Theoretical study of the optimal shape of the front profile of the lens in the eye of the scallop,Pecten

The optimal shape of the front profile of the thick lens in the eye of the scallop,Pecten is theoretically, geometric optically investigated as a function of the refractive index of the lens and the retina, as well as of the geometrical parameters of the eye. The shape of the theoretical front surfaces is compared with that of the real, experimentally determined front face of the lens. The degree of correction of the lens for spherical aberration of the reflecting spherical mirror in thePecten eye is examined. The optimal shape of the front profile of the lens depends strongly on a set of parameters, such that a certain fine tuning is required among them to assure a full correction for spherical aberration. The extreme variability of the eye parameters and the shape of the front face of the lens in the scallop is inconsistent with this fine tuning requirement. The degree of correction of thePecten lens for spherical aberration might not be as good as it could be, a possible biooptical reason for which is discussed.     

Optical characteristics of the eye of the flounder

Summary The winter flounder,Pseudopleuronectes americanus, is mildly hyperopic. However, chromatic aberration exists in significant amounts and therefore the eye may be emmetropic (zero refractive error) in natural conditions when light is restricted to shorter wavelengths. Large accommodative lens motion was observed along the direction of the pupil axis. This direction is rare among the teleosts and is the result of the unusual split origin of the retractor lentis muscle. While the lens is spherical, as in other teleosts, the retina is not uniformly distant from the lens. Rather, a vertical asymmetry exists such that dorsal and ventral portions of the retina are further from the lens than the central retina. In view of the existing large accommodative ability, this distortion of the globe is not likely to have an optical function but is probably due to the shape of the cartilagenous scleral cup supporting the eye in its extraorbital location. Further, the lens is overcorrected for spherical aberration so that rays passing through the periphery of the lens are focused further away. The value of a lens of this type is unclear.     

Spherical aberration of the fish lens: interspecies variation and age

Summary Spherical aberration of the eyes of a spectrum of freshwater fishes was determined by photographing the refractive effects of excised crystalline lenses on multiple parallel split laser beams. In general, spherical aberration is minimized by the developmentally related variation in lens refractive index. However, spherical aberration is marked and non-monotonic in a non-visual species such as the bullhead. Furthermore, the size and variability of the aberration appears to be related to visual need as indicated by diet and feeding habits. For example, the lenses of predatory sight feeders such as the pike (Esox lucius) or rock bass (Ambloplites rupestris) are optically superior to that of an omnivorous feeder as the carp (Cyprinus carpio).The effect of age was tested by examining rock bass lenses from fish two to seven years of age. Lens quality, as indicated by the amount of change in posterior focal length for beams of varying eccentricity from the optic axis, is optimum in lenses from five year old fish. The significance of this variation in lens quality is uncertain and requires further study with greater attention to specimens of advanced age.     

Optical quality of the ocular lens of the sea lamprey (<Emphasis Type="Italic">Petromyzon marinus</Emphasis>) during the mature and transformer periods of life

While larval sea lampreys exist as eyeless filter feeders for several years, they transform into free-swimming juveniles (transformers) that attach parasitically to prey fish as they develop sexual maturity. This study examines lamprey lens development and optics and, since the lens is often the only refractive component of an aquatic eye, the data also provide an indication of visual ability during transformer and adult periods of life. Seven adult sea lampreys (0.40–0.55 m) and eight transformers (0.15–0.18 m) were sacrificed, the eyes removed and lenses dissected, measured, and placed in an automated laser scanning instrument. Back vertex focal length (spherical aberration) was measured for 14 beam positions across each lens by using a digital camera to record the position of the refracted beam. Transformer lenses exhibit positive spherical aberration, with average focal lengths varying from about 2.40 mm near the lens center and 1.06 mm at the lens periphery. On the other hand, the lenses from adults are largely corrected for spherical aberration, with average focal lengths varying from 2.19 mm to 2.44 mm. This result indicates that the younger lenses do not have a gradient refractive index necessary to mitigate the aberration and that further study of this model may reveal the relation between lens embryology and the development of such a gradient.     

Chromatic aberration of a dipteran corneal lens

Summary The longitudinal chromatic aberration (variation in the position of focus with wavelength) of corneal facet lenses of the houseflyMusca domestica is measured directly. The result is shown to agree with that calculated using the thick-lens formulas, the measured lens parameters and the dispersion of the refractive index of the lenses, measured with an interference microscope. The longitudinal chromatic aberration between the two wavelengths of peak absorption of fly rhabdomeres (360 nm and 495 nm) is about 2.5 m and comparable to the depth of focus of the lens, assuming the lens to be diffraction limited. Chromatic aberration is therefore expected to have little effect on optical image quality in the fly; in particular the effect on the modulation transfer function at the receptor level and on the angular sensitivity of the rhabdomeres is insignificant.Abbreviations LCA longitudinal chromatic aberration - MTF modulation transfer function     

The eye of the blue acara (Aequidens pulcher, Cichlidae) grows to compensate for defocus due to chromatic aberration

By rearing fish in various monochromatic illuminations we investigated (1) the potential for compensation of refractive error due to chromatic aberration, (2) the contributions of the chromatic channels to emmetropization, and (3) the role of color cues in the control of eye growth. Cichlid fish (Aequidens pulcher) were reared for 6 months (12 h light/12 h dark) in monochromatic lights (623.5, 534.1, 485.0 nm; spectral purity 5–10 nm). Light levels were isoirradiant at 1.1·10¹² quanta/s/cm². Two control groups were reared in white light with down-welling illuminances of 0.2 and 33 lx. Nasotemporal diameters (NTDs) of the eyes were measured in relation to lens size. Due to the oblique axis of highest acuity vision in cichlids, NTD is considered to be a more important dimension than axial length. Variances in NTD were equally small in all rearing groups. NTDs were enlarged with increasing wavelengths of the rearing lights with highly significant values over controls in the red-light group. The wavelength-dependent size of the eyes matched the changes in focal length due to longitudinal chromatic aberration. Complete recovery from eye enlargement was observed after fish reared in red light were exposed to a white light regime for 5 weeks. Small variances in NTD in all groups indicated stringent control of eye growth in the absence of color cues. The reversibility of the increase in NTD in fish reared in red light suggests that the eyes were emmetropized by visually guided mechanisms. Eye size in fish reared in white light was intermediate between the values expected if only blue-sensitive single or the red- and green-sensitive double cones contributed to the control of eye growth. This suggests that all chromatic channels participate in emmetropizing the fish eye.     

Multifocal lenses compensate for chromatic defocus in vertebrate eyes

The focal length of the vertebrate eye is a function of wavelength, i.e. the eye suffers from longitudinal chromatic aberration. Chromatic defocus is a particularly severe problem in eyes with high light-gathering ability, since depth of field is small due to a pupillary opening that is large in relation to the focal length of the eye. Calculations show that in such eyes only a narrow spectral band of light can be in focus on the retina. For the major part of the visual spectrum, spatial resolution should be limited by the optics of the eye and far lower than the resolving power achievable by the retinal cone photoreceptor mosaic. To solve this problem, fishes with irises unresponsive to light have developed lenses with multiple focal lengths. Well-focused images are created at the wavelengths of maximum absorbance of all spectral cone types. Multifocal lenses also appear to be present in some terrestrial species. In eyes with mobile irises, multifocal lenses are correlated with pupil shapes that allow all zones of the lens, with different refractive powers, to participate in the imaging process, irrespective of the state of pupil constriction. Accepted: 6 November 1998     

The eye of the hooded seal,Cystophora cristata,in air and water

Summary Multiple refractive state measurements were made on a male and female hooded seal (Cystophora cristata) when the eyes were exposed to air and to water. The measures, made by conventional retinoscopy and by photorefraction, show that the seals are moderately hyperopic (2–3 diopters) in water and moderately myopic (2–4 diopters) in air. No significant astigmatism was noted in either medium. The absence of refractive state variation over time suggests that an accommodative mechanism is insignificant or absent, although histological study indicates that the ciliary muscle is well developed.Photokeratoscopy, carried out on two animals with two keratoscopic instruments, show that the cornea is relatively flat (30 mm, or about one-half the diameter of the eye). Furthermore the cornea is only slightly astigmatic (less than 1 diopter). The refractive power of the external corneal surface (in air), calculated from a measurement of corneal refractive index of 1.378, amounts to only 10 or 11 diopters.As in the typical fish eye, hooded seal lenses are spherical or nearly spherical in shape (24–23 mm), and have short focal lengths (30–32 mm). Focal measures for rays at varying distances from the lens center indicate that spherical aberration is well corrected.There is no indication in this seal species, of a previously reported adaptation involving a highly astigmatic cornea which together with a slit pupil can minimize the optical effect of movement from water to air.     

Sturgeons,sharks, and rays have multifocal crystalline lenses and similar lens suspension apparatuses

Crystalline lenses with multiple focal lengths in monochromatic light (multifocal lenses) are present in many vertebrate groups. These lenses compensate for chromatic aberration and create well‐focused color images. Stabilization of the lens within the eye and the ability to adjust focus are further requirements for vision in high detail. We investigated the occurrence of multifocal lenses by photorefractometry and lens suspension structures by light and electron microscopy in sturgeons (Acipenseriformes, Chondrostei) as well as sharks and rays (Elasmobranchii, Chondrichthyes). Multifocal lenses were found in two more major vertebrate groups, the Chondrostei represented by Acipenseriformes and Chondrichthyes represented by Elasmobranchii. The lens suspension structures of sturgeons, sharks, and rays are more complex than described previously. The lens is suspended by many delicate suspensory fibers in association with a ventral papilla in all groups studied. The arrangements of the suspensory fibers are most similar between sturgeons and sharks. In rays, the lens is suspended by a smaller ventral papilla and the suspensory fibers are arranged more concentrically to the lens. J. Morphol., 2012. © 2012 Wiley Periodicals, Inc.     

Terrestrial optics in an aquatic eye: The sandlance,Limnichthytes fasciatus (Creediidae,Teleostei)

The sandlance, Limnichthyes fasciatus (Creediidae, Teleostei), behaves like a marine chameleon, with independent movements of its turret-like eyes, highly-effective camouflage and rapid strikes for isolated, mobile prey at close quarters. The optical system has a fixed circular pupil, a deep pit fovea and a flattened lens unlike any other teleost lens so far described. The convex, laminated structure of the cornea is also unparalleled in a teleost which suggests that the cornea may play a refractive role that might compensate for the reduced power of the flattened lens. This suggestion has been supported in the present investigation by four independent sets of observations:- i. Purkinje images formed underwater by the cornea; ii. Measurements of the magnification of intra-corneal iridophores viewed through the corneal lenticle; iii. Measurements of the magnification produced by the dissected corneal lenticle and lens when viewed over a grating; iv. Ray tracing experiments comparing the degree of refraction produced by the lens and by the corneal lenticle. All experimental observations confirm that the cornea of the sandlance has a significant refractive role, with a power of approximately 200 D compared with a power of 550 D for the lens. This is the first report of a significant refractive role played by the cornea in a teleost. The optical system of lens plus cornea, in combination with a deep pit fovea, may be more suitable for the detection and visual localisation of small, moving, underwater prey than the conventional wide-field spherical lens system of other teleosts. The evolutionary convergence of this marine optical system and lifestyle with those of the chameleon is remarkable, given the constraints imposed by underwater optics.     

Optical performance of the penguin eye in air and water

Summary Refractive states of three species of penguins (Rockhopper, Gentoo and King) were measured in air and water. Little or no refractive error, with a trend toward slight myopia (less than two dioptres), was found in air in each case. Moderate hyperopia (8–13 dioptres) exists in water. The refractive findings of this study are similar to those of a preliminary study made with the Blackfoot penguin. The relatively small alteration of refractive state associated with the change from air to water (in contrast to an approximate change of 40 dioptres for the human eye) is attributed to the flattened shape of the cornea. The chromatic aberration measured in these species is insufficient to account for the hyperopia found underwater. The maximum reduction of hyperopia resulting from a monochromatic (blue, blue-green) aquatic habitat would only amount to two dioptres. It is speculated that the remaining hyperopia is nullified by an accommodative mechanism.This research was supported by a grant from the National Research Council of Canada. The authors are grateful for the cooperation of the Scottish National Zoological Park, Edinburgh. In particular, the authors would like to thank Mr. Kennedy for assistance in handling the penguins. The authors would like to acknowledge the original observation by Barbara Sivak concerning the flattened appearance of the penguin cornea.     

Geometric optical optimization of the corneal lens of Notonecta glauca

The optimal shape of the corneal lens of the water bug backswimmer (Notonecta glauca) and the optimal shape and position of the thin transition layer between the distal and proximal units of its cornea are theoretically determined. Using a geometric optical method, first the shape of a geometric interface between the lens units is determined, which eliminates the longitudinal spherical aberration. This interface is investigated for differently formed thick lenses when the medium in contact with the entrance surface of the lens is water or air. The optimal transition layer for the amphibious backswimmer is that, the boundaries of which are the theoretical interfaces for water and air, and the refractive index varies continuously in it. The optimal shape of the corneal lens is determined, with the disadvantageous lenses, with respect to the possible minimal spherical aberration and amount of reflected light from the transition layer, being rejected. The optimal position of the transition layer in the cornea can be obtained from the minimization of the amount of diffracted light on the marginal connection of the layers. The optimal corneal lens for backswimmer has ellipsoid boundary surfaces; the optimal transition layer in it is thin bell-shaped, at the marginal connection of which there is no dimple, the maximum of the layer is on the margin of the cornea. The shape of the theoretically optimal corneal lens, the shape and position of the theoretically optimal transition layer agree well with those of Notonecta glauca. The question posed, the geometric optical method used and the results presented are of general importance, and not only with respect to vision in the bug Notonecta, but also in the fossil trilobites, or in the wave guide theories which have been employed in similar modelling problems, in design of system of lenses without spherical aberration, for example.     

Reconstruction of the shape and optics of the lenses in the abathochroal‐eyed trilobite Neocobboldia chinlinica

Until now, the structure and optics of the calcite lenses in abathochroal trilobite eyes have not been investigated. So, the relationship of the abathochroal eye to other types of trilobite eyes has remained unclear. We have reconstructed the exact shape and optics of the lenses in the eodiscid trilobite Neocobboldia chinlinica to determine the mechanism of its abathochroal eye. The distal lens surface has a convex profile, while on the proximal lens surface there is a small central bulge, resulting in an undulating profile. Due to this bulge, the curvature and refractive power of the central region of the lens are greater than those of the peripheral zone. Consequently, the lens is bifocal. However, Neocobboldia could not take advantage of this bifocal property of its tiny lenses because of the diffraction of light and the infinite depth of field in object space. For the same reason, it is also sure that the undulating lower surface of the abathochroal lens did not evolve as a Huygensian profile, correcting for spherical aberration, as suggested earlier. This undulation is a result of the presence of the central bulge, the evolutionary significance of which remains enigmatic. On the basis of our results, we have outlined an evolutionary scenario for development of the optics of the lenses in trilobite eyes.     

Comparative visual acuity of coleoid cephalopods

The pelagic realm of the ocean is characterized by extremelyclear water and a lack of surfaces. Adaptations to the visualecology of this environment include transparency, fluorescence,bioluminescence, and deep red or black pigmentation. While thesignals that pelagic organisms send are increasingly well-understood,the optical capabilities of their viewers, especially for predatorswith camera-like vision such as fish and squid, are almost unknown.Aquatic camera-like vision is characterized by a spherical lensfocusing an image on the retina. Here, we measured the resolvingpower of the lenses of eight species of pelagic cephalopodsto obtain an approximation of their visual capabilities. Wedid this by focusing a standard resolution target through dissectedlenses and calculating their modulation transfer functions.The modulation transfer function (MTF) is the single most completeexpression of the resolving capabilities of a lens. Since theoptical and retinal capabilities of an eye are generally well-matched,we considered our measurements of cephalopod lens MTF to bea good proxy for their visual capabilities in vivo. In general,squid have optical capabilities comparable to other organismsgenerally assumed to have good vision, such as fish and birds.Surprisingly, the optical capability of the eye of Vampyroteuthisinfernalis rivals that of humans.     

Geometric optics of trilobite eyes: a theoretical study of the shape of the aspherical interface in the cornea of schizochroal eyes of phacopid trilobites

A general method is given to determine theoretically the shape of the aspherical interface that eliminates spherical aberration in an optionally shaped thick lens. The theory is applied to trilobite eyes. On the basis of the geometric optical method presented, the refractive indices and focal length of the original corneal lenses of trilobites can be determined. The shape of the aspherical interface in the cornea of some phacopid trilobites with schizochroal eyes is investigated. The theoretical aspherical interfaces agree well with the real ones.     

Dual laser flow cytometry: focal length compensation when focussing through a single lens

Dual laser operation of flow cytometers, using a single focussing lens for both beams, requires compensating for chromatic aberration of the lens. By using a prefocussing lens at a fixed position in one of the laser beams, complete focal length compensation is obtained without any loss in system performance.     

Convergence of specialised behaviour, eye movements and visual optics in the sandlance (Teleostei) and the chameleon (Reptilia)

Chameleons have a number of unusual, highly specialised visual features, including telescopic visual optics with a reduced lens power, wide separation of the eye's nodal point from the axis of rotation, a deep-pit fovea, rapid pre-calculated strikes for prey based on monocular depth judgements (including focus), and a complex pattern of partially independent alternating eye movements. The same set of features has been acquired independently by a teleost, the sandlance Limnichthyes fasciatus. Despite its underwater lifestyle, this fish displays visual behaviour and rapid strikes for prey that are remarkably similar to those of the chameleon [1]. In a direct comparison of the two species, we have revealed other, previously unsuspected, similarities, such as corneal accommodation, which was unknown in teleosts, as well as bringing together, for the first time, data collected from both species. The sandlance is the only teleost, among thousands studied, that has corneal refraction, corneal accommodation and reduced lens power, as well as sharing the other specialised optical features seen in chameleons. The independent eye movement pattern in the sandlance is also unusual and similar to that of the chameleon. The selection pressures that have produced this remarkable example of convergence may relate to common visual constraints in the life styles of these two phylogenetically disparate species.     

人眼波前像差数值表示及测量方法的研究

人眼离焦和散光两个缺陷可以通过佩戴框架眼镜、角膜接触镜、激光屈光手术得到矫正。但是,即使矫正后的眼睛屈光处于最佳状态,但仍不能获得最佳视觉敏锐度。这是因为人眼存在着光学像差。从人眼像差的测量方法和数值表示法来进行分析,并引入Zern ike多项式来表示波前像差,为用准分子激光进行眼球像差矫正提供理论依据。     

Dopamine Induces Optical Changes in the Cichlid Fish Lens

The crystalline lens in the cichlid fish Aequidens pulcher undergoes a transformation of its optical properties every dawn and dusk as the eye adapts to changes in light conditions. During dusk the transformation result in an increase of the refractive power in the lens cortex, the outermost 40 percent. The change is thought to match the optical properties of the lens to the requirements of the retina. Using a short term in vitro lens culturing system together with optical measurements we here present data that confirm that the optical properties of the lens can change within hours and that dopamine influences the optical properties of the lens. Dopamine yields dose-dependent decrease of the refractive power in the lens cortex. The D1-agonist SKF-38393 induces a similar decrease of the refractive power in the cortex, while the D2-agonist quinpirole has no effect. The effect of dopamine can be blocked by using the D1-antagonist SCH 23390. Our results suggest that dopamine alone could be responsible for the light/dark adaptive optical changes in the lens, but the involvement of other signaling substances cannot be ruled out.