Latency of peripheral saccades

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Man Cybern. SMC-7, 639-651 (1977). 18H. Von Helmholtz, Handbuch der Physiologischen Optik. Translation from German edition, edited by J. P. C. Southall.
for maintained vision," J. Opt. Soc. Am. 47, 740-744 (1957). R. W. Ditchburn, D. H. Fender, and Stella Mayne, "Vision with controlled movements of the retinal image," J. Pliysiol. (London) 145, 98-107 (19.59). 4 U. Tulunay-Keesey and L. A. Riggs, "Visibility of Mach bands with imposed motions of the retinal image," J. Opt. Soc. Am. 52,719-720 (1962). 5 A. L. Yarbus, Eye-movements and Vision (Plenum, New York, 1967), p. 86. 6 R. W. Ditchburn and A. E. Drysdale, "The effect of retinal image movements on vision. II. Oscillatory movements," Proc. R. Soc. Lond. B 197, 385-406 (1977). 7 R. W. Ditchburn and B. L. Ginsborg, "Vision with a stabilized retinal image," Nature (Lond.) 170, 36-37 (1952). 8L. A. Riggs, F. Ratliff, J. C. Cornsweet, and T. N. Cornsweet, "Disappearance of steadily fixated test objects," J. Opt. Soc. Am. 43, 495-501 (1953). 9 L. A. Riggs, personal communication. ' 0H. D. Crane and C. M. Steele, "Accurate three-dimensional eyetracker," Appl. Opt. 17, 691-705 (1978). 'IT. N. Cornsweet and H. D. Crane, "Accurate two-dimensional eye tracker using first and fourth Purkinje images," J. Opt. Soc. Am. 63, 921-928 (1973). 12 D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107-129 (1977). 13J. G. Robson, "Spatial and temporal contrast-sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 1141-1142 (1966). lID. H. Kelly, "Frequency doubling in visual responses," J. Opt. Soc. Am. 56, 1628-1633 (1966). ' 5 F. L. van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, "Spatiotemporal modulation transfer in the human eye," J. Opt. Soc. Am. 57, 1082-1088 (1967). 16 D. H. Kelly, "Adaptation effects on spatio-temporal sine-wave thresholds," Vision Res. 12, 89-101 (1972). 17 J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, S. Slappendel, "Perimetry of contrast detection thresholds of moving spatial sine wave patterns," J. Opt. Soc. Am. 68, 845-865 (1978). 18 H. D. Crane and T. N. Cornsweet, "Ocular focus stimulator," J. Opt. Soc. Am. 60, 577 (1970). 19 D. H. Kelly and R. E. Savoie, "A study of sine-wave contrast sensi3

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tivity by two psychophysical methods," Percept. Psychophys. 14, 313-318 (1973).

OSee, for example, L. A. Riggs and S. U. Tulunay, "Visual effects of

varying the extent of compensation for eye movements," J. Opt. Soc. Am. 49, 741-745 (1959). 21 Ref. 1, p. 129. 22 In subsequent papers of this series, we will consider other evidence that contrast thresholds are controlled by retinal receptive fields. 23 H. D. Crane and T. P. Piantanida, unpublished communication (1978). 24 H. D. Crane and M. R. Clark, "Three dimensional visual stimulus deflector," Appl. Opt. 17, 706-714 (1978). 25 U. Tulunay-Keesey and R. M. Jones, "The effect of micromovements of the eye and exposure duration on contrast sensitivity," Vision Res. 16, 481-488 (1976). 26 D. S. Gilbert and D. H. Fender, "Contrast thresholds measured with stabilized and non-stabilized sine-wave gratings," Opt. Acta 16, 191-204 (1969). 27 A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245-1263 (1968). 2 8L. A. Riggs and B. R. Wooten, unpublished communication (1977). 29 The form of the normal contrast sensitivity curve, and the effects of various parameters upon it, are discussed extensively in Ref. 12; 30 J. J. Koenderink, "Contrast enhancement and the negative afterimage," J. Opt. Soc. Am. 62, 685-689 (1972). 31 V. Virsu and P. Laurinen, "Long-lasting afterimages caused by neural adaptation," Vision Res. 17, 853-860 (1977). 32 D. H. Kelly, "New method of stabilizing retinal images," J. Opt. Soc. Am. 65, 1184, abstract (1973). 33 In some unpublished experiments conducted in this laboratory, H. D. Crane and T. P. Piantanida have found that the luminance of a stabilized reflectance pattern can be changed rapidly (e.g., by flickering the light source at rates above 10 Hz) without restoring its visibility, as long as the contrastof the pattern is held constant. This result is just what would be expected from the kind of retinal masking described here.

Latency of peripheral saccades Yehoshua Y. Zeevi and Eli Peli Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel (Received 14 September 1978; revised 9 January 1979) Displaying the point of gaze to the observer in addition to a point target provides a secondary visual feedback (2VFB). Eccentric fixation is achieved using a biased 2VFB to yield an experimentally imposed "eccentric fovea." The target is suddenly moved to a new position and the task is to regain it, in the "eccentric fovea." It is found that the pattern of eye-movement response consistently starts with saccadric foveal exploration of the target, but its latency has twice the duration of a regular voluntary saccade. Practice, however, makes for the shortened latency tending asymptotically to the regular saccadic duration.

sity5' 6 ; it is also known that prediction and practice 4' 7 may

INTRODUCTION When a subject is instructed to fixate on a point target and the target suddenly moves to a new position, time elapses between this displacement and the beginning of eye movement towards the new position. This effect is known as saccadic latency, and has been studied extensively ever since its existence was reported in the classic work of Dodge and Cline.' The average latency under normal conditions is approximately 200 ms, with a standard deviation of 30 ms,2-4 but is affected by a variety of factors such as stimulus amplitude and inten1274

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shorten it, whereas fatigue,8 neurological diseases, 9 and amblyopia'0 may lengthen it. All the above refers to saccades that subserve foveationthe natural mode of exploration of a suddenly appearing peripheral object of interest. Secondary visual feedback (2VFB) is a visual signal derived from continuous measurement of eye position and provides an indication of the point of gaze. 2VFB may be eccentrically displaced by biasing the measured eye position signal; subjects

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mean + 3 SD). These, such as the two indicated in the examples given in Table I, are presumably due to momentary lack of attention. Mean and SD of latencies extracted from 14 consecutive sessions are summarized in Table II and Fig. 3. Each of the peripheral saccade latency data points is averaged over 3-18 saccades, according to the number of jumps covered during the session. For each of the three subjects, we also measured the two reference points of foveal-saccadic latencies with and without 2VFB. In the first session of a peripheral saccadic task, the duration of the latency is about twice as long as the duration typical of a voluntary foveal saccade. Practice, however, tends to shorten the latency, as demonstrated in Fig. 3, tending asymptotically the regular saccadic duration.15"16 Since there is intersubject variability in the duration of foveal saccade, we normalize the data in order to compare the effect of practice on the performance of three subjects. This is shown in Fig. 4. 1278

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In our earlier report," it was shown that it is feasible to fixate with extrafoveal vision, using 2VFB. It thus becomes possible to select an extrafoveal subfield and consider it as an "eccentric fovea" in the sense of having this new fovea track and/or fixate a point target. Transition to an eccentric fovea is not a straightforward process. To begin with, there is a natural tendency to register the target within the foveal field even when eccentric fixation is achieved, and it is reasonable to assume that the system exerts inhibition to suppress that tendency. This is presumably an important factor determining the processing time required to execute the first saccade in the proper direction after closing the 2VFB loop; the same can be inferred from the fact that an untrained subject responds with the first jump in the wrong direction, in order to achieve foveation of the 2VFB signal, in which case the latency (and apparently also the processing time) is only about 200 ins. Another factor that may contribute to lengthening the reaction time of this first jump on closing the loop is the complexity of the task in terms of "programming." Unlike foveation, where the saccadic system has to program the jump with reference to the same point (namely the fovea), here the starting point is again the fovea but the end point is the "eccentric fovea," which calls for reversal of movement. The complexity is due in part to the presence of two independent point targets; indeed, it has been shown that increasing the dimensionality of the stimulus lengthens the reaction time.' 7 The currently discussed peripheral saccades have as their starting point the "eccentric fovea," where fixation can be maintained by a shift of attention," 8 combined with an inhibitory effort. In order to understand their characteristics, one must therefore consider the conditions imposed by both the starting and end points. In terms of the task, unlike the first saccade for eccentric fixation, we have here the same starting and end point. However, since, as we found, the first saccade is foveal exploration, we have the opposite of what we had in eccentric fixation: namely, the starting point is eccentric but the end point is foveal. As shown in the results, the latency in this case is about twice as long as the latency of a regular foveal saccade. While this may appear surprising at first glance, it is reasonable to assume that extra processing time is needed to eliminate the inhibitory state. The lengthening of the latency is also due to the fact that we have here, as before, a dual target situation. A consistent, important finding is the strong influence of practice on peripheral saccade latency. Normalizing the duration with respect to the latency of foveal saccades, we find that in spite of intersubject variability, due in part to visual fidelity and to individual attentive capability, the duration in the first session is about twice as long as the foveal-saccade latency, which is also the asymptote to which a subject tends within less than 14 sessions. It should be noted that there is no improvement in reaction time, the latency of the first saccade, with practice. This is consistent with Hallett's findings concerning "antisaccade" latencies. Quantitatively, we find almost twice as long reaction time in our task, in comparison with the "antisaccade" latencies. This indicates that the extra time required in order to execute the first saccade is not due solely to direction reversal which characterizes both tasks. This may provide further support for the hyYehoshua Y. Zeevi and Eli Peli

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pothesis of the existence of inhibitory signal in the dual task. In our earlier study of eccentric fixation, using 2VFB, we have shown the relationship between acuity as a function of eccentricity and performance in eccentric fixation task. It is therefore interesting to note that results of practice effect similar to ours were obtained by Johnson and Leibowitz in a study of peripheral visual resolution.' 9 However, these practice effects were not observed for the near periphery, the central field spanned in our study. ACKNOWLEDGMENTS This research was partly supported by U.S.-Israel Binational Science Foundation (BSF) Grant No. 1435 and by the Julius Silver Institute. The authors wish to thank Z. Portnoy, R. Bronwasser, and P. Segerhammer for valuable technical assistance. 'R. Dodge and T. Cline, "The angle velocity of eye movements," Psychol. Rev. 8, 125-157 (1901).

2G. Westheimer, "Mechanism of saccadic eye movements," Arch. Ophthalmol. 52, 710-724 (1954). 3 G. Westheimer, "Eye movement responses to horizontally moving visual stimulus," Arch. Ophthalmol. 52, 932-941 (1954). 4 L. Stark, G. Vossius, and L. R. Young, "Predictive control of eye tracking movements," IRE Trans. Human Factors Electron. HFE-3, 52-57 (1962). 5 L. L. Wheeless, G. H. Cohen, and R. M. Boynton, "Luminance as a parameter of the eye movement control systems," J. Opt. Soc. Am. 57, 394-400 (1967). 6 A. E. Bartz, "Eye-movement latency, duration, and response time

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as a function of angular displacement," J. Exp. Psy.chol. 64,318-324 (1962). R. B. Hackman, "An experimental study of variability in ocular latency," J. Exp. Psychol. 27, 548-558 (1940).

8W. R. Miles, "The reaction time of the eye," Psychol. Monog. 47, (whole No. 212), 268-293 (1963). R. W. Buloh, V. Honrubia, and A. Sills, "Eye tracking and optokinetic nystogmus: results of quantitative testing in patients with welldefined nervous system lesions," Annals Oto. Rhinol Laryngol. 86,

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108-114 (1977). 'OK. J. Ciuffreda, R. V. Kenyon, and L. Stark, "Increased saccadic latencies in amblyopia eyes provide further evidence for processing delays over the central retina," (private communication, 1978). "Y. Y. Zeevi, E. Peli, and L. Stark, "A study of eccentric fixation with secondary visual feedback," J. Opt. Soc. Am. 69, 669-675 (1979). 2 ' L. R. Young and L. Stark, "A discrete model for eye tracking movement," IEEE Trans. Mil. Electron. MIL-7, 113-115 (1963). 3

1 A. T. Bahill, M. R. Clark, and L. Stark, "Dynamic overshoot in saccadic eye movements is caused by neurological control signal reversals," Exp. Neurol. 48, 107-122 (1975). l4p. E. Hallett, "Primary and secondary saccades to goals defined by instructions," Vision Res. 18, 1279-1296 (1978). 5 1 Statistical trend analysis (see Ref. 16) using F test of the combined delay data (for the three subjects) indicates the existence of a trend-confidence level of 99%. The best fit linear trend is of-11.2 ± 2.1 ms/session. 6

1 A. L. Edwards, Trend analysis, in Experimental Design in Psychological Research (Rinehart, New York, 1960). 7

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Morasso, G.

Sandin, V. Tagliasco, and R.

Renato Zaccaria,

"Control strategies in the eye-head coordination system," IEEE Trans. Syst. Man Cybern. SMC-7, 639-651 (1977).

18H. Von Helmholtz, Handbuch der Physiologischen Optik. Translation from German edition, edited by J. P. C. Southall (Dover, New York, 1962). 9 1 C. A. Johnson and H. W. Leibovitz, "Practice Effects for Visual Resolution in the Periphery" (private communication, 1978).

Polarizabilities of highly ionized atoms S. 0. Kastner and M. L. Wolf Laboratoryfor Astronomy and Solar Physics, NASA-Goddard Space Flight Center, Greenbelt, Maryland 20771 (Received 12 March 1979) An extrapolation method based on a screening approximation, applied to available initial values of polarizability for low stages of ionization, is used to obtain dipole and quadrupole polarizabilities for more highly ionized members of many isoelectronic sequences. It is suggested that the derived screening constants x L and limiting ratios FL may have significant physical meaning, especially the latter which may have an interpretation in terms of hydrogenic polarizabilities.

Dipole and quadrupole polarizabilities aL=1 and aL=2 enter, for example, into the calculation of the core polarization term A, (see, e.g., Edlen') which is part of the binding energy of outer valence electrons in an atom or ion. These polarizabilities have been calculated in closed analytic form, as a function of nuclear charge Z, only for one-electron and twoelectron ions (Dalgarno, 2 Stewart 3 ). For electron number N > 2, available values of a, and a 2 drop off rapidly, especially the latter, few having been calculated along appreciable lengths of an isoelectronic sequence. Since very highly ionized atoms of iron and nickel, for example, are now being studied in laboratory and astrophysical applications, a simpler and more general approach to obtain polarizabilities for higher stages of ionization is needed. An extrapolation procedure based on a screening approximation is described here that 1279

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gives a simple closed expression for polarizabilities, yielding reasonably accurate values as judged by comparison with some reliable values in the literature. Throughout this article, polarizability of multipole order L is given in atomic units a 02L+1

GENERAL VARIATION OF POLARIZABILITIES Bokacheva and Borisova4 (BB) have given a useful discussion of the behavior of the dipole polarizability al(NZ) as a function of Z and N, indicating that in general a 1 decreases monotonically with Z and increases monotonically with N, as shown respectively in their Figs. 1 and 2. In Fig. 2, particularly, each curve shows smooth increase of a 1 along the sequence of ions of a given element Z, which at first glance

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