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Relation between border enhancement extent and retinal image blur
RELATION
BETWEEN BORDER ENHANCEMENT AND RETINAL IMAGE BLUR
EXTENT
ARM_!LFREMOLE School of Optometry. University of Waterloo, Waterloo. Ontario. Canada (Receicrd
16 Noremher 1973)
bright field on a dark ground is perceived as having a region ofenhancedbrightness adjacent to its borders. The spatial extent of this region is compared with the extent of blur of the borders m the retinal image. In agreement with Mach band theory. the two variables are found to be closely related. Only for large entrance pupils is the enhancement extent markedly smaller than half the blur zone. It is suggested that this is because it follows the physiologically effective bortion of the blur zone rather than the oblique incidence light constituting the periphery of the optical spread. Abstract-A
INTRODUCTION
A sharp stimulus border between two levels of luminance will have as its retinal correlate a finite transition zone between two levels of illuminance. This blur of the retinal image has been extensively investigated (Fry. 1955. and Ogle. 1960, for example). Within a certain range of defocus of the retinal image, the neural processes of the visual system will transform the blur to a perception of a sharp border. Thus, the extent of blur of the retina1 image cannot be perceived or measured directly. However, there are methods of obtaining an indirect measure, such as for example using the contrast threshold of visibility (Ogle, 1960). This study explores a new approach for estimating the blur of the retinal image. The method originates in observations of the border contrast phenomenon. This, as is well known. consists in that the contrast between a light and a dark area is enhanced immediately along their border. This is generally thought to be due to neural processing of the retinal image (RatIiff and Hartline. 1959; Ratliff, Hartiine and Miller, 1963; Motokawa. 1970).The increased brightness is easier to observe than the complementary increase in darkness. Preliminary observations will demonstrate that the enhanced region will increase slightly in extent when the retinal image is thrown out of focus. This increase is observable even for small amounts of defocus within the depth of focus. when no blur is perceived. While the visual system cannot perceive a slight blur of the retinal image. it can perceive the expansion of the accompanying border enhancement. That the extent of border enhancement does increase with defocus is quite compatible with the general Mach band concept. If the transition zone between the two levels of retinal illuminance is ap-
’ BSsg (19601experimented with a large range of transition zone widths at the stimulus level, including abrupt changes in luminance.
proximately sigmoidal. one would. on this theory. expect the neural system to enhance the brightness or darkness where the zone exhibits the greatest rate of change in illumination. Since this is likely to occur at the extremeties of the zone. the enhanced brightness seen along a border would thus constitute a rough demarcation of the upper end of the zone. The further assumption is made that the radius of discontinuity between the uniFormly illuminated level and the slope of the transition zone is small enough for such an effect to occur; if the discontinuity is too gradual. there witI be no enhancement (BekCsy. 1960).That the border enhancement is a Mach band and that it demarcates the extent of retinal blur is the hypothesis around which this investigation is centered. The stimulus consisted of a luminous rectangular field on a dark ground. The vertical borders of the field could be manipulated through a manual control so as to bring the enhanced regions associated with them in juxtaposition. These regions would appear to touch or merge when the field width was double the enhancement extent. This method of observing enhancement effects has been described in previous articles (Remole, 1970. 1973). The general stimulus and response situation is shown schematically in Fig. IA. where (a) represents a cross section of the stimulus luminance distribution, and (b). the hypothetical retinal distribution. (c) is a sketch of what the subject perceives. and (d) is a cross section of the perceived brightness. Figure 1H is identical to Fig. IA except that it shows the stimulus and response situation as the border enhancements are brought together to almost merge. Figure IC has been introduced merely to clarify the hypothesis and does not represent a stimulus and response situation studied in this experiment. Here. in accordance with the customary procedure of demonstrating Mach bands’. a gradual transition between two luminance levels has been introduced at the stimulus level. Except that the transition zone is much larger than that generated by
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the optical system of the eye when it is presented with a sharp border, the interpretation of the diagrams is the same as for the other figures. The working hypothesis is that the situation in Figs. IA and B is essentially the same as in C. There are, of course. differences between the two situations. Firstly. the transition zone represented by optical blur is of a relatively small order of magnitude. Furthermore, in this experiment, the situation is complicated by the visual interpretation of the transition zone as a sharp border for small amounts of defocus. The response situation is thus not just a miniature replica of that shown in Fig. 1C. As a matter of fact. the observed effect is often more like a bright halo extending from the border into the brighter of the two areas. Only with a sufficiently large amount of defocus is there a barely noticeable drop in brightness between the enhanced region and the more or less blurred border. The most prominent part of the enhanced region is not its peak, but its termination. It is the terminations of the two enhanced regions that the subject brings together when obtaining a measurement of the enhancement extent. More specifically, the hypothesis presumes that the border. when perceived as sharp, corresponds to the centre of the transition zone of the retinal image. A measure of the enhanced region as obtained by the method described would thus be a function of half the transition zone, as indicated in Fig. 1A and B. The same interpretation of the enhanced region holds when the defocus is so large that the border is perceived as blurred. The half of the transition zone that corresponds to the dark portion of the stimulus shows a continuous drop in brightness. Before a uniform level of darkness is reached, there is a region of deeper darkness, much in keeping with the hypothesis. However, this effect is much less pronounced than the corresponding brightness enhancement. Moreover, it does not lend itself to the methods used in this experiment. Therefore, only the brightness enhancement is considered in this paper. Although the measurements obtained by the subject would be a function of one half of the transition zone. they would obviously not be an exact measure of this. Rather. one would expect them to be somewhat larger, since the subject is making his judgment by the terminations rather than the peaks of the enhanced regions. To determine if the region demarcated by the border enhancement in fact is a function of the transition zone, measurements of this region were compared with estimates of the blur region of the retinal image. In a first experiment. the blur of the retinal image was controlled by varying the amount of retinal defo~u_s,the dioptral value of the stimulus serving as the independent variable. In a second experiment, the blur was varied by using the entrance pupil size as the independent variable, the amount of defocus being kept constant. In each experiment, the enhancement extent and the retinal blur were plotted. in terms of visual angle.
REMOLE
against their common independent ~ar)abk so what they could be compared with respect to magnitude. APP&RATUS AND METHOD
Figure 2 shows a plan of the apparatus. The rectanguiar observation field consisted of translucent material set in an opaque ground and uniformly transilluminated by tungsten light. The horizontal dimension of the field could be varied from about 12” at the eye to zero through a control operated by the subject. The subject would decrease the field width from its maximum size until the enhanced regions appearing along the vertical borders appeared to just touch. The extent of the enhancement was then registered mechanically on a micrometer gauge. This part of the apparatus was esscntially the same as described in previous articles (Remolr. 1970. 1973). In order to avoid after-image effects from thr: narrowed-down field comprising the two border enhancements. ample time was given between measurements. Also, each measurement was initiated with a sudden presentation of the maximum aperture. To measure the degree of defocus of the retinal image a Badal optometer arrangement was incorporated in the apparatus. A + 1040 D lens was placed with its optic axis perpendicular to the fixation axis. A point target travelling along the optic axis of the lens was superimposed on the observation held via a ~m~si~vered mirrk. The target was small enough to be seen only when approximately conjugate with the retina, when it would appear as a sharp point slightly brighter than the observation field. It was iltu. minated via a fibre optics channel receiving light from the rear of the field. Thus. except for the effect of the absorptive qualities of the tibres. the wavelength composition of the target was identical to that of the field. Measured through the semisilvered mirror. the luminance of ttie fidd was 10 cd/m’. The optometer scale was calibrated in dioptres. For each subject. the scale was adjusted so that the xro point was
PF
Fig. 2. Schematic diagram of apparatus. TS, tungsten source; P. projector; S, opal screen; A, variable aperture: AC. aperture contro1; MC. micrometer gauge; LB. lens battery; OL, optometer lens; SM, semisilvere~ mirror; OC. optometer control; DS. dioptral scale; AP. artificia! pupil; OD. right eye: OT, optometer target; PF. perceived field; FO. fihre optics channel
Border enhancement and retinal image blur conjugate with the retina when a lens battery in front of the eye produced an in-focus retinal image of the borders. When negative or positive blur of the borders was introduced, its dioptrai amount could be read from the optometer scale. For example. during negative blur. the optometer target was perceived only for a certain position beyond the zero point. In general. the subject started by first moving the optometer target in from a position beyond that conjugate with the retina until the target first appeared sharp. and its dioptral distance from the zero point was recorded. A similar reading was then obtained by moving the target away from the eye, this time starting from a position well within the plane conjugate with the retina. The dioptral midpoint of the range defined by the two readings was taken to represent the point conjugate with the retina. At all times was the subject concentrating on the field and its borders rather than the optometer target. In the first experiment. an artificial pupil of 3 mm dia was placed approx 8 mm from the cornea1 plane, behind the subject’s correction. In order to minify accommodative changes and interference from pupil constriction, the ciliary muscle and sphincter pupillae were paralyzed with @5 per cent tropicamide. The vergence of the light from the observation field at the plane of the artificial pupil was controlled by lens powers before the eye presented in quarter dioptre steps from -4.75 D to + 3.00 D. With no lenses. the vergence was - 3.00 D. Thus. a + 3.00 D lens power would produce zero vergence. In recording the incident vergence at the eye, no adjustment was made for the change in effectivity between the lens battery and the principal planes of the eye. For incidence vergences in the order of 1.00 D this would introduce an error in the measurement of the retinal blur of approx 0.01 D. Only towards the ends of the range, for values beyond 3.00 D, would the discrepancy approach 0.10 D. The discrepancy was considered to be of Little significance for this experiment. When a cycloplegic agent is used. a small amount of residual accommodative power will remain. In this experiment. the independent variable was the incident vergence provided by the dioptral value of the distance of the observation field plus the lens powers in front of the eye. However, another factor is the stimulation to accommodation inherent in the perceived nearness of the observation field, usually referred to as proximal stimulation. This activated some of the residual accommodation with the result that the zero point of the optometer setting did not correspond with zero incident vergence at the ametropic correction, The amount ofaccommodation thus activated varied with the S. amounting to 0.75 D for LH. I.00 D for AR. and 0.50 D for S MG. This amount had to be taken into account when the zero point of the optometer scale was to be placed in conjugation with the retina. That is, the lens power that produced the best focus of the observation field had to be found empirically. Since there is a dioptral range through which the borders will appear clear, the dioptral midpoint of this range was assumed to represent the best focus. The end points of the range were determined by increasing or detreasing lens power until a firs: perceptible blur of the borders appeared. In conjunction with the defocus measurements. findings were taken for the enhancement extent. using the method ’ The nodal points were chosen merely for optical convenience. The implication is not that these are centres of projection. a role which is better ascribed to entrance and exit pupil points.
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described in the introduction. Thus. for each of the three Ss tested five sets of data comparing retinal blur with enhancement extent were obtained. the incident vergence serving as the independent variable. The two dependent variables were converted to minutes of arc subtended at the eye and plotted on a common scale. Ss LH and MG had no training in this kind of observation whereas S AR had considerable training. The respective right eye distance corrections for Ss LH. AR and MG were -0.50 D. -4.00 D and -2.25, - 1~75x 180 All had normal vision with correction. Conversion of the enhancement extent into visual angle subtended approximately at the first nodal point constitutes no problem. Similarly. for large amounts of defocus. simple geometry based on the assumption that all rays pass through the paraxial focus will give a good approxtmation of the blur region. which can then be converted to visual angle subtended at the second nodal point.’ However. for small amounts of defocus, the proportion of the blur contributed by aberrations and diffraction effects becomes signiflcant. When the retinal image is optimally focused. there is a minimum blur contributed solely by these factors. To derive the extent of the transition zone between two levels of retinal illumination. these factors were considered together with the blur contributed by rays intersecting in the paraxial image plane. A formula introduced by Ogle (19601was used for this purpose:
In Ogle’s work, .: is the radius of the blur circle when a point object is used, 2” is the radius of the minimum blur circle, fis the reduced focal length of the eye. and Q is the amount of dioptral blur. In this paper. ,I represents half the transition zone rather than the blur circle radius. and z,). half the width of the minimum zone. Figure 3 is a sketch of one branch of the hyperbola described by the formula. similar to that presented in Ogle’s work. In the present study, the value of 16.78 mm was assumed for the reduced focal length, and the same value was assumed for the distance between the second nodal point and the retina (Bennett and Francis, 1962). The specification of the nodal point in converting retina1 blur to visual angle is. of course. much more critical than for the corresponding conversion of enhancement extent. where the distances involved are relatively large. In Fig. 3, the asymptotes represent the extent of retinal blur when aberrations and diffraction effects are ignored. The hyperbolic branch representing ; shows the blur when
Fig. 3. Function representing relation between optical blur and optical defocus.
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AKNLLFR~MOLL
these factors are included. There is no simple method of estlmating z,,. the minimum blur. with certainty (Ogle. 1960): its choice will have to be subject to some arbitration. Thus. whereas a good approximation can be obtained for blur caused by relatively large amounts of defocus. the estimate becomes increasingly hypothetical as the importance of zi, increases towards optimum focus. It was stated as a part of the working hypothesis that the enhancement extent would be expected to be somewhat larger than the dioptral blur. This is borne out quite well for large values of defocus. The minimum blur was chosen so that this would be true also for small amounts of defocus. Thus. it was chosen to conform with the ratio between enhancement extent and dioptral blur as found for the larger amounts of defocus. To estimate a value for this ratio. the three pairs of dependent variables at each end of the stimulus range were used. This does not, however. imply that such a constant ratio throughout the range is necessary for our hypothesis; it is merely a convenient way of presenting the data. On the other hand, there is no reason to believe that the ratio, even near zero defocus, deviates very greatly from a true one. It is worth noting that the values obtained for the minimum blur using the criterion just described are fairly consistent with values found by other authors for the minimum blur circle radius (Ogle, 1960). In the second experiment, the primary independent variable was the entrance pupil size. Whereas in the first experiment it had been a constant 3 mm dia aperture placed about 8mm in front of the cornea, the aperture was no% varied through a range of from 1 to 8 mm in dia, in I mm increments. The estimates for minimum blur used for deriving the size of the blur zone were those obtained in the first experiment, for the 3mm pupil. Since not enough was known about the aberrational characteristics of the eyes tested. variations in minimum blur due to the changes m entrance pupil size were not considered in this experiment. Results were obtained not only for the in-focus condition. but also for negative and positive defocus of 3JXl D. For the t%o situations where the retinal image was out of focus. and for the larger size entrance pupils, the estimated minimum blur would play a minor part in determining the size of the transition zone. As in the first experiment, five sets of data were obtained from each subject.
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Fig. 5. Relation between enhancement extent (0 l a) and optlcai blur (x x x 1in terms of half the transifibn zone. The independent variable is the vergencc at the artificial pupil. (000) represents a secondary band recognized h! some observers.
48). In Fig. 4, the interpretations of parts (a). fb). (c) and (d) are the same as in Fig. 1 (c) and (d) are typical subjective renderings of the response. The band more proximal to the border, contrary to the more distal band. is small enough to invite an explanation in terms of diffraction effects. At the time, it was not entirely certain which band should be taken as representative of the hypothesis. and measurements were therefore taken for both bands. Findings for the two types of
The proximal, narrower band (0 0 0) IS much more difficult to recognize than the broader band (a 0 (1 ). Sometimes it can be recognized oniy after the distal bands have been brought together for measurement and have appeared to merge. One S (LH) could recognize no such secondary band even after numerous trials. When findings are obtain&d for the proximal band. it is with considerable difficulty from the Ss point of view. Findings beyond the ranges shown in Fig. 5 were not possible_ Like the distal band, the proximal band does increase with defocus. but it lies always well within the function describing half the transition zone ( x x 2 ). This is true also for the end vaIues of the range obtained, where the estimates of the transition zone can be considered quite good. Thus. there should be little doubt that it is the distal, more easily perceived band that must be considered as pertinent to the hypothesis. A further exploration of the proximal band will not be pursued in this paper. Some other complications pertaining to the perception of the border enhancement need to be Considered. During negative defocus the distal bands are easily seen and measured. However, if tbey are brought past the distance at which they appear to touch, a dark region will develop in the centre of the fteld (Fig. 4C). This begins as a thin dark Iine when the border separation is about half that yielding a measurement of the enhancement extent. &cause it occurs only when the overlap of the original bands is considerable, it does not interfere with the type of measuremenfs performed in this study. It does, however. make impossible ai-0
border enhancement. together with findings tral blur. are shown in Fig. 5.
measurement of the proximal bands just discussed. even when these arc seen initially. The drop in bright-
RESULTS AND DISCUSSION
Quulitatice
obseraations
During the course of the experiment, it became evident that the response situation is not quite SO simple as presented in the introduction. Thus, sometimes a second band. much narrower than the first. would appear near the border. The effect occurs both during positive defocus (Fig. 4A) and negative defocus ~IFig.
for diop-
Border enhancement and retinal image blur ness of this dark band is much greater than the undulations of light and dark typical of the border effects under investigation. The relative darkness of this central band necessitates a more complex distribution of light in the transition zone than a simple sigmoid. It could be explained in terms of fundamental blur circles whose cross settion have a bimodal distribution, such as indicated in Fig. 4B (b) with a dotted line. When the borders are relatively far apart. this would make relatively little difference in the distribution except that the transition zone would be stepped rather than smooth [Fig. 4B (b)]. The blurred transition between light and dark observed during negative defocus is, in fact, less smooth than a corresponding zone observed during positive defocus. Such a step might be seen as a secondary band but would not be as bright or as pronounced as the band demarcating the termination of the transition zone. It is only during considerable overlap of the blur circles corresponding to the borders that the added effect of their central depressed areas would be great enough to introduce a depression in the retinal illuminance distribution. A simplified interpretation of this hypothesis is shown in Fig. 4C (b). where two overlapping blur circles are shown with dotted lines and their summed effect with a solid line. That the formation of the dark band begins when the border interdistance is approximately one half transition zone in angular extent agrees rather well with this interpretation. Quantitative observations
Thus, it appears that the complications described do not interfere unduly with the testing of the original hypothesis. Figure 5 summarizes the results of three Ss for enhancement extent (0 l l ) and calculated values of half the transition zone (x x x ). Except for the extreme end values, each plotted point represents the moving average of findings for three consecutive values of the independent variable, and thus constitutes the mean of 15 responses. A range of two SE. of the mean, one above and one below the plotted point, has been shown for the in-focus condition and for positive and negative defocus in the order of 3.00 D. Where the functions overlap the error bars for retinal blur are shown in insets. The vertical arrows indicate points of first perceptible blur of the borders. For all subjects, the enhancement extent follows the function representing half the transition zone. In two of the Ss, LH and AR, the expectation is borne out that the enhancement extent is somewhat larger than half the transition zone. In the third .S,GM, the two dependent variables practically coincide. Although these subjective differences between enhancement and blur could stem from genuine physiological differences. other factors are probably more important. For example. there may be significant differences in the interpretation of the criterion used for measuring enhancement. Also, individual values for the constants of the eye were not determined. For
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example, if the true position of the posterion nodal point deviates considerably from the standard value used, the calculations of retinal blur would be affected: a deviation of 1 mm would result in an error of approx 5 per cent. Figure 6 shows the results of the second experiment. where the artificial entrance pupil is the chief independent variable. For the out-of-focus condition. this is an alternative way of varying the retinal blur. The method of plotting the data is similar to that used for the first experiment. the functions being smoothed out somewhat by using moving averages for three consecutive pupil sizes. The results are similar to those in the first experiment in that the enhancement extent follows the blur extent. However, there are some deviations from the rather simple picture presented by the results from the first experiment. For large values of the entrance pupil. during out-of-focus conditions, the size of the enhancement region approaches or even drops below that of the calculated blur. This is not surprising if one considers the oblique incidence of peripheral rays and their reduced effectivity in stimulating the retina. such as is exemplified in the Stiles-Crawford effect. The enhancement extent would obviously follow the narrower portion of the transition zone representing the summation of the smaller, more effective portion of each fundamental blur circle. The enhancement extent may thus be a better indicator of changes in the effective transition zone than calculations based on optical considerations only. The decreasing slope of the function for enhancement as compared to calculated blur is evident with all the subjects (Fig. 6). However, for subject GM. the enhancement is smaller than the blur even for the 3 mm pu,pil identical to that used in the first experiment. This apparent discord between the two experiments needs some clarification. For two subjects, AR and MG. the enhancement extent in the second experiment is, for the out-of-focus condition, somewhat smaller than in the first experiment for the same pupil size and defocus. In subject LH, the discrepancy is in the opposite direction. To show the magnitude of this deviation, values from the first experiment with their accompanying error bars have been introduced in Fig. 6. The bars pertain to the results from the first experiment even when they appear to coincide with the functions obtained in the second experiment. The explanation for the often statistically significant discrepancies must lie in the inevitable differences in stimulus sequence and context for the two experiments. For example. the distribution of light in the blur accompanying changes in entrance pupil size is different from that accompanying changes in optical defocus. It is possible that the retinal adaptation effects had not been eliminated entirely, in which case there would be slight differences in the retinal pre-adaptation pattern for the two experiments. However, one would then expect the discrepancy to be of the same direction in all three subjects. A more plausible explanation is that
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Fig. 6. Relation between enhancement extent (00 l ) and optical blur ( x x x ) in terms of half the transition zone. The chief independent variable is the entrance pupil diameter.
the differences in context of the two experiments have some effect on the criterion used for the measurements. This highly subjective factor would seem to leave room for individuat. variations in this respect. In S MG. where the difference between enhancement and biur is small in the first place, even a small depression in the findings for the enhancement would cause them to drop below those for the calculated blur. Although the relation between enhancement and blur is not so simple as suggested in the original hypothesis, the fact remains that the two variables follow each other closely when the entrance pupil is about 3 mm in dia, that is. large enough to minjfy diffraction effects and small enough to eliminate relatively oblique rays. It is only when the pupil is relatively large that the enhancement deviates greatly from the calcufated blur. This indicates that the enhancement extent is a function of the physiologically effective portion of the blur zone rather than its optical spread.
REFEREYCES Bekesy G. von. [ 1960) Neural inhibitory untts of the eye and skin. Quantitative description of contrast phenomena. J. cyr. sec. Ill!. so, lO6@ 1070. Bekesy G. ran. (1972) Mach bands measured by a compensation method. l’ision Rrs. 12. 1485-1497. Bennett A. G. and Francis J. L. (1963) The eye as an optical sqtcm. In 7‘/1<~ Erc, (Edited h! Davison H). Vol 4. pp. IO-- 131. Academic Press. New York. Fry G. A. (I 955)Blur of t/w Rrrid /rmq~~. The Ohio Stale University Press, Columbus. Motokawa K. (1970) Physioloyr @Color unJ Partern I’ision. lgaku Shoin Ltd., Tokyo; Springer, Berbn. Ogle K. N. (1960) Bfurring of the retinal image and contrast thresholds in the fovea. J. o/rr. Sot. ARI.!#I; 307-315. Ratliff F. and Hardine H. K. (1959) The response ofIimul~ optic nerve fibers to patterns of ilium~~tiun on-the rccepfor mosaic. J. ~~L’IT. PliysioL 42, f24i-1255. Rat18 F.. Harthne H. K. and Miller W. H, (1963) Spatial and temporal aspects of retinal inhibitory interaction. J. oyr. sot*. .41tr.53, 1I(f 130. Kemole A. ( 1970) Spatial characteristics of the border enhancement region in a flickering field. Anr. J. Qprotu- 4’1. 779 786. Remole ,A.(1973) Extended border enhawement during intermittent iltustration: binocular effects. livin,r Rl,\. 13,
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Border enhancement
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&sum&On percolt un champ brillant sur fond sombre avec une rigIon de lummosite accrue adJ;Iccntc au bord. On compare I’extension spatiale de cette rigion B celle de flou au bord de I’image rktmlenne. En accord avec la thkorie des bandes de Mach. on trouve une relation ktroite entre ces deux varlableh. Ce n’est que pour de tres grandes pupilles que I’accroissement de luminosit-4 s‘ktend nettement mom\ que la molti de la zone de Aou. On suggere que cela provient du faalt que I’acrolssement suit la portion phvsiologiquement efficace de la zone de Rou et non la lumitre &incidence oblique qua constltue la p&iph&e de I’extension optique.
Zusammenfassung-Bei einem hellen Feld auf einem dunklen Grund nimmt man entlang dcr Kant einen Bereich erhahter Helligkeit wahr. Die riiumliche Ausdehnung dieses Bereiches wird mlt &I Kantenunschiirfe des Netzhautbildes verglichen. Die beiden Griissen sind, iibereinstimmend mit dcr Theorle der Machschen Streifen. eng korreliert. Nur bei grossen Eintrittspupillen 1st der Bereich dn Helligkeltsiiberhiihung kleiner als die halbe Unschiirfe. Das kdnnte dadurch erkliirt herden. dass mhr der ph>siologisch wirksame Teil des Unschiirfebereichs entscheidend ist. als das schriig elnfallendc Licht. das den Rand der optischen Unschiirfe ausmacht.
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Fig. 1. Sketch of the general stimulus and response situation, (a) Cross section of stimulus luminance distribution; (b) hypothetical retinal illuminance distribution; (c) field as seen by subject: (d) cross section of subjective brightness distribution. A: General situation with enhancement produced along two vertical borders. B: The enhanced regions being brought together to touch. C: Similar situation with a sloping transition zone introduced at the stimulus level.
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Fig. 4. Sketch of the general stimulus and response situation based on observations during defocus. Interpretation of (a), (b), (c) and (d) as in Fig. 1. A: Positive defocus. B: Negative defocus. C: Special effect of overlapping enhancement regions during negative defocus.
BETWEEN BORDER ENHANCEMENT AND RETINAL IMAGE BLUR
EXTENT
ARM_!LFREMOLE School of Optometry. University of Waterloo, Waterloo. Ontario. Canada (Receicrd
16 Noremher 1973)
bright field on a dark ground is perceived as having a region ofenhancedbrightness adjacent to its borders. The spatial extent of this region is compared with the extent of blur of the borders m the retinal image. In agreement with Mach band theory. the two variables are found to be closely related. Only for large entrance pupils is the enhancement extent markedly smaller than half the blur zone. It is suggested that this is because it follows the physiologically effective bortion of the blur zone rather than the oblique incidence light constituting the periphery of the optical spread. Abstract-A
INTRODUCTION
A sharp stimulus border between two levels of luminance will have as its retinal correlate a finite transition zone between two levels of illuminance. This blur of the retinal image has been extensively investigated (Fry. 1955. and Ogle. 1960, for example). Within a certain range of defocus of the retinal image, the neural processes of the visual system will transform the blur to a perception of a sharp border. Thus, the extent of blur of the retina1 image cannot be perceived or measured directly. However, there are methods of obtaining an indirect measure, such as for example using the contrast threshold of visibility (Ogle, 1960). This study explores a new approach for estimating the blur of the retinal image. The method originates in observations of the border contrast phenomenon. This, as is well known. consists in that the contrast between a light and a dark area is enhanced immediately along their border. This is generally thought to be due to neural processing of the retinal image (RatIiff and Hartline. 1959; Ratliff, Hartiine and Miller, 1963; Motokawa. 1970).The increased brightness is easier to observe than the complementary increase in darkness. Preliminary observations will demonstrate that the enhanced region will increase slightly in extent when the retinal image is thrown out of focus. This increase is observable even for small amounts of defocus within the depth of focus. when no blur is perceived. While the visual system cannot perceive a slight blur of the retinal image. it can perceive the expansion of the accompanying border enhancement. That the extent of border enhancement does increase with defocus is quite compatible with the general Mach band concept. If the transition zone between the two levels of retinal illuminance is ap-
’ BSsg (19601experimented with a large range of transition zone widths at the stimulus level, including abrupt changes in luminance.
proximately sigmoidal. one would. on this theory. expect the neural system to enhance the brightness or darkness where the zone exhibits the greatest rate of change in illumination. Since this is likely to occur at the extremeties of the zone. the enhanced brightness seen along a border would thus constitute a rough demarcation of the upper end of the zone. The further assumption is made that the radius of discontinuity between the uniFormly illuminated level and the slope of the transition zone is small enough for such an effect to occur; if the discontinuity is too gradual. there witI be no enhancement (BekCsy. 1960).That the border enhancement is a Mach band and that it demarcates the extent of retinal blur is the hypothesis around which this investigation is centered. The stimulus consisted of a luminous rectangular field on a dark ground. The vertical borders of the field could be manipulated through a manual control so as to bring the enhanced regions associated with them in juxtaposition. These regions would appear to touch or merge when the field width was double the enhancement extent. This method of observing enhancement effects has been described in previous articles (Remole, 1970. 1973). The general stimulus and response situation is shown schematically in Fig. IA. where (a) represents a cross section of the stimulus luminance distribution, and (b). the hypothetical retinal distribution. (c) is a sketch of what the subject perceives. and (d) is a cross section of the perceived brightness. Figure 1H is identical to Fig. IA except that it shows the stimulus and response situation as the border enhancements are brought together to almost merge. Figure IC has been introduced merely to clarify the hypothesis and does not represent a stimulus and response situation studied in this experiment. Here. in accordance with the customary procedure of demonstrating Mach bands’. a gradual transition between two luminance levels has been introduced at the stimulus level. Except that the transition zone is much larger than that generated by
989
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ARUL~LF
the optical system of the eye when it is presented with a sharp border, the interpretation of the diagrams is the same as for the other figures. The working hypothesis is that the situation in Figs. IA and B is essentially the same as in C. There are, of course. differences between the two situations. Firstly. the transition zone represented by optical blur is of a relatively small order of magnitude. Furthermore, in this experiment, the situation is complicated by the visual interpretation of the transition zone as a sharp border for small amounts of defocus. The response situation is thus not just a miniature replica of that shown in Fig. 1C. As a matter of fact. the observed effect is often more like a bright halo extending from the border into the brighter of the two areas. Only with a sufficiently large amount of defocus is there a barely noticeable drop in brightness between the enhanced region and the more or less blurred border. The most prominent part of the enhanced region is not its peak, but its termination. It is the terminations of the two enhanced regions that the subject brings together when obtaining a measurement of the enhancement extent. More specifically, the hypothesis presumes that the border. when perceived as sharp, corresponds to the centre of the transition zone of the retinal image. A measure of the enhanced region as obtained by the method described would thus be a function of half the transition zone, as indicated in Fig. 1A and B. The same interpretation of the enhanced region holds when the defocus is so large that the border is perceived as blurred. The half of the transition zone that corresponds to the dark portion of the stimulus shows a continuous drop in brightness. Before a uniform level of darkness is reached, there is a region of deeper darkness, much in keeping with the hypothesis. However, this effect is much less pronounced than the corresponding brightness enhancement. Moreover, it does not lend itself to the methods used in this experiment. Therefore, only the brightness enhancement is considered in this paper. Although the measurements obtained by the subject would be a function of one half of the transition zone. they would obviously not be an exact measure of this. Rather. one would expect them to be somewhat larger, since the subject is making his judgment by the terminations rather than the peaks of the enhanced regions. To determine if the region demarcated by the border enhancement in fact is a function of the transition zone, measurements of this region were compared with estimates of the blur region of the retinal image. In a first experiment. the blur of the retinal image was controlled by varying the amount of retinal defo~u_s,the dioptral value of the stimulus serving as the independent variable. In a second experiment, the blur was varied by using the entrance pupil size as the independent variable, the amount of defocus being kept constant. In each experiment, the enhancement extent and the retinal blur were plotted. in terms of visual angle.
REMOLE
against their common independent ~ar)abk so what they could be compared with respect to magnitude. APP&RATUS AND METHOD
Figure 2 shows a plan of the apparatus. The rectanguiar observation field consisted of translucent material set in an opaque ground and uniformly transilluminated by tungsten light. The horizontal dimension of the field could be varied from about 12” at the eye to zero through a control operated by the subject. The subject would decrease the field width from its maximum size until the enhanced regions appearing along the vertical borders appeared to just touch. The extent of the enhancement was then registered mechanically on a micrometer gauge. This part of the apparatus was esscntially the same as described in previous articles (Remolr. 1970. 1973). In order to avoid after-image effects from thr: narrowed-down field comprising the two border enhancements. ample time was given between measurements. Also, each measurement was initiated with a sudden presentation of the maximum aperture. To measure the degree of defocus of the retinal image a Badal optometer arrangement was incorporated in the apparatus. A + 1040 D lens was placed with its optic axis perpendicular to the fixation axis. A point target travelling along the optic axis of the lens was superimposed on the observation held via a ~m~si~vered mirrk. The target was small enough to be seen only when approximately conjugate with the retina, when it would appear as a sharp point slightly brighter than the observation field. It was iltu. minated via a fibre optics channel receiving light from the rear of the field. Thus. except for the effect of the absorptive qualities of the tibres. the wavelength composition of the target was identical to that of the field. Measured through the semisilvered mirror. the luminance of ttie fidd was 10 cd/m’. The optometer scale was calibrated in dioptres. For each subject. the scale was adjusted so that the xro point was
PF
Fig. 2. Schematic diagram of apparatus. TS, tungsten source; P. projector; S, opal screen; A, variable aperture: AC. aperture contro1; MC. micrometer gauge; LB. lens battery; OL, optometer lens; SM, semisilvere~ mirror; OC. optometer control; DS. dioptral scale; AP. artificia! pupil; OD. right eye: OT, optometer target; PF. perceived field; FO. fihre optics channel
Border enhancement and retinal image blur conjugate with the retina when a lens battery in front of the eye produced an in-focus retinal image of the borders. When negative or positive blur of the borders was introduced, its dioptrai amount could be read from the optometer scale. For example. during negative blur. the optometer target was perceived only for a certain position beyond the zero point. In general. the subject started by first moving the optometer target in from a position beyond that conjugate with the retina until the target first appeared sharp. and its dioptral distance from the zero point was recorded. A similar reading was then obtained by moving the target away from the eye, this time starting from a position well within the plane conjugate with the retina. The dioptral midpoint of the range defined by the two readings was taken to represent the point conjugate with the retina. At all times was the subject concentrating on the field and its borders rather than the optometer target. In the first experiment. an artificial pupil of 3 mm dia was placed approx 8 mm from the cornea1 plane, behind the subject’s correction. In order to minify accommodative changes and interference from pupil constriction, the ciliary muscle and sphincter pupillae were paralyzed with @5 per cent tropicamide. The vergence of the light from the observation field at the plane of the artificial pupil was controlled by lens powers before the eye presented in quarter dioptre steps from -4.75 D to + 3.00 D. With no lenses. the vergence was - 3.00 D. Thus. a + 3.00 D lens power would produce zero vergence. In recording the incident vergence at the eye, no adjustment was made for the change in effectivity between the lens battery and the principal planes of the eye. For incidence vergences in the order of 1.00 D this would introduce an error in the measurement of the retinal blur of approx 0.01 D. Only towards the ends of the range, for values beyond 3.00 D, would the discrepancy approach 0.10 D. The discrepancy was considered to be of Little significance for this experiment. When a cycloplegic agent is used. a small amount of residual accommodative power will remain. In this experiment. the independent variable was the incident vergence provided by the dioptral value of the distance of the observation field plus the lens powers in front of the eye. However, another factor is the stimulation to accommodation inherent in the perceived nearness of the observation field, usually referred to as proximal stimulation. This activated some of the residual accommodation with the result that the zero point of the optometer setting did not correspond with zero incident vergence at the ametropic correction, The amount ofaccommodation thus activated varied with the S. amounting to 0.75 D for LH. I.00 D for AR. and 0.50 D for S MG. This amount had to be taken into account when the zero point of the optometer scale was to be placed in conjugation with the retina. That is, the lens power that produced the best focus of the observation field had to be found empirically. Since there is a dioptral range through which the borders will appear clear, the dioptral midpoint of this range was assumed to represent the best focus. The end points of the range were determined by increasing or detreasing lens power until a firs: perceptible blur of the borders appeared. In conjunction with the defocus measurements. findings were taken for the enhancement extent. using the method ’ The nodal points were chosen merely for optical convenience. The implication is not that these are centres of projection. a role which is better ascribed to entrance and exit pupil points.
991
described in the introduction. Thus. for each of the three Ss tested five sets of data comparing retinal blur with enhancement extent were obtained. the incident vergence serving as the independent variable. The two dependent variables were converted to minutes of arc subtended at the eye and plotted on a common scale. Ss LH and MG had no training in this kind of observation whereas S AR had considerable training. The respective right eye distance corrections for Ss LH. AR and MG were -0.50 D. -4.00 D and -2.25, - 1~75x 180 All had normal vision with correction. Conversion of the enhancement extent into visual angle subtended approximately at the first nodal point constitutes no problem. Similarly. for large amounts of defocus. simple geometry based on the assumption that all rays pass through the paraxial focus will give a good approxtmation of the blur region. which can then be converted to visual angle subtended at the second nodal point.’ However. for small amounts of defocus, the proportion of the blur contributed by aberrations and diffraction effects becomes signiflcant. When the retinal image is optimally focused. there is a minimum blur contributed solely by these factors. To derive the extent of the transition zone between two levels of retinal illumination. these factors were considered together with the blur contributed by rays intersecting in the paraxial image plane. A formula introduced by Ogle (19601was used for this purpose:
In Ogle’s work, .: is the radius of the blur circle when a point object is used, 2” is the radius of the minimum blur circle, fis the reduced focal length of the eye. and Q is the amount of dioptral blur. In this paper. ,I represents half the transition zone rather than the blur circle radius. and z,). half the width of the minimum zone. Figure 3 is a sketch of one branch of the hyperbola described by the formula. similar to that presented in Ogle’s work. In the present study, the value of 16.78 mm was assumed for the reduced focal length, and the same value was assumed for the distance between the second nodal point and the retina (Bennett and Francis, 1962). The specification of the nodal point in converting retina1 blur to visual angle is. of course. much more critical than for the corresponding conversion of enhancement extent. where the distances involved are relatively large. In Fig. 3, the asymptotes represent the extent of retinal blur when aberrations and diffraction effects are ignored. The hyperbolic branch representing ; shows the blur when
Fig. 3. Function representing relation between optical blur and optical defocus.
992
AKNLLFR~MOLL
these factors are included. There is no simple method of estlmating z,,. the minimum blur. with certainty (Ogle. 1960): its choice will have to be subject to some arbitration. Thus. whereas a good approximation can be obtained for blur caused by relatively large amounts of defocus. the estimate becomes increasingly hypothetical as the importance of zi, increases towards optimum focus. It was stated as a part of the working hypothesis that the enhancement extent would be expected to be somewhat larger than the dioptral blur. This is borne out quite well for large values of defocus. The minimum blur was chosen so that this would be true also for small amounts of defocus. Thus. it was chosen to conform with the ratio between enhancement extent and dioptral blur as found for the larger amounts of defocus. To estimate a value for this ratio. the three pairs of dependent variables at each end of the stimulus range were used. This does not, however. imply that such a constant ratio throughout the range is necessary for our hypothesis; it is merely a convenient way of presenting the data. On the other hand, there is no reason to believe that the ratio, even near zero defocus, deviates very greatly from a true one. It is worth noting that the values obtained for the minimum blur using the criterion just described are fairly consistent with values found by other authors for the minimum blur circle radius (Ogle, 1960). In the second experiment, the primary independent variable was the entrance pupil size. Whereas in the first experiment it had been a constant 3 mm dia aperture placed about 8mm in front of the cornea, the aperture was no% varied through a range of from 1 to 8 mm in dia, in I mm increments. The estimates for minimum blur used for deriving the size of the blur zone were those obtained in the first experiment, for the 3mm pupil. Since not enough was known about the aberrational characteristics of the eyes tested. variations in minimum blur due to the changes m entrance pupil size were not considered in this experiment. Results were obtained not only for the in-focus condition. but also for negative and positive defocus of 3JXl D. For the t%o situations where the retinal image was out of focus. and for the larger size entrance pupils, the estimated minimum blur would play a minor part in determining the size of the transition zone. As in the first experiment, five sets of data were obtained from each subject.
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Fig. 5. Relation between enhancement extent (0 l a) and optlcai blur (x x x 1in terms of half the transifibn zone. The independent variable is the vergencc at the artificial pupil. (000) represents a secondary band recognized h! some observers.
48). In Fig. 4, the interpretations of parts (a). fb). (c) and (d) are the same as in Fig. 1 (c) and (d) are typical subjective renderings of the response. The band more proximal to the border, contrary to the more distal band. is small enough to invite an explanation in terms of diffraction effects. At the time, it was not entirely certain which band should be taken as representative of the hypothesis. and measurements were therefore taken for both bands. Findings for the two types of
The proximal, narrower band (0 0 0) IS much more difficult to recognize than the broader band (a 0 (1 ). Sometimes it can be recognized oniy after the distal bands have been brought together for measurement and have appeared to merge. One S (LH) could recognize no such secondary band even after numerous trials. When findings are obtain&d for the proximal band. it is with considerable difficulty from the Ss point of view. Findings beyond the ranges shown in Fig. 5 were not possible_ Like the distal band, the proximal band does increase with defocus. but it lies always well within the function describing half the transition zone ( x x 2 ). This is true also for the end vaIues of the range obtained, where the estimates of the transition zone can be considered quite good. Thus. there should be little doubt that it is the distal, more easily perceived band that must be considered as pertinent to the hypothesis. A further exploration of the proximal band will not be pursued in this paper. Some other complications pertaining to the perception of the border enhancement need to be Considered. During negative defocus the distal bands are easily seen and measured. However, if tbey are brought past the distance at which they appear to touch, a dark region will develop in the centre of the fteld (Fig. 4C). This begins as a thin dark Iine when the border separation is about half that yielding a measurement of the enhancement extent. &cause it occurs only when the overlap of the original bands is considerable, it does not interfere with the type of measuremenfs performed in this study. It does, however. make impossible ai-0
border enhancement. together with findings tral blur. are shown in Fig. 5.
measurement of the proximal bands just discussed. even when these arc seen initially. The drop in bright-
RESULTS AND DISCUSSION
Quulitatice
obseraations
During the course of the experiment, it became evident that the response situation is not quite SO simple as presented in the introduction. Thus, sometimes a second band. much narrower than the first. would appear near the border. The effect occurs both during positive defocus (Fig. 4A) and negative defocus ~IFig.
for diop-
Border enhancement and retinal image blur ness of this dark band is much greater than the undulations of light and dark typical of the border effects under investigation. The relative darkness of this central band necessitates a more complex distribution of light in the transition zone than a simple sigmoid. It could be explained in terms of fundamental blur circles whose cross settion have a bimodal distribution, such as indicated in Fig. 4B (b) with a dotted line. When the borders are relatively far apart. this would make relatively little difference in the distribution except that the transition zone would be stepped rather than smooth [Fig. 4B (b)]. The blurred transition between light and dark observed during negative defocus is, in fact, less smooth than a corresponding zone observed during positive defocus. Such a step might be seen as a secondary band but would not be as bright or as pronounced as the band demarcating the termination of the transition zone. It is only during considerable overlap of the blur circles corresponding to the borders that the added effect of their central depressed areas would be great enough to introduce a depression in the retinal illuminance distribution. A simplified interpretation of this hypothesis is shown in Fig. 4C (b). where two overlapping blur circles are shown with dotted lines and their summed effect with a solid line. That the formation of the dark band begins when the border interdistance is approximately one half transition zone in angular extent agrees rather well with this interpretation. Quantitative observations
Thus, it appears that the complications described do not interfere unduly with the testing of the original hypothesis. Figure 5 summarizes the results of three Ss for enhancement extent (0 l l ) and calculated values of half the transition zone (x x x ). Except for the extreme end values, each plotted point represents the moving average of findings for three consecutive values of the independent variable, and thus constitutes the mean of 15 responses. A range of two SE. of the mean, one above and one below the plotted point, has been shown for the in-focus condition and for positive and negative defocus in the order of 3.00 D. Where the functions overlap the error bars for retinal blur are shown in insets. The vertical arrows indicate points of first perceptible blur of the borders. For all subjects, the enhancement extent follows the function representing half the transition zone. In two of the Ss, LH and AR, the expectation is borne out that the enhancement extent is somewhat larger than half the transition zone. In the third .S,GM, the two dependent variables practically coincide. Although these subjective differences between enhancement and blur could stem from genuine physiological differences. other factors are probably more important. For example. there may be significant differences in the interpretation of the criterion used for measuring enhancement. Also, individual values for the constants of the eye were not determined. For
993
example, if the true position of the posterion nodal point deviates considerably from the standard value used, the calculations of retinal blur would be affected: a deviation of 1 mm would result in an error of approx 5 per cent. Figure 6 shows the results of the second experiment. where the artificial entrance pupil is the chief independent variable. For the out-of-focus condition. this is an alternative way of varying the retinal blur. The method of plotting the data is similar to that used for the first experiment. the functions being smoothed out somewhat by using moving averages for three consecutive pupil sizes. The results are similar to those in the first experiment in that the enhancement extent follows the blur extent. However, there are some deviations from the rather simple picture presented by the results from the first experiment. For large values of the entrance pupil. during out-of-focus conditions, the size of the enhancement region approaches or even drops below that of the calculated blur. This is not surprising if one considers the oblique incidence of peripheral rays and their reduced effectivity in stimulating the retina. such as is exemplified in the Stiles-Crawford effect. The enhancement extent would obviously follow the narrower portion of the transition zone representing the summation of the smaller, more effective portion of each fundamental blur circle. The enhancement extent may thus be a better indicator of changes in the effective transition zone than calculations based on optical considerations only. The decreasing slope of the function for enhancement as compared to calculated blur is evident with all the subjects (Fig. 6). However, for subject GM. the enhancement is smaller than the blur even for the 3 mm pu,pil identical to that used in the first experiment. This apparent discord between the two experiments needs some clarification. For two subjects, AR and MG. the enhancement extent in the second experiment is, for the out-of-focus condition, somewhat smaller than in the first experiment for the same pupil size and defocus. In subject LH, the discrepancy is in the opposite direction. To show the magnitude of this deviation, values from the first experiment with their accompanying error bars have been introduced in Fig. 6. The bars pertain to the results from the first experiment even when they appear to coincide with the functions obtained in the second experiment. The explanation for the often statistically significant discrepancies must lie in the inevitable differences in stimulus sequence and context for the two experiments. For example. the distribution of light in the blur accompanying changes in entrance pupil size is different from that accompanying changes in optical defocus. It is possible that the retinal adaptation effects had not been eliminated entirely, in which case there would be slight differences in the retinal pre-adaptation pattern for the two experiments. However, one would then expect the discrepancy to be of the same direction in all three subjects. A more plausible explanation is that
994
Fig. 6. Relation between enhancement extent (00 l ) and optical blur ( x x x ) in terms of half the transition zone. The chief independent variable is the entrance pupil diameter.
the differences in context of the two experiments have some effect on the criterion used for the measurements. This highly subjective factor would seem to leave room for individuat. variations in this respect. In S MG. where the difference between enhancement and biur is small in the first place, even a small depression in the findings for the enhancement would cause them to drop below those for the calculated blur. Although the relation between enhancement and blur is not so simple as suggested in the original hypothesis, the fact remains that the two variables follow each other closely when the entrance pupil is about 3 mm in dia, that is. large enough to minjfy diffraction effects and small enough to eliminate relatively oblique rays. It is only when the pupil is relatively large that the enhancement deviates greatly from the calcufated blur. This indicates that the enhancement extent is a function of the physiologically effective portion of the blur zone rather than its optical spread.
REFEREYCES Bekesy G. von. [ 1960) Neural inhibitory untts of the eye and skin. Quantitative description of contrast phenomena. J. cyr. sec. Ill!. so, lO6@ 1070. Bekesy G. ran. (1972) Mach bands measured by a compensation method. l’ision Rrs. 12. 1485-1497. Bennett A. G. and Francis J. L. (1963) The eye as an optical sqtcm. In 7‘/1<~ Erc, (Edited h! Davison H). Vol 4. pp. IO-- 131. Academic Press. New York. Fry G. A. (I 955)Blur of t/w Rrrid /rmq~~. The Ohio Stale University Press, Columbus. Motokawa K. (1970) Physioloyr @Color unJ Partern I’ision. lgaku Shoin Ltd., Tokyo; Springer, Berbn. Ogle K. N. (1960) Bfurring of the retinal image and contrast thresholds in the fovea. J. o/rr. Sot. ARI.!#I; 307-315. Ratliff F. and Hardine H. K. (1959) The response ofIimul~ optic nerve fibers to patterns of ilium~~tiun on-the rccepfor mosaic. J. ~~L’IT. PliysioL 42, f24i-1255. Rat18 F.. Harthne H. K. and Miller W. H, (1963) Spatial and temporal aspects of retinal inhibitory interaction. J. oyr. sot*. .41tr.53, 1I(f 130. Kemole A. ( 1970) Spatial characteristics of the border enhancement region in a flickering field. Anr. J. Qprotu- 4’1. 779 786. Remole ,A.(1973) Extended border enhawement during intermittent iltustration: binocular effects. livin,r Rl,\. 13,
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&sum&On percolt un champ brillant sur fond sombre avec une rigIon de lummosite accrue adJ;Iccntc au bord. On compare I’extension spatiale de cette rigion B celle de flou au bord de I’image rktmlenne. En accord avec la thkorie des bandes de Mach. on trouve une relation ktroite entre ces deux varlableh. Ce n’est que pour de tres grandes pupilles que I’accroissement de luminosit-4 s‘ktend nettement mom\ que la molti de la zone de Aou. On suggere que cela provient du faalt que I’acrolssement suit la portion phvsiologiquement efficace de la zone de Rou et non la lumitre &incidence oblique qua constltue la p&iph&e de I’extension optique.
Zusammenfassung-Bei einem hellen Feld auf einem dunklen Grund nimmt man entlang dcr Kant einen Bereich erhahter Helligkeit wahr. Die riiumliche Ausdehnung dieses Bereiches wird mlt &I Kantenunschiirfe des Netzhautbildes verglichen. Die beiden Griissen sind, iibereinstimmend mit dcr Theorle der Machschen Streifen. eng korreliert. Nur bei grossen Eintrittspupillen 1st der Bereich dn Helligkeltsiiberhiihung kleiner als die halbe Unschiirfe. Das kdnnte dadurch erkliirt herden. dass mhr der ph>siologisch wirksame Teil des Unschiirfebereichs entscheidend ist. als das schriig elnfallendc Licht. das den Rand der optischen Unschiirfe ausmacht.
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Fig. 1. Sketch of the general stimulus and response situation, (a) Cross section of stimulus luminance distribution; (b) hypothetical retinal illuminance distribution; (c) field as seen by subject: (d) cross section of subjective brightness distribution. A: General situation with enhancement produced along two vertical borders. B: The enhanced regions being brought together to touch. C: Similar situation with a sloping transition zone introduced at the stimulus level.
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Fig. 4. Sketch of the general stimulus and response situation based on observations during defocus. Interpretation of (a), (b), (c) and (d) as in Fig. 1. A: Positive defocus. B: Negative defocus. C: Special effect of overlapping enhancement regions during negative defocus.