A. Hughes

A schematic eye for the rabbit.

Abstract Previously published rat schematic eyes are shown to be inadequate and a new one is developed. It is demonstrated that a homogeneous lens is not satisfactory for modelling a small eye and a core lens model is provided. Attention is paid to the estimation of the confidence limits of the refractive state derived from the schematic eye computations. Other sections deal with peripheral aberrations, posterior nodal distance, exit and entrance pupils and the extent of the uniocular and binocular theoretical and observed visual fields of the rat.

An analytic, gradient index schematic lens and eye for the rat which predicts aberrations for finite pupils

Abstract Schematic eyes with a homogeneous equivalent lens are inadequate for non-paraxial optics and available versions have been invalidly fitted to non-paraxial properties. A new model eye is here analytically derived from the refractive index profile of the crystalline lens and anatomical measurements of the rat eye. It predicts spherical abberration, coma, paraxial properties and the variation of refractive state with pupil size in accord with experimental measurements. The cornea counteracts the spherical aberration and linear coma of the lens so that overall aberration is reduced and the eye is of good optical quality.The nodal point is invariant with object eccentricity in a manner advantageous to a species whose visual axis is displaced from the optic axis. The potential of the model lies in its extension to a study of such off-axis optics.

The refractive state of the rat eye

Abstract The retinoscopically determined refractive state of the rat eye is found to be 9D when the pupil is small. A calibrated fundus camera was employed for the differential ophthalmoscopy of the retinal surface vessels (+ 9D) and the choroidal vessels immediately subadjacent to the photoreceptors (−2D). Calculation from a rat schematic eye indicates the two refracted surfaces to lie + 0.136 mm and −0.03 mm respectively from the plane of focus of the optical apparatus. This sets the plane of focus in the inner segments of the photoreceptors and indicates the rat eye to be close to emmetropic when the pupil is small. The identity of the retinal surface vessel and fibre refractions with that obtained retinoscopically confirms the hypothesis of Glickstein and Millodot in this species; a retinoscopic reflex originating at the vitread retinal surface gives rise to an artefactual appearance of hypermetropia in functionally emmetropic eyes. Neurophysiological refraction of single unit receptive fields recorded from the optic nerve of the rat reveals considerable potential depth of field and is not inconsistent with an emmetropic state of the effective image shell when the pupil is small. Refraction by retinoscopy, optometry and neurophysiological assessment in the presence of a large pupil is consistent with some 6–10D of ametropia, in addition to the artefact of retinoscopy, which arises from aberrations of rays passing through the peripheral optical apparatus.

A supplement to the cat schematic eye

Abstract The uniocular and binocular fields of view of the cat eye were calculated by Vakkur and Bishop (1963) from their schematic eye but still lack confirmation by direct measurement. In the schematic eye these authors develop only the fields of view determined by the dioptric apparatus. Their assumption that the extent of the retina is not a limiting factor is shown to be invalid f or the cat so that the animal possesses differentiable optical and retinal fields. Measurements supplementary to the cat schematic eye are presented including the requisite extents of the optical and retinal, uniocular and binocular, fields as well as more information about the relative compression of the peripheral retinal image.

A useful table of reduced schematic eyes for vertebrates which includes computed longitudinal chromatic aberrations.

A schematic eye in which the dioptric apparatus has been replaced by a single refracting surface which separates air from water is a very simple and useful tool in a variety of optical calculations. Several such “reduced” model eyes for man have been based on the full schematic eye developed by Gullstrand (1909). Now that complete schematic eyes have been calculted for a variety of vertebrates it is possible to employ their parameters to generate the more convenient reduced models. The reduced eyes presented in Table 1 are developed from the published dimensions and parameters of the full schematic eyes which are conveniently summarized in Tabie 1 of Hughes (1977) where a bibhography of source papers is provided for a variety of species. The power, Ph of the reduced eyes for yellow light of the D line, ,i = 589 m& was equated with the reciprocal of the anterior focal length of the full schematic eye, HF. The posterior focal length of the reduced, water filled eye is then 1.3330.HF for yellow light. The single principal point of the reduced eye was placed at the same distance, AH, behind the cornea1 vertex, A, as the anterior principai point of the full schematic eye. The length of the reduced eye is given as the sum of AH and HF’ of Table 1 and defines the position of the effective image plane of the retina for emmetropia. The modulus of the anterior focal length is equal to the posterior nodal distance, lHF[ = NF’, so that the nodal point position is defined and the size, S, of the retinal image of an object subtending an angle Q is given by S = HF * tan CL. The radius of curvature, RC, of the refracting surface of the reduced eye, situated at H on axis, is thus defined as HN or may be computed as RC = (nai, %,&/Pa. This latter formula was then employed to obtain the power of the eye for red light, C line with i. = 656m~c, and blue light, F line with i. = 486 rnk from the published values for the dispersion of water at 20°C (Fowle, 1934) at these wavelengths; the radius of curvature of the refractive surface was held constant. The temperature chosen was considered representative of conditions under which most schematic eye measurements have been made on enucleated globes. A generalized diagram, Fig. 1, indicates the significance of the various parameters of the reduced eye. If the separation of the second principal point. H’. and the effective image plane of the retina is denoted by WE, the longitudinal refractive error by R and the power of the refracting surface by P, then for ‘x’ line light we may write nx/H’E = Px + Rx. If H’E is kept constant and the system is emmetropic for D line light, so that R, = 0, then subtracting the relationship for X line light from that for D line light gives the longitudinal chromatic difference, or aberratron, as Ro_, = --PI, f P&/nx) (Le Grand, 1967); this value is tabulated for C and F line light in Table 1 along with the corresponding whole eye powers. The change in refractive index with waselength alters not only the optical power but also the optical length of the system image space, n#‘E, in such a way as to ensure that the longitudinal aberration is always smaller than the difference in whole eye powers. The refractive indices for the ocular humors appear to be in fact somewhat higher than for water and the range of. dispersion about 25% greater, but the available information is limited; Le Grand (1967) lists a few sources and Nakao et al. (1968) tabulate dispersion information for the rabbit eye media. The computed parameters of the models are similar in magnitude to those of the full schematic eyes with the greatest deviations in the reduced parameters arising from the use of a single principal point in species whose homogeneous-lens model eye has widely separated

Irregularity and aliasing: Solution?

Although irregularity in a sampling array reduces the Moire effects caused by undersampling, it makes interpolation more sensitive to noise. The advantages of irregularity are considered with this in mind.

The refractive state of the rabbit eye: Variation with eccentricity and correction for oblique astigmatism

Abstract A calibrated fundus camera was employed for the differential ophthalmoscopic refraction of rabbit retinal surface fibres (2.2D) and choroidal vessels (0.3D) immediately subadjacent to the photoreceptors; the effective image shell of this eye is thus within 0.6D of emmenopia. The retinoscopic and refractometrically determined axial refractive state of the rabbit eye was found to be some 2D of hypermetropia. The similar magnitude of optometric refractions of the surface fibres to those obtained by retinoscopy and refractometry confirms Glickstein and Millodots hypothesis in this species: the retinoscopic reflex is thus dominated by rays originating at the vitread retinal surface and indicates an artefactual ametropia in emmetropic eyes. Away from the optic axis, at eccentricities from −20° to 90°. the rabbit eye was found to remain within 1D of emmetropia on the visual steak; the frontal field was not found to be myopic. The tangential and sagittal image shells were coincident not only for axial but also for frontal rays. The rabbit eye is thus completely corrected for oblique astigmatism in the anterior field: this is consonant with its need to employ very oblique rays for imagery in the forward fixation area whose location is subsequent upon the lateral position of its eyes.

The artefact of retinoscopy in the rat and rabbit eye has its origin at the retina/vitreous interface rather than in longitudinal chromatic aberration

Charman and Jennings (1976) concluded that the artefact of retinoscopy arises from the longitudinal chromatic aberration of the eye rather than by reflection at the retina/vitreous interface as suggested by Glickstein and Millodot (1970). Millodot and Sivak (1978) have since employed “chromoretinoscopy” (Bobier and Sivak, 1978) to establish that, although chromatic aberration is present in the eyes of small animals it is of too small a magnitude to account for retinoscopic hypermetropia. More recently, Nuboer and Van Genderen-Takken (1978) have raised, yet again, the suggestion that chromatic aberration accounts for the artefact of retinoscopy in the rabbit eye. Employing a monochromater as a light source, they claim that retinoscopy reveals the rabbit to be about 1 D myopic with blue light and 1 D hy-permetropicwith red light. This result is in conflict with that of Millodot and Sivak (1978) who used Wratten filters to show the rabbit to be hypermetropic even during retinoscopy with blue light. The results of Nuboer and Van Genderen-Takken (1978) do not satisfactorily indicate why retinoscopy without filters leads to an estimate of 2.5 D of hypermetropia in the rabbit. The suggestion that red dominance in the reflex brings about this value is not compatible with their Fig. 4 in which it is apparent that even retinoscopy with infrared light at 750 nm would not achieve a value of +2.5 D. In view of these conflicting findings it was decided that reinvestigation of rabbit and rat refraction was required. Both eyes of two rabbits and two rats with natural pupils were refracted by streak retinoscopy while the subject was under urethane anaesthesia. A working distance of 50cm was employed and allowed for in calculating the apparent refraction. Retinoscopy was first carried out in the absence of a filter. then a bright spectrum blue (Ilford 622, 375-515 nm), tricolour red (Ilford 204; >610 nm) and, finally, a spectrum blue (Ilford 602, 440-49Onm) glass mounted filter sucessively interposed either on the animal’s side of the retinoscope or between the retinoscope and the observer’s eye. Some blue interference filters were also employed in the latter position when refracting the rabbit eye. The position of the filter was not important in determining the lens required to induce reversal of the reflex movement. The results are summarised in the Table 1. The observed refractions are very similar to those of Millodot and Sivak (1978) and not compatible with the results of Nuboer and Van Genderen-Takken (1978). Retinoscopy with blue lighi brings neither rat nor rabbit near to myopia. In the rabbit this is true even when a narrowband interference filter is used in a double-pass arrangement which was precluded for the rat because of difficulty of observation. In both rat (Hughes, 1977) and rabbit (Hughes and Vaney, 1978) it has already been demonstrated that the effective image plane of the retina is nearly emmetropic and that the retinal thickness in the respective schematic eyes (Hughes, 1972; Hughes, 1979a) is just adequate to account for the artefact of retinoscopy if it arises by reflection at the retina/vitreous interface. The above chromoretinoscopic observations are compatible with these earlier findings if the chromatic aberration of the dioptric apparatus is understood as increasing or decreasing the retinal surface artefact. In an accompanying note (Hughes, 1979b) a table of reduced schematic eyes including rat and rabbit has been presented which indicates the expected longitudinal chromatic aberration of a water filled reduced eye of each species. The C-F line aberration is presented above for comparison with the retinoscopic estimate of chromatic aberration. Agreement between the simple model and the observations is good, as has been found for the human eye, but cannot be taken too seriously in the absence of more sophisticated model eyes. The basic qualitative finding of non-reversal of the artefactsign during retinoscopy with blue light is, however. substantiated.

Contact lenses change the projection of visual field onto rabbit peripheral retina.

With the exception of Choudhury (1978). previous studies of rabbit binocular cortex have employed contact lenses to prevent drying of the cornea. Bishop et al. (1962) established that a contact lens increases the posterior nodal distance of the cat eye and changes the projection of the visual field onto retina. It appeared possible that the application of a contact lens to the peripheral binocular optics of the rabbit might introduce significant error when mapping the projection of binocular cortex into the visual field and measuring the disparities of binocular units. Without an estimate of the magnitude of the effect it remained possible that the remarkable 20” divergent disparities reported for rabbit binocular units (Van Sluyters and Stewart, 1974) could have their origin in this artefact. Eyes were enucleated, supported in a cup, and punctured with a fine hypodermic needle at the superior pole. The needle was connected to a saline reservoir and the pressure of the posterior chamber maintained at 18.7 mm Hg, (Giikhan and Gokce, 1975). The posterior ciliary vessels were set horizontal, the boundary between the cornea and sclera vertical, and the optic nerve head projecting 9” forward of the 0 vertical meridan. This is equivalent to the “freeze” position of the rabbit eye (Hughes, 1971). Miniature lamps were set in front of the eye at the 90”. 80”, 72”. 64”. 46” and 36” meridia, and formed images visible transclerally through a travelling microscope positioned to the rear, Fig. 1. The horizontal shift in the image of each lamp was measured when a contact lens was put on or taken off. The eye did not move between measurements as shown by scleral landmark stability. One eye from each of 7 rabbits weighing between 2.5 and 3.5 kg was tested and the shift in the image of each lamp measured 3 times before conversion to angular representation. Application of the contact lens caused the image of the lamp centred on the 90’ meridian to shift laterally by some 0.38mm (2.3’) towards the retinal margin. The image of the lamp 26’ eccentric on the 64’ meridian shifted peripherally by some 0. IOmm (0.63”).