Spatial Frequency and the Dynamics of the Accommodation Response

When do contrast sensitivity deficits (or enhancements) depend on spatial frequency? Two ways to avoid spurious interactions

Studies across a broad range of disciplines-from psychiatry to cognitive science to behavioural neuroscience-have reported on whether the magnitude of contrast sensitivity alterations in one group or condition varies with spatial frequency. Significant interactions have often gone unexplained or have been used to argue for impairments in specific processing streams. Here, we show that interactions with spatial frequency may need to be re-evaluated if the inherent skew/heteroscedasticity was not taken into account or if visual acuity could plausibly differ across groups or conditions. By re-analysing a publicly available data set, we show that-when using raw contrast sensitivity data-schizophrenia patients exhibit an apparent contrast sensitivity impairment that lessens with spatial frequency, but that when using log-transformed data or when using generalized estimating equations, this interaction reversed. The reversed interaction, but not the overall contrast sensitivity deficit, disappeared when groups were matched on visual acuity. An analysis of the contrast threshold data yielded similar results. A caveat is that matching groups on acuity is probably only defensible if acuity differences arise from non-neural factors such as optical blur. Taken together, these analyses reconcile seemingly discrepant findings in the literature and demonstrate that reporting contrast sensitivity interactions with spatial frequency requires properly accounting for visual acuity and skew/heteroscedasticity.

Visual discomfort and depth-of-field

Visual discomfort has been reported for certain visual stimuli and under particular viewing conditions, such as stereoscopic viewing. In stereoscopic viewing, visual discomfort can be caused by a conflict between accommodation and convergence cues that may specify different distances in depth. Earlier research has shown that depth-of-field, which is the distance range in depth in the scene that is perceived to be sharp, influences both the perception of egocentric distance to the focal plane, and the distance range in depth between objects in the scene. Because depth-of-field may also be in conflict with convergence and the accommodative state of the eyes, we raised the question of whether depth-of-field affects discomfort when viewing stereoscopic photographs. The first experiment assessed whether discomfort increases when depth-of-field is in conflict with coherent accommodation-convergence cues to distance in depth. The second experiment assessed whether depth-of-field influences discomfort from a pre-existing accommodation-convergence conflict. Results showed no effect of depth-of-field on visual discomfort. These results suggest therefore that depth-of-field can be used as a cue to depth without inducing discomfort in the viewer, even when cue conflicts are large.

Accommodation steps, target spatial frequency and refractive error

PURPOSE

Errors in the accommodation response of myopes have been reported in many studies although questions remain about the exact differences in accommodation steps when compared with emmetropic individuals.

METHODS

The characteristics of the accommodation step response to large (4/1D) and small (3/2D) steps in targets with low (0.5 cpd), mid (4 cpd) and high (16 cpd) spatial frequency (SF) information was measured in myopes (MYOs) and emmetropes (EMMs).

RESULTS

In terms of step size, the larger steps showed a greater response in the 4 cpd condition than the 0.5 and 16 cpd conditions and an improved percentage correct response in the 4 cpd compared to the 16 cpd steps. In small step conditions target SF had less effect upon the magnitude of the response. In terms of refractive group differences, MYOs had a lower proportion of correct accommodation responses compared to EMMs during the small steps only, however, when correct steps were performed there were no differences in the characteristics of both large and small step responses between MYOs and EMMs.

CONCLUSIONS

These findings suggest that MYOs have some difficulty interpreting small changes in defocus to initiate or possibly fine tune a small accommodation response, however, when a correct accommodation step response is made, the MYOs accommodation plant responds in a similar manner to EMMs.

Target spatial frequency determines the response to conflicting defocus- and convergence-driven accommodative stimuli

Asthenopia, or visual fatigue, is a frequent complaint from observers of stereoscopic three-dimensional displays. It has been proposed that asthenopia is a consequence of anomalous oculomotor responses generated by conflict between accommodative and convergence stimuli. The hypothesis was examined by measuring accommodation and convergence continuously with a Shin-Nippon SRW5000 infrared autorefractor and a limbus tracking device. Subjects viewed a high contrast Maltese Cross target at three levels of Gaussian filter target blur under conditions of relatively low- and high-conflict between accommodation and convergence stimuli, the latter inducing the sensation of stereopsis. Under the low-conflict conditions accommodation was stable, but convergence-driven accommodation was dominant when the target was extremely blurred. Under the high-conflict conditions the role of convergence-driven accommodation increased systematically with the degree of target blur. It is proposed that defocus-driven accommodation becomes weak when the target comprises low spatial frequency components. Large accommodative overshoots to step stimuli that are not blurred or only mildly blurred were consistently observed and are attributed to the initial accommodative response being convergence-driven. Whereas the possibility that high-conflict conditions are a cause of asthenopia has been previously reported, this is the first evidence that they specifically affect accommodative responses while viewing stereoscopic displays.

Effect of positive and negative defocus on contrast sensitivity in myopes and non-myopes

This study investigated the effect of lens induced defocus on the contrast sensitivity function in myopes and non-myopes. Contrast sensitivity for up to 20 spatial frequencies ranging from 1 to 20 c/deg was measured with vertical sine wave gratings under cycloplegia at different levels of positive and negative defocus in myopes and non-myopes. In non-myopes the reduction in contrast sensitivity increased in a systematic fashion as the amount of defocus increased. This reduction was similar for positive and negative lenses of the same power (p = 0.474). Myopes showed a contrast sensitivity loss that was significantly greater with positive defocus compared to negative defocus (p = 0.001). The magnitude of the contrast sensitivity loss was also dependent on the spatial frequency tested for both positive and negative defocus. There was significantly greater contrast sensitivity loss in non-myopes than in myopes at low-medium spatial frequencies (1-8 c/deg) with negative defocus. Latent accommodation was ruled out as a contributor to this difference in myopes and non-myopes. In another experiment, ocular aberrations were measured under cycloplegia using a Shack-Hartmann aberrometer. Modulation transfer functions were calculated using the second order term for defocus as well as the fourth order Zernike term for spherical aberration. The theoretical maximal contrast sensitivity based on aberration data predicted the measured asymmetry in contrast sensitivity to positive and negative defocus that was observed in myopic subjects. The observed asymmetry in contrast sensitivity with positive and negative defocus in myopes may be linked to the altered accommodative response observed in this group.

Contrast and spatial-frequency requirements for emmetropization in chicks

This study examined the contrast and spatial-frequency requirements for emmetropization in chicks. Chicks were form deprived from hatching either constantly or had this treatment interrupted with 20 min of "visual stimulation" each day. Visual stimulation comprised exposure to either a normal cage environment (i.e., normal vision) or environments that were restricted in either their spatial contrast or spatial-frequency composition. Constant form deprivation resulted in high myopia (e.g. -11.8 D after 5 days), with refractive changes being much smaller in chicks allowed 20 min of normal vision each day (e.g. -3.4D). The restricted contrast environments (contrast range: 9-78%) were generally only slightly less effective than the normal cage environment in preventing form-deprivation myopia. However, in the case of restricted spatial-frequency environments, both the intermediate (0.86 cycles deg-1) and mixed spatial-frequency environments significantly reduced the form deprivation response, while both the high (4.3 cycles deg-1) and low spatial-frequency (0.086 cycles deg-1) stimuli, as well as the composites of these, were less effective in preventing form-deprivation myopia. This spatial-frequency dependence did not vary when, instead of white light, monochromatic illumination was used to eliminate chromatic aberration, although all groups showed more myopia under this condition. It is assumed that the observed inhibitory effects on form-deprivation myopia reflect the adequacy of the visual information presented during the period of visual stimulation for emmetropization in chicks. In this context, the data imply a mid-spatial-frequency tuning in the current study and a low contrast threshold which was not reached for this emmetropization process. Finally, the data hint that chromatic aberration may have some role as a cue to defocus in emmetropization.

Spatiotemporal transfer function of human accommodation

We have investigated the spatiotemporal transfer function of human "reflex" accommodation. An accommodative mechanism that is sensitive to an intermediate temporal rate of retinal image contrast change is proposed as the basis of the fine focus control hypothesis. To test the proposed mechanism accommodative responses were monitored by a dynamic infrared optometer while the subject focused on sinusoidal gratings (0.98-10.5 c/deg) which were moving sinusoidally at temporal frequencies in the range of 0.05-0.80 Hz over a 0.50 or 2.00 D peak-to-peak amplitude. The accommodative responses were best at 3 and 5 c/deg at both amplitudes of target motion. This result does not support the proposed mechanism or the fine focus control hypothesis for "reflex" accommodation. Fitting the data with first-order response functions showed little evidence of prediction. In addition, a second experiment found that the profile of the accommodative gain function is not altered by instruction at spatial frequencies above 5 c/deg in this type of dynamic accommodation experiment. The use of sinusoidally moving accommodative blur targets, particularly with careful instruction, seems to discourage voluntary accommodation in investigations of "reflex" control mechanisms 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)

A longitudinal study of the changes in the static accommodation response

The results are described of a 10-year study of the longitudinal changes in the static response of an individual subject during the approach to absolute presbyopia. The amplitude of accommodation declines linearly with age. A new finding is that the magnitude of the slope of the linear portion of the response/stimulus curve also reduces with age, as does the level of tonic accommodation.

Binocular accommodation reaction and response times for normal observers

Accommodation was recorded from right and left eyes of visually normal observers in both binocular and monocular viewing. Reaction and response times were similar in monocular and binocular viewing and are not influenced by eye dominance. Far-to-near responses were significantly quicker than near-to-far responses. The origin of this difference may be a feature of the elastic properties of the accommodation mechanism. Limited data are presented that indicate that the slowing of accommodation speed with age affects the near-to-far response disproportionally. Errors in the initial direction of response were fewer in binocular viewing in comparison with monocular viewing.

Tolerance to visual defocus

Low-resolution optical systems are more tolerant to defocus than are high-resolution systems. We wished to determine whether this principle applies to human vision. We used psychophysical methods to measure the effects of defocus in normal eyes under low-resolution conditions. Modulation transfer of sine-wave gratings was measured as a function of dioptric defocus at low and medium spatial frequencies. We defined the depth of focus at a given spatial frequency to be the dioptric range for which the modulation transfer exceeds 50% of its peak value. For dilated pupils, depth of focus increased from about 2.5 diopters (D) at 3.5 cycles/deg to about 17 D at 0.25 cycles/deg. From our results we predicted that tasks requiring only low spatial frequencies will be more tolerant to defocus than tasks requiring higher spatial frequencies. This prediction was confirmed in a letter-recognition experiment. The increasing tolerance to defocus at low spatial frequencies also implies that individuals with low acuity will be more tolerant to defocus than people with normal vision. We confirmed this prediction by measuring tolerance to defocus in 30 low-vision eyes.

Accommodation in infants as measured by photorefraction

We developed a video camera photorefractive procedure that allows on-line monitoring of accommodation from a distance of 1-2m, and have used it to study accommodation in twenty-nine 2- to 10-month-old human infants. We presented square wave gratings and random checkerboard targets at 25, 33, 50, and 100 cm from the infant. All infants altered their accommodation in the appropriate direction for changing target distances. We also presented infants with a slowly rotating circular striped target. We did not observe any systematic change in accommodation of the astigmatic infants to the rotating striped target, nor any significant change in their accommodation to stationary targets as a function of target type. Measured speeds of accommodation in infants were at least 4.6 D/sec, comparable to that found for adults.

The effects of optical vergence, contrast, and luminance on the accommodative response to spatially bandpass filtered targets

The steady-state monocular accommodative response was measured using a new type of stimulus, a spatially bandpass filtered luminance distribution known as a difference of Gaussian or DOG. The independent variables were: spatial frequency, optical vergence, contrast, and mean luminance. High-contrast DOGs of varying peak spatial frequencies were presented monocularly over a range of target optical vergences. In addition, DOGs were presented at a fixed dioptric vergence (1) over a range of contrasts with a constant mean luminance, and (2) over a range of mean luminances with a constant contrast. The magnitude of the accommodative error was found to depend on the total stimulus condition, i.e. the particular level of each independent variable. Changes in retinal-image contrast from the background (zero-defocus) level, which were brought about by the errors of accommodation under the various stimulus conditions, were mathematically determined and were used to calculate the "accommodative (contrast discrimination) Weber fractions". Comparisons between accommodative and psychophysical contrast discrimination data revealed that there are limits to the degree of shared processing of contrast discrimination information between accommodation and visual perception.

Modulation dependence of the accommodation response to sinusoidal gratings

The steady-state, monocular, accommodation response to sinusoidal grating targets (spatial frequencies 0.67, 2.0, 6.0 and 18 c/deg) at effective distances between 0.2 and 1.0 m was measured with a laser optometer, as a function of the grating modulation. In general, only a rather weak dependence of the response on modulation was observed. The results are discussed in terms of the theoretical modulation of the retinal image as a function of defocus. It is argued that the accommodative system usually works to produce a contrast in the grating image which is well above the detection threshold. Considerable inter-subject differences in response were observed, suggesting that a variety of strategies may be employed by different subjects when engaged upon the same voluntary accommodation task.

Viewing distance and the sustained detection of high spatial frequency gratings

Although conventional visual acuity tests measure the ability to resolve fine detail, many visual tasks demand prolonged detection. By evaluating the ability to maintain visual resolution, we observed that detection of stimuli subtending a small but constant visual angle depends on viewing distance and is probably determined by accommodative control. Detection was longest when viewing distance corresponded to the individual observer's accommodative resting, or tonus, position and fell off markedly for further distances. Since most visual assessment procedures involve a momentary detection criterion, they will not predict the ability to sustain accommodation and may thus overestimate visual resolution for prolonged viewing tasks.

Accommodative stimulus/response function in human amblyopia

Three parameters are essential to describe static accommodative behavior in a comprehensive, quantitative manner: the slope of the stimulus/response curve, the depth of focus, and the tonic response. These parameters were obtained in amblyopes, former amblyopes, strabismus without amblyopia, and normals. Results showed that the accommodative response in the amblyopic eye was characterized by a reduction in the slope of the stimulus/response curve and increased depth of focus. Similar abnormalities but of lesser magnitude were found in the non-dominant eye of some former amblyopes and some strabismus without amblyopia. Orthoptic therapy always increased the slope of the stimulus/response curve in the amblyopic eye. We believe that the reduced accommodative responses found in amblyopic eyes reflect a primary sensory loss over the central retinal region that occurs as a result of prolonged, early, abnormal visual experience associated with the presence of strabismus and/or anisometropia.

The effect of contrast on sustained detection

During a 1 min observation, the percentage of time a high spatial frequency grating can be detected is influenced by the contrast and spatial frequency of a second, superimposed and orthogonally-oriented sine wave grating. Increasing contrast of the second pattern aids detection of the first by providing a more effective accommodative stimulus. The function relating spatial frequency and the minimum contrast needed to activate accommodation is similar in shape to the classical contrast sensitivity function. However, an order of magnitude more contrast is required to stabilize accommodation than is required to simply detect a pattern. These results suggest that performance on visual tasks requiring sustained rather than brief detection may be markedly impaired under low contrast conditions.

Spatial frequency dependence of accommodative responses in amblyopic eyes

Monocular, steady-state accommodative responses were measured as a function of spatial frequency of simple sinusoidal gratings presented at high contrast and target vergence levels in amblyopes, as well as in strabismics without amblyopia and in visually-normal control subjects. In general, spatial frequency dependence of the accommodative response was the rule. However, the amblyopic eyes exhibited markedly reduced accommodative responses over most of the spatial frequency range tested, and this was attributed to reduced accommodative controller gain in the sensory pathways involved in the control of accommodation in the amblyopic eye. Due to the diversity of accommodative response spatial frequency profiles found across all groups, the results suggest that reflex, voluntary, and higher-level perceptual aspects of accommodation may interplay in a complex manner in the act of accommodation on a simple sinusoidal grating.