A. Terry Bahill

The main sequence, a tool for studying human eye movements

Abstract The astronomical term “main sequence” has been applied to the relationships between duration, peak velocity, and magnitude of human saccades over a thousandfold range of magnitude. Infrared photodiodes aimed at the iris-sclera border and a digital computer were used in experiments to derive the main sequence curves. In the pulse width modulation model, the duration of the controller signal pulse determines saccadic amplitude and peak velocity. The high-frequency burst of the oculomotoneurons needs to be only one-half the duration of the saccade, because of the “apparent inertia” of the eyeball.

Overlapping saccades and glissades are produced by fatigue in the saccadic eye movement system

Abstract Saccadic eye movements and their neurological control signals change significantly as the human fatigues. Electronic instrumentation with a band-width extending from DC to 1 kHz enabled the recording of anomalous looking saccadic eye movements that occurred as the subjects physiological state changed. Fatigue can produce: overlapping saccades in which the high-frequency saccadic bursts should show large pauses; glissades in which the high-frequency bursts should be much shorter than appropriate for the size of the intended saccades; and low-velocity, long-duration, non-Main Sequence saccades in which the motoneuronal bursts should be of lower frequency and longer duration than normal. As few as 30 saccades of 50 deg magnitude or a longer sequence of saccades as small as 10 deg can produce these aberrant eye movements and their concomitant neuronal firing pattern variations. The effects of fatigue could explain some of the variations between and spread within published data for velocity vs amplitude of human saccadic eye movements. Measuring the resistance to eye movement fatigue could become either a common clinical tool for diagnosing specific or general disease states, or a research tool for studying dyslexia or fatigue.

Dynamic overshoot in saccadic eye movements is caused by neurological control signal reversals

Three quite different types of overshoot occur in saccadic eye movements; each has unique characteristics determined by distinct neuronal control patterns. Most saccades have dynamic overshoot; it is more prevalent among, and more prominent in, small saccades. Dynamic overshoot is caused by nonrandom reversals of the neuronal control signals. It is a monocular phenomenon. The return velocities for dynamic overshoot are equal to saccadic velocities and are much larger than vergence velocities.

Smooth pursuit eye movements in response to predictable target motions

The human smooth pursuit eye movement system has a latency of about 150 msec. However, this study shows that humans can learn to perform zero-latency tracking of targets that move with continuous velocity and amplitude-limited acceleration. Superposition of eye velocity and target velocity records, for our unique target waveforms, demonstrated that the subject was using the correct waveform and not just approximating it with a sinusoid or some other simple waveform. Calculation of the mean square error between target and eye position gave a quantitative measure of how well the human can track. The mean square error between target and eye position was 0.32 deg2 for one thousand seconds of steady-state tracking by seven subjects. For several cycles at a time all subjects were able to reduce this error to less than 0.1 deg2.

Frequency limitations of the two-point central difference differentiation algorithm

A two-point central difference algorithm is often used to calculate the derivative of a function. This estimate is only valid over a limited frequency range. Therefore, the algorithm can be modeled as an ideal differentiator in series with a low-pass filter. The filter cutoff frequency is a function of the time between the points. We discuss the accuracy and limitations of using this algorithm on human saccadic eye movement data. To calculate the velocity of saccadic eye movements the algorithm should have a cutoff frequency of 74 Hz or above.

Frequency Limitations and Optimal Step Size for the Two-Point Central Difference Derivative Algorithm with Applications to Human Eye Movement Data

There are many algorithms for calculating derivatives. The two-point central difference algorithm is the simplest. Besides simplicity, the two most important characteristics of this algorithm are accuracy and frequency response. The frequency content of the data prescribes a lower limit on the sampling rate. The smoothness and accuracy of the data determine the optimal step size. We discuss the low-pass filter characteristics of this algorithm and derive the optimal step size for two types of human eye movement data. To calculate the velocity of fast (saccadic) eye movements, the algorithm should have a cutoff frequency of 74 Hz. For typical slow (smooth pursuit) eye movements, a step size of 25 or 50 ms is optimal.

Glissades-Eye Movements Generated by Mismatched Components of the Saccadic Motoneuronal Control Signal

Abstract Human saccadic eye movements have three types of overshoot: dynamic overshoot, lasting 10–30 ms; glissadic overshoot, lasting 30–500 ms; and static overshoot, which is amended—after a delay of about 200 ms—by a subsequent corrective saccade. Glissades are the slow drifting eye movements occasionally seen at the end of saccadic eye movements. Glissades are hypothecated to be produced by mismatches in the pulse and step components of the motoneuronal controller signals. Glissades are not vergence eye movements, although the dynamics are similar.

Model emulates human smooth pursuit system producing zero-latency target tracking

Humans can overcome the 150 ms time delay of the smooth pursuit eye movement system and track smoothly moving visual targets with zero-latency. Our target-selective adaptive control model can also overcome an inherent time delay and produce zero-latency tracking. No other model or man-made system can do this. Our model is physically realizable and physiologically realistic. The technique used in our model should be useful for analyzing other time-delay systems, such as man-machine systems and robots.

Eye Movements during Reading: Case Reports*

&NA; Since the time of Javal, it has been well established that normal reading eye movement patterns have 3 principal components: (1) small saccades that move the eyes from word to word, (2) large saccades that return the eyes to the beginning of the next line, and (3) fixation pauses between each saccade for information processing. We discuss the vision analysis results and show the quantitative reading eye movement records, measured with the infrared photoelectric method, of 5 patients examined in the Neuro‐optometry Clinic. The reading records showed a wide variety of behavior: 1 patient performed normal reading movements, 1 “slow reader” manifested an excessive number of fixations as well as extended fixational durations, another “slow reader” only exhibited an excessive number of fixations, a patient with dyslexia performed backward reading movements, and 1 patient exhibited nystagmus superimposed upon the reading pattern.

Sensitivity Analysis, a Powerful System Validation Technique

A sensitivity analysis is a powerful technique for understanding systems. This heuristic paper shows how to overcome some of the difficulties of performing sensitivity analyses. It draws examples from a broad range of fields: bioengineering, process control, decision making and system design. In particular, it examines sensitivity analyses of tradeoff studies. This paper generalizes the important points that can be extracted from the literature covering diverse fields and long time spans. Sensitivity analyses are particularly helpful for modeling systems with uncertainty.