A Cybernetic Model of Accommodation

Otis S. Brown, McDonnell Douglas Aerospace
Ronald J. Hooker, George Washington University
Peter R. Greene, Harvard University & BGKT Ltd.
Jason S. Moore, The United States Naval Academy
Stirling A. Colgate, The Los Alamos National Laboratory

This Paper was delivered to the 1996 Annual Engineering in Medicine & Biology Society Symposium.


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.


This paper's objective is to clarify the predictions that are implied in earlier block diagrams of the accommodation system. The diagrams do not provide active outputs which can be compared directly with the experimental data. The actual building of a working model from a block-diagram concept is challenging and will define, after review, the behavior of the normal system.

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.


Light rays from objects travel through the cornea, lens and ultimately arrive at the retina. At the retina they form a blur-circle which varies in size. The lens control system must act to drive the lens-plant towards the null (or in-focus) condition.


Optically, all eyes have dead-band. Dead-band varies, and is inversely proportional to the size of the aperture. The eye's dead-band in day-light is approximately +/- 0.6 diopters, and at night, +/- 0.3 diopters. Dead-band occurs because the lens of the eye can be varied in power without any detectable change in the sharpness of the image at the surface of the retina. [1]

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
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
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.


The basic concept of a null-seeking network and system is that a cone/neuron will turn-on when struck by a photon of light. The output of the network depends only on the presence of light or no-light, and not on its intensity. A Charge Coupled Device (CCD) could be developed as an analog of this retina characteristic. [2] (A comparator amplifier, following the cone can be used to accomplish this conversion of an analog signal to a on-off level.) Figure 3.

Figure 3
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.


When the signal blooms from being out-of-focus (positive or negative), more cones will detect photons, and the summations of neuron firing increases. This action produces an increase in output voltage, as the image goes out-of-focus. Figure 4. Lens control can occur only after the blur-circle strikes additional cones.

Figure 4
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.


The retina senses the increasing voltage which is used by the control system (in combination with a dither signal) to produce a null-seeking action. The dither, or noise will -- on the average -- center the lens in the middle of the dead-band. This system will produce sharp focus for perhaps 80 percent of this time when the eye is viewing an object. Obviously, we are not objectively aware of the short excursions that occur when the lens exceeds the edge of the dead-band as the system scans the range of sharpest focus. Figure 5.

Figure 5
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.


To center the lens, continual lens motion must be induced in the system. This can be accomplished by a sine-sweep, dither, or some other noise-type of signal. In the case of the eye, random motion (noise - from 0.25 to 4 hertz) is seen in lens motion -- as measured by an infrared optometer. [3,4] The need for this type of signal should be obvious to most control-system designers, where static friction or dead-band exist in the control system.


The full implementation of the control system requires some mechanical changes in the "plant" to simulate the eye's behavior. The manner in which the muscles support the eye's lens has been discussed in many other texts and dissertations. [5]

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.

Figure 6
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.

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. [4] A graphic sketch is shown in Figure 5.


The complete block diagram of the retina-lens system that captures the basic accommodation characteristic has been previously published. See Figure 7 [6] The action of the model is such that when the eye is looking at infinity (zero diopters) visual environment, the lens will oscillate between +/- 0.6 diopters, as long at the individual looks at infinity.

Figure 7
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.


Our next step is to convert the block diagram into an analog computer and to compare the output with the response as seen by an infrared optometer. A major feature of the model is the requirement that the system must have a stand-by, or reference position when blur cannot be detected. A control system will typically drift into the stops, unless a reference signal is supplied. This simulation is accomplished by a switch which selects a -1.0 volt level when the eye is in "conscious darkness", or if blur cannot be detected. A typical value for the dark focus of the normal eye is -1.0 Diopters. [3] Figure 8.

Figure 8
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.


The above presentation is a simplified version of accommodation. In future model enhancements, we will incorporate a tonic accommodation amplifier which will show that tonic accommodation will track the average value of accommodation. This response has been suggested in a previous study. [3] We can also expect that the tonic accommodation system will show a time-constant response of approximately 100 days. [7]


Previous models of accommodation have restricted their attention to the muscles that surround the lens of the eye. This model concentrates on the image processing and feedback control that must occur at the surface of the retina.


We acknowledge the long-term assistance of Dr. Karel Montor, The United States Naval Academy, and Dr. David Guyton, Professor of Ophthalmology, The Wilmer Institute. Their commitment to the development of new concepts, and their concern for the welfare of others, has been an inspiration to all of us. The development of this paper would have been impossible without their dedicated support.

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.


1. Hung, G., Ciuffreda, K., Semmlow, J., Hokoda, S., "Model of Static Accommodative Behavior in Human Amblyopia", Trans. on Biomedical Eng., Vol. BME-30, No. 10, pp. 665-672, Oct 1984

2. Langenbacher, H. T., Fossum, E. R., and Kemeny, S., "CMOS Active-Pixel Image Sensor With Intensity-Driven Readout", Jet Propulsion Laboratory, NASA Tech Briefs, January 1996

3. Baker, R., Brown, B., Garner, L., "Time Course and Variability of Dark Focus", Investigative Oph. & Visual Science, Vol. 24, pp. 1528 - 1531, Nov 1983

4. Suzumura, A., "Accommodation in Myopia", Department of Oph., Aichi Medical U., Proceedings of the 2nd International Myopia Conference, 1978

5. Greene, P. R., "Mechanical Aspects of Myopia", Ph.D. Dissertation, Harvard University, Division of Engineering and Applied Physics, Feb. 1978

6. Semmlow, J., Hung, G., "A Quantitative Theory of Control Sharing Between Accommodative and Vergence Controllers", IEEE Transactions on Biomedical Engineering, Vol BME-29, No 5, pp. 364-370, May 1982

7. Brown, O., Young, F., "The Response of a Servo Controlled Eye to a Confined Visual Environment", The 18th Annual Rocky Mountain Bioengineering Symposium, pp. 41-44, 1981

Back to I SEE home page...