resolving power of the optics based on consideration of diffraction and the objective measurements of the quality of the optics of man in vivo have

Transcription

1 576 J. Phy8iol. (1965), 181, pp With 13 text-figures Printed in Great Britain OPTICAL AND RETINAL FACTORS AFFECTING VISUAL RESOLUTION BY F. W. CAMPBELL AND D. G. GREEN* From the Physiological Laboratory, University of Cambridge (Received 27 April 1965) If a scene containing fine spatial detail is viewed at constant high photopic luminance, there are two main factors which limit the perception of the fine detail-the quality of the optics of the eye forming the image on the retina and the ability of the retina (coupled to the brain) to resolve the details of that image. In the past there have been many theoretical studies of the potential resolving power of the optics based on consideration of diffraction and the chromatic and spherical aberrations of the eye. It is only recently that objective measurements of the quality of the optics of man in vivo have been obtained (Flamant, 1955; Westheimer & Campbell, 1962; Krauskopf 1962; R6hler, 1962). As will be demonstrated, it is not possible to use these findings to determine the relative weighting that should be given to the optics and the retina in determining a given threshold. This paper reports the results of experiments using an improved version of the well-known interference fringe technique (Le Grand, 1937; Byram 1944; Westheimer, 196; Arnulf & Dupuy, 196) which theoretically allows a sinusoidal pattern of very high contrast to be formed directly on the retina. The practical difficulty in using this technique is to obtain a light source of high intrinsic brightness and coherence with which to form high-luminance interference fringes on the retina; this has been solved by using a neon-helium gas laser. By decreasing the contrast (Fig. 1) of the interference fringes with another source of light it was possible to determine the contrasts on the retina at which the fringes are just detected. Thus a measure of the resolving power of the retina-brain is obtained without prior modification by the optics of the eye. Measurements have also been made of the visual resolution of external gratings whose intensity varied sinusoidally with distance across the gratings and which were imaged on to the retina by the optical components of the eye. By comparing the threshold contrasts of these external sinusoidal gratings with thresholds for sinusoidal fringes of the same spatial frequency formed through interference, the quality of the * Present address: Nobel Institute for Neurophysiology, Stockholm, Sweden.

2 VISUAL RESOLUTION 577 retinal image has been measured by determining the optical transfer function of the eye (Linfoot, 1964). Effects of pupil size and focus have also been measured and compared with the performance of ideal optical systems. CB Distance Fig. 1. Contrast is defined as (Im,-I)/(Im +I,. Three contrast ratios are illustrated: 1-,.5 and -5. Note that the mean luminance level remains constant. Spatial frequency is defined as the reciprocal of the angular distance between successive maxiima in the sinusoidal intensity distribution. The spatial frequency that can just be detected is thus a measure of visual acuity. METHODS Formation of interferencefringe8 To form the sinusoidal patterns on the retina the interference property of coherent light was used. Two beams of monochromatic light from a coherent source, a neon-helium laser, were focused in the plane of the pupil near the nodal points of the eye. The beams diverge within the eye and both illuminate a patch on the retina. A fringe pattern is produced by interference where the beams overlap on the retina. The maxima and minima occur where the path difference between the two beams is such that the wave fronts are in phase and add, or out of phase and destructively interfere. The resulting intensity distribution is given by a X) I(x) = I1+I2+2V(I112)os(A-a), (1) where I., 12 are the intensities of the two beams, A the wave-length of the light, a the separation of the two coherent sources, and x the angular distance in radians along the retina. When the two beams are equal in intensity the fringes are of unity contrast. The apparatus is shown diagrammatically in Fig. 2. The neon-helium laser (Bradeley Ltd., 37 Physiol. 181

3 578 F. W. CAMPBELL AND D. G. GREEN Type-LH 61) was powered from a radio frequency source of 6 W. When fitted with concave mirrors the laser generated a slightly divergent beam with a uniphase front (TEMOO) at A = m,u. In this mode the maximum output was about 1 mw. The beam from the end of the laser was made sufficiently divergent with a -5D spectacle lens (L1) to fill the 1 cm aperture of the 1 cm focal length microscope objective (L2) placed at a distance of about 15 cm. To separate the light into the required two portions, the beam was divided by passing it through a thin pellicle (RP) placed at 45 to the axis of the beam. The beam reflected from the pellicle was reflected a second time from a front aluminized mirror (M1) and directed on to L2. The direct beam was found to be slightly brighter than the reflected beam and therefore a neutral density filter (NF) was placed in the path of the direct beam to equate them. Fig. 2. F _PI L v3 mtl Diagram (not to scale) of the apparatus used to form interference fringes on the retina. See text for description. The observer placed his eye so that the double image of the source was at the nodal point of the eye. This position was not critical since, for an emmetropic eye, the fineness of pattern on the retina is essentially independent of where the beams come to focus. The subjects verified that they could move their heads back and forth over several inches without being able to detect any change in the frequency of the fringes observed. The viewing was Maxwellian with the lens (L2) seen to be evenly flashed with light. In this position the observed grating filled a circular field of about 3 diameter. From eqn. (1) the formula relating the separation of the images of the source at the nodal point to the separation of successive maxima in intensity on the retina is a = A/a, where a is the visual angle between successive maxima expressed in radians, A is the wavelength of the light in air and a is the separation of the images in air. In these experiments, A = m/ct and a was measured directly with a measuring microscope (not shown in Fig. 2). In order to change a, the distance between the mirror (M1) and the pellicle (RP) was varied and the mirror re-aligned to direct the reflected beam on to lens L2. Varying the content of the vertical interference fringes formed at the retina while keeping the retinal illurnination constant was done with the arrangement shown in Fig. 2. The filament of a small 36 W tungsten lamp is focused by lens L3 on to the microscope objective (L2) after reflexion by a mirror (M2). This mirror is placed just above the level of the two laser beams so as just to miss them. The colour of the light is determined by an interference filter (F) selected to match the colour of the laser beams. The light from the tungsten lamp is non-coherent and it simply dilutes the contrast of the fringe interference pattern. The luminance of the tungsten source was adjusted so as to produce a field equal in luminance to that of the laser field. In order to vary the amount of contrast dilution and keep the mean luminance constant, a polaroid (P.) is placed in the tungsten beam at right angles to the angle of polarization of the laser beams. The laser light is already plane polarized owing to the presence of windows at either end of the gas discharge tube orientated at the Brewster

4 VISUAL RESOLUTION 579 angle. A second polaroid (P2) is mountedin a rotating holder and placed before the objective (L,) so that it intercepts all three beams. As this second polaroid is rotated it varies the ratio of the intensities of the laser to the tungsten light, but keeps the total light flux reaching the microscope objective constant. Thus, rotation of the polaroid varies only the contrast, and it does so as sin2, where is the angle of rotation in degrees. Formation of sinusoidal gratings The method used to generate a vertical sinusoidal grating target was based on that of Schade (1956) as modified by J. G. Robson, in which grating patterns are generated on the face of an oscilloscope. The oscilloscope selected was a Telequipment (Type D33R) with a green phosphor (P1) Contrast calculated from input voltage Fig. 3. The measured contrast of a grating pattern formed on the oscilloscope screen plotted against the modulation voltage which was applied to the modu. lation grids of the cathode ray tube. Measurements were made by scanning a 2 c/deg sinusoidal pattern with a linear photocell and narrow slit. The vertical axis was driven through one of the oscilloscope's vertical amplifiers at 1 kc from an oscillator giving a triangular wave-form output. The horizontal axis was driven by the oscilloscope's own internal time base at a frame frequency of 5 c/s or higher. To form the desired pattern on the face of the cathode-ray tube, the second vertical amplifier was disconnected from the second beam and its output applied through a capacitor to the beam brightness control grid of the cathode-ray tube. This amplifier was then driven from a sine-wave oscillator. With suitable synchronization of the oscilloscope from the sine-wave oscillator it was possible to generate gratings on the screen over a large range of spatial frequencies. The modulation depth of the grating pattern could be varied by changing the magnitude of the 37-2

5 58 F. W. CAMPBELL AND D. a. GREEN voltage reaching the control grid of the cathode ray tube. In practice this was done by changing the output of the oscillator and the gain of the second vertical amplifier. By direct measurement of the patterns on the screen, with a linear photocell, it was determined that the screen could be run at a luminance of about 1 cd/m2 and with the contrast of the gratings proportional to the voltage applied to the control grid from zero to about -5 contrast (Fig. 3) I Spatial frequency (c/deg) Fig. 4. The spatial frequency response of the oscilloscope. Measurements were made by photo-electrically scanning the screen with the modulation voltage held constant. The spatial frequency of the sinusoidal gratings is expressed in c/deg as if viewed from a distance of 57 in. from the screen. In front of the oscilloscope was placed a sheet of white cardboard having a 2 in. by 1-3 in. aperture. This cardboard was illuminated to the same brightness and colour as the oscilloscope screen with a tungsten lamp and colour filter. To standardize the contrast of the grating, a low spatial frequency square-wave grating was put on the screen. A calibrated neutral density filter was placed in front of the brighter half cycle of the grating and the modulating voltage was adjusted until a match, as determined by eye, was obtained with the darker half cycle. This contrast setting was calculated to be -26. Other contrast settings were taken as proportional to this voltage (Fig. 3). The subject determined the magnitude of the modulating voltage at which the grating was just detectable and this peak-to-peak voltage was then measured. The spatial frequency of the grating was calibrated in terms of the oscillator frequency, which could be read to about 1 %. The resolution of the gratings on the oscilloscope face was found to be independent of spatial frequency up to about 45 c/deg. at a viewing distance of 57 in. (Fig. 4).

6 VISUAL RESOLUTION 581 RESUJLTS Resolution of interference fringes by the retina-brain No difficulty is encountered in measuring the threshold for sinusoidal interference fringes at frequencies up to 35-4 c/deg, for the fringes are seen over a large part of the visual field. However, at higher frequencies the perception of the pattern is confined more and more to the central region of the fovea. As the fixation axis of the eye wanders about, the small area of the field resolving the fringes also drifts (rather like the drifting of an after-image formed at the fovea). Inexperienced observers are often unable at first to see fringes of high frequency even when the fringes are presented at 1% contrast. However, if the observers are trained to fixate for a few seconds on some dust particle present in the lens system of the microscope objective and to look for the fringes appearing near the fixation object, they quickly learn to perceive the grating and to retain the perception in the absence of voluntary fixation. It is also advantageous to measure the threshold contrast by first setting the contrast suprathreshold and then lowering it until the grating disappears. At very high spatial frequencies the fringes are perceived in a region subtending about half a degree in diameter. It is difficult to recognize it as a grating, for its dominant appearance is that of a scintillating area brighter than the surrounding field and also desaturated in colour compared with the rest of the field. This effect is well described by Byram (1944). It is presumably due to 'beating' between the periodic fringes and the regular pattern of the retinal mosaic. Another phenomenon also increases the difficulties of making accurate measurements at higher spatial frequencies. If a grating is observed at suprathreshold contrast for a period of more than about 1 sec, it tends to fade from view. It will reappear if the eye is closed for a second or so, or if the observer switches to his other eye, or if one of the interference beams is cut off temporarily to remove the interference pattern. In practice we were able to control this fading by making the observations rapidly, taking only a few seconds to reduce the contrast from some suprathreshold value down to the threshold value. A check at this value was made by observing with the other eye to ensure that the grating was not visible. As will be pointed out in the Discussion, we have been able to resolve gratings at lower contrast than some other workers. It is likely that one of the reasons for this is due to the greater care that has been taken in this study to control the factors mentioned above. In Fig. 5 the results are shown for subjects D. G. G. and F. W. C., obtained at a retinal illumination of 5 td. Contrast sensitivity is plotted

7 7 582 F. W. CAMPBELL AND D. G. GREEN on a log. scale and spatial frequency on a linear scale. Smooth curves have been drawn by eye through the results. For spatial frequencies higher than 1 c/deg the threshold contrast for detecting the fringes is a steadily increasing function of spatial frequency. In Fig. 5, where contrast is plotted on a logarithmic scale and spatial frequency is plotted on a linear scale, this high frequency portion of the curve, from 1 c/deg on upwards, is closely fitted by a straight line. That is, the contrast sensitivity is decreasing exponentially with increasing spatial frequency _ Ca 1 - * O. I.., oq _ Spatial frequency (c/deg) Fig. 5. Contrast sensitivity for interference fringes formed by a coherent source of A = m,u. Measurements were made at a retinal illumination of 5 td. Results obtained for two subjects are shown as open circles, F. W. C. (4 yr) and closed circles, D. G. G. (27 yr). The smooth curves have been drawn by eye through the measurements. Resolution of the over-all visual system In the previous section, the resolving power of the retina-brain was determined for interference patterns modulated in intensity sinusoidally. External gratings with similar modulation were then used to determine the resolution of the over-all visual system. This was done by generating the

8 VISUAL RESOLUTION 583 gratings on an oscilloscope screen and measuring the contrast threshold as in the previous experiment. The fundamental advantage of using a sine modulated grating is that the modulation remains sinusoidal even when imaged by a poorly focused or imperfect optical system. The effect of all aberrations and focus settings is a reduction in contrast of the grating pattern in the image plane. Two main factors affect the quality of images formed on the retina by the optics of the eye-focus and pupil size. 1 r 3., 4., 9 1 Ic; i 4. 4., Q 4._ -Q _ v a) 1 L Lens power, dioptres Fig. 6. The effect on contrast sensitivity of changing the refractive power of the eye of subject D. G. G. Measurements at four spatial frequencies are illustrated. The eye was homatropinized and a 2 mm diameter pupil was used. The points are the average of three measurements. *, 3 c/deg;, 22 c/deg; O, 9 c/deg; *, l 5 c/deg. Focus. To change the refractive power of the eye a range of spectacle lenses was placed near the cornea and the subject viewed the test gratings through a 2 mm diameter pupil. The eye was atropinized to eliminate the effects of fluctuations of pupil size and accommodation. The results are shown in Fig. 6 for the four spatial frequencies of 1-5, 9, 22 and 3 c/deg. It can be seen that there is a symmetrical decrease in

9 584 F. W. CAMPBELL AND D. G. GREEN sensitivity around a well defined lens power of D. As the viewing distance was 57 in., the refractive error of this eye is + -8 D at infinity in the vertical meridian. It is clear that the rate of change of contrast sensitivity with change of refractive power is greater at higher spatial frequencies. Cs ' 1 X 1 -ia~ ~ ~ ~~~ptalfeunc cdg Spatial frequency (c/deg) Fig. 7. The effect on contrast sensitivity of increasing the refractive power of the eye by,.5, 1 and 2- D over a wide range of spatial frequencies. The eye of the subject (D. G. G.) was homatropinized and a 2 mm diameter pupil was used. The points are the average of three measurements. *, 1-5 D;, 2* D; El, 2-5 D; *, 3-5 D. In the next experiment the contrast sensitivity for the emmetropic eye and for three values of myopia were determined (.5, 1 and 2 D). The results on D. G. G. using a 2- mm diameter pupil are shown in Fig. 7. Not unexpectedly, the contrast sensitivity decreases at all higher spatial frequencies with progressive de-focusing. PUpil size. Using the + 1X5 D lens to render the eye in focus for the viewing distance, the effect on the contrast sensitivity of various pupil sizes was determined. Neutral density filters were placed before the eye to compensate for the change in retinal illumination due to changes in pupil area. The retinal direction effect (Stiles & Crawford, 1933) was taken into account. Pupil diameters of 2-, 2-8, 3-8 and 5-8 mm were used. For the

10 VISUAL RESOLUTION 585 sake of clarity, the results of only three of these are shown in Fig. 8. The general shape of the three sets of measurements of contrast sensitivity is similar to that found for the retina alone (Fig. 5), but in all instances the contrast sensitivity for the fringes on the retina is higher than that for the 'over-all' visual system. '2 -I - Ca 1 [ C) '2 Po 4 1 I ai I l Spatial frequency (c/deg) Fig. 8. The effect on contrast sensitivity of changing the diameter of the artificial pupil. The eye (subject D.G.G.) was in focus for the viewing distance and was homatropinized. The points are the average of three measurements., 2- mm pupil; *, 3-8 mm pupil; A, 5-8 mm pupil. Determination of the contrast transfer function of the optics In Fig. 9 the open circles represent the contrast sensitivity obtained with a 2 mm diameter pupil and emmetropic correction as in Fig. 8. The continuous curve represents the contrast sensitivity of the retina alone (D. G. G.) obtained by means of interference fringes as in Fig. 5. In the upper portion of Fig. 9 are plotted the ratios of the contrast sensitivities for Over-all/Retinal (closed circles). The ratio scale is on the right side of the figure. This ratio can be interpreted as the reduction in contrast of the image falling on the retina due to optical defects in the eye's refractive system. This follows from the assumption that the threshold sensitivity

11 586 F. W. CAMPBELL AND D. G. GREEN for a sinusoidal fringe pattern formed on the retina by interference is the same as for a similar grating imaged thereon by the optics of the eye, providing the measurements are made at identical wave-lengths and luminances. In these experiments, the only available suitable oscilloscope had a green phosphor with a spectral luminance peaking at 53 m,t and with a half-width of + 3 m,u. The only available laser had its emission at 632*8 m,u. In order to justify interpreting the over-all/retinal ratio of contrast c; f 1 1 F _. 1 5v -2 u -1 - r. W IC v- Q 1 I'- c '.,4.%.` - I II Spatial frequency (c/deg) Fig. 9. The open circles are transferred from Fig. 8 (2 mm pupil). The continuous smooth curve is transferred from the results of D. G. G. in Fig. 5. The closed circles are the ratios of the contrast sensitivities and represent the contrast transfer function for the optics of the eye. A smooth curve has been drawn through the ratios. sensitivity as a measure of the optics, we have assumed that the resolving power of the visual system is not significantly different for lights of equal luminance at wave-lengths of 53 and 632f8 m,u. This assumption seems reasonable, for it is in agreement with the findings of Brown, Kuhns & Adler (1957), who show visual acuity to be equally good over most of the visual spectrum. As these workers tested visual acuity with high-contrast

12 VISUAL RESOLUTION 587 gratings, it could be argued that their experiments do not exclude the possibility that the shape of the contrast sensitivity curve is wave-length dependent. To test this possibility the contrast sensitivity of subject D. G. G. was measured using the oscilloscope screen viewed through Ilford spectrum filters (nos. 67 and 621). These filters, in combination with the spectral emission of the phosphor and the sensitivity of the eye, gave a test field coloured blue and orange. With a spectroscope, it was determined that the peak wave-lengths of each field were about 48 and 6 m,t. The fields were of equal luminance and produced a retinal illumination of 3 td. 1. *8 6.6 i p4 p._ 4 V S Spatial frequency (c/deg) Fig. 1. Calculated contrast transfer functions for the in-focus eye of D.G.G. at four pupil diameters,, 2 mm; V, 2-8 mm; E, 3.8 mm; A, 5-8 mm. The ratio of contrast sensitivity for each colour at eighteen spatial frequencies ranging from 3 to 3 c/deg was determined. Inspection of the results showed no difference in the shape of the two curves. The mean ratio for all spatial frequencies of Blue/Orange was found to be s.e The ratio does not differ significantly from unity. It may be concluded that at these two wave-lengths there is no difference in the contrast

13 588 F. W. CAMPBELL AND D. G. GREEN sensitivity, nor is there evidence that the shape of the contrast sensitivity curve is affected by using these widely differing wave-lengths. In Fig. 1, the over-all/retinal ratios ofthe contrast sensitivities are given for pupil diameters of 2-, 2-8, 3-8 and 5-8 mm. For spatial frequencies greater than 3 c/deg. the contrast ratio is highest for the 2*8 mm pupil, but for frequencies lower than 3 c/deg the optimum pupil size is 2 mm. The optics compared with a perfect diffraction-limited system It is interesting to compare the measured transmission properties of the eye with those that would be obtained with a system free from geometrical aberrations and limited only by diffraction. This may be done conveniently by adopting the convention at present used in physical optics (Hopkins, 1962; Linfoot, 1964). Contrast ratio on a linear scale is plotted against the spatial frequency normalized to the diffraction cut-off '6 5 A A I I I Normalized spatial frequency Fig. 11. The results shown in Fig. 1 have been normalized to the diffractionlimited cut-off frequencies set by each pupil size. If the eye were an ideal diffaction-limited optical system, the results should all lie close to the curve labelled 'diffraction-limited optical system'. *, 2 mm pupil; V, 2-8 mm pupil; U, 3-8 mm pupil; A, 5-8 mm pupil. This is done by dividing each grating frequency by the so-called cut-off frequency for each aperture size (Fig. 11). The cut-off frequency is the line frequency above which no fine structure appears in the image (IAnfoot, 1964). That a definite frequency exists with this property was first pointed out by Duffieux (1946).

14 VISUAL RESOLUTION 589 The top curve in the figure is the normalized frequency response for an aberration-free optical system limited only by diffraction at A = 53 mru. Smooth lines have been drawn by eye through the contrast ratios obtained for various pupil diameters. Increasing deviation of the results with increase in pupil size from the perfect diffraction limit is probably due to the addition of the effects of spherical aberration. -o O* W te v -6 %% os os Normalized frequency Fig. 12. The effect of defocus on the optical transfer function. The continuous lines are drawn by eye through the results. Each interrupted line represents the transfer function of an ideal optical system suffering only from diffraction and defocus. (Subject, D. G. G. Pupil diameter, 2 mm. A = 53 m,.) Upper frame: *, 1-5 D; A, 2-5 D. Lower frame: *, 2- D;, 3-5 D. In the next experiment, the effect on the contrast sensitivity of increasing the refractive power of the eye by, -5, 1 and 2- D was measured for a 2 mm pupil. The results were processed as previously described to determine the optical component, using the contrast sensitivity already determined for the retina-brain (Fig. 5). In Fig. 12 the results have been displayed on a normalized frequency scale as was done in the previous experiment. The interrupted lines are theoretical curves for a 2 mm aperture system free from geometrical aberrations and suffering only from defects of focus. Each interrupted line has been computed taking

15 59 F. W. CAMPBELL AND D. G. GREEN into account the size of the pupil, the wave-length of the light and the degree of focus error. This was done according to the theoretical method described by Hopkins (1962) and using computational results kindly supplied by Dr E. H. Linfoot. The fit is good. The remaining deviations may be accounted for by the small amounts of lateral chromatic and spherical aberration still present at a pupil diameter of 2 mm. As the half band-width of the spectral luminance of the oscilloscope phosphor was + 3 m#t around 53 m, the probable magnitude at these limits of the longitudinal chromatic aberration is about -25 D (Campbell, 1957). Unfortunately, the magnitude of spherical aberration varies greatly from subject to subject and is difficult to measure at small apertures. We hope to compute corrections for these aberrations at a later date. DISCUSSION Measurements of threshold contrast have been made by Westheimer (196) and by Arnulf & Dupuy (196), using fringes formed upon the retina by interference. Unfortunately, it is difficult to compare quantitatively their data with our results. In the case of Westheimer (196) the comparison is impossible owing to ambiguity in his published scale of threshold contrasts. Comparison of our results with the threshold curves of Arnulf & Dupuy (196) shows that their contrast thresholds are about three times higher than our measurements, even when we repeated the experiment at their lower retinal illumination (5 td.). However, considering the differences in the techniques, such discrepancies are small. In general terms, the measurements obtained in these three ways show similar trends of contrast threshold with spatial frequency. Arnulf & Dupuy (196) have made suprathreshold contrast matches between gratings formed directly by interference on the retina and gratings imaged on to the retina. The gratings formed by the optics have a lower contrast than the interference gratings owing to the attenuation by the optical system. By taking the ratio of this difference in contrast, the contrast transfer characteristics of the optics can be determined. Their results for a 2-5 mm diameter pupil are shown in Fig. 13 compared with the mean results obtained by us for a 2-8 mm pupil. The agreement is good at the few spatial frequencies they used. Flamant (1955), Westheimer & Campbell (1962), Krauskopf (1962) and Rohler (1962) have attempted to establish the quality of the retinal image by examining photographically or photo-electrically the reflected light coming from a fundus image. As their data have been obtained after the light has passed twice through the optics, calculation is required to find the quality of the retinal image formed by the normal single passage. Flamant's results are shown in Fig. 13.

16 VISUAL RESOLUTION 591 The squares represent Flamant's calculations of the contrast transfer function for a single passage (natural pupil; probably 3-4 mm diameter). Westheimer & Campbell (1962) obtained almost identical results with a 3 mm pupil and Krauskopf similarly confirmed Flamant's result with data obtained at a pupil diameter of 5 mm. Their results are not shown. 1. " mm pupil 5.8 mm pupil 2-5\ 2 A Spatial frequency (c/deg) Fig. 13. The interrupted curves represent the mean contrast transfer functions obtained by us at pupil diameters of 2-8 and 5-8 mm (see Fig. 1). The calculations of Flamant of a single passage through the optics are shown as squares. The measurements of Arnulf and Dupuy for a 2-5 mm pupil are shown as circles. R6hler's results are also not shown because his measurements were not made at frequencies higher than 1 c/deg. The interrupted curves represent the mean contrast transfer functions obtained by us at pupil diameters of 2-8 and 5-8 mm (see Fig. 1 for raw data). It is clear that our results indicate that the quality of the optical image is much better than was estimated by the four groups who independently used the double-passage technique. The ophthalamoscopic technique requires considerable skill in the alignment of the optical apparatus, in the adjustment of the electronics, and in the selection and training of the subjects. Furthermore, the calculations required to obtain the single-pass optics from the &loublepass data depend on a number of untested assumptions about the nature of the reflecting (or diffusing) surface at the fundus. These difficulties and uncertainties could lead to the conclusion that the quality of the image is worse than it is in reality. Preliminary experiments with an improved version of the double-pass apparatus have given results closer to the

17 592 F. W. CAMPBELL AND D. G. GREEN optical transfer function found in this paper than that obtained by the previous four groups. This suggests that further attempts should be made to improve the double-pass technique. There has been speculation on the extent to which an optical interpretation can be given to the increased contrast required for the detection of a grating with increasing spatial frequency. Ooue (1959) and Flamant (1955) have taken the extreme view that a grating is detected when a given contrast is achieved at the retina. Our results permit a quantitative assessment of the relative role of optics and nervous system in the detection of gratings at higher spatial frequencies. For example, inspection of Fig. 9 shows that over the range 3-4 c/deg the optical attenuation (indicated by the change in the contrast ratio) increases by a factor of Over this same range the attenuation by the nervous system measured by interference fringes increases by a factor of 2-4 (Fig. 9). Thus, in this example, using a 2 mm pupil, the attenuation due to the nervous system is approximately twice as great as that due to the optics. In the case of the over-all contrast sensitivity the optics will contribute only one third of the attenuation in this high frequency range. Of course, for pupil diameters greater than about 2-4 mm, and particularly for de-focused images, the optics will contribute to the over-all attenuation to a much greater extent. SUMMARY 1. With a neon-helium laser as a light source, interference fringes were produced on the retina directly, thus by-passing the effects of the optics of the eye. 2. Threshold contrasts for resolution of these interference fringes were measured. It was found that the contrast sensitivity decreased roughly exponentially with increase in spatial frequency. 3. The contrast sensitivity of the over-all visual system was measured with similar sinusoidal gratings displayed on an oscilloscope. At all spatial frequencies the contrast sensitivity was found to be lower than that obtained with the interference fringes. 4. By finding the ratio between the contrast sensitivities measured by these two techniques, the contrast reduction due to the optics of the eye was calculated. The effects of changes in pupil size and focus on the quality of the retinal image was determined. For an eye with a 2 mm diameter pupil the measured optical attenuation agrees with that predicted for a diffraction-limited system. With increasing pupil size the performance of the optics deviated progressively from a perfect optical system. 5. These results establish that the quality of the optics is substantially better than that determined by recent ophthalmoscopic methods.

18 VISUAL RESOLUTION 593 This investigation was supported by a United States Public Health Service research grant (NB 546-1) and a grant from the W. H. Ross Foundation. D.G.G. was supported by a National Science Foundation Postdoctoral Fellowship. We are pleased to acknowledge the constructive advice of Dr J. G. Robson, Dr E. H. Linfoot, Dr H. H. Hopkins, and the technical assistance of Mr T. Holland. REFERENCES ARNULF, A. & DupuY,. (196). La transmission des contrastes par le systeme optique de l'oeil et les seuils des contrastes retiniens. C.R. Acad. Sci., Paris, 25, BROWN, J. L., KuHNs, M. P. & ADTI, H. E. (1957). Relation of threshold criterion to the functional receptors of the eye. J. opt. Soc. Amer. 47, BmAM, G. M. (1944). The physical and photochemical basis of visual resolving power. Part II. Visual acuity and the photochemistry of the retina. J. opt. Soc. Amer. 34, CAMPBELL, F. W. (1957). The depth of field of the human eye. Optica Acta, 4, DuPFEux, P. M. (1946). L'int6grale de Fourier et ses applications a l'optique. (Bescancon: privately printed.) FLAMANT, F. (1955). etude de la repartition de lumiere dans l'image r6tinienne d'une fente. Rev. Opt. (th6or. instrum.), 34, HoPKiNS, H. H. (1962). 21st Thomas Young Oration. The application of frequency response techniques in optics. Proc. phys. Soc. Lond. 79, KRAUSKOPF, J. (1962). Light distribution in human retinal images. J. opt. Soc. Amer. 52, LE GRAND, Y. (1937). La formation des images retiniennes. Sur un mode de vision eliminant les d6fauts optiques de l'aeil. 2e R6union de l'institute d'optique, Paris. LINFOOT, E. H. (1964). Fourier Methods in Optical Image Evaluation. London and New York: The Focal Press. OOUE, S. (1959). Response function of the eye. J. appl. Phys., Japan, 28, R6O1ER, R. (1962). Die Abbildungseigenschaften der Augenmediern. Vision Res. 2, SCHADE,. H. (1956). Optical and photoelectric analog of the eye. J. opt. Soc. Amer. 46, STns, W. S. & CRAWFORD, B. H. (1933). The luminous efficiency of rays entering the eye pupil at different points. Proc. Roy. Soc. B, 112, WEST EiMER, G. (196). Modulation thresholds for sinusoidal light distributions on the retina. J. Physiol. 152, WESTHEIMER, G. & CAMPBErL, F. W. (1962). Light distribution in the image formed by the living human eye. J. opt. Soc. Amer. 52, Physiol. 181