An analysis of retinal receptor orientation II. Predictions for psychophysical tests. Jay M. Enoch and Alan M. Laties

Transcription

1 An analysis of retinal receptor orientation II. Predictions for psychophysical tests Jay M. Enoch and Alan M. Laties With the use of histologic techniques, it was shown that retinal receptors in several species are directed toward a point near the front of the eye lens. Because of inherent limitations in histologic methods, evidence concerning photoreceptor orientation obtained by a different technique would be of value. The psychophysically determined Stiles-Crawford effect (directional sensitivity of the retina) provides a valuable test of the anatomical findings. In this paper the theoretical basis for such a test is developed and working hypotheses have been proposed. One model calls for retinal receptors to be directed toward the center of the exit pupil of the eye (anterior pointing hypothesis), and a second requires the photoreceptors to point toward the center of the retinal sphere (center pointing hypothesis). The direction of the maximum of the photopic Stiles-Crawford function would be different for the two working hypotheses at extrafoveal points. Similarly, the integrated effective visual stimulus magnitude would be different for each of the two alternative proposals. The questions raised in this paper are significant because they can help clarify the "why" of retinal receptor optical properties. Key words: retinal receptor orientation, Stiles-Crawford effect, optical properties of retinal receptors, retinal illuminance, effective visual stimulus. In prior communications the orientation of photoreceptors with reference to the optical landmarks of the eye 1 ' 2 and to each other 3 was discussed. In several species the From the Department of Ophthalmology, Washington University School of Medicine, and the Oscar Johnson Institute, St. Louis, Mo., and the Department of Ophthalmology, Hospital of the University of Pennsylvania, Philadelphia, Pa. Supported in part by Research Grant No. 5 RO1 EY and Career Development Award No. 5 K3 EY (to Jay M. Enoch) and in part by a Research to Prevent Blindness Research Professorship and by Research Grant No. 9 RO1 EY (to Alan M. Laties) of the National Eye Institute, National Institutes of Health, Bethesda, Md. Manuscript submitted March 10, 1971; revised manuscript accepted Oct. 5, photoreceptors were found to be coaxially aligned with a point D near the front of the eye lens along the line of sight (Fig. 1) and thus to have a graded differential orientation. Because of the inherent limitations of the anatomical techniques used, evidence about photoreceptor orientation gathered by independent means would be of value. The Stiles-Crawford effect 4 in psychophysics is an obvious alternative to anatomical methods, and the present communication addresses itself to the means by which critical psychophysical studies can be performed. The expected displacement of the maxima of sets of Stiles-Crawford functions are derived for points away from the principal line of sight for two different hypothetical conditions. In the first, photoreceptors are assumed to be normal to the globe and to point toward its cen-

2 960 Enoch and Laties Investigative Ophthalmology December 1971 Cornea Retina AE = mm ED = " DO =9.312 " AO = = OF' =11.4 mm 1 +- AF' = mm* DF" = mm AI = 3.6 mm 9 L -" 9 3 (1.2144) Gullstrand Schematic Eye Made Emmetropic Fig. 1. Constants and angles used in the analysis are shown on this schematic drawing. A ray is incident in the center of the entrance pupil of the emmetropized Gullstrand schematic eye ( ). After refraction, it continues on as if it had passed through the center of the exit pupil (D) to its retinal intercept P n. O is located at the center of the retinal sphere. ter; while in the second, photoreceptors are assumed to be everywhere aligned coaxial to a point along the line of sight passing through the center of the exit pupil of the eye. One of the two hypotheses presented predicts a decentration of the photopic directional sensitivity function in the entrance pupil of the eye for nonfoveal test points. Such a decentration would result in a reduction of the effective visual stimulus. An analogue device provided determinations of stimulus magnitude changes predicted for different Stiles-Crawford peak decentrations and different pupil sizes. This paper is a logical extension of histologic studies of photoreceptor orientation and of the analyses of relationships of photoreceptors to the eye 2 and to each other. 3 In the quantitative analysis which follows, it is assumed that one "law" or organizational format pertains to the entire retina. The possibility exists, however, that different regions of the retina exhibit different orientational properties. Such a multilaw concept was suggested by Stiles 5 as part of an analysis of a paper by Aguilar and Plaza. 0 Only limited Stiles-Crawford data exist for nonfoveal points and local variations in orientation have been discribed. This paper provides a theoretical framework for studies just completed. Working hypotheses Center pointing hypothesis (CPH). All receptors point toward the center of the retinal sphere. That is, they are radially distributed about the center of that sphere, point 0 in Fig. 1. Anterior pointing hypothesis (APH). All receptors are directed toward an anterior point in the eye; ideally they point toward the center of the iris aperture stop (the source of light) as imaged by the eye lens. That point is the center of the exit pupil of the eye, point D on Fig. 1. In this and in previous papers, 2 ' 3 descriptions of the anterior pointing hypothesis treat D as a uni-

3 Volume 10 Number 12 Retinal receptor orientation tary locus. When one considers peripheral lens characteristics and the limitations inherent in histologic observations, it may well be as valid to consider D a distribution of points, the characteristics of which have not yet been fully defined. Interreceptor differences in orientation for either hypothesis are very small. 3 In fact, the angular and spatial differences predicted are so small that they are beyond the resolution capabilities of present electron microscopic techniques for tissue sections. Alternative hypotheses describing orientational characteristics may be formulated. For example, all receptors may be regarded as being parallel to each other. As a general theory of photoreceptor orientation, this proposal must be rejected. If all photoreceptors were parallel to the foveal elements, cells at the equator of the eye would be flat against the external limiting membrane, and those situated beyond that point would have to be bent back upon themselves. All anatomic evidence indicates that such a model is not valid. As a more limited model, applying to a small region at the posterior pole of the eye, the hypothesis deserves consideration. Recently just such a proposal was advanced by Heath and Walraven 7 - s on the basis of Stiles- Crawford measurements of the central four degrees. Since the degree of receptor tilt within 2 degrees of the fovea is of so low an order as to be within the measurement error of present histologic techniques, discrimination between parallel orientation and the other possibilities presented is not possible by anatomical means. The necessary equations which allow consideration of this third working hypothesis are included in this manuscript. The authors hope Dr. Heath will extend his studies to more peripheral points in which a critical comparison between differing hypotheses can be more easily accomplished. Analysis In Fig. 1, a chief ray is directed toward the center of the entrance of the pupil of the the eye (E). When refracted by an optical system having the properties of the Gullstrand schematic eye, this ray passes through the center of the iris (I) and leaves the rear lens surface as if it had origin at a point D in the center of the exit pupil of the eye. The ray, whose angle of incidence at E is designated by Qi, leaves point D with an angle of G,?. In Fig. 1 if one assumes (1) that the iris is coincident with the anterior surface of the unaccommodated lens of the eye, (2) that the iris is centered on (and the fovea lies on) the optic axis of the eye, and (3) that the rays are paraxial, then small angle assumptions hold and the simple relationship shown in Equation 1, may be defined by performing a chief ray trace. e, = e 3 (1.2144) (1) The refracted ray DP n is incident at retinal point? n. Q s is the angle the refracted chief ray makes with the optical axis of the eye. Point O lies at the center of the retinal sphere. Modifying the Gullstrand schematic eye in order to make it emmetropic, F' serves as the center of the fovea and as the secondary focal point of the optical system of the eye. Angle P n OF', 0, is the angular displacement of the chief ray intercept P n from the fovea as measured at the center of the retinal sphere. The radius of the retinal sphere (OP n or OF' designated by r) is estimated from available reports of ocular dimensions. 9 The values of the several dimensions used in this analysis are shown on Fig. 1. The distance AF' and the derived value DF' are based on the characteristics of the emmetropized Gullstrand eye shown in Equation 2. d = DF' - r (2) In triangle DOP n, d and r are constants. Interestingly, point O lies near, but not necessarily precisely at, the center of rotation of the eye. That is, the center of the retinal sphere, O, must also lie near the center of the scleral sphere. The second assumption listed above will have to be considered further. A correction factor will have to be introduced for nonalignment of the fovea, the pupil center, and the optic axis. A number of different formulas may be used to describe the relationships between the factors considered in the model. In the initial analyses Equations 3, 4, and 5 have been found most useful. 2 ' 3 0 = e 3 + (3) sine O 3 sine sine 0 (4) r cot = esc 0 + cot 0 (5) d As the angle of incidence of the chief ray

4 962 Enoch and Laties Investigative Ophthalmology December 1971 a k "= a k (0.9094) Entrance Pupil Exit Pupil Fig. 2. In the center pointing hypothesis, the receptors are coaxial with the radii of the retinal sphere. With increase in angle 0, the forward projection of these photoreceptor axes to the pupillary plane results in marked displacements of that projection in the exit (and hence entrance) pupil. If the peak of Stiles-Crawford effect reflects the central tendency of receptor orientations, in the CPH, one would expect displacements of the S-C maximum in the entrance pupil which would increase as i or 0 becomes larger. (Oj) increases, the resultant angle of refraction (0,9) increases, and the length of the chief ray projection to the retina (x) becomes shorter. As Q 3 increases, 0 and 6., increase and 0 2 decreases. Coincidentally with an increase in 0 i5 the effective aperture of the iris becomes foreshortened in the plane of 0* as a function of cos 0*. This is the familiar horizontal narrowing of the iris on lateral view. To some extent the resultant reduction in visual stimulus magnitude is overcome by the shortening of the distance x as 0,? becomes larger. As x becomes shorter, the angle subtended by the bounds of the exit pupil becomes larger at point P n. The image quality in the peripheral retina is poor because the retinal surface does not lie in the image plane and because the aberrations are marked. Hence, the straightforward integration of energy (having origin at some infinitely distant point) irradiating all parts of the iris aperture and directed toward Point P n may not be too valid for large angles 0. Further, because of uncertainties regarding the validity of the schematic eye models for far peripheral points, predictions for these retinal areas are not without hazard. Fortunately, in order to make judgments regarding the two hypotheses presented in this discussion, the status of the far periphery need not be evaluated. As indicated, the authors assume that a single-orientation "law" holds for the entire retina. The Stiles-Crawford effect is a measure of retinal directional sensitivity for angles of incidence at the retina limited by the aperture of the pupil. Considering only photopic stimuli, one may argue that if the retina is directionally sensitive, the peak of the Stiles-Crawford function reflects the orientational tendency of the directionally sensitive elements located in the retinal sampling area. By finding the direction of maximum sensitivity at different points from the fovea outward, it should be possible to gain an independent measure of retinal receptor orientation, a measure which avoids many of the pitfalls common to histologic techniques. If receptors (inner and outer segments taken as a unit) at point P n are coaxial with the center of the exit pupil of the eye (APH), the maximum of the Stiles-Crawford function (for different angles of incidence Qi) will remain centered in the entrance pupil of the eye. On the other hand, if the receptors point toward the center of the retinal sphere (CPH), the maximum of sensitivity would displace rapidly in the eye pupil when angle i is increased. This point becomes obvious when looking at Fig. 2. Even for modest values of 0,-, the extension of the line P,,0 to the exit pupil results in substantial displacement of that line intercept (a k ") from the line F'D. The magnitude of the displacement, a k ", is given by the simple relationship shown in Equation 6. a k " = d tan 0 (6)

5 Volume 10 Number 12 Retinal receptor orientation. II 963 Translating a point in the exit pupil to a comparable point (a lc ) in the entrance pupil results in Equation 7. a k = a k "/ (7) This latter relationship is derived from paraxial ray trace with the use of the constants of the unaccommodated Gullstrand schematic eye. From these relationships, one may compute the predicted displacement (from the center of the entrance pupil) of the maximum of the photopic Stiles-Crawford effect. Starting with either Equation 1 or a modified version of it, Q 3 may be computed from given values of Q t. Given r, d, and Q 3, and using the law of sines (Equation 4), 9, may be determined. Knowing Q 3 and Q 1} one may solve for 0 (Equation 3). Then a k may be computed from Equations 6 and 7. If all receptors were parallel to the optic axis, the displacement would be a k " = r sin 0, or a k " = x sin 0 3. In this instance, the projection of the axis of the receptor to the pupillary plane falls on the opposite side of the pupil from that considered in Fig. 2. Equation 1 has also been computed for tan 0, = tan ( ). Frankly, doubt arises as to the proper form one must use when the limits of 0 = sin 0 = tan 0 breakdown (at about eight degrees) and when models derived from paraxial optics are no longer valid. The argument has been developed in a manner such that induced errors are small. Fig. 3 is a plot of a k for the two working hypotheses. The prediction for the center pointing hypothesis, the computation of which was just described, is given by the curve marked O. The anticipated result for the anterior pointing hypothesis (with receptors pointing at the exit pupil of the eye) is defined by the line designated D. Note how rapidly values on the O line increase. The entrance pupil of the eye rarely exceeds 8 mm. or a value of a fc (radial displacement from the center of the entrance pupil) of 4 mm. This means that, for values 0 7 of 15 degrees or more, the Stiles-Crawford maximum for receptors 5 4 >H e c 1-2 L Fig. 3. These are the predictor curves for the direction of maximum sensitivity for the APH (line D) and the CPH (curve O). Stated simply, the anterior pointing hypothesis predicts the nondisplacement of the S-C peak for nonfoveal points while the center pointing hypothesis predicts a rapid displacement of a k as j increases. (See comments below on the meaning of minus values of a*.) pointing toward the center of the retinal sphere (CPH) will fall outside the 8 mm. diameter pupillary boundary. Thus, one may determine the general character of receptor orientation by studying the Stiles- Crawford function in the fovea, parafovea, and near periphery of the retina. That is, properties determined in the first 20 degrees of eccentricity from the fovea should provide the necessary information. Measurement problems When angle 0i is not small, the designation and control of a k becomes complex. In Fig. 4, the problem becomes apparent. Here E lies at the center of the entrance pupil. The ray XE is a chief ray incident in the entrance at an angle 0 from the normal (optic axis of the eye). WV is a ray which is parallel to XE but displaced by

6 964 Enoch and Laties Investigative Ophthalmology December 1971 Entrance Pupil Fig. 4. This drawing illustrates one problem which arises when Oi becomes large. If = 0 degrees, the image of the exit pupil of the Stiles-Crawford instrument lies in the entrance pupil of the eye. With oblique incidence that image rotates about point E. This complicates the optics, and results in a displacement of the stimulus in the entrance pupil. distance A/ from XE. The intercept of this ray in the entrance pupil plane is U, which is located a distance of A k from E. If one assumes that the aperture stop of the Stiles- Crawford apparatus is imaged with its center at E with increasing 9.;., its rotated projection at point V lies increasingly out of the plane of the entrance pupil of the eye, and A k becomes increasingly larger than A fc '. Angle UEV = 9i and triangle UVE is a right triangle (Equation 8). cos Q[ = and a k = a : / sec 0, (8) a k This complex problem can be readily dealt with experimentally if limited focal adjustment of the aperture plane is possible in the Stiles-Crawford apparatus and if the entrance pupil plane of the eye may be visualized (or duplicated on a ground glass or other screen which may be viewed by the experimenter during the experiment). That is, a k may be measured directly (instead of measuring a k ') and blur of a projected aperture in the entrance pupil plane may be corrected. A special added problem, the refraction of light at the vitreous-retinal interface, has been brought to our attention by L. Lipetz. While the index of refraction of the vitreous is readily determined in fact, is well known the inner retinal index (or concentration of solids) has not been defined. Pending determination of inner retinal index, consideration of this matter will be deferred. Given the small distances involved, it is probable that the magnitude of the inner retinal deflection of ray DP n (Fig. 1) is small. The foveal incline presents a special problem from this point of view a point made many years ago by Walls. 10 A major problem not considered in this paper is local variation in the receptor orientation, described by O'Brien and Miller 11 and verified by Enoch. 12 One must distinguish local orientation of a small group of receptors from the general tendency of the retinal area. Histologically, differences in orientation between retinal groups of a few degrees are difficult to measure. 1 By careful application of the Stiles-Crawford technique, that is, using a bite bar, field stop adjustment, and monitoring eye position and focus, some estimate of local variations may be obtained. The O'Brien-Miller technique allows rapid evaluation only of local differences in orientation as reflected through the visual neural network. The existence of local variation of photoreceptor orientation requires that great care be employed when making Stiles- Crawford measurements for the purposes considered here. Only limited weight can be placed on the data of one observer or on one or two points determined in one meridian. Further, the use of small test field areas can lead, for these reasons, to erroneous conclusions. Although local variation in photoreceptor orientation makes it imperative that precise technique and careful evaluation be employed, it does not make the problem insoluble. Since one is interested primarily in the direction of the maximum, a technique described by Enoch 13 might be adapted. That is, instead of holding one aperture constant in the entrance pupil and translating a second aperture as is usually done, one can move both apertures simultaneously across the entrance pupil (e.g., separating Vz mm.

7 Volume 10 Number 12 Retinal receptor orientation. II c ^ 2 o / i / X * / / \ \ As / V y / \\ // / \ a OD. Nasal L. G L OD. TemporalL. 6^ 0.5. Nasal L. 9i O.S. Temporal L. & "or further in the indicated direction" * Identical points \ \ \ \ \ s \ V -3 L Fig. 5. The data of Aguilar and Plaza G have been fit to the hypothetical functions present in Fig. 3. Obviously, these data do not allow a choice between the two hypotheses. Other available data, when plotted in this manner, are equally ambiguous. The arrows tagged on certain points indicate that the direction of maximum sensitivity fell at the edge of the observer's pupil or beyond. The one set of data is dashed because of partial overlap with another set. The two points identified with the asterisk on the ordinate are the same data point (see text). aperture images about 2 mm.). The observer may then compare the brightnesses of the projections of these two apertures on the retina (bipartite field type of display two halves separated a bit). The directional sensitivity maximum should bisect the locus of the two points in the aperture stop when the two retinal images appear equally bright. The technique described assumes Stiles-Crawford function symmetry, normal photoreceptor orientation, and no vignetting. Further, angle 0i should not be so large that the factors considered in Equation 8 are of consequence. One must specify 0 i5 the position of the Stiles-Crawford directional sensitivity maximum in the entrance pupil, and the direction of translation of the maximum in relation to the angle of incidence 0*. This point becomes clearer on examination of Fig. 2. If the center pointing hypothesis is valid, the maximum (designated by a k ) would be translated to the same side of the entrance pupil as the direction of origin of the ray incident at E. Thus if the ray defining 0 originated as an angular displacement in the nasal field, the maximum of the Stiles- Crawford effect for the CPH would be displaced nasally in the entrance pupil. Information available from prior reports is too scant to allow full consideration of our hypotheses. Although Aguilar and Plaza G considered the problem of Stiles- Crawford effects away from the fovea in some detail, their description of experimental controls was limited and their data were obtained from experiments on the two eyes of one observer. In Fig. 5, Aguilar and Plaza's complex data are plotted on the predictor curves developed in Fig. 3. On the basis of their data, plots of their Stiles-Crawford function maxima could be

8 966 Enoch and Laties Investigative Ophthalmology December i _ J Equivalent Diameter of Entrance Pupil 2 mm 4mm 6mm 8mm SCE (Crawford) Non-integrated, set to match the 2mm diam. peak D e c e n t r a t i o n i n t h e E n t r a n c e P u p i l ( m m ) Fig. 6. Mean data obtained using the analogue instrument. There are integrations of the stimulus imaged in the integrating sphere. Four different equivalent diameter entrance pupils were employed. These were displaced from the center of the rotating disc in equivalent millimeter steps. For comparison, the Crawford J1 function has been plotted with data obtained using an equivalent 2 mm. entrance pupil. The arrow on the ordinate points toward the four data points plotted on Fig. 7 (in which these same points appear as a cross and three black points). made only to the nearest millimeter. If the peak of the Stiles-Crawford function were not centered in the entrance pupil for foveal fixation (e.g., when testing in the horizontal meridian), the displacement (a k ) would be plotted differently for nasal field values of 0s than for the temporal field values. Plus values of ak indicate that the peak was displaced in the same sense as 0i; minus values indicate the reverse displacement. Plus values (and minus values) indicate common (or opposed) angular orientation of these two factors. Thus on Fig. 5 (asterisks), we see the apparent anomaly of the same point plotted at two different points on the ordinate. Although several authors have presented data on the directionality of the peripheral retina, none is in a form suitable for the analysis of the problems raised in this report. 14 ' 17 Integrating the Stiles-Crawford (S-C) function It is important to estimate the effect of a displacement of the peak of the S-C

9 Volume 10 Number 12 Retinal receptor orientation. II 967 function on the magnitude of the visual stimulus. One may also use such information to distinguish between working hypotheses. Further, this material is added in order to provide a more complete analysis, in the same sense as that presented by Stiles and Crawford' 1 in their original paper. If the peak of the Stiles-Crawford function is not centered in the pupil, the effect is to reduce the effective visual stimulus. In order to quantify the decrement in stimulus, one must integrate the Stiles-Crawford function (of the first kind) across the entrance pupil of the eye and adjust that value for the effect of pupil decentration, making due correction for entrance pupil size. Method. A simple analogue measuring device was developed for this purpose. A disc with a representative S-C function drawn on it was rotated at high speed. It was illuminated by two direct current-supplied tungsten microscope illuminators. This rotating disc was imaged by a lens on the limiting aperture of an integrating sphere. The measured output of a calibrated photomultiplier provided the necessary integrations. Black flocked paper was used in areas not painted white. All measurements were in the form of the ratio, target measurement: measurement of a uniform background of black flocked paper. The S-C function chosen was the one proposed by Crawford (Equation 9). Four "eny = e-0.105r 2 (9) trance pupil" masks of different diameter were placed sequentially in front of the S-C distribution generated by this technique. The masks were centered or decentered in equivalent millimeter steps. Computed ratios for the different size masks which were located at given positions relative to the center of the rotating pattern are presented in Fig. 6. By setting the equivalent decentration in millimeters equal to au, values of Ot and 0 could be derived (Fig. 6, top). The validity of the analogue device as an integrator of the defined function was tested in two ways. A 2 mm. pupil is slightly larger than the sampling entrance pupil aperture used in Stiles-Crawford measurements. That is, the diameter of the aperture traversed across the pupil when making such determinations generally is of the order of 0.3 to 1.0 mm. While somewhat larger, a 2 mm. pupil should not differ markedly in effect from the reference function (Equation / - Arbitrarily Set (Ordinate only) * - Entrance Pupil Centered, Remaining Points Log Equivalent Entrance Pupil Area (mm 2 ) Fig. 7. This figure shows relative stimulus magnitude for different size entrance pupils of the eye ;ls for two conditions. Perfect additivity would be predicted if there was no directional sensitivity. The integrated (representative) SCE function would be followed if the observer's directional sensitivity function were centered in the entrance pupil (and the eye integrated energy falling at the retina on the basis of this factor alone). 1S These two curves are presented here to test the validity of the analogue model. Obviously, the four plotted points taken from Fig. 6 fit the integrated SCE function well. 9). The dashed distribution of Fig. 6 represents Equation 9 with its maximum value set equal to the zero-displacement measurement for the 2 mm. equivalent entrance pupil. The two distributions are closely matched. As a second test, values obtained for the entrance pupils centered condition (points lying on the ordinate indicated by the arroio) were plotted on Fig. 7. This is simply the effect of integrating the photopic Stiles-Crawford function for different size enhance pupils. The two curves plotted on Fig. 7 were taken from Enoch. 1S Perfect additivity represents the stimulus values one would predict for different size pupils if no S-C effect existed (as is assumed when computing photopic trolands and not correcting for the S-C effect). When correction is made for the directional sensitivity of the retina, the Integrated SCE curve is obtained. In psychophysical trials, added problems arise. 1S The four measured values on the ordinate of Fig. 6 were plotted on Fig. 7. The equivalent 2 mm. diameter entrance pupil was plotted at the cross mark. The remaining three points were then plotted. When this was done, they all fell on the predictor line. Thus, in this second test of this analogue integrator, a good result was obtained.

10 968 Enoch and Laties Investigative Ophthalmology December 1971 A small shadow, which was present near the edge of the "entrance pupil" mask, proved to be a limited source of error in these determinations. The shadow resulted from the necessary small separation of the rotating disc and the aperture. This factor was slightly greater for larger decentrations of the apertures and was proportionally greater the smaller the aperture diameter. Receptors not pointing at the center of the entrance pupil receive less stimulus. The predicted reduction in stimulus magnitude is given by each curve (Fig. 6). If the receptors point toward the center of the retinal sphere (CPH), sensitivity would be expected to fall off as O increases. Curves are presented for the different size entrance pupil apertures. This is an "aperture" effect and hence i? independent of test procedure employed. That is, regardless of whether or not one measures absolute threshold, increment threshold (static perimetry), flicker, visual resolution, etc., all determinations would be subject to this form of alteration in stimulus magnitude as f ( i). If center pointing is present, this characteristic would be present and should be detectable. If the receptors are directed toward the center of the exit pupil (APH), no fall-off in sensitivity as a function of 0 ( woidd occur due to aperture characteristics (for values of < limited to values shown in Fig. 3). In disturbances of receptor orientation which result in displacement of the primary S-C function, 12 ' la > 19 one would predict a loss in sensitivity comparable to that shown in Fig. 6. For each millimeter the peak of the S-C function is displaced in the entrance pupil, mean receptor orientation would be altered by 2.5 degrees. The relationship between a t and Q> for the center pointing hypothesis, and a k = O for 6 f = 0 should not be confused. It is evident from these analogue data that disturbances of several degrees in receptor orientation are probably required before meaningful decrements in visual resolution occur. 20 Discussion The psychophysical consequences of two hypothetical models of photoreceptor orientation have been calculated. The expected loci of maxima of sets of photopic Stiles-Crawford functions for parafoveal points are different in the two models. This permits the formulation of a number of clear tests between the working hypotheses. No allowance is made in the calculations for local variance in receptor orientation. Correction will have to be made for the displacement of the fovea from the optical axis of the eye. That correction will vary as a function of meridian tested. It is not possible to extend the predictions to the retinal periphery because of the limitations inherent in calculations based on the schematic eye and paraxial optics. Despite these limitations, the models described are of substantial value in understanding human receptor orientation. Simply stated, we believe differential receptor orientation is necessary for effective receptor function. The orientation characteristics common to photoreceptors in several species serves as witness to this generalization. 1 ' 3 The light-receiving structures of photoreceptors are cylinders or cones in form. Photosensitive pigment is oriented coplanar to membranous discs within the outer segments (for an example, refer to Liebman 21 ). The photoreceptors are transparent and are separated near the external limiting membrane by processes from the Miiller cells and by fibrils from the pigment epitheilum at their distal ends. The interstitial space formed by these cellular processes has a lower index of refraction, i.e., it has lower concentrations of proteins and lipids than those of the receptor outer segment (and part of the inner segment). The combination of high-index transparent cells separated by a low-index surrounding medium 22 " 24 results in the creation of fiber optics elements which, when taken together, form a bundle. In addition, the fibrils from the pigment epithelium (projecting between the receptors) contains dark melanin granules in many species. As a consequence of their form and surroundings, both rods and cones are directionally transmitting and directionally sensitive. The directional sensitivity of cones is widely accepted. Although controversial, the evidence for directional sensitivity of rods is steadily accumulating. 15 ' is, 22, when considering this problem, it must be remembered that the entrance pupil aperture allows evaluation only of directional sensitivity (Stiles-Crawford ef-

11 Volume 10 Number 12 Retinal receptor orientation. II 969 feet) over a few degrees of incidence at the retina in the human being, approximately ± 10 degrees. Here we refer to the angle subtended at the retina by the iris aperture rather than the retinal locus. That angle is translated to the entrance pupil plane by ray trace. The arguments presented above are not limited to apertures of ± 10 degrees. 7 Oriented photolabile pigment acts much like a polarizer. Probability of absorption of nonpolarized light follows a V2 (1 + cos 2 a) function, e.g., at an angle of incidence of 45 degrees only a 75.0 per cent probability of absorption exists. Further, a fiber optic element, like a microscope objective, has a limiting aperture, its numerical aperture (for an example refer to Kapany- S ). This aperture defines the limiting angle within which the fiber or receptor can contain (couple-in) energy. Dark melanin pigment sheathing in many species reinforces this effect. Since these properties are all present in rods, they, too, must be directionally sensitive. It is interesting that in the histologically all rod retina of Gecko gecko, the same anterior pointing properties were observed as were found in mixed rod-cone retinas of primates. 3 In order to be visually effective, photoreceptors in the mid to peripheral retina would ideally have an anterior pointing orientation. Assume a receptor is located at the equator of the eye and is directed toward the center of the retinal sphere (point O). If d were set equal to r (Fig. 1) radiant energy reaching this receptor would be incident at an angle of 45 degrees. The source of the visual stimulus (as seen by the receptor), the exit pupil aperture, would be somewhat foreshortened. Since a cell pointing at O most probably has its maximum sensitivity in the direction toward which it points, it would be receptive to and integrate stray light incident over a broad solid angle. Of course, the stray light absorbed would vary as a function of its angle of incidence at the cell. The summed amplitude of the stray light might well exceed the direct signal from the pupil. Melanin sheathing and pigment orientation would tend to further limit the direct signal absorbed in such a case. One is led to a number of conclusions, if this is a valid argument. Namely, the photolabile pigment in the receptor outer segment is oriented in order to more effectively absorb the light guided to it by the receptor acting as a fiber optics element. The receptor is a fiber optics element and is often sheathed by pigment to protect it from stray light. Thus, for effective function, the fiber optics element must be directed toward the source of light (ideally the center of the exit pupil of the eye) in order to receive the signal (visual stimulus) with high efficiency. One key aspect of the problem of photoreceptor orientation has not been considered here. That is, it is important to define the mechanism(s) which determine orientation at birth and maintain and correct it during life. A discussion of some phases of this problem was recently presented by Laties and Enoch. 3 A recent paper by Bourdy 20 touches on some aspects of this problem. Enoch and Hope 30 will shortly present an initial experimental analysis of theoretical arguments discussed in this paper. REFERENCES 1. Laties, A.: Histological techniques for the study of photoreceptor orientation, Tissue Celll: 63, Laties, A., Liebman, P., and Campbell, C. E. M.: Photoreceptor orientation in the primate eye, Nature 218: 172, Laties, A., and Enoch, J. M.: An analysis of retinal receptor orientation. I. Angular relationships of neighboring photoreceptors, INVEST. OPHTHALMOL. 10: 69, Stiles, W. S., and Crawford, B. H.: The luminous efficiency of rays entering the pupil at different point?, Proc. R. Soc. Lond. Series B. 112: 428, Stiles, W. S.: The directional sensitivity of the retina, Ann. R. Coll. Surg. Engl. 30: 73, Aguilar, M., and Plaza, A.: EfTecto Stiles- Crawford en vision extra-foveal, An. Soc. Real. Esp. Fisica y Quim. A. 50: 119, 1954.

12 970 Enoch and Laties Investigative Ophthalmology December Heath, C, and Walraven, P.: Receptor orientations in the central retina, J. Opt. Soc. Am. 60: 733, Heath, G.: Directional sensitivity of retinal receptors, J. Opt. Soc. Am. 60: 736, Duke-Elder, S., editor: System of ophthalmology, vol. II. The anatomy of the visual system, ed 2, London, 1961, Henry Kimpton. 10. Walls, G.: The vertebrate eye, Bloomfield Hills, Mich., 1942, Cranbrook Inst. of Science. 11. O'Brien, B., and Miller, N. : A study of the mechanism of visual acuity in the retina. W.A.D.C. Technical Report No , Wright Patterson Air Force Base, Ohio, 1953, Wright Air Development Center. 12. Enoch, J. M.: The current status of receptor amblyopia, Doc. Ophthalmol. 23: 130, (The O'Brien-Miller 11 experiment appears in a rather inaccessible document. The technique has been described in some detail in this paper.) 13. Enoch, J. M.: Receptor amblyopia, Am. J. Ophthalmol. 48: (Part II) , Crawford, B. H.: The luminous efficiency of light entering the eye pupil at different points and its relation to brightness threshold measurement. Proc. R. Soc. Lond. Series B 124: 81, Flamant, F., and Stiles, W. S.: The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths, J. Physiol. (Lond.) 107: 187, Flamant, F.: Contribution a l'etude du phenomene Stiles-Crawford, Rev. Opt. 28: 44, Westheimer, G.: Dependence of the magnitude of the Stiles-Crawford effect on retinal location, J. Physiol. 192: 309, Enoch, J. M.: Summated response of the retina to light entering different parts of the pupil, J. Opt. Soc. Am. 48: 392, Enoch, J. M.: The retina as a fiber optics bundle. Appendix B, in Kapany, N.: Fiber optics, principles and applications, New York, 1967, Academic Press, Inc., pp Ohzu, H., Enoch, J., and O'Hair, J.: Optical image modulation by the fresh isolated retina and retinal receptors, Vision Res. In press. 21. Liebman, P.: Retinal cell microspectrophotometry, Ann. N. Y. Acad. Sci. 157: 250, Briicke, E. ( ): Cited (and elaborated on) in Von Helmholtz, H.: Handbook of physiological optics, vol. 1, ed. 3, (English translation by Southall, J. (1924), New York, 1962, Dover Publications, Inc., p. 229.) 23. Barer, R.: Refractometry and interferometry of living cells, J. Opt. Soc. Am. 47: 545, Sidman, R.: The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy, J. Biophys. Biochem. Cytol. 3: 15, Enoch, J. M.: Nature of the transmission of energy in the retinal receptors, J. Opt. Soc. Am. 51: 1122, Enoch, J. M.: Optical properties of the retinal receptors, J. Opt. Soc. Am. 53: 71, Enoch, J., and Glismann, L.: Physical and optical changes in excised retinal tissue: Resolution of retinal receptors as a fiber optics bundle, INVEST. OPHTHALMOL. 5: 208, Kapany, N.: Appendix N, in Strong, J.: Concepts of classical optics, San Francisco, 1948, J. H. Freeman Co., pp Bourdy, C: Eft'et Stiles-Crawford, et fixation, Vision Res. 10: 859, Enoch, J. M., and Hope, G. M.: An analysis of retinal receptor orientation III. Results of initial psychophysical tests, INVEST. OPHTHAL- MOL., to be submitted.