9 10 11 these stimuli exceeded the amplitude of accommodation of the older observers and were therefore arguably inappropriate to examine the dynamic accommodation responses of the middle-aged eye. 
The aim of this study was to examine changes in accommodation dynamics that occur with age. A modest change of accommodation stimulus (1.05 D) was used, which lay well within the amplitude of accommodation of all the subjects who participated in the study. The stimulus vergence was varied sinusoidally so that gain and phase lag characteristics of the accommodation response could be determined. The stimulus amplitude was kept constant, rather than being scaled to take account of the age-related decline in the subject’s amplitude of accommodation. This was intended to demonstrate more clearly any deterioration in the performance of older subjects and to represent more realistically the impact of failing accommodation dynamics in real-world accommodative tasks. Reaction and response times were also measured using abrupt step changes in target vergence. 
Methods
Subjects
Nineteen subjects, 18 to 49 years of age, participated in the main experiment. This age range was chosen to provide a spread of accommodation abilities. All had normal distance and near visual acuity and no visual abnormalities. All had normal amplitude of accommodation for their age, and none had near vision symptoms. The lowest subjective amplitude as measured with natural pupils on the near point rule was 3.75 D, in comparison to the stimulus range of 1.33 to 2.38 D. Each subject received a full optometric examination before inclusion into the study to establish refractive error, visual acuity, accommodation amplitude, and absence of ocular anomaly. Any refractive error present was corrected, as necessary, by a soft contact lens: No subject had uncorrected astigmatism greater than 0.50 DC. Informed consent was obtained after an explanation of the experimental protocol. All procedures complied with the Declaration of Helsinki. All subjects were either students or staff at Glasgow Caledonian University. 
Apparatus
Accommodation was continuously recorded using a modified Canon Auto Ref R1 infrared optometer (Fig. 1) . 15 16 The instrument’s capacity to record accommodation levels statically is maintained, so that both static and continuous measures are possible. This optometer is particularly suited to the study of accommodation because it has an open field view and because the stimulus is presented as a real object in real space. This is achieved using an inclined semireflecting mirror that reflects infrared light for measurement and transmits visible light for vision. This arrangement reduces the potential for proximal effects to influence accommodation responses. 17 Each subject used the standard headrest provided for the Canon optometer, which had been modified to provide a bite-bar. A dental impression was made for each observer before recording: the use of headrest and bite-bar reduced artifact from head movement that might otherwise have contributed to the noise of the accommodation records. Accommodation was recorded monocularly from the eye preferred by the subject, and the other eye was occluded. 
The accommodation stimulus was a high-contrast single Snellen letter transparency (limb width, 1.09 mm) mounted onto the pen support base of an X–Y plotter (Bryans 60,000). A function generator (Phillips PM 5133) was used to drive this base sinusoidally. The target was back-illuminated by an electroluminescent panel, which provided a target luminance of 36 cd/m2 and was attached to the target. The target was viewed directly, in free space and oscillated sinusoidally over a distance from 42 cm (2.38 D) to 75 cm (1.33 D), which lay well within the amplitude of accommodation of all observers. When the distance sinusoid is inverted to convert the stimulus strength into diopters, some small distortions in the resulting vergence sinusoid are introduced. The vergence sinusoid is flattened at the far end of the cycle and is sharper at the near end of the cycle. A Fourier analysis of this vergence “sinusoid” shows that the mean level and amplitude of the fundamental sinusoidal oscillation are reduced slightly to an amplitude of 0.51 D, oscillating about a mean level of 1.78 D: the amplitude of higher harmonics was small enough to be ignored. Eleven frequencies (0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 Hz) randomly presented were used; each recording was 10.24 seconds long, and 10 were made for each frequency. The free space viewing arrangement for the target meant that its angular subtense was not held constant during the cycle of oscillation. The change in target limb subtense throughout the cycle was modest, from 8.92′ at 42 cm to 5.0′ at 75 cm. 
Abrupt changes in target vergence from 2.38 to 1.33 D and vice versa were provided using two single letter targets, one being positioned at 42 cm the other at 75 cm from the eye: these were identical with those used for the sinusoidal changes. Each target was back-lit by an electroluminescent panel attached to the target and mounted on a rotary solenoid so that it could be rotated independently into and out of the axis of the observation system. The rise and fall times of these targets were measured as 0.1 seconds. These step measurement response data were used to provide reaction and response times for comparison with phase lag data. 
Procedure
The subjects were shown the apparatus before recording, and the target movements were explained to them. As the target oscillated, its movement across the plotter platter was readily audible. Hence, the behavior of the targets was entirely predictable, and the requirements of each subject made very clear. We noted above that a size cue was present, throughout the cycle, because the target subtended a slightly larger visual angle when at the near (42-cm) end of its cycle. During recording, encouragement was given and reinforced when good records were evident. Subjects were discouraged from blinking during the recording, but some blinking did occur, especially from the older subjects who found the task difficult. No subjects could be considered experienced in accommodation studies. All were told to keep the target as clear as possible at all times and were given plenty of practice to familiarize themselves with the task before recording was started. 
Calibration
Calibration was carried out in the following manner. Once a satisfactory continuous record had been achieved with the instrument operating in its dynamic mode, recordings were made of the step changes from 2.38 to 1.33 D and vice versa. Each recording lasted for 10.24 seconds; because the sampling rate was 100 Hz, 1024 measures of accommodation level were collected, and one step change only was made during that time. In this way the change in optometer output in voltage units contained in the record of the step change was established to provide the number of these units per diopter value for calibration. Four measurements (two for far-to-near and two for near-to-far) were taken to provide one calibration trial, and three trials were taken during the time spent with each observer, interspersed with the recordings for oscillating targets to provide a calibration sampling throughout the experiment. Hence, 12 measurements of the response amplitude in voltage units to a single step change were made for calibration purposes. 
Corresponding accommodation response amplitudes in absolute dioptric units were measured with the optometer (which had previously been calibrated with a model eye) by taking 10 static measures of accommodation for the near (2.38 D) and then the far (1.33 D) target positions. These were then averaged, and the difference established the averaged dioptric size of the accommodation response amplitude for the 1.05-D stimulus amplitude. 
The final calibration value for each observer was made by averaging all the results from the three calibration trials in voltage units and dividing this value by the averaged size of the static response to the step in diopters, thereby providing a final average optometer output in voltage units per diopter value for calibration to quantify gain. 
The room lights were kept on when pupil size allowed. For some older subjects room illumination was switched off, and mydriasis was necessary to keep recordings free from pupillary artifacts. Mydriasis was achieved using two drops of 2.5% phenylephrine and was used on the 35-, 37-, 40-, 41-, 42-, 45-, 46-, and 49-year-old subjects. Mydriasis was not required for the 43- or 44-year-old subject. 
Results
Sinusoidal Stimuli
Typical Responses.
Some typical accommodative sinusoidal responses to the 0.05- and 0.6-Hz sinusoids for three subjects (21, 37, and 45 years of age) are illustrated in Figure 2 . The ordinate values (in diopters) on these figures refer to the response only, and the position and size of the stimulus (lower trace and with correct phase) on the ordinate scale were arbitrary for presentational reasons. The older subject clearly shows reduced gain and increased phase lag in comparison to the other two subjects. As shown in Figure 2D , some notching was evident in the response“ sinusoid” that may be caused by the superimposition of fluctuations caused by arterial pulse on the responses. 18 Note that this response terminates with a blink, which leads to a sudden saturation of the signal at the end of the run, and a couple of blinks can be seen at the beginning of the 45-year-old’s response to the 0.05-Hz stimulus (Fig. 2E)
During recording it became noticeable that sometimes subjects were having difficulty maintaining an accommodative response to the oscillating stimulus. Two examples are shown in Figure 3 . In Figure 3A 3a young (27-year-old) subject cannot maintain the accommodative tracking for the 0.9-Hz stimulus midway through the trial and regains it at the end. In Figure 3B , for a 38-year-old subject, the dynamic response to the 1.0-Hz frequency is seen to diminish throughout the trial, and tracking is lost completely toward the end. A lack of symmetry was sometimes noted in the time spent accommodating to the far target (1.33 D) in comparison to the time spent accommodating to the near target (2.38 D). An example of this is shown in Figure 4 , and it is clear that the subject (27-year-old) spent more time fixating the target at the 2.38-D stimulus level than he did when the target was at the 1.33-D stimulus level, giving the “sinusoid” response function a distinctively asymmetrical sawtooth-like appearance. The power spectrum from a Fourier analysis of this response is shown in Figure 4B : some power resides in the second and third harmonics, suggesting that the dynamic response is not a linear system. Possible ageing effects on the form of the responses have not been further explored in this study, and this could be an interesting aspect of future work. 
It is worth noting that several volunteers, who seemed normal, could not be admitted into the study because trials showed that they were unable to accommodate to the sinusoidal vergence changes of the stimulus. The reasons for this are unknown, because all had normal vision with normal accommodation amplitudes, and none had any near vision symptoms or difficulties. All said that the target went blurred during the cycle, and they were unable to make it go clear. This provides a reminder that, even though free space viewing was used, the arrangement did not provide a normal visual environment for accommodation for these particular subjects, possibly because they normally relied on binocular cues, particularly convergence, to initiate accommodation. 
Gain.
Gain was defined as the quotient of the peak-to-trough response change divided by that of the stimulus. Hence, a gain of 1.0 implies that the subject has accommodated to the sinusoidally varying target with exactly the amplitude required by the stimulus. 
Graphs of gain versus age for each frequency used are shown in Figure 5 . Straight lines have been fitted to the data to indicate trends, although it may be that other fitting functions would be more appropriate in some cases. Note that gain values tend to decline with frequency and age. The standard deviations for individual subjects reflect variability in the subject’s responses (see Fig. 4 ) rather than measurement errors: The same applies to phase measurements (see below). 
Phase.
Phase lag was measured directly off the recordings. The mean time lag, tL (in seconds), for each response peak and trough with respect to the corresponding stimulus extremum was determined, and the corresponding phase lag was expressed as tL × f × 360°, where f is the temporal frequency of the stimulus. Graphs of the variation of phase lag with age for each frequency used are shown in Figure 6 . Straight line fits are again used to indicate general trends in the data. The familiar increase in phase lag at the higher frequencies is evident, as is the fact that a marked increase in phase lag occurs with age only at higher frequencies. 
Step Stimuli
Typical accommodation changes for abrupt step changes in accommodation from 2.38 to 1.33 D and from 1.33 to 2.38 D are shown in Figure 7 . Near-to-far and far-to-near reaction and response times were read directly off the records. The initial and final steady state levels were first estimated by averaging the response on either side of the step. The reaction time was taken as the time interval between the known instant of stimulus change and the time at which the response just started to change from the initial steady-state level. The response time was taken as that between the latter time and that when the response just reached its final steady-state level. Most of the uncertainty in these estimates was caused by the natural fluctuations in accommodation. Regression analysis of age against various response characteristics is summarized below in Table 1
When data for all subjects were pooled, mean reaction times were 0.34 ± 0.10 seconds (far-to-near) and 0.35 ± 0.10 seconds (near-to-far). Mean response times were 0.53 ± 0.18 seconds (far-to-near) and 0.56 ± 0.24 seconds (near-to-far). No significant difference exists between near-to-far and far-to-near reaction times (paired t-test: diff = −0.013; t = −0.673; P = 0.51), and no significant difference exists between near-to-far and far-to-near response times (paired t-test: diff = −0.039; t = 1.03; P = 0.32). It can be seen that in general there is no strong effect of age on reaction or response times. 
In Figure 8a comparison is made of predicted phase lag based on the individual reaction times and the corresponding measured phase lag for the 1.0-Hz frequency stimulus. At 1-Hz the simple reaction time prediction is that the phase lag will be 360R degrees, where R is the reaction time in seconds. Observed lags become substantially longer than the predictions for the older subjects. Similar but reduced effects are observed at lower frequencies. 
Discussion
In considering these data, we again emphasize that during the measurements the sinusoidal changes in stimulus vergence were entirely predictable, there being plentiful cues to target distance. Subjects were given every encouragement to keep the target clear at all times, and the modest amplitude of the stimulus change (0.52 D) meant that the stimulus always lay well within the amplitude of accommodation of the subjects, whatever their age. 
One striking feature of the results, evident in Figures 5 and 6 , is the existence of substantial intersubject variability between the responses of individuals of similar age (see also Ref. 13) : These differences did not correlate in any obvious way with the conventional amplitudes of accommodation of the individuals concerned. It may be that some subjects were better able to make use of the available monocular cues to target position and were less disturbed by the absence of normal binocular cues; alternatively they may have been capable of providing a stronger voluntary input to help drive their accommodation. 
In general, it was found that gain decreased with age at all temporal frequencies, with the relative changes being smaller at higher frequencies. Thus, over the frequency range studied (Fig. 5) , gain varied more for younger subjects than it did for the older ones. At the lower frequencies, some of the subjects had gains in excess of unity, suggesting that under these viewing conditions responses are facilitated by the predictable nature of the task, allowing some voluntary accommodation to augment the response. At higher temporal frequencies gain values are low (e.g., ≈0.4 at 1.0 Hz) and reduce only slightly with age, showing that this is a difficult task for all subjects, irrespective of their ages. Phase lags tend to increase with age (Fig. 6) , with the increase being much more pronounced at higher frequencies. This evidently implies some slowing of the accommodation system with age when a constant amplitude of stimulus is used. However, it must be remembered that such a stimulus represents a larger fraction of the available amplitude of accommodation for older subjects. It is possible that if the stimulus amplitude had been scaled with the subjective amplitude of the subjects, these increased phase lags would have been absent. Such scaling would not, however, be representative of real-world tasks. Evidently a presbyope could always “respond” to a zero stimulus change. 
It is important to note that the increase in phase lag must be attributed to a response change with age rather than to changes in reaction time. This is well illustrated by Figure 8 . The phase lags at 1.0 Hz predicted on the basis of individual reaction times to step changes in stimulus, like the reaction times themselves, show little variation with age. Predicted lag at 1 Hz is simply 360R degrees, where R is the reaction time in seconds. The young observers have a measured phase lag somewhat smaller than that calculated from their reaction times, suggesting that they were able to make use of the predictability of the task to reduce the lag. In contrast, older subjects, although attempting to follow the same predictable changes, have lags in excess of those calculated from their reaction times, indicating an ageing effect in the dynamic responses. 
Since a mydriatic was used to dilate the pupils of many of the older subjects, it was possible that their slower responses might in some way have been due to the drug, rather than to the effects of age. A control experiment was therefore carried out in which accommodation responses across the same range of temporal frequencies were recorded for two young subjects (26 and 27 years of age) in each of two conditions: with no drug and, on a separate occasion, half an hour after instillation of 2 drops of 2.5% phenylephrine. When the gains and phase lags of the responses without and with the drug were compared, one subject showed no change, but in the other the drug tended to reduce gains and to increase phase lags. 
It is well known that phenylephrine 2.5% modestly reduces the static amplitude of accommodation. 19 20 The control experiment showed that adverse effects may also be induced in the dynamic responses. Hence, it is possible that some of the changes with age seen in Figures 5 and 6 could be due to phenylephrine masking the full capacity for accommodation in those older subjects for whom mydriasis was necessary. However, the 43- and 44-year-old subjects in the main experiment received no mydriatic (see the Procedure section): it is evident in Figures 5 and 6 that their results follow the same trends as those for the rest of the older subjects, implying that mydriasis is unlikely to have any major effect on the results. The effect of mydriatics on accommodation dynamics deserves further investigation. 
In view of the finding of systematic changes with age in dynamic characteristics to sinusoidal target vergence change, it might seem paradoxical that no significant age changes in the response times to abrupt step changes in target vergence were detected (Table 1) . It must be remembered, however, that an abrupt step, random in time, cannot be predicted, so that younger subjects are unable to use the voluntary control of accommodation, which enhances their gain for low frequency sinusoidally changing stimuli. Moreover, because gains are low at higher temporal frequencies, the markedly increased phase lags at these frequencies for older subjects have only a minor impact on the step response. Thus, step response characteristics are a less sensitive indicator of accommodation changes with age than are studies of sinusoidally changing stimuli at a range of temporal frequencies. 
The present gain and phase results for 20- and 45-year-old subjects, derived from the line fits of Figures 5 and 6 , are compared in Figure 9 with those found by several previous investigators, 21 22 23 24 who used young subjects and roughly similar stimulus amplitudes. It can be seen that there is broad agreement. It is, of course, likely that experimental details such as target luminance, contrast, size, and color will influence values of gain and phase for subjects of similar age from one study to the next. In particular, those studies in which the stimulus was presented through a Badal system, thereby eliminating size cues, tend to record lower gains. 21 22 23 24  
The step reaction and response times found in the present study are also very similar to those found by other authors. 25 26 27 An increase with age in the response time to step changes in stimulus has been reported in some studies, 9 10 11 12 13 although many of these used inappropriately large changes in stimulus, so that the higher stimulus level lay outside the amplitude of accommodation of the older subjects. 
Although the effects are not statistically significant (see Table 1 ), possibly because of the large intersubject variations, it is interesting that the magnitude of the response changes elicited by the 1.05-D stimulus steps (1.33–2.38 D) used for calibration appears to reduce with age (Fig. 10) . There is some indication that most of the decline occurs after approximately 40 years of age. A similar decline has been observed by Fukuda et al., 11 who used a step change between 3.0 and 0.5 D and subjects 22 to 61 years of age. Ramsdale and Charman 28 explain such changes in terms of a reduction with age in the slope of the static accommodation response/stimulus curve. Effectively, the useful subjective amplitude of accommodation, within which the stimulus must lie for clear vision, is the objective amplitude of accommodation supplemented by the total ocular depth of focus. Thus, as the objective amplitude diminishes through life while the objective depth of focus remains approximately constant, 29 the slope of the response/stimulus curve, which approximates to the objective divided by the subjective amplitude, diminishes. The slope change would be expected to become much more obvious at 40 years of age or older, 29 when the total depth of focus becomes a substantial fraction of the subjective amplitude. The changes in response/stimulus slope lead to a decrease with age in the magnitude of any step response. 
In summary, several effects of age on dynamic accommodation have been shown in the present study, even though stimuli lay within the amplitude of static accommodation of all subjects. For stimulus vergences changing sinusoidally with time, gain tends to decline with age and phase lag to increase. However, these effects are quite modest, and it is striking that subjects can continue to respond into their late 40s to stimuli varying at 1 Hz. Within the available amplitude of accommodation, the dynamic characteristics of the older accommodation system remain quite efficient. Schaeffel et al. 13 have previously remarked that the speed of accommodation in response to step changes varies remarkably little between 20 and 45 years of age. The major practical problems associated with the approach of presbyopia are, then, those due to the decline in the amplitude of accommodation, rather than to the loss of dynamic facility. 
It is difficult to reconcile this finding with models of presbyopia depending solely on changes in the elastic constants of the lens, 2 3 4 which predict marked changes in both the static and dynamic characteristics. We note, however, that Fisher’s 4 measurements of lens elasticity show only small changes below the age of approximately 40 and that, in any case, a single value of modulus may not adequately characterize an inhomogeneous structure like the lens. It must be remembered that the outer cortical fibers of the older lens are, due to lens growth throughout life, as youthful (and, possibly, elastic) as those of the young lens. Thus, if the dynamics of lenticular change in response to small stimulus changes depend primarily on the elastic properties of the outer cortex of the lens, reasonable dynamic efficiency may be retained into middle age. More significantly it may be, as remarked by Koretz et al., 30 in relation to the constancy with age in the changes per diopter of accommodation in lens thickness and other axial dimensions, that with age the lens and other relevant parts of the anterior segment “develop in a compensatory manner to preserve… the general form of the accommodative process.” The multifactorial nature of accommodative changes with age has, of course, been emphasized by many authors. 31 32 33  
 
Figure 1.
 
Diagram of the apparatus used. Accommodation was measured both statically and continuously on a Canon Auto Ref R1 optometer. Targets positioned at 42 and 75 cm, respectively, were mounted onto rotatory solenoids and could be swung into the visual axis to provide step-change accommodative stimuli. A third target was mounted onto the penholder base of an X–Y plotter and driven sinusoidally along the visual axis. This target was removed when step changes were being recorded.
Figure 1.
 
Diagram of the apparatus used. Accommodation was measured both statically and continuously on a Canon Auto Ref R1 optometer. Targets positioned at 42 and 75 cm, respectively, were mounted onto rotatory solenoids and could be swung into the visual axis to provide step-change accommodative stimuli. A third target was mounted onto the penholder base of an X–Y plotter and driven sinusoidally along the visual axis. This target was removed when step changes were being recorded.
Figure 2.
 
Typical accommodation responses for a 21-year-old subject (A, B), a 37-year-old subject (C, D), and a 45-year-old subject (E, F) for stimuli oscillating at 0.05 Hz (A, C, E) and at 0.6 Hz (B, D, F). In (D) some notching is evident in the response, perhaps caused by arterial pulse. The lower trace in each part of the figure represents the stimulus with correct phase but amplitude was arbitrary and adjusted to avoid the response trace for display purposes.
Figure 2.
 
Typical accommodation responses for a 21-year-old subject (A, B), a 37-year-old subject (C, D), and a 45-year-old subject (E, F) for stimuli oscillating at 0.05 Hz (A, C, E) and at 0.6 Hz (B, D, F). In (D) some notching is evident in the response, perhaps caused by arterial pulse. The lower trace in each part of the figure represents the stimulus with correct phase but amplitude was arbitrary and adjusted to avoid the response trace for display purposes.
Figure 3.
 
Examples of response fatigue. In (A) a 27-year-old observer loses accommodative tracking to a 0.9-Hz stimulus midway through the recording and then regains it. In (B) the response (1.0-Hz stimulus) declines throughout the recording (38-year-old observer).
Figure 3.
 
Examples of response fatigue. In (A) a 27-year-old observer loses accommodative tracking to a 0.9-Hz stimulus midway through the recording and then regains it. In (B) the response (1.0-Hz stimulus) declines throughout the recording (38-year-old observer).
Figure 4.
 
Responses for a 27-year-old observer to a 0.4-Hz stimulus showing a sawtooth-like pattern (A). Fourier analysis shows that most of the subsidiary power lies in the second and third harmonics (B).
Figure 4.
 
Responses for a 27-year-old observer to a 0.4-Hz stimulus showing a sawtooth-like pattern (A). Fourier analysis shows that most of the subsidiary power lies in the second and third harmonics (B).
Figure 5.
 
Graphs of mean gain against age for the eleven frequencies used. Error bars represent standard deviations.
Figure 5.
 
Graphs of mean gain against age for the eleven frequencies used. Error bars represent standard deviations.
Figure 6.
 
Graphs of mean phase lag against age for all eleven frequencies used. Errors bars represent standard deviations.
Figure 6.
 
Graphs of mean phase lag against age for all eleven frequencies used. Errors bars represent standard deviations.
Figure 7.
 
Typical accommodation responses to the step change in target vergence 2.38 to 1.33 D above (A) and 1.33 to 2.38 D below (B) for a 21-year-old observer.
Figure 7.
 
Typical accommodation responses to the step change in target vergence 2.38 to 1.33 D above (A) and 1.33 to 2.38 D below (B) for a 21-year-old observer.
Table 1.
 
Analysis of the Correlation with Age of Reaction Time, Response Time, Velocity, and Response Magnitude
Table 1.
 
Analysis of the Correlation with Age of Reaction Time, Response Time, Velocity, and Response Magnitude
Correlation with Age F Degrees of Freedom P Sig
Far-to-near reaction time 0.092 1,18 0.77 NS
Near-to-far reaction time 6.37 1,18 0.02 sig; y = −0.004x+ 0.48; r = 0.52
Pooled reaction times 4.02 1,36 0.061 NS
Far-to-near response times 0.001 1,18 0.97 NS
Near-to-far response times 1.7 1,18 0.21 NS
Pooled response times 0.56 1,36 0.47 NS
Response velocity 0.45 1,18 0.51 NS
Response magnitude 4.2 1,18 0.06 NS
Figure 8.
 
Graph of measured and predicted (from reaction times) phase lags at 1.0 Hz against age.
Figure 8.
 
Graph of measured and predicted (from reaction times) phase lags at 1.0 Hz against age.
Figure 9.
 
Plots of gain (A) and phase lag (B) as a function of temporal frequency of a sinusoidally changing stimulus as found in the present experiments and by other investigators. Open circles: Data for 20-year-old subjects, values derived from the regression line fits of Figures 5 and 6 , 0.52-D stimulus amplitude, with blur, color, and size cues. Solid circles: Data for 45-year-old subjects. Continuous lines: Kruger and Pola, 21 mean of four 23-year-old subjects, 1.0-D stimulus amplitude, with blur, color, and size cues. Heavy dashed lines: Ohtsuka and Sawa, 22 mean of four 29-year-old subjects, 1.5-D stimulus amplitude, with no size cues. Lightly dashed lines: van der Wildt et al., 23 data from one young subject, 0.5-D stimulus amplitude, with no size cues. Dot and dashed lines: Stark et al., 24 data of one subject, 0.5-D stimulus amplitude, with no size cues.
Figure 9.
 
Plots of gain (A) and phase lag (B) as a function of temporal frequency of a sinusoidally changing stimulus as found in the present experiments and by other investigators. Open circles: Data for 20-year-old subjects, values derived from the regression line fits of Figures 5 and 6 , 0.52-D stimulus amplitude, with blur, color, and size cues. Solid circles: Data for 45-year-old subjects. Continuous lines: Kruger and Pola, 21 mean of four 23-year-old subjects, 1.0-D stimulus amplitude, with blur, color, and size cues. Heavy dashed lines: Ohtsuka and Sawa, 22 mean of four 29-year-old subjects, 1.5-D stimulus amplitude, with no size cues. Lightly dashed lines: van der Wildt et al., 23 data from one young subject, 0.5-D stimulus amplitude, with no size cues. Dot and dashed lines: Stark et al., 24 data of one subject, 0.5-D stimulus amplitude, with no size cues.
Figure 10.
 
Graph of the variation of size of the calibration step response with age. Error bars represent SDs.
Figure 10.
 
Graph of the variation of size of the calibration step response with age. Error bars represent SDs.
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Figure 1.
 
Diagram of the apparatus used. Accommodation was measured both statically and continuously on a Canon Auto Ref R1 optometer. Targets positioned at 42 and 75 cm, respectively, were mounted onto rotatory solenoids and could be swung into the visual axis to provide step-change accommodative stimuli. A third target was mounted onto the penholder base of an X–Y plotter and driven sinusoidally along the visual axis. This target was removed when step changes were being recorded.
Figure 1.
 
Diagram of the apparatus used. Accommodation was measured both statically and continuously on a Canon Auto Ref R1 optometer. Targets positioned at 42 and 75 cm, respectively, were mounted onto rotatory solenoids and could be swung into the visual axis to provide step-change accommodative stimuli. A third target was mounted onto the penholder base of an X–Y plotter and driven sinusoidally along the visual axis. This target was removed when step changes were being recorded.
Figure 2.
 
Typical accommodation responses for a 21-year-old subject (A, B), a 37-year-old subject (C, D), and a 45-year-old subject (E, F) for stimuli oscillating at 0.05 Hz (A, C, E) and at 0.6 Hz (B, D, F). In (D) some notching is evident in the response, perhaps caused by arterial pulse. The lower trace in each part of the figure represents the stimulus with correct phase but amplitude was arbitrary and adjusted to avoid the response trace for display purposes.
Figure 2.
 
Typical accommodation responses for a 21-year-old subject (A, B), a 37-year-old subject (C, D), and a 45-year-old subject (E, F) for stimuli oscillating at 0.05 Hz (A, C, E) and at 0.6 Hz (B, D, F). In (D) some notching is evident in the response, perhaps caused by arterial pulse. The lower trace in each part of the figure represents the stimulus with correct phase but amplitude was arbitrary and adjusted to avoid the response trace for display purposes.
Figure 3.
 
Examples of response fatigue. In (A) a 27-year-old observer loses accommodative tracking to a 0.9-Hz stimulus midway through the recording and then regains it. In (B) the response (1.0-Hz stimulus) declines throughout the recording (38-year-old observer).
Figure 3.
 
Examples of response fatigue. In (A) a 27-year-old observer loses accommodative tracking to a 0.9-Hz stimulus midway through the recording and then regains it. In (B) the response (1.0-Hz stimulus) declines throughout the recording (38-year-old observer).
Figure 4.
 
Responses for a 27-year-old observer to a 0.4-Hz stimulus showing a sawtooth-like pattern (A). Fourier analysis shows that most of the subsidiary power lies in the second and third harmonics (B).
Figure 4.
 
Responses for a 27-year-old observer to a 0.4-Hz stimulus showing a sawtooth-like pattern (A). Fourier analysis shows that most of the subsidiary power lies in the second and third harmonics (B).
Figure 5.
 
Graphs of mean gain against age for the eleven frequencies used. Error bars represent standard deviations.
Figure 5.
 
Graphs of mean gain against age for the eleven frequencies used. Error bars represent standard deviations.
Figure 6.
 
Graphs of mean phase lag against age for all eleven frequencies used. Errors bars represent standard deviations.
Figure 6.
 
Graphs of mean phase lag against age for all eleven frequencies used. Errors bars represent standard deviations.
Figure 7.
 
Typical accommodation responses to the step change in target vergence 2.38 to 1.33 D above (A) and 1.33 to 2.38 D below (B) for a 21-year-old observer.
Figure 7.
 
Typical accommodation responses to the step change in target vergence 2.38 to 1.33 D above (A) and 1.33 to 2.38 D below (B) for a 21-year-old observer.
Figure 8.
 
Graph of measured and predicted (from reaction times) phase lags at 1.0 Hz against age.
Figure 8.
 
Graph of measured and predicted (from reaction times) phase lags at 1.0 Hz against age.
Figure 9.
 
Plots of gain (A) and phase lag (B) as a function of temporal frequency of a sinusoidally changing stimulus as found in the present experiments and by other investigators. Open circles: Data for 20-year-old subjects, values derived from the regression line fits of Figures 5 and 6 , 0.52-D stimulus amplitude, with blur, color, and size cues. Solid circles: Data for 45-year-old subjects. Continuous lines: Kruger and Pola, 21 mean of four 23-year-old subjects, 1.0-D stimulus amplitude, with blur, color, and size cues. Heavy dashed lines: Ohtsuka and Sawa, 22 mean of four 29-year-old subjects, 1.5-D stimulus amplitude, with no size cues. Lightly dashed lines: van der Wildt et al., 23 data from one young subject, 0.5-D stimulus amplitude, with no size cues. Dot and dashed lines: Stark et al., 24 data of one subject, 0.5-D stimulus amplitude, with no size cues.
Figure 9.
 
Plots of gain (A) and phase lag (B) as a function of temporal frequency of a sinusoidally changing stimulus as found in the present experiments and by other investigators. Open circles: Data for 20-year-old subjects, values derived from the regression line fits of Figures 5 and 6 , 0.52-D stimulus amplitude, with blur, color, and size cues. Solid circles: Data for 45-year-old subjects. Continuous lines: Kruger and Pola, 21 mean of four 23-year-old subjects, 1.0-D stimulus amplitude, with blur, color, and size cues. Heavy dashed lines: Ohtsuka and Sawa, 22 mean of four 29-year-old subjects, 1.5-D stimulus amplitude, with no size cues. Lightly dashed lines: van der Wildt et al., 23 data from one young subject, 0.5-D stimulus amplitude, with no size cues. Dot and dashed lines: Stark et al., 24 data of one subject, 0.5-D stimulus amplitude, with no size cues.
Figure 10.
 
Graph of the variation of size of the calibration step response with age. Error bars represent SDs.
Figure 10.
 
Graph of the variation of size of the calibration step response with age. Error bars represent SDs.
Table 1.
 
Analysis of the Correlation with Age of Reaction Time, Response Time, Velocity, and Response Magnitude
Table 1.
 
Analysis of the Correlation with Age of Reaction Time, Response Time, Velocity, and Response Magnitude
Correlation with Age F Degrees of Freedom P Sig
Far-to-near reaction time 0.092 1,18 0.77 NS
Near-to-far reaction time 6.37 1,18 0.02 sig; y = −0.004x+ 0.48; r = 0.52
Pooled reaction times 4.02 1,36 0.061 NS
Far-to-near response times 0.001 1,18 0.97 NS
Near-to-far response times 1.7 1,18 0.21 NS
Pooled response times 0.56 1,36 0.47 NS
Response velocity 0.45 1,18 0.51 NS
Response magnitude 4.2 1,18 0.06 NS
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