JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Absolute Threshold before and after Correction of Oblique-Ray AstigmatismLUCIA RONCHI

National Institute of Optics, 50125 Arcetri, Firenze, Italy(Received 20 January 1971)

Threshold luminance was determined at various eccentricities along the horizontal nasal meridian of thedark-adapted retina of one subject. If test-flash duration is brief, threshold is almost independent of eccen-tricity, in the range investigated. If the duration exceeds, say, 12 ins, sensitivity deteriorates beyond 400.Luminance-time relationships reveal that the total integration time decreases as the distance from thefovea is increased beyond 400. This, however, is no longer the case when oblique-ray astigmatism is suitablycorrected; total integration time attains an unexpected value (1 s) and sensitivity, as determined with long-duration flashes, increases as eccentricity is increased. The relation between size of the minimal-blur diskand size of receptive field is discussed.INDEX HEADING: Vision.

The present paper deals with the relation between theabsolute threshold and retinal eccentricity in far-peripheral vision. This topic has attracted the attentionof other investigators.' 2 However, as far as we know,test-flash duration has not yet been adequately takeninto account, although its possible influence wasrecognized.

Thus, for instance, Bartlett3 quotes the findings ofDe Groot et al., according to which night-vision sensi-tivity decreases with eccentricity beyond about 100 or15°. This result applies with a small target, exposed fora long time. According to Bartlett, somewhat differentfunctions are expected for other sizes and durations,because the gradients for temporal and spatial sum-mation differ with retinal location. In turn, Pirenne4

asserts that the difference between cone and rodthreshold is larger for a steady source than for a briefflash, on account of the greater range of temporal sum-mation of rods. Recently, Kishto' stressed that changesof flash duration would also affect the threshold, atthose retinal points which show the same degree oftemporal summation.

Traditionally, the integrative properties of the retinahave been investigated by recording the luminance-time relation. The intriguing aspect of the problem isthat temporal summation is somehow related to spatialsummation, which, in turn, depends on the size of thereceptive field.1

Now, the image cannot be rendered as small aswanted, because of the minimal-blur disk of dioptricorigin. Thus, the relation between receptive-field sizeand minimal image size must be elucidated.

At photopic levels, for which the pupil is narrow,the minimal-blur disk subtends a few minutes of arcand is usually smaller than the foveal receptive field.7

As adapting luminance is decreased, the size of the blurdisk increases, because of the increased pupil size. Inthe neighborhood of absolute threshold it attains itsmaximum value. The computation of the distributionof illuminance, at retinal points far from the fovea, iscomplicated.8 -10 It is generally believed that the retinalimage deteriorates strongly as eccentricity exceeds,say, 40°, because of the interplay of the typical off-axis

aberrations, coma, and oblique-ray astigmatism." Afull description of these phenomena is given in Amesand Proctor's early paper.'0 In turn, the receptive-fieldsize, for the dark-adapted retina, is known to increasewith eccentricity. According to Hallett"2 and Glezer,"it attains about 60' diameter at 300 or 400 from thefovea. For greater eccentricity, precise data are notavailable.' The density of photoreceptors is known todecrease in the far-peripheral retina,' but the basis forthe differences of local sensitivity is not receptordensity.

Additional hypotheses, involving secondary neurons,must be invoked.'

Our experimental data show that the correction ofoblique-ray astigmatism leads to an increase of thetotal integration time. This might mean that, undernatural viewing conditions, beyond 400 from the fovea,the minimal-blur disk is greater than the receptive field.However, the estimate of the apparent length of the(astigmatic) streak-like image of a 6' circular spot, theluminance of which is close to absolute threshold, doesnot exceed 50' in the far periphery."

Thus, there are two possibilities at least: either thereceptive field decreases beyond 400, or the interactionbetween subliminal stimuli fails to be a simple linearsummation over such an area.

APPARATUS AND METHOD

The light emitted by a 2800 K incandescent-filamentlamp is concentrated at a plane where a revolving diskis placed. The length of the slit pierced in the diskcontrols the flash duration. Both the rise and decaytimes of luminance amount to about 1 Ins. Luminanceis varied by use of neutral Kodak Wratten filters. Thelight impinges on a ground glass covered by an opaquediaphragm in which a hole is pierced. The size of thehole controls the size of the test spot. In our experi-ment, the test spot subtends at the eve about 6' of arc.The viewing distance is 1 m.

Prior to each session, the subject adapts her eye tothe darkness for 30 min. The session lasts 1 h. Monoc-ular vision is employed.

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VOLUME 61, NUMBER 12 DECEMBER 1971

1706LUCIA RONCHI

For each selected eccentricity and duration, absolutethreshold is determined. Spot luminance assumes fivedifferent values, differing from one another by steps of0.1 log units, in order to cover the range where visionis uncertain. For each value, 15 responses are recorded.Threshold is estimated from the plot of perceptionprobability vs log luminance. The subject is emme-tropic and highly experienced in visual experiments.

EXPERIMENTAL FINDINGS

Figure 1 shows the luminance-time relationshiprecorded at 100. As expected, it approximates thatpredicted by Bloch's law. That is, total integrationtakes place up to durations no greater than 100 Ins.Then, partial summation takes place. The slope of theplot, throughout this range, is about 0.58. This agreeswith the result reported by Connors'6 for stimuli ofsmall subtense. Figure 2 refers to an eccentricity of400. Total integration time attains about 70 ins. Theslope of the branch covering the range of partial sum-mation is 0.51. At 600, the plot clearly shows a totalintegration time briefer than the minimum durationhere considered, that is, 10 ins. The slope of the long-duration branch [Fig. 3, plot (a)] is about 0.30.

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During the course of the sessions, the subject reportssome changes of the appearance of the target from onetrial to the next. This may be due to spontaneousfluctuation of accommodation." In some trials, thetarget appears streak-like, either horizontal or vertical,or even oblique. In others, it appears as a patch withfuzzy contours or like an intense point surrounded bya diffuse halo. Multiple patterns are also perceived. Inorder to minimize the effects of this source of varia-bility, the retinal image was suitably modified, with theaid of lenses. These were fitted in a special frame. Inorder to avoid the oblique-ray astigmatism of the lensitself, it was placed perpendicular to the line joiningthe test spot to the center of observer's pupil. In thisway, the fixation light is viewed by the naked eye.

Let us consider first the case in which the image isdrastically brought out-of-focus with the aid of a +3-diopters spherical lens. Under these conditions thesubject perceives a large and blurred image. The log

' + t + tluminanceXtime product increases with stimulus dura-0 0 0 0 0 0 0 tion as shown in Fig. 3, plot (b). These data indicateIn r- o Ln o o 0

- N ' ( that, under the conditions described, partial summationD U R AT I0 N - s takes place in the range for duration 10-400 Ins. The

iminanceXtime product vs stimulus slope is now 0.21.Eccentricity, 100 nasal. When a +3-diopters cylindrical lens is used, which

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December 1971 THRESHOLD AND CORRECTION OF ASTIGMATISM

produces a long streak-like pattern, the situation is asshown in Fig. 3, plot (c). The slope is now 0.46.

Apparently, the natural viewing condition corre-sponds to an intermediate situation between the twoextreme cases. This might be due to the change fromone pattern to another, according to the state ofaccommodation.

Thus, confirming some data previously reportedby us,'8 the peripheral retina is characterized by verybrief total integration times.

We then tried to correct oblique-ray astigmatism byuse of crossed cylinders of suitable powers and orien-

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tations. The percept of a point-like target was theo (a ) criterion for the choice of the power of the correcting

lenses. Note, however, that the correction as a functionof eccentricity is ineffective if the subject's attitude isnot relaxed, when, presumably, accommodation fluc-tuates strongly.

As shown in Figs. 4 and 5, the luminance-timerelation, at 50° and at 600, shows a total integrationtime as long as 1 s, and the slope of the long-durationbranch equals unity. The powers of the two cylindricallenses used for the dioptric correction, at 60°, are

,D (b) +0.5 diopter, horizontal axis, and - 1.25 diopters,vertical axis.

Figure 6 shows some data recorded under naturalviewing conditions, at various eccentricities. Each

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FIG. 5. Logarithm of luminanceXtime product vs stimulusduration, recorded at an eccentricity of 600 after correction ofoblique-ray astigmatism.

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LUCIA RONCHI

We might infer that the properties of the big re-40 ms ceptor units, far from the fovea, are not spatially

uniform. Perfect linear summation of subliminal stimulitakes place over their core, whereas the summationover the area surrounding it is not linear. Let us recallthat nonlinearity of temporal integration, within the

looms limit of the currently adopted critical duration, issuggested by Battersby and Schuckman,'9 under someexperimental conditions at least.

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curve refers to a test flash of a given duration; at anyeccentricity, pupil area was corrected in order to takeinto account the change of the entering flux, accordingto the cosine of the incidence angle. For brief durations,say, below 16 ins, threshold luminance is more or lessconstant across the retina. For long flashes, thresholdluminance increases with eccentricity when it exceeds,say, 35°.

After correction of oblique-ray astigmatism, sensi-tivity is practically constant, whatever the eccentricity,when flash duration is brief. For long-duration flashes,on the other hand, sensitivity increases as eccentricityis increased. This is the case, for instance, for the 400-msflash, as shown in Fig. 7.

DISCUSSION

The correction of oblique-ray astigmatism increasesboth the total integration time and the slope of thelong-duration branch of the luminance-time rela-tionship.

The nature of the reported changes is the same asthat found for central and paracentral vision, when thetest flash becomes less than receptive-field size."6 Thus,it is as if the correction of oblique-ray astigmatismrenders the minimal-blur disk smaller than the retinalunit. This is not expected, because the estimate of theapparent length of the astigmatic pattern,'" beyond400, does not exceed 50'. Also the receptive-field size,estimated by extrapolating data available"3 up to 400,should be no less than 1°.

aberrations might be responsible for the known abilityof the peripheral retina to detect time changes ofstimulation.

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ECCENTRICITYFIG. 7. Log test-spot luminance, at threshold, vs eccentricity,

in the far periphery, after correction of oblique-ray astigmatism.Flash duration, 400 ms. Cosine correction for pupil area wasapplied.

I; . Let us consider now the variation of sensitivity across. 6 the retina. Data shown in Figs. 6 and 7 confirm the

expectations. 2 - 4 As stimulus duration increases, sensi-

tivity decreases when total integration time decreases.Accumulation of subliminal stimuli takes place withinthe critical duration. The longer the stimulation,

- 12.5 ms beyond this limiting value, the less opportunity seemsto exist for linear summation within the receptors, so

5- lms that the stimulus becomes less efficient.2 0

I We emphasize that correction of oblique-ray astig-50° 600 matism is advantageous in some respects (by increasing

)lute threshold, v critical duration it leads to an increase of sensitivity),i. Cosine correction but it is detrimental in others. Critical duration isder natural viewing directly related to the temporal unit response, which,

in turn, is inversely related to the time-resolving power.In other words, it is as if the existence of off-axis

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THRESHOLD AND CORRECTION OF ASTIGMATISM

This is shown by the data reported below. The dark-adapted retina is presented with an intermittentstimulus, at a rate of 2 cps, test-spot size being 6'.First, the absolute threshold is determined. Then,luminance is increased by small steps, and the taskconsists of describing what is seen. Just above threshold,the observer perceives an irregular time distribution ofbrightness, probably due to Poisson-like fluctuationof quantal content of the beam. When the spot lumi-nance exceeds a given value, the situation changes,and the observer perceives the typical sensation offlicker. Let us recall that light adaptation involves adecrease of the duration of the unit response.2"

Under natural viewing conditions, at 600, the ratioof flicker-threshold luminance to absolute-thresholdluminance is about 5. After correction of oblique-rayastigmatism, this ratio becomes as great as 10. Thehypothesis that differences of summation might beascribed solely to differences of receptor density is notacceptable,3 because mechanisms located at levels morecentral than the retina are known to be also involved.' 9

REFERENCES

' L. L. Sloan, Am. J. Ophthalmol. 30, 70 (1947).2 G. Meur, Vision Res. 5, 435 (1965).3 N. R. Bartlett, in Vision and Visual Perception, edited by

C. H. Graham (Wiley, New York, 1965), p. 154.4 M. H. Pirenne, in The Eye, edited by H. Davson (Academic,

London, 1962), Vol. 2, p. 160.5 B. N. Kishto, Vision Res. 10, 745 (1970).6 E. Baumgardt, J. Gen. Physiol. 31, 269 (1948).7 K. N. Ogle, J. Opt. Soc. Am. 51, 862 (1961).8 G. A. Fry, Blur of the Retinal Image (The Ohio State Uni-

versity, Columbus, 1955).9 Y. Le Grand, Optique Pihysiologique (Ed. de la Rev. d'Opt.,

Paris, 1955), Vol. 3, p. 136.'0 A. Ames and C. A. Proctor, J. Opt. Soc. Am. 5, 22 (1921)."Reference 10, p. 139.12 E. P. Hallett, Vision Res. 3, 9 (1963).13 V. P. Glezer, Vision Res. 5, 497 (1965).14 G. Osterberg, Acta Ophthalmol. Suppl. 6 (1935).15 L. Ronchi and 0. Novakova, Atti Fond. G. Ronchi 25, 402

(1970).16 M. M. Connors, J. Opt. Soc. Am. 60, 958 (1970).17 M. Millodot, Vision Res. 8, 73 (1968).18 L. Ronchi and 0. Novakova, J. Opt. Soc. Am. 61, 115 (1971).19 W. S. Battersby and H. Schuckman, Vision Res. 10, 263

(1970).20 R. M. Boynton and R. S. Das, Science 154, 1581 (1966).21 G. Sperling and M. M. Sondhi, J. Opt. Soc. Am. 58, 1133

(1968).

NOBEL PRIZES

Gerhard Herzberg, Ives Medalist, an Honorary member of the Optical Society ofAmerica, has been awarded the Nobel Prize in Chemistry for his contributions to theknowledge of electronic structure and geometry of molecules, particularly free radicals.A review of Dr. Herzberg's new book, Spectra and Structures of Simple Free Radicals: AnIntroduction to Molecular Spectroscopy, appears on p. 1718.

The Nobel Prize in Physics was at the same time awarded to Prof. Dennis Gabor, forhis invention of holography.

1 709December 1971