On the linearity of accommodation dynamics

Seeing the future: Predictive control in neural models of ocular accommodation

Ocular accommodation is the process of adjusting the eye's crystalline lens so as to bring the retinal image into sharp focus. The major stimulus to accommodation is therefore retinal defocus, and in essence, the job of accommodative control is to send a signal to the ciliary muscle which will minimize the magnitude of defocus. In this article, we first provide a tutorial introduction to control theory to aid vision scientists without this background. We then present a unified model of accommodative control that explains properties of the accommodative response for a wide range of accommodative stimuli. Following previous work, we conclude that most aspects of accommodation are well explained by dual integral control, with a “fast” or “phasic” integrator enabling response to rapid changes in demand, which hands over control to a “slow” or “tonic” integrator which maintains the response to steady demand. Control is complicated by the sensorimotor latencies within the system, which delay both information about defocus and the accommodation changes made in response, and by the sluggish response of the motor plant. These can be overcome by incorporating a Smith predictor, whereby the system predicts the delayed sensory consequences of its own motor actions. For the first time, we show that critically-damped dual integral control with a Smith predictor accounts for adaptation effects as well as for the gain and phase for sinusoidal oscillations in demand. In addition, we propose a novel proportional-control signal to account for the power spectrum of accommodative microfluctuations during steady fixation, which may be important in hunting for optimal focus, and for the nonlinear resonance observed for low-amplitude, high-frequency input. Complete Matlab/Simulink code implementing the model is provided at https://doi.org/10.25405/data.ncl.14945550.

Monocular accommodation response to random defocus changes induced by a tuneable lens

Accommodation of the human eye relies on multiple factors and visual cues that include object size, monochromatic and chromatic aberrations, and vergence. Yet, even in monocular conditions, accommodation corrects for defocus. Studies of eye growth in chicks have addressed whether the retina can decode the sign of defocus as this may play a role for emmetropization and possibly also accommodation. However, findings have not been unambiguous and questions remain. Here, we report on monocular accommodation studies of emmetropic and myopic human subjects to clarify whether foveal vision drives accommodation in the correct direction by removing out-of-focus blur potentially before relying on other cues. Subjects viewed monocularly a green target at 1-meter distance while being presented with a random sequence of negative defocus step changes induced by a pupil-conjugated current-driven tuneable lens. The natural pupil was constricted by a pupil-conjugated motorized iris using three different diameters and target brightness was set with a liquid crystal variable attenuator. A Hartmann-Shack wavefront sensor with an infrared beacon captured real-time changes of defocus and Zernike polynomial coefficients up to 4th radial order. We find that the young adult eye accommodates reliably in the correct direction but with a latency of 300-700 ms. The findings are discussed in relation to an absorption model of light in outer segments that breaks the defocus symmetry and thus may serve as a plausible guide for accommodation and emmetropization.

Stimulus Unpredictability in Time, Magnitude, and Direction on Accommodation

SIGNIFICANCE

The effect of predictability in changes of time, magnitude, and direction of the accommodation demand on the accommodation response latency and its magnitude are insignificant, which suggests that repetitive accommodative tasks such as the clinical accommodative facility test may not be influenced by potential anticipation effects.

PURPOSE

The purpose of this study was to investigate the effect of stimulus' time, magnitude, and direction predictability, as well as their interactions, on accommodation latency and response magnitude.

METHODS

Monocular accommodative response and latency were measured in 12 young subjects for nine different conditions where the stimulus accommodative demand changed several times in a steplike fashion for a period of 120 seconds. Each change in accommodative demand could have different time duration (i.e., 1, 2, or 3 seconds), magnitude (1, 2, or 3 diopters), and/or direction (i.e., accommodation or disaccommodation). All conditions were created permuting the factors of time, magnitude, and direction with two levels each: random and not random. The baseline condition was a step signal from 0 to 2 diopters persisting for 2 seconds in both accommodative demands. After each condition, subjects were asked to provide a score from 1 to 5 in their perceived predictability.

RESULTS

Friedman test conducted on the perceived predictability of each condition resulted in statistically significant differences between the nine conditions (χ = 56.57, P < .01). However, repeated-measures analysis of variance applied to latency and accommodative response magnitude did not show significant differences (P > .05). In addition, no correlation was found between the perceived predictability scores and both latency and accommodative response magnitudes between the most predictable and the most unpredictable conditions.

CONCLUSIONS

Subjects were able to perceptually notice whether the stimulus was predictable or not, although our results indicate no significant effect of stimuli predictability on either the accommodation latency or its magnitude.

Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays

From the desktop to the laptop to the mobile device, personal computing platforms evolve over time. Moving forward, wearable computing is widely expected to be integral to consumer electronics and beyond. The primary interface between a wearable computer and a user is often a near-eye display. However, current generation near-eye displays suffer from multiple limitations: they are unable to provide fully natural visual cues and comfortable viewing experiences for all users. At their core, many of the issues with near-eye displays are caused by limitations in conventional optics. Current displays cannot reproduce the changes in focus that accompany natural vision, and they cannot support users with uncorrected refractive errors. With two prototype near-eye displays, we show how these issues can be overcome using display modes that adapt to the user via computational optics. By using focus-tunable lenses, mechanically actuated displays, and mobile gaze-tracking technology, these displays can be tailored to correct common refractive errors and provide natural focus cues by dynamically updating the system based on where a user looks in a virtual scene. Indeed, the opportunities afforded by recent advances in computational optics open up the possibility of creating a computing platform in which some users may experience better quality vision in the virtual world than in the real one.

Ocular motor triad with single vision contact lenses compared to spectacle lenses

AIM

Theoretically myopes are required to exert more accommodation and vergence when wearing single vision contact lenses compared to glasses and hypermetropes less. This study aims to quantify the effects clinically.

METHOD

Thirty subjects (21 female, nine male, average age 21.0+/-2.2 years) with a range of refractive errors (-7.87 D to +3.50 D) viewed in a random order, static targets at 0.1, 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 D accommodative demand that were matched for angular subtense. The subjects were fully corrected with spectacles and daily disposable contact lenses to their full prescription. Accommodation was monitored objectively with the PowerRefractor and Shin-Nippon SRW5000 and vergence and pupil size with the PowerRefractor.

RESULTS

Myopes exerted greater accommodative effort for viewing near targets with contact lenses than glasses and hypermetropes less (r(2)=0.35, p=0.001 PowerRefractor). Myopes also exerted greater vergence effort for viewing near targets with contact lenses than glasses and hypermetropes less (r(2)=0.22, p<0.01).

CONCLUSION

Theoretical calculation of the accommodative and vergence requirements with glasses compared to contact lenses reflect clinical findings, although there is reasonable variability between individuals.

Accommodation as a function of age and the linearity of the response dynamics

The changes with age in the accommodation responses to dynamic stimuli can reveal useful information on the factors underlying presbyopia development. Analysis of the monocular accommodation responses of 19 normal observers (ages 18-49 years) to stimuli whose vergence varied sinusoidally with time at different temporal frequencies (peak-to-peak stimulus 1.33-2.38 D, at 0.05-1.00 Hz) showed that at all ages both the gain and phase of the response were essentially linear functions of the temporal frequency. Extrapolation of least-squares, regression line fits to the gain data for each subject gave the gain at zero frequency, G0, and the cut-off frequency, fc, at which the gain fell to zero. G0 reduced with age but fc remained essentially constant at about 1.7 Hz, up to at least the age of about 40. The magnitude of the response to step stimuli covering the same stimulus range was well correlated with the value of G0. The linear changes in phase lag with temporal frequency corresponded to simple time delays td. The time lag varied from close to zero for the youngest subjects to about 0.5 s for the subjects in their late forties. There was substantial variation between the responses of subjects of similar age: those subjects with high values of G0 also tended to have low values of td, both effects probably being due to the superior ability of some individuals to predict the sinusoidal changes in the accommodation stimulus. Comparison of theoretical step responses, derived by applying linear theory to the parameters obtained from the results for the sinusoidal stimuli, with the actual responses to unpredictable steps for the same subjects supports the view that prediction effects and other possible factors make linear theory inapplicable to this type of data. The results are discussed in the context of current ideas on the development of presbyopia: it is suggested that the constancy of fc with age is the result of the ciliary body maintaining its efficiency, whereas the fall in G0 and increase in td result from increases in lens rigidity.

Accommodation dynamics as a function of age

Experiments are described in which the dynamic accommodation response to a stimulus whose vergence was varying sinusoidally with time between 1.33 and 2.38 D was measured as a function of frequency for 19 subjects, with ages distributed between 18 and 49 years. Response to abrupt stimulus change between the same levels was also measured. The results showed that at any age, for the sinusoidal stimuli, gain fell with frequency and phase lag increased: at fixed frequency, gain fell with age and phase lag increased. Neither reaction nor response times for step stimuli changed with age. Analysis of the sinusoidal data suggests the possible existence of a cut-off frequency of about 2 Hz, which varies little with age and above which the system cannot respond. The phase data is compatible with the existence of a frequency-independent time delay, which increases with age from about 0.17 s at 20 years to 0.48 s at 40 years. The results are discussed in terms of current knowledge of the factors contributing to the development of presbyopia.

Dynamics of the accommodation response to abrupt changes in target vergence as a function of age

The dynamic accommodation responses to small, abrupt changes in an accommodation stimulus were studied in two experiments. In the first, responses of 19 subjects with ages distributed between 18 and 49 years were measured for step stimuli of +/- 1.05 D. In the second, responses to small step stimuli (+/- 0.75, +/- 1.75 D) were recorded for a group of six 'young' (mean age 22, range 16-26 years) and six 'old' (mean age 42, range 36-48 years) subjects. In both experiments, the low target vergences always lay within the accommodation range of all subjects. Whether the data were analysed in terms of simple reaction and response times, or in terms of the frequency response, no marked systematic changes with age were found in the dynamics of the response in either of the experiments. It is concluded that, for small stimuli within the amplitude of accommodation, the response dynamics over the adult age range studied remain remarkably constant, even though the amplitude progressively reduces with age as complete presbyopia is approached.