Abstract

The purpose of this experiment is to measure the latency to onset of the contraction of the pupil, as a function of the size of positive steps in luminance, starting at various luminance levels to which the eye has been adapted prior to the stimulus steps. In the past, latency of the pupil response has been inaccurately measured, owing to the difficulty of separating the end of the latent period from the slow beginning of contraction. To overcome this, a digital curve-fitting technique involving a time delay followed by a modified second-order step response was developed. Latency was defined as the time delay giving the most accurate fit.

Because the curve-fitting procedure needed a response with less random variation than is normally present, an average was used. Such averaging was first justified by using the standard deviation to show that there is probably no significant variation of latency for responses of a given subject under identical stimulus conditions. This analysis also showed that 20 responses is an efficient number to average for the pupil-contraction system.

The excellent agreement between each average experimental response and the computed fit verified the value of delay used in the computation. Latency, thus defined for each stimulus condition, was found to be primarily a function of luminance during the step and only secondarily of the ratio of the step change of luminance to the adaptation luminance.

© 1969 Optical Society of America

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References

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  1. L. Stark, Proc. IRE. 49, 1925 (1959).
    [Crossref]
  2. M. Clynes, Ann. N. Y. Acad. Sci. 98, 806 (1962).
    [Crossref] [PubMed]
  3. D. Green, Ph.D. thesis, Northwestern University (1964).
  4. E. Adrian and R. Matthews, J. Phys. 64, 279 (1927b).
  5. E. Johnson and N. Bartlett, J. Opt. Soc. Am. 46, 167 (1956).
    [Crossref] [PubMed]
  6. H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
    [Crossref]
  7. N. Bartlett and S. MacLeod, J. Opt. Soc. Am. 44, 306 (1954).
    [Crossref] [PubMed]
  8. B. Arden and R. Weale, Proc. Roy. Soc. (London) B142, 258 (1954).
  9. J. Roufs, Vis. Res. 3, 81 (1963).
    [Crossref]
  10. O. Lowenstein and I. Loewenfeld, Am. J. Ophthalmol. 48, 87 (1949).
  11. O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
    [PubMed]
  12. M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).
  13. L. Kumnick, J. Geront. 11, 391 (1956).
    [Crossref]
  14. R. Feinberg and E. Pololak, in Behavior, Aging and the Nervous System, by A. Welford and J. Birren (C. C. Thomas, Springfield, Ill.1965).
  15. Further description of the search procedure and a complete Fortran program for the procedure can be found in the thesis, “Effect of Adaptation Level and Stimulus Amplitude on Latency to Contraction of the Human Pupil Reflex,” by R. E. Lee, which is available from University Microfilms, Inc. as Order No. 66-10, 810.

1964 (1)

O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
[PubMed]

1963 (2)

M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).

J. Roufs, Vis. Res. 3, 81 (1963).
[Crossref]

1962 (1)

M. Clynes, Ann. N. Y. Acad. Sci. 98, 806 (1962).
[Crossref] [PubMed]

1959 (1)

L. Stark, Proc. IRE. 49, 1925 (1959).
[Crossref]

1956 (2)

1954 (2)

N. Bartlett and S. MacLeod, J. Opt. Soc. Am. 44, 306 (1954).
[Crossref] [PubMed]

B. Arden and R. Weale, Proc. Roy. Soc. (London) B142, 258 (1954).

1952 (1)

H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
[Crossref]

1949 (1)

O. Lowenstein and I. Loewenfeld, Am. J. Ophthalmol. 48, 87 (1949).

1927 (1)

E. Adrian and R. Matthews, J. Phys. 64, 279 (1927b).

Adrian, E.

E. Adrian and R. Matthews, J. Phys. 64, 279 (1927b).

Alpern, M.

M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).

Arden, B.

B. Arden and R. Weale, Proc. Roy. Soc. (London) B142, 258 (1954).

Barr, L.

M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).

Bartlett, N.

Clynes, M.

M. Clynes, Ann. N. Y. Acad. Sci. 98, 806 (1962).
[Crossref] [PubMed]

Feinberg, R.

R. Feinberg and E. Pololak, in Behavior, Aging and the Nervous System, by A. Welford and J. Birren (C. C. Thomas, Springfield, Ill.1965).

Green, D.

D. Green, Ph.D. thesis, Northwestern University (1964).

Hartline, H.

H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
[Crossref]

Johnson, E.

Kawabata, H.

O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
[PubMed]

Kumnick, L.

L. Kumnick, J. Geront. 11, 391 (1956).
[Crossref]

Lee, R. E.

Further description of the search procedure and a complete Fortran program for the procedure can be found in the thesis, “Effect of Adaptation Level and Stimulus Amplitude on Latency to Contraction of the Human Pupil Reflex,” by R. E. Lee, which is available from University Microfilms, Inc. as Order No. 66-10, 810.

Loewenfeld, I.

O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
[PubMed]

O. Lowenstein and I. Loewenfeld, Am. J. Ophthalmol. 48, 87 (1949).

Lowenstein, O.

O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
[PubMed]

O. Lowenstein and I. Loewenfeld, Am. J. Ophthalmol. 48, 87 (1949).

MacLeod, S.

MacNichol, E.

H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
[Crossref]

Matthews, R.

E. Adrian and R. Matthews, J. Phys. 64, 279 (1927b).

McCready, D.

M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).

Pololak, E.

R. Feinberg and E. Pololak, in Behavior, Aging and the Nervous System, by A. Welford and J. Birren (C. C. Thomas, Springfield, Ill.1965).

Roufs, J.

J. Roufs, Vis. Res. 3, 81 (1963).
[Crossref]

Stark, L.

L. Stark, Proc. IRE. 49, 1925 (1959).
[Crossref]

Wagner, H.

H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
[Crossref]

Weale, R.

B. Arden and R. Weale, Proc. Roy. Soc. (London) B142, 258 (1954).

Am. J. Ophthalmol. (2)

O. Lowenstein and I. Loewenfeld, Am. J. Ophthalmol. 48, 87 (1949).

O. Lowenstein, H. Kawabata, and I. Loewenfeld, Am. J. Ophthalmol. 57, 569 (1964).
[PubMed]

Ann. N. Y. Acad. Sci. (1)

M. Clynes, Ann. N. Y. Acad. Sci. 98, 806 (1962).
[Crossref] [PubMed]

Cold Spring Harbor Symp. Quant. Biol. (1)

H. Hartline, H. Wagner, and E. MacNichol, Cold Spring Harbor Symp. Quant. Biol. 17, 125 (1952).
[Crossref]

J. Gen. Physiol. (1)

M. Alpern, D. McCready, and L. Barr, J. Gen. Physiol. 47, 265 (1963).

J. Geront. (1)

L. Kumnick, J. Geront. 11, 391 (1956).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. (1)

E. Adrian and R. Matthews, J. Phys. 64, 279 (1927b).

Proc. IRE. (1)

L. Stark, Proc. IRE. 49, 1925 (1959).
[Crossref]

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

B. Arden and R. Weale, Proc. Roy. Soc. (London) B142, 258 (1954).

Vis. Res. (1)

J. Roufs, Vis. Res. 3, 81 (1963).
[Crossref]

Other (3)

D. Green, Ph.D. thesis, Northwestern University (1964).

R. Feinberg and E. Pololak, in Behavior, Aging and the Nervous System, by A. Welford and J. Birren (C. C. Thomas, Springfield, Ill.1965).

Further description of the search procedure and a complete Fortran program for the procedure can be found in the thesis, “Effect of Adaptation Level and Stimulus Amplitude on Latency to Contraction of the Human Pupil Reflex,” by R. E. Lee, which is available from University Microfilms, Inc. as Order No. 66-10, 810.

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Figures (8)

Fig. 1
Fig. 1

X ¯ is the ensemble of a large number of equal-amplitude steps with a latency varying uniformly between limits T1 and T2. X ¯ can be seen to have a form which is completely unrepresentative of the individual members. The lowest curve, σ, is the standard deviation of X ¯. In the region where X ¯ fails to represent the form of its members, the increase of σ gives warning of erroneous results.

Fig. 2
Fig. 2

A normalized average pupil contraction, X ¯, obtained from the average of 20 individual pupil responses. The standard deviation of this average response is also shown, labeled σp, plotted against the same 2-sec time scale. A slight increase of the standard deviation σp is found to be associated with the end of the steeply contracting portion of the response. A gaussian variation of latency within the limits suggested by the dashed curves labeled X(T + 0.025) and X ¯(T − 0.025) would cause the increase of standard deviation shown at the bottom, labeled σΔL. This is larger than the increase of σp as well as earlier and indicates that latency variation, if present, is probably less than ±25 msec.

Fig. 3
Fig. 3

X ¯ is the normalized average pupil contraction resulting from L1 = −0.4 log10 td and ΔL = 3.0 log10 td. The curve labeled COMP is the best-fitting second-order step response, plus exponential, beginning after a time delay which was obtained by the computer. The excellent fit near the beginning is taken as evidence of the accuracy of this value of latency.

Fig. 4
Fig. 4

Curves marked with tic marks and labeled X ¯ are averages of 20 individual responses. Curves without tic marks and labeled COMP are the computer best fits to the associated X ¯ curve. The upper set was arbitrarily displaced by a quarter unit for clarity. The lower curves show excellent agreement between X ¯, the normalized experimental average, and COMP, the computer fit. This indicates that the weighting of the error minimizes the effects of an artifact in the later portions of the average response. The experimental average, X ¯, of the upward pair of curves contains an artifact, possibly an undetected blink, in the early portion of the response. The computer fit can be seen to be poor despite the weighting of the error but shows that such a poor fit can be easily detected visually. All responses were plotted and checked visually and those where there was any visible area between the curves were discarded.

Fig. 5
Fig. 5

Latency vs adaptation luminance L1 in log trolands. The figures marked on the curves indicate the sizes of the stimulus step in luminance, expressed in log10 units. Thus the numeral 4 above the abscissa value of 0.9 log10 td indicates that the step consisted of a multiplication of 104 times the adaptation level of 0.9 log10 td while the ordinate shows that the latency for this stimulus situation is 210 msec. The data in the figure reveal an inverse linear relationship between latency and logarithm of the adaptation luminance.

Fig. 6
Fig. 6

Latency vs adaptation luminance L1 in log10 trolands. The data points are those presented in Fig. 5 and are expressed in the same form. The straight lines represent the best equispaced lines which can be fitted to the data under the assumption that all lines should have the same slope, the average of the slopes obtained by a best linear fit of the data without any restrictions.

Fig. 7
Fig. 7

Latency vs luminance during the step measured in log10 trolands and with step size in log units again indicated by the numeral. Note that plotting against L2 as a parameter has greatly compressed the data, indicating the relative importance of this quantity in determining latency.

Fig. 8
Fig. 8

Latency vs luminance during the step. The presentation here is the same as in Fig. 7 except that the individual data points have been omitted for clarity and the best equidistant, parallel straight lines fitted by the computer and shown vs L1 in Fig. 6 are here shown vs L2, with a resultant compression of the data due to the importance of L2 in determining latency. The lines do not exactly superimpose, so that the step size, ΔL, while less important than L2, is still a parameter affecting latency.

Equations (2)

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X ( t ) av = 1 N i = 1 N X i ( t )             and             σ ( t ) = { 1 N i = 1 N [ X i ( t ) - X ( t ) av ] 2 } 1 2 .
Δ t = 312 - 18.6 log L 2 - 5.0 log Δ L msec ,