We found that there is no direct relationship between phase and gain of the oculomotor system. The difficulty lies in the fact that the exact nature of the desired biological state eludes us. Dallas and Jones (4) also studied the response of the oculomotor system to band-limited Gaussian - random motion.
EXPERIMENTAL APPARATUS AND DATA PROCESSING This chapter describes the experimental apparatus and data
Contact lenses should be designed so that they are comfortable and follow the movements of the eye without slipping. The limbal arch is specially designed to avoid contact with the limbus, which contains most of the pain receptors. The other end of the tube is attached to a water manometer, which is used to apply suction between the lens and.
SUCTION TUBE
SCLERAL PORTION
CONTOURS OF
CORNEA
VISUAL AXIS
CORNEAL BULGE
LIMBAL ARCH
CENTER OF
ROTATION OF EYE
To measure lens slip, rectangular grids of very precisely spaced grooves were machined on the inner surface of the lens;. These grids were located roughly on the scleral part of the lens and extended from the corneal part to the temporal edge as shown in Figure 2. Lens slip was measured by observing the movement of the scleral blood (through a 24X Wild M-5 stereomicroscope) vessels against the grid.
POLYETHYLENE TUBE TO
MANOMETER
NASAL
TOP VIEW
LAMP
LEFT LENS
LAMP POWER
FRONT VIEW
The assembly was then slipped onto the end of the stem protruding from the contact lens, as shown in Figure 2. The wires and polyethylene tube were attached to the subject's head during the experiment in such a way as to minimize termination with free eye movements. The subject's head was positioned so that the bulb at the end of the stem was placed directly over the rectangular guides leading to the photomultiplier tubes as shown in Figure 2. 4.
HORIZONTAL OUTPUT VERTICAL OUTPUT
LENS M-MIRROR
BS - BEAM SPUTTER RP- ROOF PRISM
AS S- APERTURE AND SHUTTER W - OPTICAL WEDGE
LIGHT SOURCE
5 cm from the center of rotation, just as it was on the contact lens stem. Then the blades were allowed to return to their original positions and the artificial eyeball was rotated using the micrometer screw until the same tension change was achieved. The same setup was also used to check the linearity range of the PMTs and associated electronics.
MIN ARC
DOWN
MIN ARC 60
TEMPORAL
INTRODUCTION: FIXATION PATTERNS OF THE EYE WHEN VIEWING STATIONARY TARGETS
The literature now contains a number of articles describing the nature of the spontaneous eye movements that occur during fixation. Westheimer (22) reported that smooth motion of a target gave rise to smooth pursuit eye movements, and Rashbass (14) showed that the speed of the smooth pursuit movement matched that of the target. Rashbass and Westheimer (15, 16) have demonstrated the independence of the conjugate and vergence mechanisms during tracking tasks.
INTERPLAY OF FLICKS AND DRIFTS IN BINOCULAR FIXATION
The direction of flicks for the right eye is plotted against the direction for the left. The retinal difference on the mean becomes marginally larger, although the significance of the change is not high. The pattern traced by the visual axis of the occluded eye has little correspondence to the target structure.
We now want to quantify the effect of flicking and drifting on the overall fixation pattern of the visual axis. The influence of the target structure on the fixation pattern is clearly shown in the diagrams in Figure 4. F1gµre 4,5, Equ1probab111ty ellipses represent the position of the visual axes before and after the flick.
Those points between the horizontal axis and the slope line -1 (sectors A) represent movements that start in the correct direction and do not come close to the target. The lateral correction of the fixation error as a function of the error at the onset of the eye movements was continued. Therefore, we calculated the regression surfaces describing the dependence of the correction on the fixation errors of the left and right eyes.
Thus, we can plot the fixation errors for the left and right visual axes along X and Y, respectively, and the correction of an eye movement along z. Slopes of the regression plots between the correction in one eye and the fixation errors in both eyes. The slope of the regression line between binocular corrective eye movements and misalignment of the visual axes.
PREPARATION OF EXPERIMENT AND DATA REDUCTION FOR TRACKING EXPERIMENTS
Because of the finite distance between the recording and playback heads, analog recordings contain a constant lag between stimulus and response. The Cooley-Tukey algorithm (2, 3) was used to calculate Fourier transforms of individual functions. A sampling interval of 6t (1/52 s) determines the Nyquist frequency:. and the record length T dictates a spectral resolution equal to twice the width of the 6f frequency field.
By properly choosing the g(T) window, many variations of segmental averaging are then possible. In addition, some points were represented by a symbol to distinguish different curves on the same graph. In some experiments, a 1 cps signal was falsely introduced into the eye movement recordings.
However, none of the frequencies present in the stin1uli were equal to 1 cps; we therefore) de-. 0 cps for the vertical component of the stimulus, and another sixteen frequencies for the horizontal. Fourier transforms of target motion and eye movements were computed as described in Chapter VI.
Figure 3 shows these power spectra for subjects GSC and SAM, respectively, when the stimuli consisted of the 4-frequency bands listed in Table 7-1.
LEFT EIE
STIMULUS
MIN ARC
SECCJNOS
BETWEEN TIME MARKS
START
FREQUENCY (CPS)
FREQUENCY £CPS)
Despite the apparent randomness of the target movement, both subjects nevertheless managed to follow the dot closely enough so that, in general, the resulting eye movements consisted only of those frequencies present in the stimulus. In addition, for subject GSC, vertical and horizontal eye movements contain only those frequency components present in the vertical and the horizontal stimuli, respectively. That is, the vertical eye movements contain certain frequencies that are only present in the horizontal component of the stimulus.
The eye movements in these experiments are small enough that there should be no cross-talk between vertical and horizontal movements due to the geometry of muscle action. It is true that with large eye movements, the superior and inferior rectus, which mediate vertical movements of the visual axis, can also cause horizontal movement of the visual axis. However, the medial and lateral rectus, which mediate horizontal movement, work to produce no vertical movement from the primary position even with large movements of the eye.
The crosstalk must occur at or before the nuclei of the extraocular motor neurons. For subject GSC, there are essentially no frequencies in the eye movements that are not present in the stimuli. 5 shows the power spectra of the following eye movements when the stimulus spectrum is increased to 7 and.
Some input frequencies are missing from the response, and there are some spurious frequencies present in the eye movement recording that are not present in the stimuli.
FREQUENCY CCPSJ
We will first examine the gain of the eye movements relative to target movement at the stimulus frequencies for the four 4-frequency bands described above. 6d shows the increase in decibel as a function of frequency for the vertical and the horizontal movements of the left eye for both subjects. Slope of the regression line between magnitudes of eye movements and log frequency for the 4-frequency band.
If there is a true preference for the higher frequencies within a band, both the gain and the absolute value of the eye movement should increase with frequency. 1, most points fall very close to the values previously obtained in the four-frequency band experiment (slightly lower for horizontal motion). All three lines slope upward, and the value of the slope increases as the test frequency increases.
Figure ?.?(d)s Gain of the oculomotcr system Subject SAM Left horizontal eye movements Binocular fixation co N I N. Figure ?.8(d): Phase la.g of the oculomotor system Subject SAM Left horizontal eye movement~ Binocular vision N. In this case, however, one would have to be most imaginative to derive a transfer function which adequately describes the gain behavior of the oculomotor system for the four 4-frequency bands.
However, it now appears that the "delay time" in the oculomotor system is a function of the target movement.
LOW~
BANDWIDTH
MEDIUM BANDWIDTH
HIGH
HIGH/
Curve 1: Values measured by Dallos & Jones (1) Curve 2: Least-means-squared approximation to
Curve 1 assuming that phase lag is result of constant delay
FREQUENCY (CFS)
Phase lag of the oculomotor system for tracking targets whose motion consists of Gaussian random motion Curve 1: Values measured with. If the oculomotor system works in a similar way, then after the bandwidth of the target movement is increased, we would expect the delay time to increase accordingly to convey the added information. In this case, we would expect small changes in the average delay time as the target motion bandwidth increases, but the average information transfer rate should decrease.
1 /R, the inverse of the average rate of information transfer, and the relationship can be approximated by a straight line fitted by the least-mean-squares criterion. Despite the fact that the scores are somewhat scattered, the derived parameters are remarkably similar for the two subjects. As the brightness of the target decreased, the phase delay increased for a given target motion and at a given frequency.
I shows the power spectra of the spontaneous eye movements made during binocular fixation of a stationary point. 1 shows that the attenuation is approximately 26 - 28 dB/decade, a very good agreement considering that the expected error in the calculation of the power spectra is 3 dB at a 90 percent confidence level. However, we found that dE/dt is constant (equation 6) across the bandwidth of the oculomotor system (up to about 3 cps).
3 shows the power spectra for tracking movements of the left eye of subjects GSC and SAM, respectively; those of the right eye are similar.
LEFT VERTICAL SUBJECT GSC
BINOCULAR VIEWING
LEFT HORIZONTAL SUBJECT GSC
LEFT VERTICAL SUBJECT SAM
LEFT HORIZONTAL SUBJ3CT SAM
