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

Contribution of the gradient refractive index and shape to the crystalline lens spherical aberration and astigmatism

The optical properties of the crystalline lens are determined by its shape and refractive index distribution. However, to date, those properties have not been measured together in the same lens, and therefore their relative contributions to optical aberrations are not fully understood. The shape, the optical path difference, and the focal length of ten porcine lenses (age around 6 months) were measured in vitro using Optical Coherence Tomography and laser ray tracing. The 3D Gradient Refractive Index distribution (GRIN) was reconstructed by means of an optimization method based on genetic algorithms. The optimization method searched for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens in 18 different meridians. Spherical aberration and astigmatism of the lenses were estimated using computational ray tracing, with the reconstructed GRIN lens and an equivalent homogeneous refractive index. For all lenses the posterior radius of curvature was systematically steeper than the anterior one, and the conic constant of both the anterior and posterior positive surfaces was positive. In average, the measured focal length increased with increasing pupil diameter, consistent with a crystalline lens negative spherical aberration. The refractive index of nucleus and surface was reconstructed to an average value of 1.427 and 1.364, respectively, for 633 nm. The results of the GRIN reconstruction showed a wide distribution of the index in all lens samples. The GRIN shifted spherical aberration towards negative values when compared to a homogeneous index. A negative spherical aberration with GRIN was found in 8 of the 10 lenses. The presence of GRIN also produced a decrease in the total amount of lens astigmatism in most lenses, while the axis of astigmatism was only little influenced by the presence of GRIN. To our knowledge, this study is the first systematic experimental study of the relative contribution of geometry and GRIN to the aberrations in a mammal lens.

Pig lenses in a lens stretcher: implications for presbyopia treatment

PURPOSE

To investigate porcine lenses in a lens stretcher with regard to presbyopia corrective procedures.

METHODS

A lens stretching device was designed, which allows to simultaneously determine all relevant geometrical and optical parameters at each stretch position. The setup was used to compare the optical and geometrical lens properties of young slaughter pigs (n = 5) with older sows (n = 7).

RESULTS

The change of optical power with stretching is about five times larger for young porcine lenses than for sows. For young pigs, the gradient index profile of the crystalline lens significantly contributes to the induced accommodation amplitude.

CONCLUSIONS

We have shown that sow lenses are a suitable model for in vitro experiments on possible treatments for presbyopia. The rapid decrease in the induced accommodation amplitude with age may be explained by a reduced change of all geometrical lens parameters, which in turn leads to a smaller contribution of the gradient index profile to accommodation.

The gradient index lens of the eye: an opto-biological synchrony

The refractive power of a lens is determined largely by its surface curvatures and the refractive index of its medium. These properties can also be used to control the sharpness of focus and hence the image quality. One of the most effective ways of doing this is with a gradient index. Eye lenses of all species, thus far, measured, are gradient index (GRIN) structures. The index gradation is one that increases from the periphery of the lens to its centre but the steepness of the gradient and the magnitudes of the refractive index vary so that the optics of the lens accords with visual demands. The structural proteins, the crystallins, which create the index gradient, also vary from species to species, in type and relative distribution across the tissue. The crystallin classes do not contribute equally to the refractive index, and this may be related to their structure and amino acid content. This article compares GRIN forms in eye lenses of varying species, the relevance of these forms to visual requirements, and the relationship between refractive index and the structural proteins. Consideration is given to the dynamics of a living lens, potential variations in the GRIN form with physiological changes and the possible link between discontinuities in the gradient and growth. Finally, the property of birefringence and the characteristic polarisation patterns seen in highly ordered crystals that have also been observed in specially prepared eye lenses are described and discussed.

Model of accommodation: contributions of lens geometry and mechanical properties to the development of presbyopia

PURPOSE

To determine the relative importance of lens geometry and mechanical properties for the mechanics of accommodation and the role of these elements in the causes and potential correction of presbyopia.

SETTING

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey, USA.

DESIGN

Experimental study.

METHODS

Finite element methods and ray-tracing algorithms were used to model the deformation and optical power of the human crystalline lens during accommodation. The mechanical model treats the lens as an axisymmetric object, and the optical model incorporates a gradient refractive index. Using these models, the accommodation of a broad range of lenses with different geometries and mechanical properties were investigated.

RESULTS

The most significant result was that reshaping the 45-year-old lens to the geometry of the 29-year-old lens, while retaining the mechanical properties, restored the former's accommodation amplitude to 72% to 94% of that of the 29-year-old lens, depending on ciliary body displacement. That is, reshaping can add 1.8 to 3.7 diopters of accommodation. A sensitivity analysis showed that this result was robust over a wide range of mechanical and geometrical properties.

CONCLUSION

The study results suggest that a significant amount of the loss of accommodation is due to changes in lens geometry.

Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.

Refractive index distribution in the porcine eye lens for 532 nm and 633 nm light

AIMS

To measure the refractive index distribution in porcine eye lenses for two wavelengths from the visible spectrum: 532 and 633 nm, in order to determine whether there are any discernible wavelength dependent differences in the shape of the profile and in the magnitude of refractive index.

METHODS

Rays were traced through 17 porcine lenses of the same age group and of similar size. Ray trace parameters were used to calculate the refractive index distributions for 633 nm light in all 17 lenses and for 532 nm light in 10 lenses. The effect of the refractive index at the edge of the lens, on the rest of the profile, was considered because the mismatch between refractive index at the lens edge and the refractive index of the surrounding gel necessitated a further step in calculations.

RESULTS

The shape of the refractive index distributions is parabolic. There is a small wavelength dependent difference in the magnitude of the refractive index across the profile and this increases very slightly into the centre of the lens. The value of the refractive index at the edge of the lens does not appreciably affect the index profile.

CONCLUSIONS

The wavelength dependent differences in refractive index between light of 633 and 532 nm are small but discernible.

Schematic eye with a gradient-index lens and aspheric surfaces

A new schematic eye with aspheric surfaces and a radially varying refractive-index distribution lens is proposed. Image quality and spherical aberration are determined by use of ray tracing, and the results are presented as spot diagrams and compared with five existing model eyes. The proposed model provides the best image quality and lowest spherical aberration.

Model of the optical system of the human eye during accommodation

A model of the human eye with a gradient index crystalline lens is presented. The crystalline lens shape at different accommodation levels is described by a single function which is a combination of hyperbolic cosine functions and hyperbolic tangent functions. Using the experimental data published in the literature a model of the variations of the external lens shape was created. Formulae for the lens shape parameters and gradient index distribution for different accommodation levels are given.

Analysis of Inhomogeneous Optical Systems by the Use of Ray Tracing. II. Three-dimensional Systems with Symmetry

We describe a new approach to the index reconstruction of three-dimensional optical systems with rotational symmetry, which is based on sampling ray paths that lie in the sagittal plane. Since the observed rays are distorted by the optical system itself, they cannot be used directly for index reconstruction. We present an iterative procedure to compute the true ray paths and then to find the index distribution. The utility of the method is verified on the model problem.

Investigation of dispersion effects in ocular media by multiple wavelength partial coherence interferometry

We report on quantitative measurements of group refractive indices and group dispersion in water and in human ocular media such as the cornea, the aqueous humor, the lens, artificial intraocular lenses, as well as a total value averaged over the media along the axial eye length of normal subjects and pseudophakic patients in vivo using dual beam partial coherence interferometry. Different optical thickness values due to the dispersion of the cornea are demonstrated using two spectrally displaced light sources. The displacement can be used to indirectly calculate the group dispersion of the human cornea in the spectral region between 810 nm and 860 nm. If the object under investigation is dispersive, resolution is limited due to a broadening of the detected signals. This broadening increases with group dispersion, i.e., the extent to which the group refractive index of the medium varies with wavelength and thickness of the tissue under investigation as well as with the spectral bandwidth of the light source. Measurements of the group dispersion in the cornea, lens and vitreous of pseudophakic and normal human eyes, show that the cornea and the lens are more dispersive than water-by a factor of about 5 and 2, respectively-in the investigated spectral region. The cornea is approximately threefold more dispersive than the human crystalline lens, the aqueous humor is less dispersive than water and the group dispersion of all ocular components together, averaged over the axial length of normal and pseudophakic eyes, was only slightly higher compared to that of water. Since the highly dispersive cornea and lens together have only a thickness of about one sixth of that of the axial eye length, it seems that their contribution to the group dispersive effect along the whole axial eye length is only small.

Refractive index contours in the human lens

The refractive index values along the equatorial and sagittal planes of lenses of varying ages were measured using a reflectometric fibre optic sensor. In younger lenses (from the third decade) and in one older lens, the index profiles from the two planes did not concur when plotted on a normalized scale refuting, in these lenses, the assumption of concentric, isoindicial contours which follow the shape of the lens. Agreement between the normalized profiles did occur with all other lenses investigated (aged 47 and older).

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.

The refractive index along the optic axis of the bovine lens

This study aimed to measure the refractive index values along the optic axes of adult bovine lenses. An optic fibre reflectometric sensor was used for this purpose. Seventeen lenses were examined and over the weight range studied there were no apparent age-related trends in the index gradient. The peak index values varied from 1.432 to 1.442. There was a greater variation in the edge index values, which may have reflected differences in hydration on lens surfaces or may be indicative of a slight decrease in surface index with age.

Variations in refractive index and absorbance of 670-nm light with age and cataract formation in human lenses

A newly-developed fibre-optic sensor (wavelength of 670 nm) was used to measure the index gradient in 16 human lenses ranging in age from 38 to 78 years. Two of these lenses had nuclear cataract. The refractive index, calculated from the proportion of reflected light at the sensor/sample interface, appeared to increase with age and further with cataract formation. This was not consistent with previous studies. The increased losses of reflected light, which gave apparent increased values of refractive index, were reconsidered to be resulting from light absorption and an estimate of relative absorption was made by deducting excess light loss from a base level expected to yield the maximum index value. The characteristics of the relative absorption are similar to those of a red fluorophor reported in other studies.

Refractive Index of the Human Corneal Epithelium and Stroma

BACKGROUND

The refractive index of the cornea must be determined to optically perfect keratorefractive procedures. There are very few empirical measurements of the human corneal refractive index described in the literature. Throughout its depth, the cornea demonstrates regional variations in physiological properties such as swelling/de-swelling characteristics. These properties suggest there may be a difference in the refractive index between the anterior and posterior corneal surfaces.

METHODS

The refractive index of the human corneal epithelium of 10 eyes was measured, in vivo, using a modified hand-held refractometer. The refractive indices of the anterior and posterior surfaces of the bare stroma of fresh human corneas were measured using a bench model Abbe refractometer.

RESULTS

The mean refractive index of the epithelium, stromal anterior and posterior surfaces were 1.401 (SD +/- 0.005), 1.380 (SD +/- 0.005), and 1.373 (SD +/- 0.001) respectively.

CONCLUSIONS

The refractive index of the cornea is not uniform. The calculated dioptric power of the corneal epithelium is approximately -1.40 diopters (D). The varying refractive index does not significantly affect the total dioptric power of the cornea. The varying refractive index of the cornea has the potential to significantly contribute to the overall optical performance of the eye in relation to refractive surgery. The results should be incorporated into mathematical models, comparing and contrasting the optical performance of the eye before and after surgery.

Surface refractive index of the eye lens determined with an optic fiber sensor

The use of a fiber-optic sensor for measurement of the refractive index on the surface of eye lenses is described. The technique makes use of the fact that the amount of light reflected at the interface of two media (Fresnel reflectance) depends on the refractive-index difference between them. The sample is probed with a single-mode fiber, and the refractive index is calculated from the proportion of light reflected at the probe-sample interface.

Modeling the power of the aging human eye

A hypothesis is presented that may explain why the aging eye does not become myopic with age. The power of the eye lens is predicted with a modeling approach to determine how the form of the refractive-index gradient within the lens can change to maintain a constant power in spite of age-related curvature increase. Methods used include published age-dependent data on the optical parameters of the eye, a mathematical model of the lens based on elliptical isoindicial contours, and a refractive-index profile that can be expressed as a power series in the distance from the lens center. The kinds of change in profile required to prevent the eye from becoming myopic as its lens grows are shown.

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.