A Cybernetic Model of Accommodation
Over the past fifteen years we have evaluated numerous models of accommodation. Our task is to clarify these models by designing an automatically focused camera, with major emphasis of the capability of the retina to sense blur and feed this information back to the eye's lens for accurate focal adjustment.
Depth-of-field, or dead-band, poses a significant obstacle for the designer of an automatically focused camera. Our approach is to use noise to provide a scanning, or dither motion so that the lens will spend 80 percent of its time in sharp focus. Retina detection of blur can be simulated by a Charge Coupled Device (CCD), designed to produce a null when sharpest focus is achieved. The nature of blank-field accommodation is judged, and a prediction made about its long-term behavior.
Thus, for instance, the noise that is seen in the system is not a defect, but rather is an essential design requirement of a system that has dead-band. A scanning signal must be present if the system is to maintain accurate focal control. Other capabilities of this system, such as blank-field accommodation are part of the design, and are included in this model. The available measurements confirm most of the analog computer's predictions for the eye's dynamic focal control.
A source point of light will produce a blur-circle on the retina. When this circle is larger than the retina cones, several cones "fire" producing multiple outputs. As the blur circle is focused to a point of light, only one cone will fire, producing a null. This null will exist throughout the dead-band. Because of this physical characteristic of the eye, a design-around of the control-system must be accomplished to deal with it, if the system is to maintain continuous sharp focus on the retina. Dead-band is schematically shown in Figure 1 and 2.
Figure 1: Shows how an expanding "disk of light" or blur circle falls on a wider area of neurons when the lens is moved towards and away from the retina. When the disk is smaller than the diameter of a neuron, only one neuron is triggered. This depth-of-field is approximately +/- 0.6 diopters.
Figure 2: Demonstrates how lens motion relative to the retina creates variously a "disk-of-light", or blur circle. For a certain range of motion, no blur is produced on the surface of the retina.
Figure 3: Demonstrates how an "artificial retina" can be designed to sense blur. While the retina probably uses a more sophisticated method of determining blur, an auto-focus camera could be designed and would work using this basic blur detection strategy.
Figure 4: This figure demonstrates the nature of the signal produced by the artificial retina. Through the area of dead-band, the signal is constant. When the blur-circle begins to exceed the edge of the dead-band, a rising signal is produced.
Figure 5: This diagram shows how the accommodation system behaves in actual operation. Since blur cannot be detected when the lens is inside the dead-band the focal state of the lens will "drift" until it exceed the edge of the dead-band. The system must use negative feedback to "kick" the lens towards and into the dead-band. This type of motion is seen with an infrared optometer.
Because of a need for high focal accuracy we cannot build a sphincter-muscle-lens system. We can, however, build a "plant" that will accomplish the same result. For this model, we show a lead-screw that is driven by a Direct Current (DC) motor. Thus by high-gain amplification of the output of the retina, and by lead-screw adjustment of the lens, we can insure that the lens is always servoed to the output of the retina for continuous focal adjustment. Figure 6.
The lead-screw will constantly change the focal position of
the lens and the sharpness of focus on the retina. This type of
signal is seen in the human eye, and is a normal condition. The
continual motion of the lens will cause the retina to provide a
changing signal. Proper use of this signal insures that the lens
is within the dead- band most of the time. The net result of this
control-action is a signal almost identical to the neurological
signal seen when the output of an infrared optometer is recorded
on a strip-chart recorder.  A graphic sketch is shown in
Figure 6: This model of an auto-focus camera shows how the signal derived from the surface of the retina is used to control the positioning of the lens relative to the retina. While more difficult to design, the lens power could be changed by using the lead-screw to change the power of the lens -- rather than the position of the lens. The control-system would behave in the same manner in either case.
Figure 7: This diagram shows the basic building signal processing blocks of the accommodation system. The model produces an output (lens power) that is almost identical to the measurements made with an infrared optometer.
When the object is moved closer, say to -3.0 diopters, the lens of the eye will change by +3.0 and then oscillate by +/- 0.6 diopters. Thus we have designed a visual control system that continuously monitors and tracks its visual environment. This model is consistent with other proposed dynamic models for the eye.
Figure 8: This diagram shows the implementation of the various accommodation blocks into a design that will work to effectively control the lens power of the eye.
CYBERNETICS: [From Gr, kybernetes, steersman, governor.] Comparative study of the control system formed by the nervous system and brain and mechanical-electrical communication systems, such as computing machines.
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