A wide-angle gradient index optical model of the crystalline lens and eye of the octopus.

Cephalopods and fish have had no common ancestor since the Cambrian, and their eyes are a classic example of convergent evolution. The octopus has no cornea, and immerson renders the trout cornea optically ineffective. As a result, the nearly spherical lens is responsible for all refraction in these eyes. In spite of the fact that the octopus lens consists of two joined parts, while the trout lens consists of one part, we show here that their optical properties are very similar. An index gradient bends rays within these lenses, adding power and correcting spherical aberration. High spherical symmetry in both lenses strongly reduces other monochromatic aberrations and yields a wide field of vision, advantageous in attack and evasion. The octopus Mattheissen's ratio, 2.83, an inverse measure of light-gathering power, lies above the trout value of 2.38 but within the range of values reported for fish. Strong uncorrected longitudinal chromatic aberration is nearly identical in both animals as a result of similar lens protein optical properties, and will limit resolution. We discuss how animal lifestyle requirements and lens material properties influence the design of these eyes.

Chromatic and monochromatic optical resolution in the rainbow trout.

The modulation transfer function due to measured longitudinal chromatic aberration was calculated for the otherwise unaberrated eye of the adult rainbow trout (Oncorhynchus mykiss) under daylight conditions assuming light absorption by single retinal cone pigments, and by photopic mechanisms involving interaction between cones. The adult trout eye, with its large immobile pupil, is limited by chromatic aberration to resolution much lower than the diffraction limit, consistent with the low acuity reported for fish. This low resolution can be considered a design trade-off cost of a bright image. The measured monochromatic modulation transfer function is similar to that calculated due to chromatic aberration alone, showing that these independent aberrations are approximately balanced in the fish eye. The effect of changes in receptor length, pigment density, water depth, and pupil size upon the chromatic resolution was calculated. The calculated chromatic modulation transfer function will hold approximately for other teleost eyes with lens larger than about 1 mm.

A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout.

Trout lens external shape and internal refractive index gradient structure were measured and used to construct an optical lens model that predicts by ray tracing the average longitudinal spherical and chromatic aberration, focal length and image quality. The nearly spherical shape of the lens was measured from photographs, and the internal refractive gradient structure was measured directly with a special Pulfrich areal refractometer. Longitudinal spherical aberration and back focal length were measured using a simplified Hartmann test using laser beams and a Schlieren test which additionally made refractive index gradient fine structure visible and detected scattering, axial symmetry and structural irregularity. Axial focus shift caused by longitudinal chromatic aberration was measured using a star test. The model lens was then incorporated into a model trout eye based on vertical and horizontal eye frozen sections. Calculated model function yields insight into the relation between eye and lens structure and optical behaviour. Semi-random secondary structural features act as perturbations on the basic model, and will result in point image fine structure.

Image formation by the crystalline lens and eye of the rainbow trout.

The image of a distant unresolved point (point image or PI) and modulation transfer function (MTF) of the eye and lens of the trout were recorded with high spatial (0.3 micron) and dynamic (4096 grey levels) resolution for various entrance aperture sizes and focal positions in monochromatic light, and in broadband light simulating sunlight absorbed by a retinal cone pigment. The PI is irregular, with streaks, wisps and speckle, as a result of lens structural irregularity and diffraction of light scattered within the lens and cornea. Maximum diameter of a diffraction-limited aperture area of the eye is about 0.3 mm. Axially spaced multiple foci are caused by irregular and discontinuous zonal spherical aberration. Lens substance dispersion causes strong longitudinal chromatic aberration, resulting in a broadband PI with concentric coloured haloes. Incident linearly polarized light is slightly depolarized in the PI. The nature of the image is discussed relative to lens and cornea structure, optical modelling and vision. Human subjective entoptic phenomena analogous to those observed objectively in the trout are described.

Aquatic vision and the modulation transfer properties of unlighted and diffusely lighted natural waters.

The modulation transfer function (MTF) of well-mixed unlighted and diffusely lighted samples of clear natural waters for path lengths up to 4 m was measured. The measuring conditions simulated the situation for horizontal aquatic vision. In unlighted water, the MTF decreased relatively slowly with increasing path length and spatial frequency up to 150 c/deg. We interpret this as the result of low-angle forward scattering of light from the target. For diffusely lighted water, the MTF fell much more rapidly with path length, but was nearly independent of spatial frequency. Here, scattering of ambient light into the light path contributes an additional veiling glare or path radiance, which is independent of spatial frequency but degrades the MTF strongly with increasing path length. These scattering processes are independent of wavelength in the visible spectrum. The modulation transfer properties of these waters do not preclude high aquatic visual acuity. However, the useful range of high acuity vision in diffusely lighted water is much less than for unlighted water. This places special requirements upon the design of high-acuity aquatic eyes.

The optics of the spherical fish lens.

The optical design of the fish eye is particularly simple because immersion renders the cornea optically ineffective and the lens is nearly spherical in shape. Measurements have shown that an approximately parabolic gradient of refractive index exists within the lens. If full internal and external spherical symmetry of the lens applies, the geometrical-optical behaviour of the lens is then a function only of the refractive index of the surrounding medium, that of the lens core and cortex, and of the form of the index gradient. The theoretical optical performance of models of the spherical fish lens is calculated by means of the ray-tracing program Drishti as a basis for understanding the optical design of real fish and aquatic eyes. Models based on the gradients proposed by earlier workers are shown to be unable to predict reported spherical aberration and image quality. A model of the fish lens with a polynomial gradient is proposed that yields spherical aberration, image quality and chromatic aberration similar to that reported for the fish.

The refractive structure and optical properties of the isolated crystalline lens of the cat.

Direct measurements of the shape and internal refractive index distribution of the isolated cat lens were used to construct individual optical models of the lenses from the left eyes of five cats. The right eyes were used in a companion study of the optics of the cat eye. The lens refractive index spatial distribution and dispersion were measured with a specially designed Pulfrich areal refractometer. Agreement of calculated ray paths through these models with the observed paths of laser beam fans incident parallel to, and at an oblique angle to the lens axis indicates that the models, which contain no freely adjustable parameters, are good physical and optical representations of the isolated (accommodated) crystalline lenses.

Optical quality of the eye of the cane toad Bufo marinus.

The wide-angle optical quality of the cane toad eye was measured using a single-pass intraocular optical fibre microprobe, a double-pass projection method and high magnification ophthalmoscopy to photograph individual photoreceptors. The cane toad eye is a wide angle optical device with a horizontal field of nearly 200 deg and a large relative aperture (ca f/1). Its image quality, which is poor compared to diffraction-limited performance, decreases relatively little towards the periphery. Rough matching was found between image quality and the potential resolution of the rod array, although undersampling occurs for small pupils. Undersampling probably also occurs for the cone and ganglion cell arrays. The relative rotational symmetry of the topographic distribution of image quality precludes direct matching to the topography of the visual streak at the ganglion cell layer although it remains to be determined whether it is matched to the receptor distribution.

Visibility of photoreceptors in the intact living cane toad eye.

Photoreceptors are invisible under the usual conditions of viewing the fundus; light reflected from other structures obscures them. Individual photoreceptors are shown to be visible in the intact living eye of the cane toad when viewed with intense oblique illumination from one side. The photoreceptors act like optical waveguides in channelling light from the sclera to the observer. If the retinal mosaic were so fine as to oversample the image, the optical system would not be able to resolve a single mosaic element. The fact that adjacent photoreceptors are seen as separate spots of light, using the eye's optical system, indicates that oversampling of the optical image by the retinal mosaic is not occurring.

Physical forces involved in pseudophacodonesis and iridodonesis.

Studies of high-speed motion pictures of the eyes of patients after extracapsular (EC) and intracapsular (IC) cataract extraction show that pseudophacodonesis and iridodonesis are the result of oscillations of the fluids in the anterior segment of the eye. These oscillations, initiated by movement of the eye, result in shearing forces on the corneal endothelium which may result in damage. Similar motion of the vitreous causes shearing forces which may damage the retina.

Anomalous disperison of rhodopsin in rod outer segments of the frog.

Linear-retardation spectra of single frog-rod outer segments were measured by use of a microspectrophotometer equipped with polarizing optics. The recorded transmitted-flux variation was reduced to a rhodopsin anomalous-dispersion spectrum by use of the Jones calculus. This anomalous dispersion is compared with theoretical predictions.