Note that both the closed-loop system gain and time constant are reduced by 1/(1 + GMKds). The increase of open-loop time constant was observed by Qi, and is compatible with the negative feedback model. Qi neither reported what happened to the steady-state (no object) fmn when the muscle was cut, nor considered the effect considered of not cutting the contralateral MOT at the same time the ipsilateral muscle was cut. The contralateral eye was not stimulated with a moving object, neither was it masked. Hence eye movements caused by changes in frequency to the intact contralateral MOT could enter the system.
It is clear that the fly's CSEM system is more complex than the models suggested here. Qi observed that the positive peaks in the IF Afmn in response to sinusoidal stripe motion (in the preferred direction toward the rear of the animal) had a nearly 90° phase lead to the object position. However, close inspection of the phase of the negative peaks of Afmn caused by the object moving toward the front of the fly (null direction) showed that they led object position by a fixed angle between 70° and 80°, generally constant over 0.5 to 2.0 Hz object oscillation frequency. Qi suggested that this phase difference could mean different mechanisms were involved for perception of front-to-back and back-to-front motion. That is, two separate DS systems were involved.
That the fly visual system is far more complex than currently imagined is substantiated by recent behavioral observations on blowfly flight dynamics by van Hateren and Schilstra (1999). The motions of the head and thorax of free-flying blowflies were studied using magnetic sensors. They observed that flying flies performed a series of short, saccade-like turns at a rate of about 10/s in a fixed order, beginning with a roll. The rolled thorax next pitched up (head up), then yawed, resulting in a turn. Finally, the thorax rolled back to a level position. The saccades had amplitudes up to 90°, but 90% were smaller than 50°. Most amazing was the maximum angular velocity, about 2000°/s, and maximum angular acceleration, about 105°/s2. To conserve angular momentum, a fly's head exhibited counter rolls to the thorax rolls. Yaws of the thorax were accompanied by faster turns of the head, starting later and finishing earlier than the thorax saccades. Between the high angular velocity head and thorax saccades, the thorax and head are well stabilized, as head velocities are generally less than 100°/s for roll, pitch, and yaw. During this "stabilized" phase of flight, the fly's CSEM system can operate, and visual information is available to stabilize and direct flight. During thorax saccades, the fly's inertial navigation sensors, the halteres, may be stimulated, providing a different flight stabilization modality (see Section 2.7). The countermovements of head to thorax appear to be for preserving inertial stabilization in flight.
In closing, contemplate the evolved purpose of the dipteran CSEM system. From experiments on fixed insects, it appears that one effect of the medial ommatidia tracking a moving object is to provide a longer integration time for low-contrast, moving objects by the retinula cells involved. The object moves at ve < vo with respect to these receptors. Qi (1989a) shows that a better retinula cell signal-to-noise ratio results from slowing the apparent object motion. The overall CSEM system can also provide the animal with yaw stabilization signals, and also advise the flying insect of its relative velocity with respect to objects in its visual space.
A fly does not have binocular vision, but the optical axes of its most medial ommatidia of the left and right eyes apparently overlap at a distance of several head diameters in front of the insect. This fact leads to a final question that needs answering: Does the CSEM system permit vergence, i.e., fixation on a moving object coming straight at (or away from) the fly? An interesting experiment would be to move a test object toward and away from the front of the head on the animal's centerline. If vergence occurs, the IF of both NMOTs should decrease together to track an approaching object, and vice versa.
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