Abstract

A generalization of the “clamping” method is described and its application to the pupil light-reflex servo-mechanism illustrated. The relationship between this environmental clamping and more classical input-output analysis is demonstrated by the accuracy of predictions from the transfer function and is discussed theoretically. Separation of linear and nonlinear factors in system behavior in the oscillatory model has interesting experimental consequence.

© 1962 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).
  2. L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
    [CrossRef] [PubMed]
  3. L. Stark, M. Iida, and P. A. Willis, Quart. Progr. Rept., Research Laboratory of Electronics, MIT60, 229 (1961).
  4. G. Marmont, J. Cellular Comp. Physiol. 34, 351 (1949).
    [CrossRef]
  5. K. S. Cole, Arch. sci. physiol. 3, 253 (1949).
  6. J. L. Bower and P. M. Schultheiss, Introduction to the Design of Servomechanisms (John Wiley & Sons, Inc., New York, 1958).
  7. G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls (John Wiley & Sons, Inc., New York, 1957).
  8. L. A. MacColl, Fundamental Theory of Servomechanisms (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1945).
  9. H. M. James, V. B. Nichols, and R. S. Phillips, Theory of Servomechanisms (McGraw-Hill Book Company, Inc., New York, 1947).
  10. S. J. Mason and H. G. Zimmermann, Electronic Circuits, Signals, and Systems (John Wiley & Sons, Inc., New York, 1960).
  11. L. Stark, Proc. Inst. Radio Engs.,  47, 1925 (1959).
  12. L. Stark and F. Baker, J. Neurophysiol. 22, 158 (1959).
  13. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) 112b, 428 (1933).
    [CrossRef]
  14. L. Stark and T. N. Cornsweet, Science,  127, 588 (1958).
    [CrossRef]
  15. See reference 6, p. 168.
  16. See reference 6, pp. 84–85.
  17. See reference 10, pp. 418–422, 572–574.
  18. W. R. Evans, Control System Dynamics (McGraw–Hill Book Company, Inc., New York, 1954).

1959 (2)

L. Stark, Proc. Inst. Radio Engs.,  47, 1925 (1959).

L. Stark and F. Baker, J. Neurophysiol. 22, 158 (1959).

1958 (2)

L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
[CrossRef] [PubMed]

L. Stark and T. N. Cornsweet, Science,  127, 588 (1958).
[CrossRef]

1957 (1)

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

1949 (2)

G. Marmont, J. Cellular Comp. Physiol. 34, 351 (1949).
[CrossRef]

K. S. Cole, Arch. sci. physiol. 3, 253 (1949).

1933 (1)

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) 112b, 428 (1933).
[CrossRef]

Atwood, J.

L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
[CrossRef] [PubMed]

Baker, F.

L. Stark and F. Baker, J. Neurophysiol. 22, 158 (1959).

Bower, J. L.

J. L. Bower and P. M. Schultheiss, Introduction to the Design of Servomechanisms (John Wiley & Sons, Inc., New York, 1958).

Campbell, F. W.

L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
[CrossRef] [PubMed]

Cole, K. S.

K. S. Cole, Arch. sci. physiol. 3, 253 (1949).

Cornsweet, T. N.

L. Stark and T. N. Cornsweet, Science,  127, 588 (1958).
[CrossRef]

Crawford, B. H.

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) 112b, 428 (1933).
[CrossRef]

Evans, W. R.

W. R. Evans, Control System Dynamics (McGraw–Hill Book Company, Inc., New York, 1954).

Gould, L. A.

G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls (John Wiley & Sons, Inc., New York, 1957).

Iida, M.

L. Stark, M. Iida, and P. A. Willis, Quart. Progr. Rept., Research Laboratory of Electronics, MIT60, 229 (1961).

James, H. M.

H. M. James, V. B. Nichols, and R. S. Phillips, Theory of Servomechanisms (McGraw-Hill Book Company, Inc., New York, 1947).

Kaiser, J. F.

G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls (John Wiley & Sons, Inc., New York, 1957).

MacColl, L. A.

L. A. MacColl, Fundamental Theory of Servomechanisms (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1945).

Marmont, G.

G. Marmont, J. Cellular Comp. Physiol. 34, 351 (1949).
[CrossRef]

Mason, S. J.

S. J. Mason and H. G. Zimmermann, Electronic Circuits, Signals, and Systems (John Wiley & Sons, Inc., New York, 1960).

Newton, G. C.

G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls (John Wiley & Sons, Inc., New York, 1957).

Nichols, V. B.

H. M. James, V. B. Nichols, and R. S. Phillips, Theory of Servomechanisms (McGraw-Hill Book Company, Inc., New York, 1947).

Phillips, R. S.

H. M. James, V. B. Nichols, and R. S. Phillips, Theory of Servomechanisms (McGraw-Hill Book Company, Inc., New York, 1947).

Schultheiss, P. M.

J. L. Bower and P. M. Schultheiss, Introduction to the Design of Servomechanisms (John Wiley & Sons, Inc., New York, 1958).

Sherman, P. M.

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

Stark, L.

L. Stark, Proc. Inst. Radio Engs.,  47, 1925 (1959).

L. Stark and F. Baker, J. Neurophysiol. 22, 158 (1959).

L. Stark and T. N. Cornsweet, Science,  127, 588 (1958).
[CrossRef]

L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
[CrossRef] [PubMed]

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

L. Stark, M. Iida, and P. A. Willis, Quart. Progr. Rept., Research Laboratory of Electronics, MIT60, 229 (1961).

Stiles, W. S.

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) 112b, 428 (1933).
[CrossRef]

Willis, P. A.

L. Stark, M. Iida, and P. A. Willis, Quart. Progr. Rept., Research Laboratory of Electronics, MIT60, 229 (1961).

Zimmermann, H. G.

S. J. Mason and H. G. Zimmermann, Electronic Circuits, Signals, and Systems (John Wiley & Sons, Inc., New York, 1960).

Arch. sci. physiol. (1)

K. S. Cole, Arch. sci. physiol. 3, 253 (1949).

J. Cellular Comp. Physiol. (1)

G. Marmont, J. Cellular Comp. Physiol. 34, 351 (1949).
[CrossRef]

J. Neurophysiol. (2)

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

L. Stark and F. Baker, J. Neurophysiol. 22, 158 (1959).

Nature (1)

L. Stark, F. W. Campbell, and J. Atwood, Nature 182, 857 (1958).
[CrossRef] [PubMed]

Proc. Inst. Radio Engs. (1)

L. Stark, Proc. Inst. Radio Engs.,  47, 1925 (1959).

Proc. Roy. Soc. (London) (1)

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) 112b, 428 (1933).
[CrossRef]

Science (1)

L. Stark and T. N. Cornsweet, Science,  127, 588 (1958).
[CrossRef]

Other (10)

See reference 6, p. 168.

See reference 6, pp. 84–85.

See reference 10, pp. 418–422, 572–574.

W. R. Evans, Control System Dynamics (McGraw–Hill Book Company, Inc., New York, 1954).

L. Stark, M. Iida, and P. A. Willis, Quart. Progr. Rept., Research Laboratory of Electronics, MIT60, 229 (1961).

J. L. Bower and P. M. Schultheiss, Introduction to the Design of Servomechanisms (John Wiley & Sons, Inc., New York, 1958).

G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls (John Wiley & Sons, Inc., New York, 1957).

L. A. MacColl, Fundamental Theory of Servomechanisms (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1945).

H. M. James, V. B. Nichols, and R. S. Phillips, Theory of Servomechanisms (McGraw-Hill Book Company, Inc., New York, 1947).

S. J. Mason and H. G. Zimmermann, Electronic Circuits, Signals, and Systems (John Wiley & Sons, Inc., New York, 1960).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Pupil response to steady-state, light-flux changes. Ordinates and abscissas as marked. This is a typical response showing dominant fundamental response with harmonic distortion, high-frequency noise, nonstationarity of response, and low-frequency drifting.

Fig. 2
Fig. 2

Experimental apparatus. Two main portions of the apparatus are (a) servo-controlled light stimulation, and (b) direct-recording, area measurement by invisible-infrared energy.

Fig. 3
Fig. 3

Calibration. A linear fit was used for simplicity. Calibration is necessary because of variation in iris-infrared reflectance from subject to subject.

Fig. 4
Fig. 4

Optical arrangement for (a) normal “closed loop”, and (b) “open-loop” operating conditions.

Fig. 5
Fig. 5

Block diagram of the “clamping box” arrangement. Note the new closed loop formed from the pupil system and the clamping-box external-intensity control in tandem. The locus of the “cut” for opening the pupil loop is also shown.

Fig. 6
Fig. 6

Instability-oscillation experiment. The development of maintained sinusoidal oscillations can be noted. Record selected to show difficulties which can arise, namely, saturation of range of light-intensity control by slow fluctuations of area. The absence of phase shift in electronic portions of tandem system is clearly illustrated. Pupil phase lag is 180°, frequency 1.4 cps, pupil gain −6 decilog.

Fig. 7
Fig. 7

Instability oscillation with introduced phase shift. Phase shift due to electronic system is −20°. Pupil phase lag is 200°, frequency 1.6 cps, pupil gain −5 decilog.

Fig. 8
Fig. 8

Double-instability oscillations illustrate certain nonlinear features of pupil system as explained in text. For rapid oscillations pupil phase lag is 203°, frequency 1.3 cps, pupil gain −11.1 decilog; for slow oscillations, pupil-phase advance is 65°, frequency 0.18 cps, pupil gain −9.3 decilog.

Fig. 9
Fig. 9

Frequency characteristics illustrated as Bode plot of both high-gain instability—oscillation experiments (squares) and driven-response experiments (filled circles). Heavy solid lines are empirical fits to steady-state experiments; the dashed and thin continuous lines are asymptotes. Numbers indicate number of different experiments whose values fall too closely together to be plotted separately.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

G = Δ F p / Δ F i ,
G = Δ A · I ¯ / Δ I · A ,
G ( s ) = 0.16 e 0.2 s / ( 1 + 0.1 s ) 3
G = ( Δ A / A ¯ ) / ( Δ I / I ¯ )
% area change / % illuminance change .
G p × G c b = G t s = 1.
ϕ p + ϕ c b = ϕ t s = 180 ° ,