Gerald H. Cohen

Eye-Movement Responses to Step and Pulse-Step Stimuli*

A spot of light is presented to an observer who tracks its movement visually, doing so as quickly and accurately as possible. The positions of the eye are continuously recorded so that direction and magnitude of eye movements as a function of time can be assessed. Without warning, the target spot steps from its resting position, moving 6° horizontally to one side, followed after a time W by a 12° step in the opposite direction. The result is a pulse-step pattern of target motion with the time interval W msec defining the pulse duration. The directions of the pulse and step are always opposite but otherwise are unpredictable. Trials consisting of pulses followed by steps are intermixed randomly with a larger number of trials consisting of 6° steps alone. The experiments demonstrate that the visual system is sometimes able to cancel an eye-movement response to a pulse, on the basis of information contained in the subsequent step, to which it responds instead. As the step is delayed by progressively longer pulses, the probability increases that a response to the pulse will occur. If a response does occur in the direction of the step, it begins about 325 msec after the beginning of the step. This latency is independent of pulse time W and is about 40 msec longer than the latency of responses to steps presented alone. It is concluded that the visual system utilizes this 40 msec to operate upon a latent response to a pulse, and thereby to cancel its overt manifestation (eye movement) before initiating a response to the second, incompatible stimulus.

Luminance as a Parameter of the Eye-Movement Control System*

A study of the eye-movement control system shows the dependence of many of the system parameters on target luminance and contrast. Saccadic reaction time was found to decrease from a high value toward a fixed minimum as target luminance was increased, whether with a zero background (high contrast) or a fixed low contrast with respect to the background. The magnitude of the visual dead zone created when target luminance went below foveal threshold was also measured as a function of target luminance. The closed-loop gain of the eye-movement control system for ±2° sinusoidal target motion was measured as a function of luminance for high- and low-contrast targets. The results showed two changes of system gain as target luminance was decreased: (a) There was a decrease of the high-frequency response associated with target energies (luminance-by-time products) falling below a critical value required to produce visual sensation, resulting in a cutoff frequency; (b) for high-contrast targets only, there was an over-all decrease of system gain as target luminance was decreased, for luminances well above foveal threshold and for frequencies well below cutoff. This latter, unexplained effect cannot be interpreted as resulting from an increase of retinal latency, the effect of a visual dead zone, or the lack of sufficient target energy for visibility. A similar tracking experiment was performed for “unpredictable” target motion. Several changes were observed in the response of the eye-movement control system, and these were related to the effects of luminance upon system parameters and target predictability.

Using color substitution pupil response to expose chromatic mechanisms

It is well known that pupillary threshold shows a scotopic spectral behavior, even for foveal stimuli. However, when two scotopically balanced fields at different wavelengths are alternated, the pupil shows a constriction response at each transition, exposing innervation from chromatic mechanisms. Using a suitable model for pupillary innervation, this substitution response is systematically studied for different wavelengths and radiant power levels to yield (within the accuracy of the assumptions of the model) spectral threshold curves for the chromatic mechanism as indicated by the pupil. Four mechanisms have thus been identified, having peak sensitivities near 450, 525, 580, and 495 nm. We propose that these represent the blue, green, red and scotopic mechanisms as maintained before the level of the lateral geniculate body.

Latency Variation in Human Pupil Contraction Due to Stimulus Luminance and/or Adaptation Level*

The purpose of this experiment is to measure the latency to onset of the contraction of the pupil, as a function of the size of positive steps in luminance, starting at various luminance levels to which the eye has been adapted prior to the stimulus steps. In the past, latency of the pupil response has been inaccurately measured, owing to the difficulty of separating the end of the latent period from the slow beginning of contraction. To overcome this, a digital curve-fitting technique involving a time delay followed by a modified second-order step response was developed. Latency was defined as the time delay giving the most accurate fit.Because the curve-fitting procedure needed a response with less random variation than is normally present, an average was used. Such averaging was first justified by using the standard deviation to show that there is probably no significant variation of latency for responses of a given subject under identical stimulus conditions. This analysis also showed that 20 responses is an efficient number to average for the pupil-contraction system.The excellent agreement between each average experimental response and the computed fit verified the value of delay used in the computation. Latency, thus defined for each stimulus condition, was found to be primarily a function of luminance during the step and only secondarily of the ratio of the step change of luminance to the adaptation luminance.

Optimizing the Use of the Criterion Response for the Pupil Light Reflex

Light flashes stimulate one eye by Maxwellian view. The change of pupil diameter of the contralateral eye is the measured response. The effects of stimulus magnitude, stimulus field size, and subject selection are examined. The stimulus is adjusted until the response is some predetermined (criterion) amount. Thus, even though the system is nonlinear, the different possible stimuli which yield this criterion response are equivalent. We show that to utilize the criterion response technique optimally it is necessary to (1) use large-field stimulation, (2) obtain complete curves of response magnitude vs retinal illuminances on potential subjects, (3) select subjects having steep slopes on these curves, (4) select the value of the criterion response to be centered in the steeply-sloped portion of the curve. Failure to observe these rules may result in data of little value.

A Method of Characteristics and Invariant Imbedding for Distributed Control Problems

Abstract A method of characteristics and invariant imbedding is introduced for solving optimal control problems for hyperbolic systems. Advantages over existing methods are illustrated by means of examples.

An analysis of optimal control system algorithms

Currently, there are methods available which were derived in the field of computer science to analyze and evaluate algorithms implemented in computer programs. The subject of this paper will involve a combination of three of these methods with a rather rigorous simulation of three invariant imbedding algorithms in a manner strictly slanted toward their usefulness and importance in control system applications. The algorithms used to solve the problems and special solution formulations of the problems are presented first. Then, the numerical routines which provided the most efficient implementation of the problems in their algorithmic form are explained. And last, the adaptation of the analysis techniques to the problems is shown to aid in understanding the final conclusions drawn.

Instrumentation for Automated Study of Human Pupil Responses

Instrumentation has been developed for studying the responses of the human pupil to different kinds of visual stimuli. This involves stimulating the eye visually, acquiring pupillary diameter data samples, analyzing them, and displaying and storing the results All of these functions are controlled by a minicomputer. The apparatus is a convenient research tool for studying the visual system of color-normals and color-defectives by observing pupillary behavior.

Computer-assisted diagnosis of strabismus.

A program for use on a microcomputer was developed to assist in the diagnosis of strabismus. The matrix consists of 41 separate disorders and 59 facts (history and examination findings). The facts are answered in a yes/no format. The relationship between the fact and the disorder is weighted as to whether the fact is always present, usually present, sometimes present, not related, unlikely to be present, not usually present, or never present. The computer makes the diagnosis (or diagnoses) indicating the most likely disorder when several are possible from the information given. Over 300 patient files were tested with the program. Of the last 50 records reviewed (70 disorders), the computer diagnosis agreed with the clinical diagnosis in 91% of the cases. Continued refinement of the program should be able to improve this accuracy.