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A note on the refraction and image formation of the rat's eye
A NOTE ON THE FORMATION
REFRACTION AND IMAGE OF THE RAT’S EYE M. T. BLCXK*
Department of Physiology, ~nb~
University Makal
School, Elba
(Received 19 December 1968) INTRODUCTION
Two BROADLY opposed views are held regarding the refractive state of the rat’s eye. Many authors, for example JOHNSON (1901), WALLS(1942) and RCKXON-DWIGNEAUD (1943), express the opinion that the rat, in common with all small eyed nocturnal mammals, exhibits a marked hypermetropia. Statements about its degree are either vague or variable, and discussion of the optical performance is entirely qualitative. LASHLEY (1932), however, claims that the rat is severely myopic and furnishes some meas~ements of the optical characteristics of the eye, together with a brief account of the retinal structure. It is Lashley’s work that has received the most attention and the more specific claim of 3D of myopia occurs in two recent neurophysioIo~c~ investigations of the rat’s visual pathway (BROWNand ROJAS,1965; MONTERO, BHJGGEand BEITEL,1968). Whereas other inv~tigators estimated the refraction of the rat’s eye by retinoscopy or ophthalmoscopy, LASHLEY (1932) adopted the curious procedure of observing through the sclera of the excised eye the images focused by the dioptric system. One is left to deduce that the eyes examined were about 12.5D myopic (8 cm being the object distance for sharpest focus) and in one case as much as 16aSD. From the single estimate of nodal point position, the total refractive power would appear to be of the order of 350D. Two criticisms may be made of this method: excised eyes quickIy lose their shape, and the image plane is not well detined, possibly lying diffusely within the sclera. It must be emphasized that quite small shifts in the plane of focus imply SizeabIe changes in refraction when dealing with a system of high refractive power. Much the same criticism applies to Lashley’s attempt to determine the eye’s resolving power-the scleral image is simply not good enough to permit a decision as to whether or not the living eye is capable of resolving two points of light. Lashley is at pains to show that the performance of the rat’s optical system is at its best when viewing objects closely, as in the jumping stand visual discrimination situation (LASHLEY, 193Oa). But his statement that “the eyes . . . form clear images of objects within the more significant range of the animal’s activity” does not stand up to analysis, It is well known that the rat, given the possibility, will be guided by the grosser, more distant visual cues offered by the environment @ZEBB, 1938; L,UHLEY,1938); at close range the rat has its nose and vibrissae to falI back on and only uses vision as a last resort. The weight of evidence lies in favour of hype~e~opia, although it is difficult to account for the observations of BROWNand ROJAS(1965) and of MONTERO er al. (1968). *Present address: Department of Physiology. Queen E&tab&h Colkgc, C!anpda Hill Road, London, W.8.
706
M. T.
BLOCK
METHODS
Refraction was carried out by plane mirror retinoscopy on the atropinized eyes of intact, anaathctized rats. Values were oaasionaily checked by dim ophthalm~opy. Eye dimensions were measured either from frozen sections or directly from the intact cornea and excised lens. The refractive in&x of the equivalent thick lens was obtained from the vertex powers of lenses of known dimensions in air-the inverted aerial image of a distant object was viewed under a microscope. The lens was stopped down with an artificial pupil of about i mm dia. to obviate the negative spherical aberration. A few nodal point estimates were attempted from measurement of the separation of tram sclerally viewed images of pairs of lights subtends known angles at the eye. Pupil sizes in intact animals under various conditions were measured under the dissecting microscope. With the exceptions of pupil size ~~~rnen~, which were done on pigmented animals, and nodal point estimates, which were carried out on albinos, pigmented and albino animals were used alike. The rats were between 250 and 350 g in weight and were over six months old. RESULTS AND DISCUSSION
Table I sedates the data on eye dimensions. The refractive index of the equivalent iens is calculated to be l-61-a high value that must result from the variation in refractive index of the lens material from centre to periphery (even higher effective indices of around 1e65 occur in fish). The refractive index of the humours was found to be 1.34 in an AbW refractometer and the cornea1 refractive index was assumed to be l-38. In constructing the schematic eye the average figures for radii of curvature and separations of refracting surfaces were combined with the appropriate refractive indices to define the cardinal points of the system. Since the estimates of axial length were not very reliable the retinal position was defined by adding in a hypennetropia of 9D (see below). Figure 1 and Table
FIG. 1. The schematic eye showing the positions of the cardinal points of Table 2.
A Note on the Refraction and Image Formation of the Rat’s Eye
707
2 summarize the values of the schematic eye. it is seen that there is a tolerable agreement
between the observed and schematic values of posterior nodal distance.
TABLE1. MEW
Dimension
FOR.v.xEMATIc EYE
Standard deviation
Mean
comeai thickness
@25lxlrn 088mm 2+8omm 1*/l mm z75mrn 1.85 mm 1.72 mm 3.01 mm -l-P3 D
Cornea-lens distance Lens thickness Lens-retina distance Anterior comeal radius Anterior lens radius Posterior lens radius Posierior nodal distance Ametropia
No. of ohs.
0.01
7
012 O-09 @29 bll 0.14 0.14 0.70 1.6
I 10 7 13 I I 5 30
Image-back
Refractive index of lens Front radius (mm)
Back radius On&
l-89 1‘79 1.83
1.75 1.68 f.74
TABLE
Thickness
surface
Refractive index
I:: 2.81
@92 @84 0.85
1.61 1*61 1.62
2. THEVALUES OF~~~HE~~AT~CEY~:
Radius of curvatun @r@
Separation (rw
Anterior cornea St
2-75
0.25
I.38
Posterior cornea $2
2.50
@88
1.34
Anterior lens S3
I.85
2.80
1.61
Posterior lens S4
1.72
1.78
l-34
Surface
Refractive index
Refractive power
f_ 1380 16D\ 1220 324D $ fig
1 26333
Retina Ss Cardinal points First principal point Sewnd principal point First focal distance Second focal distance First nodal point Second nodal point Retina Posterior nodal distance
SIP1 SlPZ PlFr SIFI P2F2 SF2 SINI S1N2 w5 N2S5
1.66 3.09 1.55 4.14 5.80 2.59 271 568 2.97
Pupil dimensions and positions Real Entrance
Exit
Diameter z Distance from St 1.16
z 077
%z 0.98
M. T.
708
Broac
The position of the receptor plane
For a hypermetropia of 9D the distance between the posterior focal plane, Fz, and the assumed receptor plane, Ss, is 120 CL.A similar hypermetropia in the eye of a cat (refractive power 78D according to VAKKURand BISHOP,1963) or a man (60D) would result in separations of 2.0 mm and 2.8 mm respectively. The question of the precise location of the plane of reflection used in retinoscopy assumes considerable importance (HIRSCHBERG,1882). If the eye were emmetropic for the receptor plane, then reflection from a plane behind the receptors would suggest a myopia, while reflection from in front would create an appearance of hypermetropia. The furthest structure likely to be involved in reflection of light is the lamina vitrea. There remains the possibility of reflection from before the receptors, although this would tend to reduce the eye’s sensitivity. Some reflection does take place from structures anterior to the receptors. When refracting the rat’s eye with a plane mirror retinoscope a clear “with” movement of the reflex is seen until a correcting lens of + 10D is placed at the eye (working distance 1 m). From this point up to about f20D the movement of the reflex is equivocal and shows no obvious reversed point. Above +20D there is a clear “against” movement. The simplest explanation is that +9D corresponds to the “hypermetropia” of the furthest reflecting
DISTANCE PLANE
Of
250-m
FROM
HYPERMITROPIA
FIO.
__f
2. The relationship between the refractive error of a plane and its displacement from the focal plane F2. @set shows a section of retina drawn to the same scale.
A Note on the Refraction and image Formation of the Rat’s Eye
709
plane at, or perhaps a little beyond, the receptor layer while significant reflection from retinal structures occurs up to some 120 p in front of the furthest plane. This distance accords very closely with the thickness of the retina (Fig. 2). In the cat’s eye an extended reflecting structure of the same dimensions would make for equivocation over a mere 0.6D. The hypermetropia of the receptors has been taken as that indicated by the change from “with” to “equivocal”, the mean value for 30 eyes being i-9.3D (S.E.M. = f Oq3D). Fupii size and depth of focus The smallest pupil diameter measured under light urethane anaesthesia and in intense illumination was O-2 mm. Many observations were carried out on animals used for eleotrophysiological recording experiments and in these cases pupil diameters ranged from just below 0.4 mm up to 1a2 mm, depending upon the state of the animal. This range is similar to that found by LASHLEY {1932) for the conditions of tests on detailed vision. Taking 26 as the visual acuity of the pigmented rat (LASHLEY’S best figure-1930b, 1938), and 0.5 mm for the apparent (entrance) pupil diameter it is possible to arrive at an approximate idea of the depth of focus. Since the posterior nodal distance (NzSs) is 2.97 mm, the retinal distance corresponding to the minimum separabile is 0.022 mm. The exit pupil has a diameter of 0.62 mm and is situated at 4.91 mm from the retina. If a point source at the eye’s near point gives rise to a blur circle whose diameter is equal to the retinal minimum separabile, then the distance of its image from the exit pupil can be found by simple geometry. In this case that distance is 5.09 mm, putting the image 60 p beyond the second focal plane. The near point vergence is thus 5D (see Fig. 2) corresponding to a distance of 20 cm. The limiting exit pupil size that gives no depth of focus is 0.9 mm for an apparent diameter of 0.8 mm. The schematic eye appears to be consistent with the known visual performance of the rat. There is a di~culty for el~rophysiolo~~al experiments in which stimuli are presented in the visual field. The simplest procedure to adopt is to ensure that the naturat pupil remains small (ADAMS and FORRESTER, 1968)-an artificial pupil would be an acceptable alternative-but if the eye is atropinized it would seem essential to introduce an optical correction. Pupil size and retinal illumination The retinal illumination, I, of a distant object is given by
where p is the pupil diameter, D the total refractive power, and i a constant depending on the intrinsic brightness of the object and transmission losses in various media. If r is the posterior nodal distance, then D = i and
Thus only if the ratio of pupil diameter to posterior nodal distance rises is there any gain in retinal illumination. The m~mum entrance pupil seen in atropinized eyes is 4~5 mm, corresponding to a real pupil of about 3 mm if the considerable spherical aberration of the cornea is taken into account. p2Dz is found to be 2.22 as against 0.23 for man
710
M.T. BLOCK
(p=8.0 mm-DUKE-ELDER, 1932) and 1.19 for the cat (p=+14 mm-VAKKvR and BISHOP,1963). The difference between the rat and human eye is striking and undoubtedly
significant; the comparison between rat and cat is vitiated by the abnormal circumstances of measurement-it would be necessary to know the physiological relationship between pupil diameter and light intensity. The tapetum of the cat should have the effect of allowing a given illumination of the receptors at relatively smaller pupil aperture: it would, therefore, not be surprising if the maximal light gathering capacity of the cat’s dioptric apparatus were inferior to that of the rat. Eyeshine does not seem to occur in small eyed nocturnal animals, but is only prominent in some large eyed types, for example the cat and the owl, which have a superior acuity. This suggests that the significance of the tapetum may not lie simply in an increase in retinal illumination for its own sake. The small eye with its relatively poor acuity-the acuity of the cat is five to six times better than that of the ratcan tolerate a greater degree of effective ammetropia before the acuity suffers. Acuity is in any case of less consequence to the small mammal; hunted rather than hunter, identifying by smell rather than sight. As the pupil dilates to let in more light, there occurs, presumably, an overall increase in the aberration of the dioptric system. The effect of aberration will be more detrimental to the acuity and visually oriented behaviour of the larger animal. The tapetum, by forestalling the rise in pupil area, may act to preserve visual acuity. A proper consideration of the variation in optical performance as pupil diameter increases would depend upon accurate knowledge of the lens aberration. The cornea1 refracting surface shows spherical aberration the effect of which will be to bring light passing in the outer regions of the pupil to a focus before light in the paraxial region. It is interesting to note that this type of aberration might, up to a point, lead to no increase in blur patch size in an eye whose retina falls short of the paraxial focal point. The lens has a negative spherical aberration as a consequence of the graduation of refractive index from surface to core-rays passing through the lens periphery suffer less refraction than those through the middle. How far lens aberration may compensate that of the cornea is unknown. REFERENCES ADAMS, A. D. and FO~RE.YTER, J. M. (1968). The projection of the rat’s visual field on the cerebral cortex. Quart. JI exp. Physiol. 53, 327-336.
BROWN,J. and Rorti, J. A. (1965). Rat retinal ganglion cells: receptive field organization and maintained activity. J. Neurophysiol. 28, 1073-1090. DUKE-ELDER, S. (1932). Development form and function of the visual apparatus. Textbook of Ophthulmology, Vol. I, Henry Kimpton, London. HEB& D. 0. (1938). Studies of organization of behaviour, I. Behaviour of the rat in a field orientation. J. camp. Psychol. 25, 333-353. Archs Anat. Physiol. Lpz. Physioi. HIRSCHBmG, J. (1882). Zur vergleichenden Ophthalmoskopie. Abteibmg 81-92. JOHNSON,L. J. (1901). Contribution to the comparative anatomy of the mammalian eye, chiefly based on ophthalmoscopic examination. Phil. Trans. R. Sot. SW, l-82. LASHLEY,K. S. (1930a). The mechanism of vision I. A method for the rapid analysis of pattern vision in the rat. J. genet. Psychol. 37,453-460. LAsHLay, K. S. (1930b). The mechanism of vision III. The comparative visual acuity of pigmented and albino rats. J. genet. Psychol. 37,481484. LASHLEY,K. S. (1932). The mechanism of vision V. The structure and image forming power of the rat’s eye. J. camp. Psycho!. 13, 173-200. LAsmey, K. S. (1938). The mechanism of vision XV. preliminary studies of the rat’s capacity for detail vision. J. gen. Psychol. 18. 123-194. Motmrao, V. M., BRUGGE, J. F. and Barm~, R. E. (1968). Relation of visual field to lateral geniculate body in the albino rat. J. Neurophysiol. 31,221-236.
A Note on the Refraction and Image Formation of the Rat’s Eye
711
WCHON-DWIGNEAUD, A. (1943). Les Yeux ef III Vision ah VerrtWs, Mason, Paris. VAIUCUR, G. J. and BISHOP,P. 0. (1963). The schematic eye in the cat. Vision Res. 3, 357-381. WALLS,G. L. (1942). The Vertebrate Eye md its Adrrptive Ru&tion, reprinted 1963, Hafner, New York. Abstrsct-Measurements on excised rats’ eyes have provided a basis for the construction of a schematic eye. Refraction of the rat has reveaIed a hypermetropia of 9D for the receptor plane. Combining the v&es of the schematic eye with estimates of pupil size it can be shown that the known visual acuity of the rat can be accounted for and that the eye has a considerable depth of focus. Possible implications of the enlargement of the pupil to increased retinal illumination are discused. R&III&--Les mesures sur des yeux de rats exci& out permis & construire un oeil sch&natique. La &fraction du rat rCv&leune hyperm&ropie de 9 D dam le plan du &cepteur. En combinant les vaieurs de l’oeil sch&natique avec des estimations de ia dimension pupillaire, on peut rendre compte de l’acuiti visuelle du rat et on trouve pour son oeil une profondeur de foyer co&l&able. On discute les effets possible-s des variations de la pup& sur lV&&rement r&&en. Zusammenfawmg-Mesungen an enukleierten Rattenaugen haben eine Gruudlagc fii deu Aufbau eines schematischen Auges geliefert. Die Refraktion der Ratte hat fti die Rezeptorenebene eine Hypermetropie von 9D gezeigt. Man kann beweisen, dass die belcannte Sehsch&fe der Ratte durch eine Verbindung der Werte des schematischen Augea mit Sch&ungeu der Pupillenweite N e&&en ist und das das Auge eine betrilchtliihe Tiefens&rfe be&t. Miigliche Folgerungeu einer ~p~ene~eite~g w&rend einer Erh6hung der Ne~ut~le~h~g werden tirtert. Pewoiwe - H3MepeHpuI 3rzyfcneHpowmrbIx rna3 ~pbrcbx IIOCliOBawHCM J$JIfi nocrpoemw cxeMam~ecxor0 rrua. P&pamm ma3a Rparcb~xapasrepa3yercr rrdnepMeqmn.fe~ 9 ~OIIqxii2 B IIIIOCKOCIH pe~etrropoa. Ko~6mi~pya BewpHHbI CxeMawmxoro rna3a c 0qeaRahui ~en.mnnw 3pam MO=O rxo~a3am, 9~0 333ecrxw paaee ocrpora spemrn EpbICbI MOXCeT 6bITb o6wtcaezza 3 Tro Ex rna3 EMeeT 3Ba¶JiTenbEyxo rny63my +oKyca. MaeTcr 303~0xwxoe 3Haseaae pacnnspe~ spanra m yBenweHHR orsemermoc-rsi CeTsafKB.
REFRACTION AND IMAGE OF THE RAT’S EYE M. T. BLCXK*
Department of Physiology, ~nb~
University Makal
School, Elba
(Received 19 December 1968) INTRODUCTION
Two BROADLY opposed views are held regarding the refractive state of the rat’s eye. Many authors, for example JOHNSON (1901), WALLS(1942) and RCKXON-DWIGNEAUD (1943), express the opinion that the rat, in common with all small eyed nocturnal mammals, exhibits a marked hypermetropia. Statements about its degree are either vague or variable, and discussion of the optical performance is entirely qualitative. LASHLEY (1932), however, claims that the rat is severely myopic and furnishes some meas~ements of the optical characteristics of the eye, together with a brief account of the retinal structure. It is Lashley’s work that has received the most attention and the more specific claim of 3D of myopia occurs in two recent neurophysioIo~c~ investigations of the rat’s visual pathway (BROWNand ROJAS,1965; MONTERO, BHJGGEand BEITEL,1968). Whereas other inv~tigators estimated the refraction of the rat’s eye by retinoscopy or ophthalmoscopy, LASHLEY (1932) adopted the curious procedure of observing through the sclera of the excised eye the images focused by the dioptric system. One is left to deduce that the eyes examined were about 12.5D myopic (8 cm being the object distance for sharpest focus) and in one case as much as 16aSD. From the single estimate of nodal point position, the total refractive power would appear to be of the order of 350D. Two criticisms may be made of this method: excised eyes quickIy lose their shape, and the image plane is not well detined, possibly lying diffusely within the sclera. It must be emphasized that quite small shifts in the plane of focus imply SizeabIe changes in refraction when dealing with a system of high refractive power. Much the same criticism applies to Lashley’s attempt to determine the eye’s resolving power-the scleral image is simply not good enough to permit a decision as to whether or not the living eye is capable of resolving two points of light. Lashley is at pains to show that the performance of the rat’s optical system is at its best when viewing objects closely, as in the jumping stand visual discrimination situation (LASHLEY, 193Oa). But his statement that “the eyes . . . form clear images of objects within the more significant range of the animal’s activity” does not stand up to analysis, It is well known that the rat, given the possibility, will be guided by the grosser, more distant visual cues offered by the environment @ZEBB, 1938; L,UHLEY,1938); at close range the rat has its nose and vibrissae to falI back on and only uses vision as a last resort. The weight of evidence lies in favour of hype~e~opia, although it is difficult to account for the observations of BROWNand ROJAS(1965) and of MONTERO er al. (1968). *Present address: Department of Physiology. Queen E&tab&h Colkgc, C!anpda Hill Road, London, W.8.
706
M. T.
BLOCK
METHODS
Refraction was carried out by plane mirror retinoscopy on the atropinized eyes of intact, anaathctized rats. Values were oaasionaily checked by dim ophthalm~opy. Eye dimensions were measured either from frozen sections or directly from the intact cornea and excised lens. The refractive in&x of the equivalent thick lens was obtained from the vertex powers of lenses of known dimensions in air-the inverted aerial image of a distant object was viewed under a microscope. The lens was stopped down with an artificial pupil of about i mm dia. to obviate the negative spherical aberration. A few nodal point estimates were attempted from measurement of the separation of tram sclerally viewed images of pairs of lights subtends known angles at the eye. Pupil sizes in intact animals under various conditions were measured under the dissecting microscope. With the exceptions of pupil size ~~~rnen~, which were done on pigmented animals, and nodal point estimates, which were carried out on albinos, pigmented and albino animals were used alike. The rats were between 250 and 350 g in weight and were over six months old. RESULTS AND DISCUSSION
Table I sedates the data on eye dimensions. The refractive index of the equivalent iens is calculated to be l-61-a high value that must result from the variation in refractive index of the lens material from centre to periphery (even higher effective indices of around 1e65 occur in fish). The refractive index of the humours was found to be 1.34 in an AbW refractometer and the cornea1 refractive index was assumed to be l-38. In constructing the schematic eye the average figures for radii of curvature and separations of refracting surfaces were combined with the appropriate refractive indices to define the cardinal points of the system. Since the estimates of axial length were not very reliable the retinal position was defined by adding in a hypennetropia of 9D (see below). Figure 1 and Table
FIG. 1. The schematic eye showing the positions of the cardinal points of Table 2.
A Note on the Refraction and Image Formation of the Rat’s Eye
707
2 summarize the values of the schematic eye. it is seen that there is a tolerable agreement
between the observed and schematic values of posterior nodal distance.
TABLE1. MEW
Dimension
FOR.v.xEMATIc EYE
Standard deviation
Mean
comeai thickness
@25lxlrn 088mm 2+8omm 1*/l mm z75mrn 1.85 mm 1.72 mm 3.01 mm -l-P3 D
Cornea-lens distance Lens thickness Lens-retina distance Anterior comeal radius Anterior lens radius Posterior lens radius Posierior nodal distance Ametropia
No. of ohs.
0.01
7
012 O-09 @29 bll 0.14 0.14 0.70 1.6
I 10 7 13 I I 5 30
Image-back
Refractive index of lens Front radius (mm)
Back radius On&
l-89 1‘79 1.83
1.75 1.68 f.74
TABLE
Thickness
surface
Refractive index
I:: 2.81
@92 @84 0.85
1.61 1*61 1.62
2. THEVALUES OF~~~HE~~AT~CEY~:
Radius of curvatun @r@
Separation (rw
Anterior cornea St
2-75
0.25
I.38
Posterior cornea $2
2.50
@88
1.34
Anterior lens S3
I.85
2.80
1.61
Posterior lens S4
1.72
1.78
l-34
Surface
Refractive index
Refractive power
f_ 1380 16D\ 1220 324D $ fig
1 26333
Retina Ss Cardinal points First principal point Sewnd principal point First focal distance Second focal distance First nodal point Second nodal point Retina Posterior nodal distance
SIP1 SlPZ PlFr SIFI P2F2 SF2 SINI S1N2 w5 N2S5
1.66 3.09 1.55 4.14 5.80 2.59 271 568 2.97
Pupil dimensions and positions Real Entrance
Exit
Diameter z Distance from St 1.16
z 077
%z 0.98
M. T.
708
Broac
The position of the receptor plane
For a hypermetropia of 9D the distance between the posterior focal plane, Fz, and the assumed receptor plane, Ss, is 120 CL.A similar hypermetropia in the eye of a cat (refractive power 78D according to VAKKURand BISHOP,1963) or a man (60D) would result in separations of 2.0 mm and 2.8 mm respectively. The question of the precise location of the plane of reflection used in retinoscopy assumes considerable importance (HIRSCHBERG,1882). If the eye were emmetropic for the receptor plane, then reflection from a plane behind the receptors would suggest a myopia, while reflection from in front would create an appearance of hypermetropia. The furthest structure likely to be involved in reflection of light is the lamina vitrea. There remains the possibility of reflection from before the receptors, although this would tend to reduce the eye’s sensitivity. Some reflection does take place from structures anterior to the receptors. When refracting the rat’s eye with a plane mirror retinoscope a clear “with” movement of the reflex is seen until a correcting lens of + 10D is placed at the eye (working distance 1 m). From this point up to about f20D the movement of the reflex is equivocal and shows no obvious reversed point. Above +20D there is a clear “against” movement. The simplest explanation is that +9D corresponds to the “hypermetropia” of the furthest reflecting
DISTANCE PLANE
Of
250-m
FROM
HYPERMITROPIA
FIO.
__f
2. The relationship between the refractive error of a plane and its displacement from the focal plane F2. @set shows a section of retina drawn to the same scale.
A Note on the Refraction and image Formation of the Rat’s Eye
709
plane at, or perhaps a little beyond, the receptor layer while significant reflection from retinal structures occurs up to some 120 p in front of the furthest plane. This distance accords very closely with the thickness of the retina (Fig. 2). In the cat’s eye an extended reflecting structure of the same dimensions would make for equivocation over a mere 0.6D. The hypermetropia of the receptors has been taken as that indicated by the change from “with” to “equivocal”, the mean value for 30 eyes being i-9.3D (S.E.M. = f Oq3D). Fupii size and depth of focus The smallest pupil diameter measured under light urethane anaesthesia and in intense illumination was O-2 mm. Many observations were carried out on animals used for eleotrophysiological recording experiments and in these cases pupil diameters ranged from just below 0.4 mm up to 1a2 mm, depending upon the state of the animal. This range is similar to that found by LASHLEY {1932) for the conditions of tests on detailed vision. Taking 26 as the visual acuity of the pigmented rat (LASHLEY’S best figure-1930b, 1938), and 0.5 mm for the apparent (entrance) pupil diameter it is possible to arrive at an approximate idea of the depth of focus. Since the posterior nodal distance (NzSs) is 2.97 mm, the retinal distance corresponding to the minimum separabile is 0.022 mm. The exit pupil has a diameter of 0.62 mm and is situated at 4.91 mm from the retina. If a point source at the eye’s near point gives rise to a blur circle whose diameter is equal to the retinal minimum separabile, then the distance of its image from the exit pupil can be found by simple geometry. In this case that distance is 5.09 mm, putting the image 60 p beyond the second focal plane. The near point vergence is thus 5D (see Fig. 2) corresponding to a distance of 20 cm. The limiting exit pupil size that gives no depth of focus is 0.9 mm for an apparent diameter of 0.8 mm. The schematic eye appears to be consistent with the known visual performance of the rat. There is a di~culty for el~rophysiolo~~al experiments in which stimuli are presented in the visual field. The simplest procedure to adopt is to ensure that the naturat pupil remains small (ADAMS and FORRESTER, 1968)-an artificial pupil would be an acceptable alternative-but if the eye is atropinized it would seem essential to introduce an optical correction. Pupil size and retinal illumination The retinal illumination, I, of a distant object is given by
where p is the pupil diameter, D the total refractive power, and i a constant depending on the intrinsic brightness of the object and transmission losses in various media. If r is the posterior nodal distance, then D = i and
Thus only if the ratio of pupil diameter to posterior nodal distance rises is there any gain in retinal illumination. The m~mum entrance pupil seen in atropinized eyes is 4~5 mm, corresponding to a real pupil of about 3 mm if the considerable spherical aberration of the cornea is taken into account. p2Dz is found to be 2.22 as against 0.23 for man
710
M.T. BLOCK
(p=8.0 mm-DUKE-ELDER, 1932) and 1.19 for the cat (p=+14 mm-VAKKvR and BISHOP,1963). The difference between the rat and human eye is striking and undoubtedly
significant; the comparison between rat and cat is vitiated by the abnormal circumstances of measurement-it would be necessary to know the physiological relationship between pupil diameter and light intensity. The tapetum of the cat should have the effect of allowing a given illumination of the receptors at relatively smaller pupil aperture: it would, therefore, not be surprising if the maximal light gathering capacity of the cat’s dioptric apparatus were inferior to that of the rat. Eyeshine does not seem to occur in small eyed nocturnal animals, but is only prominent in some large eyed types, for example the cat and the owl, which have a superior acuity. This suggests that the significance of the tapetum may not lie simply in an increase in retinal illumination for its own sake. The small eye with its relatively poor acuity-the acuity of the cat is five to six times better than that of the ratcan tolerate a greater degree of effective ammetropia before the acuity suffers. Acuity is in any case of less consequence to the small mammal; hunted rather than hunter, identifying by smell rather than sight. As the pupil dilates to let in more light, there occurs, presumably, an overall increase in the aberration of the dioptric system. The effect of aberration will be more detrimental to the acuity and visually oriented behaviour of the larger animal. The tapetum, by forestalling the rise in pupil area, may act to preserve visual acuity. A proper consideration of the variation in optical performance as pupil diameter increases would depend upon accurate knowledge of the lens aberration. The cornea1 refracting surface shows spherical aberration the effect of which will be to bring light passing in the outer regions of the pupil to a focus before light in the paraxial region. It is interesting to note that this type of aberration might, up to a point, lead to no increase in blur patch size in an eye whose retina falls short of the paraxial focal point. The lens has a negative spherical aberration as a consequence of the graduation of refractive index from surface to core-rays passing through the lens periphery suffer less refraction than those through the middle. How far lens aberration may compensate that of the cornea is unknown. REFERENCES ADAMS, A. D. and FO~RE.YTER, J. M. (1968). The projection of the rat’s visual field on the cerebral cortex. Quart. JI exp. Physiol. 53, 327-336.
BROWN,J. and Rorti, J. A. (1965). Rat retinal ganglion cells: receptive field organization and maintained activity. J. Neurophysiol. 28, 1073-1090. DUKE-ELDER, S. (1932). Development form and function of the visual apparatus. Textbook of Ophthulmology, Vol. I, Henry Kimpton, London. HEB& D. 0. (1938). Studies of organization of behaviour, I. Behaviour of the rat in a field orientation. J. camp. Psychol. 25, 333-353. Archs Anat. Physiol. Lpz. Physioi. HIRSCHBmG, J. (1882). Zur vergleichenden Ophthalmoskopie. Abteibmg 81-92. JOHNSON,L. J. (1901). Contribution to the comparative anatomy of the mammalian eye, chiefly based on ophthalmoscopic examination. Phil. Trans. R. Sot. SW, l-82. LASHLEY,K. S. (1930a). The mechanism of vision I. A method for the rapid analysis of pattern vision in the rat. J. genet. Psychol. 37,453-460. LAsHLay, K. S. (1930b). The mechanism of vision III. The comparative visual acuity of pigmented and albino rats. J. genet. Psychol. 37,481484. LASHLEY,K. S. (1932). The mechanism of vision V. The structure and image forming power of the rat’s eye. J. camp. Psycho!. 13, 173-200. LAsmey, K. S. (1938). The mechanism of vision XV. preliminary studies of the rat’s capacity for detail vision. J. gen. Psychol. 18. 123-194. Motmrao, V. M., BRUGGE, J. F. and Barm~, R. E. (1968). Relation of visual field to lateral geniculate body in the albino rat. J. Neurophysiol. 31,221-236.
A Note on the Refraction and Image Formation of the Rat’s Eye
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WCHON-DWIGNEAUD, A. (1943). Les Yeux ef III Vision ah VerrtWs, Mason, Paris. VAIUCUR, G. J. and BISHOP,P. 0. (1963). The schematic eye in the cat. Vision Res. 3, 357-381. WALLS,G. L. (1942). The Vertebrate Eye md its Adrrptive Ru&tion, reprinted 1963, Hafner, New York. Abstrsct-Measurements on excised rats’ eyes have provided a basis for the construction of a schematic eye. Refraction of the rat has reveaIed a hypermetropia of 9D for the receptor plane. Combining the v&es of the schematic eye with estimates of pupil size it can be shown that the known visual acuity of the rat can be accounted for and that the eye has a considerable depth of focus. Possible implications of the enlargement of the pupil to increased retinal illumination are discused. R&III&--Les mesures sur des yeux de rats exci& out permis & construire un oeil sch&natique. La &fraction du rat rCv&leune hyperm&ropie de 9 D dam le plan du &cepteur. En combinant les vaieurs de l’oeil sch&natique avec des estimations de ia dimension pupillaire, on peut rendre compte de l’acuiti visuelle du rat et on trouve pour son oeil une profondeur de foyer co&l&able. On discute les effets possible-s des variations de la pup& sur lV&&rement r&&en. Zusammenfawmg-Mesungen an enukleierten Rattenaugen haben eine Gruudlagc fii deu Aufbau eines schematischen Auges geliefert. Die Refraktion der Ratte hat fti die Rezeptorenebene eine Hypermetropie von 9D gezeigt. Man kann beweisen, dass die belcannte Sehsch&fe der Ratte durch eine Verbindung der Werte des schematischen Augea mit Sch&ungeu der Pupillenweite N e&&en ist und das das Auge eine betrilchtliihe Tiefens&rfe be&t. Miigliche Folgerungeu einer ~p~ene~eite~g w&rend einer Erh6hung der Ne~ut~le~h~g werden tirtert. Pewoiwe - H3MepeHpuI 3rzyfcneHpowmrbIx rna3 ~pbrcbx IIOCliOBawHCM J$JIfi nocrpoemw cxeMam~ecxor0 rrua. P&pamm ma3a Rparcb~xapasrepa3yercr rrdnepMeqmn.fe~ 9 ~OIIqxii2 B IIIIOCKOCIH pe~etrropoa. Ko~6mi~pya BewpHHbI CxeMawmxoro rna3a c 0qeaRahui ~en.mnnw 3pam MO=O rxo~a3am, 9~0 333ecrxw paaee ocrpora spemrn EpbICbI MOXCeT 6bITb o6wtcaezza 3 Tro Ex rna3 EMeeT 3Ba¶JiTenbEyxo rny63my +oKyca. MaeTcr 303~0xwxoe 3Haseaae pacnnspe~ spanra m yBenweHHR orsemermoc-rsi CeTsafKB.