Ocular refraction at low illuminations

F&ion Ret.

Vn!. 6, pp. ?I?-237.

OCULAR

Pergamon

Press

1966.

Printed

REFRACTION

in

Great Britain.

AT LOW ILLUMINATIONS’

J. MELLERIO Department of Physiological Optics, Institute of Ophthalmology, Judd Street, London, WC.1

HAS been known for many years that the refraction of the eye changes as illumination is reduced, a phenomenon known as “night myopia”. It is arguable whether this name is really suitable, for the refraction changes are not simple. This phenomenon has been the subject of much work and some controversy, and the literature is scattered. This paper is the result of an attempt to collect the relevant data and present in a “nutshell” the reasons for these changes of refraction.

IT

Early work The first mention that illumination affects refraction was made by LORD RAYLEIGH in 1883. He discovered that hecould see small objects more clearly in dim light if he wore glasses of- 1 dioptre power. JACKSON (1888), and BBRANECK and VERREY (I 892) both expected the eye to become myopic in the dark-Jackson because of the enhanced spherical aberration due to large pupils, and Beraneck and Verrey because they thought that light stimulated the choroidal blood-vessels to fill and that their emptying in the dark would cause the retina to move away from the lens. CHARPENTER (1902) confirmed that eyes became myopic in dim light, but SCHOUTE (1903) found only slight changes towards hyperopia. OGATA and WEYMOUTH (1918) measured the refraction of eyes at various perimetric angles and showed that 40 per cent of those measured became more myopic as the angle

increased, until at, and beyond, 4”, a constant value of about -0.37 D was obtained. Homatropine and artificial pupils did not alter this myopia, which, they argued, was due to “parafoveal cupping”. They also noted that in 10 per cent of the eyes examined, there was a slight change towards myopia on proceeding from bright to dim illuminations. WIBAUT (1919) measured the myopia of his own eyes and found that at near darkness it reached a constant value of -1.25 D, and was independent of the illumination below about 3.5 log stilbs. He went on to demonstrate in 14 eyes the effects of chromatic aberration, and suggested that this, coupled with the shift of wavelength of maximum retinal sensitivity from photopic to scotopic conditions, and “parafoveal cupping” of the retina, were the causes of this myopia. He also showed that it took a few minutes for the myopia to approach a plateau and that homatropine did not alter the value of this myopia. The only other relevant work prior to 1940 was that of FERREE and RAND (1933, 1935). They found that in dim conditions the near point retreated from the eye, and that the changes, though small in normal eyes, were greatest in presbyopes. The changes were due to increasing aberrations and reduced depths of focus brought about by enlarged pupillary diameters, diminished visual acuity and “inherent perceptive changes”. 1 This paper forms part of a Ph.D. thesis submitted to the University of London, 217

J. MLLLEHIO

21s

During the second world war, much w:ork was done on “night vision”. but little was published until the late 1940s. Using subjective methods. OTERO and DLIRAN (1941) demonstrated 2 D of night myopia. A year later (OTERO and DURAN, 1942) they explained this myopia as the result of an increase in accommodation of the crystalline lens invoked to reduce the spherical aberration of the eye. As IVANOFF (1947a) was to show in greater detail, the spherical aberration of most eyes is strongly undercorrected when accommodation is relaxed, but is overcorrected at about 4 D of accommodation: somewhere in between. Because the night myopia shown by Otero and Duran usually 1.5 D, the eye is aplanatic. was mostly accommodative, instillation of homatropine reduced the myopia to very IOH levels. LE GRAND (1942) concluded that night myopia was due to chromatic aberration and the Purkinje shift, together with spherical aberration revealed by enlarged pupils. RONCHI (1943) thought that only the former explanation applied. OTERO and DLJRAN (1943) replied that this was not the case, for they had measured night myopia with coloured lights and found that throughout the visible spectrum the myopia was about 2 D. This. and the fact that atropine abolished the myopia, led them to state once again that night myopia was mainly due to the effect of the lens, and that the ocular aberrations played only a small part. During his work with Otero, DURAN (1943) had been able to show that in dim light the amplitude of accommodation was reduced and that below 7.5 log stilbs the eye became presbyopic, and once presbyopic it remained about 2 D myopic of its bright light refraction. It was thought that this represented the “rest point” of accommodation. Other workers who have demonstrated presbyopia and a myopic rest point of accommodation include CARELLO (~~~~),CHIN~~~HORN(~~~~),IVANOFF(~~~~),KATZ(~~~~-~).O~ERO~~~CABELLO(I~~~). OTERO, VIG~N and GALVEZ (1950), SIEBECK (1953). and WALD and GRIFFIN (1947). Katz considered that in darkness it was the lack of a retinal image that caused the eye to accommodate. A similar effect had been noted by LUCKIESH and MOSS (1940) in bright conditions. They presented their subjects with stimuli for convergence to infinity, but with no stimulus to accommodation. This form of myopia is termed empty field or space myopia, and was investigated by CAMPBELL and WHITESIDE (1953), who pointed out that it was a hazard for air pilots. CABELLO (1945) measured the time course of the onset of night myopia and, like WIBAUT (1919), found that it took a few minutes to reach its maximum value. After 5 min it was 1.5 D and after a further 10 min it increased slowly to 2 D. This, he argued, represented the two phases of night myopia, first the action of the lens, and secondly, and more slowly, the adaptation of the rods and the completion of the Purkinje shift. WHITESIDE (1952) found that the onset of night myopia was complete after IO set, whilst SCHOBER (1948), using very crude methods, could find no time-lag. HEATH (1962) employed an automatic i.r. optometer, and found that about 5 min were necessary for the myopia to reach its full value, but that it was very irregular and showed large fluctuations. CAMPBELL. ROBSON and WESTHEIMER (1959). using similar techniques, showed that accommodation fluctuated in bright light, and that, with empty visual fields, the fluctuations decreased in amplitude.

More

recent

work

By 1946-7 evidence of the several causes of night myopia had been published, and the next ten years were mainly concerned with filling in details and confirmatory experiments.

OcuitarRefraction at Low illuminations

219

IVAN~FF (1946, 1947a, 1947b) measured the chromatic aberration of several eyes and also extended the work of AMESand PROCTOR(192 1) by measuring spherical aberration at different values of accommodation. At the same time GRIFFIN and WALD (1946) and WALD and GRIFFIN (1947) were measuring these aberrations and calculated that the chromatic aberrationipurkinje shift caused about 0.4 D of night myopia-a figure similar to that obtained by Ivanoff. The mean value for the night myopia in the 1947 study was -0.6 D, ranging from -3.4 D to +I.4 D. The large range of values between subjects should be noted, for it is a feature of ocular behaviour, especially in dim illuminations; and the fact that some subjects become hyperopic and not myopic should not be lost from view (SCHOUTE, 1903). Wald and Griffin explained these variations in terms of fluctuant involuntary accommodation and said “the average eye is fairly well corrected for spherical aberration”. Enlargement of the pupils would, they argued, increase the spherical aberration of the eye were it not that the cornea becomes flatter towards its periphery, so countering this aberration. ivanoff had noted this for an unaccommodated eye, and RIOS-SASIAIN (1948) pointed out that in his study the magnitude of night myopia was greatest with the smallest pupils. OTERO, PLAZA and Rios (1948), again using telescope eyepiece settings as a measure of night myopia, found that in monochromatic light, which avoids the effects of chromatic aberration, there was a mean of 1.2 D myopia present. With artificial pupils they showed that no more than 0.4 D of this was due to spherical aberration. In 1950, OTERO, VIG~N and G.&LVEZemployed a different technique to strengthen their evidence that accommodation played the major role in night myopia. They photographed the third Purkinje image from the anterior lens surface, because the size of the image provides a useful measure of its curvature and hence of accommodation. They found that with flash photography they could photograph eyes in the dark, for the photograph was taken before any response to the dash-bight could occur. Otero et ai. gave a mean figure of just over one dioptre for the accommodation of their subjects in the dark. KOOMEN, SCOLNIK and TOUSEY (1951) measured night myopia with subjective techniques, and showed that, whereas homatropine did not greatly alter the value, small artificial pupils drastically reduced the myopia. They were convinced that about 0.4 D of night myopia was due to chromatic aberration and the Purkinje shift, and the remaining larger portion to spherical aberration. In reply to this paper, O~ERO and AGUILAR (1951) repeated their experiments with artificial pupils, but still failed to find that spherical aberration was a major cause of night myopia. As a result, KOOMEN ef al. (1953a) repeated the experiments of Otero and his colleagues, and photographed the third Purkinje image. They failed to find any increase in accommodation in dim light and only a very small effect in one of their three subjects in darkness. There followed more articles by both groups upholding their previous findings (KOOMEN et al., 1953b; OTERO, 1953; AGUILAR and YUNTA, 1952). That no one thought that intersubject variations might be the explanation for these conflicting results is surprising, for Koomen used only three, and Otero six subjects. CAMPBELL (1953) used 13 subjects and fovea1 scotoma fixation for his Purkinje image photographs, and showed that there was a mean myopia of -0$4 D in darkness. Campbell summed up the causes of night myopia as: (a) chromatic aberration combined with the photopicjscotopic spectral sensitivity change in the retina,

J. MELLERIO

220

(b) spherical aberration which became effective in some people as pupil diameter increased in low illuminations. and (c) a certain amount of fluctuant accommodation. More recent work of BOUMAN and VAN DEN BRINK (1952) and CHIN and HORN (1956) shows that any of these factors may be important in an individual. Causes

qf accommodative

night m>sopia

Several reasons for the accommodative element of night myopia ha\e been put fcorward. I. Ivanoff, and originally Otero, suggested that some accommodation occurred so as to make the eye aplanatic. In the conditions of illumination that cause night myopia. vision is mediated by the rods, and acuity is low. The retinal images in the extra-fovea] regions will be distorted by spherical aberration, but accommodation will improve them somewhat (IVANOFF, 1947a), although too much accommodation would also degrade these images. The final amount of accommodation must be something of a compromise. and as JIM~NEZLANDI and CABELLO (1943) showed, correction of night myopia with spectacle lenses improves acuity and lowers the visual threshold (OTERO, PLAZA and SALAVERRI. 1949). 2. KtiHL (1949), and latterly Otero, maintained that it was the rest point of accommodation in the absence of retinal images that was responsible for accommodative night myopia. This idea, that the rest point of accommodation lay between the far and the near points, caused considerable difficulty, for it seemed that when the eye was adjusted to its far point, negative accommodation was required: the accepted theories of accommodation could not explain how this might be achieved. Eventually the idea of ciliary muscle tone was brought forward. When there is no stimulus to accommodation, the inhibition of the ciliary parasympathetic nerve supply is reduced, so allowing a certain amount of accommodation to take place. And from a teleological viewpoint, one to two dioptres of accommodation in dim light could be advantageous, for this is a distance corresponding to about an arm’s length. 3. Night convergence also occurs in dim light and darkness, as well as in bright. empty fields, and Ivanoff has suggested that accommodative night myopia is really only convergence-induced accommodation (see below). In a subject’s eye accommodative night myopia may well result from any or all of these factors. Ametropia

and night myopia

Studies by C.ARRERAS (1951) and IRVING (1957) considered the amounts of night myopia present in ametropic eyes. The subject’s ametropia was corrected, and telescope Carreras found little difference eyepiece settings were used as a measure of the myopia. (
cau.m of night mJ?opia

RONCH~ (1947,

spherical

aberrations,

1948) has suggested that besides the myopia caused the lens is pushed forwards through the enlarged

by chromatic and pupil by pressure

Ocular Refraction at Low Illuminations

221

from the vitreous. Whilst this would make the eye myopic, it does not account for the Purkinje image evidence, nor explain why, when the pupil is dilated with a mydriatic, the eye does not become myopic. BIESSELS(1954) could explain night myopia only in terms of oblique astigmatism of the eye. This astigmatism, although present in bright light, is masked by fovea1 vision until scotopic conditions apply. JENKINS (1963) has measured this astigmatism and finds that it can amount to 0.4 D, a finding shown in passing by KOOMEN et al. (1949). Useful review articles on night myopia have been published by PALACIOS(1944), OTERO (1951), KNOLL (1952) and IRVING (1957). Night convergence

IVANOFF and BOURDY (1954), IVANOFF (1955) and BOURDY (1955) published papers showing that as illumination is reduced, convergence gradually approaches a limiting value of about 2 m angles, no matter whether the subject had been fixating a near or far object in bright light. Ivanoff extrapolated the synergy that exists between accommodation and convergence in bright light to dim conditions, and maintained that this night convergence was the cause of accommodative night myopia and night presbyopia. OTERO, AGUILAR and SAURAS(1958) re-examined this phenomenon and showed that the link between convergence and accommodation could be broken. FINCHAM (1962) carried out a more detailed study, and showed that if any retinal images were present in dim light, fusional convergence occurred, but that if it were completely dark and the visual field were empty, convergence disappeared and the optical axes became set for the far point, even though accommodative night myopia remained unchanged. The link between these two mechanisms may be broken, but in monocular viewing conditions, convergence does occur. The reasons for this behaviour are presumably to ensure that in darkness the eyes cover a large field of view, as they are not converged, and that as soon as any object is discerned, the eyes converge to fuse its retinal images. The night near response

The demonstration of accommodative night myopia and night convergence led to the idea that there might be a complete night near response which includes night miosis (WEALE, 1960). This is an interesting idea, for, as we have seen, pupil diameter is an important factor in ocular refraction. However, if night miosis occurs, it would be expected that the enlarging pupil in reducing illuminations would interfere with, or mask, the miosis. Consideration of the pupil light reflex indicates that it is the pupil steady state light response that must be examined, for as the illumination falls the night near response will gradually take effect and any miosis it causes will be superimposed on the steady state pupil curve. A study of the pupil steady state light response curves published in the literature was therefore undertaken, to see if they showed irregularities that could be due to duality of pupil control. The pupil steudy state light response

Seven sets of data were found covering this response, REEVES(1920 curve 7. Fig. 1) published a curve for illuminate the test field (size and distance unspecified), measuring the pupil diameter. The curve is substantially

and are redrawn in Fig. 1. six subjects, using white light to and a photographic method of smooth.

222

J. MELLEKIO

COUVREUX (1924 curve 1 Fig. 1) produced similar data with white light and a field size The slight irregularity at about of 25”. but did not state how many eyes were examined. 4.8 log stilbs in an otherwise smooth curve cannot be considered significant. FERREEand RAND’S (1932, curve 8, Fig. 1) mean result for five subjects was obtained with a test field of about 180”, and white light. The curve, although rather steep. shows a break at about 2-3 log stilbs and the mean slopes of the two portions are significantly different from each other (P=O.O25).

FIG. 1. The steady state pupil diameter (mm) in reducing illumination. The curves are redrawn from the literature as follows: 1. COUVREUX (1924). 2. LYTHGOE (1933). 3. CRAWFORD (1936), displaced upwards by 2 mm. 4. SPRING and STILES (1948). displaced upwards by 3 mm. 5. SPRING and STILES (1948). “Admiralty” curve displaced upwards by 3 mm. 6. FLAMANT (1948). displaced upwards by 5 mm. 7. REEVES (1920). displaced upwards by 6 mm. 8. FERREE and RAND (1932), displaced upwards by 7 mm. 9. Present study, displaced upwards by 7 mm.

LYTHGOE (1932, curve 2, Fig. 1) produced a curve from five subjects with white light and a 180” test field. His results showed just how large the variations in pupil response between subjects can be, and although his mean curve shows slight irregularities, they are not significant. One subject did show a large irregularity, however, but it is not possible to calculate its significance. CRAWFORD (1936, curve 3, Fig. I) used ten subjects, white light and a test field of 55’ for his curve. He fitted a hyperbolic tangent curve to his points, but there is an obvious irregularity in the mean curve, which is significantly different (P=O.O25) from the curve he fitted.

223

Ocular Refraction at Low Illuminations

SPRING and STILES (1948) published two sets of data. One (curve 4, Fig. 1) was the result of their experiments with twelve subjects and a test field of 50”, the other (curve 5) was an “Admiralty” curve obtained from fifty-two subjects. They noted that both curves contained irregularities, and stated that in their curve it was due to the even greater irregularities in the responses of some of their subjects. FLAMANT (1948, curve 6, Fig. 1) used a photographic method for measuring the pupil size of her forty subjects, and employed the darkening evening sky as her test field. In her mean curve, the point of inflexion is very marked and must be significant although it is impossible to calculate a significance from the data given. Figure 2 shows the curves she published from eight individual subjects. Only curve 15 in Fig. 2 has irregularities that may not be significant. Flamant considered the irregularities were caused by the pupil being under the control of two mechanisms, and later, ALPERN, KITAI and ISAACSON (1959) said that these two mechanisms must be the rod and cone systems of the retina. In order to find out if these irregularities were caused by night myopia or another mechanism, the following experimental work was undertaken.

I I9 -

”

”

”

’ ”

I

1817 16 15 14 I3 I2 4 I II f “0 IOC?

9a76-

16

5432-

FIG. 2. The eight pupil steady state light responses published by FLAMANT (1948). The numbers refer to the subjects and are taken from the original paper. The pupil diameter is in millimetres. Curve 9 is correctly plotted, curves 13-40 are displaced upwards by 1, 2,4, 5, 7, 8, and 12 mm respectively.

224

.I. MELLERIO METHODS

Since methods of measuring pupil diameter and the state of accommodation were required, the pupil of the eye and the third Purkinje image were photographed simultaneously on one negative. APPARATUS Figures 3 and 4 show diagramatically the arrangement ofthe apparatus. The mirror M directs the subject’s gaze on to the target T, which has the form of a fine cross drawn on white card, with a pin-hole at the centre, so that a small, just suprathreshold, red spot can be provided for experiments performed in the dark by bulb B and red filter R. The disc wheel W holds eight lenses which vary the vergence of the light from the target, and K is a holder for neutral density filters to control the test field luminance. It also holds an llford 626 yellow spectrum filter used to purify the sodium yellow light that illuminates the target from sodium lamp N

Q R.E

Q 1.E

T

I

R

FIG. 3. A diagrammatic plan of the apparatus. The key is: M, a plane mirror: S, converted slit-lamp (see Fig. 4); W, lens disc with 8 lenses; K, filter holder for neutral density filters and an Ilford 626 filter; T, the target with a central pin-hole; R, dense red fiiter; B, torch bulb; N, sodium lamp and lamp-house; J, 6-m. diameter condenser lens; V, car head-lamp bulb and housing; P; and Pz, two 10; prisms. base together; L. com~n~ting lens; f, Edixa camera. and condenser J. V is a car headlamp bulb. which is used in conjunction with an llford 204 red filter in K, so as to provide red test fields. All the apparatus to the right of the lens disc W is enclosed in a light tight box. The camera C (Edixa 50 mm f I .9 lens and 30 mm extension tube) is focused on the subject’s left eye by the rack mechanism provided. The two 10’ prisms, PI and Pe, cause two images to be formed on the negative, one of the third Purkinje image, and one of the pupil. The lens L keeps the pupil image in focus on the film, for the plane of the pupil lies in front of that of the Purkinje image. The source of illumination is a converted slit lamp, S, mounted on an arm so that it can swing round the eye. Figure 4 shows this more clearly. An image of the filament of the 12 V 48 W bulb A is formed via the lenses D and E, and split into two, Qt and Qz. by the two small silvered right prisms HI and Ha. F is a yellow filter included to reduce both light scatter in the eye and the effects of chromatic aberration of the optics. G is a shutter that provides the short flash of light by which the photograph is taken. The length of the flash is kept below about O-05 set so that the photograph is taken before any signs of a light response of the eye occur. The subject’s head is fitted in the head-rest of the slit-lamp.

Ocular Refraction

at Low illuminations

225

Subjects were first examined with a slit-lamp and then with a Fincham coincidence optometer, in order to ensure that the eye was normal and that a pupil light response and a near response were present. The eye was also refracted. Subjects with sluggish pupils or high ametropias were excluded. All the remaining 25 were tried in the apparatus, but some could not sit still for long, others had drooping eyelids that hid their pupils, and yet more had Purkinje images that were too diffuse to measure; they were all excluded. Finally, nine subjects were studied. Procedure

The procedure in an experiment was as follows. The subjects were light-adapted in a bright room (15 cd-ft-” at bench top level) for 5-10 min before sitting down at the apparatus. The Purkinje images were found and the camera focused. Then the room lights were turned off and the first 16 pictures were taken with the illumination at maximum, two frames with the target being viewed through each of the eight lenses in W. These lenses were presented in a random manner so that the pupil diameter and Purkinje images could be “calibrated” (for the apparent target distance was known). Then the target was viewed through that lens which made it appear farthest away (0.4 D), and the illumination was reduced to darkness, and then back to bright again, the remaining 26 photographs being taken. The reason for taking the photographs in both reducing and increasing illuminations was to see if there were any hysteresis in the pupil system-none was found within the limit of these experimental conditions. For recovery from the flash of exposing light and for any changes due to different test luminances to take place, 15 to 20 set were allowed between each photo~ph. For the last frame of the film, a millimetre rule was placed at the position of the subject’s pupil so as to provide a scale for calculation of pupil diameter and third image size.

FIG. 4. A diagram of the modified slit-lamp S in Fig. 3. The key is: A, I2 V, 48 W, car headlight bulb; D and E, lenses; F, yellow filter; G, shutter; HI and HZ, two small silvered right-angle prisms used to split the beam and form two images of the lamp filament at Q1 and Qz.

J. MELLERIO

‘26

The film, Ilford FP3, was then processed and measured (with a measuring microscope fitted with an eyepiece graticulef. Subjective measuring errors were minimized by allowing only one person to measure aft the films. Because of the distortion introduced by prism Ps, the pupil diameter was measured in the vertical meridian. As the anterior lens surface is not spherical. eye movements could mean that the Purkinje image might be formed by different parts of the lens surface and this would lead to erroneous results. Accordingly, during measurement of the film the position of the image within the pupil opening was checked to see that it remained constant. This proved a sensitive method of checking. and any frames where movement occurred were discarded. Film shrinkage or warping could not be detected. The errors involved in measuring the films were estimated as pupil diameter 7. -= 0.03 mm. 7 :: 001 units. image size The errors of measuring target luminance were estimated as sodium yellow, relative to other points = = 0.05 log stilbs. absolute - _t 0.14 log stilbs. Red light. relative to other points = % 0.11 log stilbs. absolute -= 7 0.18 log stilbs. RESULTS

Before the results could be plotted, it was necessary to know the exact magnitude of the stimulus to the retina. Luminance of the test field is not a measure of retinal stimulus, so it must be expressed in retinal illumination units. This unit is the troland, but the definition of the troland does not take into account pre-retinal absorption nor the Stiles-Crawford effect. The calculation of effective trolands, which makes allowances for these factors. is not an easy matter. in the present experiments, long wavelength light was used. and as it is the shorter waveIengths that are absorbed most, the pre-retinal absorption factor can be put equal to zero (but see WEALE, 1961). The Stiles-Crawford effect can be regarded as reducing the size of the effective pupil in the calculation of effective photopic trolands (?G’~)

where S, is this effective pupil area in square millimetres and I is the luminance of the test surface in nits (cd-m-s). The difficulty lies in the fact that the Stiles-Crawford effect is predominantly a cone effect, so when a range of illuminations is used, it is necessary to form an estimate of the way in which the effect varies as more or less cones are stimulated. CRAWFORD (1937) gave an equation which fitted his measurements of I,I as

where I? is the ratio of the flux of a beam of light travelling through the centre of the pupil to that travelling through the periphery, at radius r, for equal luminosity and U. h, and c. are constants, He also measured the manner in which b varied with illumination. and it is from his figures that values of log ttiP were calculated from values of log stilbs. The total effective flux through the whole pupil is given by the equation R

Fp-2n.

D.

i 0

q . I’ . th

where D is the flux density at the pupil, R is the pupillary radius and r is the radius of an elemental annulus within the pupil. This equation assumes that the pupil is circular and that the point of entry for maximum light efficiency is at its centre, and also that the integration of the Stiles-Crawford effect is additive (STILES and CRAWFORD, 1933).

Ocular

227

Refraction at Low Iitumin~tions

It follows that

and substituting

Crawford’s

equation

for q we have

s R

se = 2n

e-b(r+c)” . r . dr

0

This equation is best integrated graphically and Fig. 5 shows S, plotted against pupil radius for various luminances. It must be remembered that q varies with the wavelength of the test light; it is maximal around 570 rnp, but the greatest changes are towards the shorter wavelengths and not the long. As yellow and red light were used in this study, the probable effect is that the corrections applied for the Stiles-Crawford effect are too iarge. Combined results

All subjects’ results were combined to produce one set of graphs. Figure 6 shows mean pupil diameter and mean image size plotted against target distance (an increase of image size indicates a decrease of accommodation). The dashed lines have been fitted by least squares, and show that for a change in accommodation of 1.5 D, there is a corresponding change of pupil diameter of about 0.1 mm.

40

6

30

E *T 20

IO

0

0

I

2 Rlmmsl

3

4

FIG. 5. The effective pupil area, S, (mm’), plotted against pupil diameter, R (mm), for the different luminances shown (log stilbs). Use of this graph to find a value of S, in the calculation of retinal ilIuminaGon (effective troiands) corrects for the apparent loss of stimulus caused by the Stiles-Crawford effect. The magnitude of this effect increases between 5 and ‘5 log stilbs: below and above these values the ;Tand the 2 log stilb curves should be used. The dashed curve (labelled ER”) shows the uncorrected pupil area.

t

Ocular

Refraction at Low iiluminntions

229

Figure 7 shows pupil diameter and image size plotted against log illumination. The dashed line in the image plot is a fitted linear equation in terms of the illumination and the points 3 and 4’Iog stilbs are not significantly different from it. The dashed line in the pupil plot is the fitted parabola, P = 6438 - 0.22 x - 0.03 ~2 where x is (5Slog stilbs) and P the pupil diameter. The curve is not completely smooth, but none of the irregularities is large or significant. This curve is shown in Fig. 1 (curve 9) and is displaced there to the right relative to the other curves because of the small field size and monochromatic light used. The mean data did not show irregularities of the kind found in the literature. so an examination of the individuals’ results was undertaken. PUPIL

FIG. 8. The mean results of subject H.K. At the top are the pupil and image calibration plots. and beneath the results measured at different illuminations. An increase of image size indicates relaxation of accommodation. The size of the points has been drawn to include the estimated errors of measurement. Refraction of subject: j-4 D sph.

Figures 8 and 9 show the mean results of two subjects plotted with the calibrations at the top, and the trials below. The results of the other seven subjects were very similar in general outline to the two represented here, and differences will be discussed as appropriate. For five subjects the plots of calibration image size show that their accommodation was related to fixation distance. One subject could not make use of the information provided, and his accommodation was erratic. Two myopes (-$ and - 14 D) relaxed accommodation as far as their far points, beyond which their accommodation was erratic, and the last subject-a slight hyperope-behaved like a myope of - 1 D. Generally, the pupil calibration P

J.

230

MELLEK~O

curve followed the accommodation curve; that of subject H.K. is a good example whilst that of C. is not. The effect of reducing jll~rninatjon on accoll~modat~on can be stated brieBy thus-all the subjects (except one) showed that accommod~tjon entered a plateau where it remained unaltered over the middle of the range of illuminations used, To reach this plateuu. five of the subjects (including H.K. and C.) had to relax their accommodation. whilst two increased it, and in one more it remained unchanged. The last subject was the one that did not exhibit an accommodation plateau-his plot was erratic. PUp:L

c*

IMAGE

56

1 FIG. 9. The mean results of subject C. Details as for Fig. 8. Refractian

of subject: ‘IIi D sph.

In the dimmest ~l~urnj~ations H.K, increased her accommodatjon by 1 D, and two more subjects aiso accommodated. In three others accommodation remained almost unchzmged and in one more it retaxed slightly. In the two myopes, of which C. was one (-2 5). accommodation relaxed in dim light and darkness to values that appeared to be beyond their far points. This was a surprising observation and the ---l& D myope, subject W., was refracted with cycloplegics to make sure that he was not a false myope. There have been other reports that some people become hyperopic in dim light rather than myopic (e.g. WARD and GRIFFIN, 1947). and IRVING (1957) photographed the third Purkinje images of two myopes and found that they also relaxed their accommodation beyond their far points in the dark. He repeated the experiment with an i.r. optometer, but with this technique found that the eyes were myopic.

Ocular Refraction at Low Illuminations

231

It is difftcult to explain this pl~enomenon for it looks as though some compensatory lengtl~ening of the eyeball takes place in darkness to keep the refraction of the eye constant and myopic whilst the lens relaxes. Eye movements affecting the Purkinje images have been ruled out, so this cannot be an artifact. Perhaps some activity of the extra-ocular muscles involved in night convergence can reduce the tension on the zonule fibres and at the same time elongate the eyeball, which in myopes has a thin wall. The individual pupil response curves all show small irregularities, and one or two curves show larger ones, but the largest is H.K.‘s and it is significant. The point at 1.3 log rd, is significantly different (P=O.Ol) from a parabola fitted through the remaining points. It is also different (P=O*OS) from a straight Iine joining the points at O-9 and I-9 log t& It is also at this level of illumination that her accommodation begins to increase.

Having found a subject with a pupil irregularity, it was decided to see if its appearance could be modified. Unfortunately, there is no drug that will paralyse accommodation without affecting the pupil, so an experiment was designed to cut out the stimulus to the rods. The apparatus and procedure already described were used except that the test field size was reduced to 1”. Subject H.K. was employed and fixation tests showed she could maintain accurate fixation on the centre of the field. The stimulus was delivered directly to an area of the retina which contained very few rods. Light scattered in the eye also stimulated the more peripheral rods, although the total rod stimulus was a lot less than with the 5” field, The results with the small field were similar to those obtained with the larger field, except that the irregularity occurred at a slightly lower value of illumination, but was not diminished in size. The experiment was then repeated, again using H.K., but with a 5” field and red light. The use of red light meant that the rods were hardly stimulated. The results showed that the irregularity was absent from the pupil response curve, but also showed that accommodation had not changed in reducing illumination. It was therefore not possible to compare these results fairly with those obtained in yellow light. DISCUSSION Frequency qf the irregularity Returning to the survey of the literature on the pupil steady state light response, it is possible to form an estimate of the frequency with which the pupil irregularities occur, as shown in Table 1. TABLE

Investigation

I

No. of subjects ---___-~

No. with not iceable irregularities --__

*FERREE and RAND (1932) LYTHGOE (1932) *CRAWFORD (1936) *FLAMANT (1948) SPRUNG and STILES (1948) Present study

6 5 10 40 12 9

Total

82

~-

4;

2 2 9 35? 6 1

33 40 90 88 50 I1

55

67

3.

232

MELLERIO

The investigations marked by asterisks had significant irregularities in their total mean curves. It is impossible to calculate from the data published whether an individual’s irregularity is significant, so the criterion used was whether or not the individual’s published curve had a marked irregularity. The reason why only 1 out of 9 (1 I per cent) of subjects in the present study is included in the table is because here it has been possible to apply strict significance tests to the individual results. To some extent, then, the frequency figure of 67 per cent is arbitrary, and it should only be used as a rough guide. Causes of the irregularity

Four causes of the irregularities in the pupil response curves will be considered. (1) The Stiles-Crawford efict. The sudden onset of this effect at a given illumination could cause some small irregularity in the pupil response, but since the results were plotted in terms of effective trolands (allowances having been made for the Stiles-Crawford effect) and the irregularity still appeared (Fig. 8), this cannot be a cause. (2) Rod/cone change-over. This idea was put forward by ALPERN, KITAI and ISAACSON (1959). The input to the pupil system (here defined as all the receptors. nerve fibres, connections, and muscle fibres involved in pupillary behaviour) of the light response can be either by the rods or by the cones (ALPERN and CAMPBELL,1962; ALPERN et af.. 1959; BOUMA. 1965), in spite of much old evidence that only cones are pupillomotoric (e.g. HESS, 1909). Apart from the different spectral sensitivities that the two receptors show, rods have a lower pupillomotor threshold, show better summation and have smaller pupillomotor efficiencies than cones. Visually, AGUILAR and STILES (1954) showed that rods became saturated at 5.5 log stilbs, and this must apply also to their pupillomotor function. The rod pupillomotor threshold can also be determined from visual data (SCHWEITZERand BOUMAN,1958) and lies at about $5 log stilbs. Similarly, the cone pupillomotor threshold will be about 6.5 log stilbs, and an upper luminance limit to the pupil response will occur when the pupil curve levels out and the pupil ceases to respond to increasing illumination. presumably because of mechanical limitations within the iris. This level is reached at approximately 0.0 log stilbs, and cannot be due to cone saturation, as all the visual pigment is not bleached until about 6.0 log photopic trolands (about 5 log stilbs, WEALE, 1963). From the figures given above, it is possible to construct two theoretical curves of the pupil steady state light response when being driven either wholly by cones, or wholly by rods. Figure 10 shows these two curves. When an area of retina that contains both rods and cones is stimulated (as was the case in previous work in the literature), the pupil response will be some resultant of the activities of the two inputs to the pupil system. The simplest resultant will be obtained by straight addition of the rod and cone responses: P’ = aR -j- bC

where P’ is the resultant pupil response, R and C the rod and cone responses, and a and h weighting factors which are dependent upon how many rods and cones are present, and on their pupillomotor efficiencies. The dotted line in Fig. 10 is this resultant, calculated for equal numbers of equally efficient rods and cones, i.e. a=b=0.5. The correctness of this addition assumption can be challenged, but there are only two simple alternatives. One is that the resultant is obtained by the addition of weighted logarithmic functions: logP’=flogR+glogC

Ocular Refraction at Low Illuminations

233

only apply when both rods and cones are above threshold, and then the shape of the resultant would not differ greatly from that obtained by simple addition. The other alternative is that represented by the dashed line in Fig. 10. The resultant follows whichever of the two inputs is the most sensitive, but this has a serious drawback-it would involve suppression of the cone response below about 3.5 log stilbs, and suppression of the rod response above this value. Whilst it would be possible to think of two separate mechanisms that behave in this manner, simple addition of the rod and cone responses appears to be an easier and physiologically more likely explanation.

This could

7 6 t

Log stilbs FIG. 10. Hypothetical

rod only and cone only pupil steady state light response. For explanation, see the text.

As can be seen in Fig. 10, either resultant is smooth and does not contain irregularities. However, if the slope of the rod curve was much steeper, and the value given by Aguilar and Stiles for rod saturation too high by as much as 2 or 3 log stilbs, then the resultant could flatten out into a plateau. But this seems highly unlikely, and, in any case, it would not produce irregularities of the kind found with subject H.K. or in Flamant’s data. It is interesting to note that most of the steady state pupil curves from the literature show two distinct phases, as expected from Fig. IO-one of small slope in low iliumjnations, and the other of greater slope in higher illuminations, corresponding to the activities of the rods and cones-and that the irregularities can occur in either portion. In the “Admiralty” curve of Spring and Stiles (see Fig. 1) the irregularity is in the rod portion, whilst in Crawford’s results, the irregularity is in the cone section. It can be concluded, then, that duality of input to the pupil system (rod/cone changeover) cannot cause the kinds of irregularities that have been found. (3) Sphincter/dilator change-over. Just as there is duality of input to the pupil system, so there is duality in the output effector. The iris is made up of two opposing muscles innervated by two opposing nervous supplies. if it were supposed that at low illuminations the dilator muscle and the sympathetic nervous system controlled the pupil diameter, and at higher illuminations the control

234

J. MCLLERIO

passed to the sphincter muscle and the parasympathetic nervous system (or vice versa). and that this transition of control from one system to the other were not smooth, then irregularities would be seen in the pupil steady state light response curves. But such irregularities could only take the form of plateaux and could not be like those that have been found. The evidence presented by LOEWENFELD (1958), on dilation of the pupil. should dispose of this idea of a change-over of control within the iris at a given illumination. (4) The night near response. Because duality in the input and output of the pupil system cannot cause irregularities in the light response curves, their origin must lie between the retinal receptors and the iris. The idea that they can be caused by two mechanisms is sound. and they could be brought about in one of two ways. Either one mechanism operates at low illuminations and changes over to another at high illuminations, a scheme disposed of by Loewenfeld. or two mechanisms both struggle for control over a range of illuminations. Now when illumination is reduced, gradually night myopia occurs. together with night convergence (if the conditions are correct), and night miosis may follow this night near response. But, at the same time, the pupil will “try” to increase in size due to the failing light reflex. These two opposing mechanisms must struggle for nervous control of the pupil, and eventually the pupil will dilate fully because of the lack of light. It is this struggle that causes the pupil to behave in an irregular way, until the stronger reflex (the failing light reflex) wins. The variation in occurrence of this irregularity amongst subjects can be explained by the relative strengths of the two reflexes involved. The probable cause of the pupil irregularities found in some subjects must therefore be the action of a night near response.

CONCLUSIONS

The survey of the literature shows that in most people the eye is rendered myopic by one or more of the following factors in reducing illuminations. (a) The change in the spectral sensitivity of the retina from photopic to scotopic conditions (the Purkinje shift) coupled with the chromatic aberration of the eye account for about 0.4 D of this myopia. (b) Spherical aberration of the eye, together with the large pupils produced by low illuminations, can cause large amounts of myopia (up to 1 D) in some people. (c) Accommodation of the lens which tends towards a constant value at and near darkness, but which nevertheless shows large fluctuations, can introduce up to 1.5 D of myopia in some subjects. There are also a few people who tend to become hyperopic instead of myopic in dim light, and others whose refraction does not change. Convergence also occurs in reducing illuminations, provided there is sufficient detail in the field of view for fusion to be possible. If the field is completely empty (or totally dark) then the axes of the eyes are set to infinity. Also, the pupil of the eye dilates up to a maximum constant value, but during the dilation some people’s pupils show irregularities that might be quite small, or be large points of inflexion. The cause of these irregularities does not lie in either rod,cone function, or sphincterjdilator muscle function, but is possibly the result ofa night near response, in which accommodative night myopia and night convergence are involved.

Ocular Refraction at Low Illuminations

235

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CRAWFORD, B. H. (1936). Dependence of pupil size upon the external light stimuli under static and variable conditions. Puoc. R. Sot. B. 121, 376-395. CRAWFORD, B. H. (1937). The luminous efficiency of light entering the eye pupil at different points and its relation to brightness threshold measurements. Proc. R. Sot. B. 124, 81-96. DURAN, M. (1943). Los valores umbrales de la miopia noctuma. An. Fis. Quim. 39, 579-584. FERREE, C. E. and RAND, G. (1932). Relation of the size of the pupil to intensity of light, and the speed of vision and other studies. J. esp. Ps.vchol. 15, 37-55. FERREE, C. E. and RAND, G. (1933). The effect of the intensity of illumination on the near point of vision and a comparison of the effect for presbyopic and non-prebyopic eyes. Trans. illwn. Engng Sot. (N. Y.) 28, 590-611.

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Abstract-A survey of literature concerned with ocular refraction at reduced illuminations reveals that most eyes become myopic with approaching darkness. The three causes of this myopia are considered and evidence for a night near response presented. The pupil steady state light response, as reported by several authors, was examined and found to contain irregularities. It is shown that the cause of these irregularities cannot be the duality of retina1 receptor input, but that it probably lies with the night near response. RCsumQ-Un examen de la litterature concemant la r&fraction oculaire en faible lumiere r&v&le que la plupart des yeux deviennent myopes & I’approche de I’obscurit6. On considere les trois causes de cette myopie et on ptisente des arguments en faveur d’une rkponse. nocturne de p&s. On examine la rkponse B la lumi&e de la pupille en &at stable, d’aprks divers auteurs, et on y trouve des irrkgularitts. On montre que la cause de ces ir&gularit& ne peut pas ttre la dualite titinienne, mais &side plus probablement dans la rkponse nocturne de p&s. Zusemmenfassung-Ein Literaturstudium zeigt, dass die meisten Augen mit zunehmender Dunkelheit myop werden. Die drei Ursachen dieser Myopie werden betrachtet und Beweise fiir eine “might near response” erbracht. Die Pupillenreaktion auf Dauerlicht, wie sie von mehreren Autoren beschrieben wird, wurde untersucht. Es wurde gefunden, dass sie Unregelmlssigkeiten enthllt. Es wird gezeigt, dass die Ursache dieser Unregelmiissigkeiten nicht die Dualitlt des retinalen Rezeptoreingangs sein kann, sondern dass sie wahrscheinlich mit der “might mear response” zusammenhlngt. Pe3HtMe--0630p

JleTepaTypbl, KaCZltoIlUifiC5I ~fjIpaKUIiI4 rJla3a IIpki IIOHHECHHOM OCBClUeHklIiIlOKaSbIBacT, WO 60JIbWiHCTBO I-Jla3CTaHOBIlTCR MWOUWieCKWMW IIpki IE~XOAeKTcMHOTe. PaCCMaTpaBaIoTCnTPElnpe~lrHbI3TO#MaOUnURn~AcTaBnncTCR B~PO~THOC o6ancHue “night near response”. IGbmo RccnenoBaHo nocTonHcTB0 peaKuuZi 3pPIKaHaCBCT,KaKcoo6LUaeTc~HcKOTOpbIMU aBT0pat.N HHB$i~eHO,YTO OHUHeiJCrYJIlIPHbI. nOKa3bIBacTC& YTO 3TOa IippWyJIRpHOCTb He MOXET 6bITb 06bRCHeHa ABOfiCTBCHHOZt IlpHpOllOfipWcIlTOpOB Cc'PIaTKEi,KOTOPbIe BKJIH)WH)TCR B PCaKUUIO. BCPOSTHO, wo oHa cBn3aHa c “night near response.”