Image quality of the human eye for eccentric entrance pupils

The human eye has a considerable amount of chromatic aberration and a moderate amount of spherical aberration. If a small artificial pupil is placed in front of such optics and moved away from the centre towards the periphery the chromatic aberration will result in lateral colour shifting, and the spherical aberration will cause coma. Starting from available experimental data on the chromatic aberration and the spherical aberration, modulation transfer functions (MTF's) are calculated for central and eccentric positions of small pupils placed in front of the human eye. These calculations may help to separate optical and retinal contributions to the well-known reduction of visual acuity measured with eccentric pupils. It appears that measurements with pupils smaller than 1 mm in monochromatic light can be considered optically as diffraction limited. Changes of visual acuity found in this way must be assigned to the retina.     

Chromatic aberration and optical power of a diffractive bifocal contact lens.

Although diffractive contact lenses have been well documented in theory, no definitive experimental data have been reported which confirm that the near image is in fact created by diffraction rather than by refraction. We have tested the diffraction hypothesis for one type of diffractive contact lens (the Hydron Echelon bifocal) experimentally by measuring its longitudinal chromatic aberration in isolation and when worn on the eye. The basis of this test is that, according to theory, diffractive lenses should have chromatic aberration which is opposite in sign to that measured for the eye. Objective measurements of chromatic aberration were made with a focimeter when the lens was in a wet cell. Subjective measurements were made with a Badal optometer when the lens was worn on the eye. Four control experiments were conducted to provide baseline measurements of the eye's chromatic aberration, against which we compared the results obtained for the diffractive contact lens. The data were also compared with conventional measurements of refractive error obtained by standard subjective techniques and by an automated infrared refractor. Our results showed that the longitudinal chromatic aberration of the diffraction image of the Echelon bifocal lens was about one-half that obtained under the four control conditions: for the naked eye, for the nondiffraction image of the Echelon lens, or for either image of a refractive bifocal contact lens (CIBA Bisoft). These results are consistent with the theoretical prediction that the negative chromatic aberration of a diffractive contact lens should partially cancel the positive chromatic aberration of the human eye.(ABSTRACT TRUNCATED AT 250 WORDS)     

Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils.

Chromostereopsis has been attributed previously to interocular differences in foveal transverse chromatic aberration (TCA). We tested this hypothesis by measuring chromostereopsis as a function of the separation of small artificial pupils. We also measured the monocular transverse chromatic aberration under the same conditions. Our results show that chromostereopsis with small pupils can be precisely accounted for by the interocular difference in monocular transverse chromatic aberration. This relationship is closely predicted by a simple water eye model.     

THE CHROMATIC ABERRATION ADJUSTMENT IN LASER OPTOMETRY

The issues involved in designing chromatic aberration corrections in laser optometry are reviewed. There is considerable disagreement regarding both the magnitude of human eye chromatic aberration and the value that should be assumed for the reference wavelength. Also important are the observer's accommodative state, target luminance wavelength, laser wavelength, intersubject dioptric variations, and several other factors. The appropriate solution for most experiments appears to be to report no chromatic aberration adjustment at all; rather, the investigator should provide basic technical information from which interested readers can make their own corrections, depending on the assumptions of importance to them.     

Human axial chromatic aberration found not to decline with age

Millodot (1976) reported a dramatic decline in the amount of axial chromatic aberration of the human eye with age. The present study represents a failure to replicate that finding using a more standard procedure. No difference in chromatic aberration was found between a young and an older group of observers. Also, the chromatic aberrations of two observers which had been measured 25 years previously showed no decline when these measurements were repeated, even though their ages at first and second testing straddled the period over which Millodot reported the most change in chromatic aberration.     

The value of the red-green test

The causes of chromatic aberration were elucidated by Newton in 1704, though in regard to the eye the phenomenon has been a subject of controversy. The chromatic aberration of the eye has long been used to determine refraction. In principle, blurred coloured circles are visible which depend on the chromatic aberration of the eye and lead to perception of different contrasts in the dark optotypes presented in the two coloured fields, depending on the real ametropia or correction conditions. Uniform perception of contrast by the subject is used as the criterion for correction. As regards the red-green test, it appears doubtful that the results are not influenced by protanopia and brunescent cataract. Therefore, the contrast thresholds of 8 protanopic patients and 5 patients with brunescent cataract were examined. This was done using special red and green lenses (produced by VEB Carl Zeiss Jena) under individual conditions with Landolt's rings. Characteristic differences in the contrast thresholds for red and green were found. For bichromatic tests no procedure has been defined, and neither the wave-lengths to be used nor the reference wavelength have been laid down. The results can be affected by numerous physical, physiological and pathological factors. The accuracy and practical usefulness of red-green tests are questionable. Therefore, it does not appear justified to equip ophthalmological examination instruments for such tests.     

Theory and measurement of ocular chromatic aberration

We have determined the transverse chromatic aberration of the human eye by measuring the apparent offset of a two-color vernier viewed foveally through a displaced, pinhole aperture. For the same subjects, we also determined the longitudinal chromatic aberration for foveal viewing by the method of best focus. In both cases, the results were closely predicted by a simple, reduced-eye optical-model for which transverse and longitudinal chromatic aberration are directly proportional, with the constant of proportionally being the amount of displacement of the pinhole from the visual axis. Further measurements revealed that the natural pupil was closely centered on the visual axis for two subjects and slightly displaced in the temporal direction for three other subjects. One implication of these results is that, although the eye has substantial chromatic aberration, the pupil is positioned so as to minimize the transverse component of the aberration for central vision, thereby optimizing foveal image quality for polychromatic objects.     

Effect of ocular chromatic aberration on monocular visual performance

This brief review outlines the theory of ocular chromatic aberration and describes the three primary forms in which the aberration appears: chromatic difference of focus, chromatic difference of magnification, and chromatic difference of position. Our central theme is that all three aspects of chromatic aberration have as their common basis the chromatic dispersion of light. The magnitude of each form of the aberration is related to the others by simple linear formulas in which a key parameter is the location of the pupil relative to the nodal point of the eye. The way in which retinal image quality is affected by chromatic aberration is described and we assess the impact of the aberration on visual performance.     

Achromatizing the human eye

Ocular chromatic dispersion manifests itself as wavelength-dependent image planes, image sizes, and image positions, and it has been suggested that ocular chromatic aberration is the most important of the eye's optical aberrations. Most attempts to correct for the eye's chromatic aberration (achromatize the human eye) have concentrated on correcting the wavelength-dependent image planes or chromatic difference of refractive error (CDRx). There are two optical techniques that correct for CDRx (special achromatizing lenses and multiple channel display systems) by making the ocular image planes of all wavelengths coincident. A different approach simply avoids the effects of ocular CDRx by using small pupils which effectively make all images diffraction-limited irrespective of wavelength-dependent differences in image planes. Theoretical and experimental evidence shows that achromatizing lenses provide an accurate correction for CDRx. In spite of the pre-eminence of chromatic aberrations, and the effectiveness of the corrections, no obvious improvements in vision accompany correction. We show that loss of retinal image quality due to CDRx may be subthreshold (less than ocular depth of focus). We also show that achromatizing methods can introduce their own chromatic aberrations that can easily exceed those present in the uncorrected eye. The precise location of the eye with respect to the achromatizing device determines the amount of these additional aberrations. Therefore, in order to achromatize the eye effectively, careful control of eye position is essential.     

The effect of chromatic dispersion on pseudophakic optical performance

AIM: Monochromatic and chromatic aberrations limit the visual performance of pseudophakic eyes. Chromatic aberration is caused by the chromatic dispersion of optical materials which can be characterised by their Abbe numbers. This study examines how chromatic dispersion affects pseudophakic optical performance at different wavelengths and spatial frequencies. METHODS: Abbe numbers were measured for acrylic and silicone intraocular lenses (IOLs). A schematic eye model based on cataract population data was used to compute monochromatic and photopic polychromatic modulation transfer functions (MTFs) for pseudophakic eyes with aspheric IOLs. IOL Abbe numbers were varied without changing other eye model parameters to determine how chromatic dispersion affects pseudophakic MTF and chromatic difference of refraction. Additional calculations were performed for (1) acrylic or silicone materials and (2) high-pass optical filters blocking either UV radiation or UV radiation and short wavelength visible light. RESULTS: Shorter wavelengths account for approximately two thirds of pseudophakic chromatic difference of refraction or longitudinal chromatic aberration. Increasing Abbe number (reducing chromatic dispersion) decreases total chromatic difference of refraction and increases photopic polychromatic MTF. For a specific spatial frequency, there is an effective pseudophakic depth of wavelength over which a particular MTF level is achieved or exceeded. Depth of wavelength narrows with decreasing Abbe number or increasing spatial frequency. Blue-blocking IOL chromophores improve photopic MTF performance by less than 1.5%. CONCLUSIONS: Most pseudophakic longitudinal chromatic aberration arises from the chromatic dispersion of IOLs rather than the cornea and other ocular media. Increasing the Abbe number of optic materials improves overall pseudophakic optical performance. Optical transmission of medium and high spatial frequency modulation information has a spectrum similar to photopic luminous efficiency, accounting for the inability of blue-blocking chromophores to improve photopic pseudophakic contrast sensitivity significantly and demonstrating the excellent mutual adaptation of modulation transfer by the eye's optics and management of that data by the retina and brain.     

Psychophysical measurement of the blur on the retina due to optical aberrations of the eye

The blur on the retina in the horizontal meridian due to monochromatic and chromatic aberrations has been measured using a novel psychophysical technique. Longitudinal chromatic aberration gives the dominant blur for pupil sizes of 4-5 mm, followed by monochromatic aberrations, and blur due to optical transverse chromatic aberration. In some eyes, coma was present as a result of a displacement of the axis of symmetry from the centre of the pupil, but in three eyes, coma was present without spherical aberration. The technique also allows a measurement of the effective pupil centre relative to the geometric centre and a partial analysis of the relative positions of the reference axes of the eye.     

Le Grand eye for the study of ocular chromatic aberration

In this technical note we study the prediction of ocular chromatic aberration which provides Le Grand's complete theoretical eye model. Theoretical computations of the longitudinal chromatic aberration are lower than experimental results. However, we show that experimental results of the chromatic difference of position (CDP) agree with theoretical predictions. The fit of the CDP for this model is practically the same as the one obtained for the Thibos reduced eye.     

Investigating sources of variability of monochromatic and transverse chromatic aberrations across eyes

Schematic eye models have typically been used to explain the average monochromatic and chromatic imaging properties of the eye. Both monochromatic aberrations and transverse chromatic aberration are known to vary widely across subjects. However, to our knowledge, the ability of schematic eye models to predict these individual variations has not been tested experimentally. We used a spatially resolved refractometer to measure the monochromatic aberrations and the optical transverse chromatic aberration (oTCA) in a group of 15 eyes. By recording the 1st and 4th Purkinje images for five directions of gaze, we also estimated the tilt, misalignment of ocular surfaces (front surface of the cornea and back surface of the lens) and off-axis position of the fovea (angle alpha), as well as pupil centration. We conclude that, contrary to expectations none of those factors are major contributors to the variability in monochromatic aberrations and oTCA in this group of eyes. Simulations show that corneal curvature and corneal conicity are also unlikely to account for the observed relation between monochromatic aberrations and oTCA. Our results suggest an important contribution of corneal irregularities to those aberrations.     

The longitudinal chromatic aberration of the human eye, and its correction

The human eye suffers from longitudinal chromatic aberration, and this has been thought to average approximately 1.75 D between 420 and 660 nm. In many vision experiments the aberration may be a serious problem, and a number of lenses have been designed to correct it, two of which have recently been commercially available. These achromatising lenses produce an equal but opposite aberration to that of the average eye, and the power of the eye/lens combination should then be independent of wavelength. Recent measures of the eye's longitudinal aberration suggest that the average may be substantially greater than the above value, in which case lenses based on this figure should be inadequate. Using a Badal optometer we determined the far points for 20 subjects with each of the recent lenses, and without either, at nine wavelengths over the above range. Consistent with the early studies we found an average aberration of 1.82 D (SD 0.15 D). Both lenses performed as specified, and none of our subjects had over 0.48 D of residual aberration when corrected with either.     

Longitudinal chromatic aberration of the human eye and wavelength in focus

The wavelength in focus on the retina was determined for 14 observers from measurements of the longitudinal chromatic aberration of the eye. Measurements were made at two viewing distances: 3 m and 40 cm. The results show a large amount of individual variability for the wavelength in focus at each distance. The range of values at 3 m was 457 to 593 nm with a mean of 518 nm, and 375 to 548 nm with a mean of 468 nm at 40 cm. The chromatic aberration measured at 3 m is the same as previously reported data by other investigators for distant viewing. The average results of this study indicate very little difference for the chromatic aberration measured at near compared to distant viewing but, again, considerable individual variability exists.     

The effects of longitudinal chromatic aberration and a shift in the peak of the middle-wavelength sensitive cone fundamental on cone contrast

Longitudinal chromatic aberration is a well-known imperfection of visual optics, but the consequences in natural conditions, and for the evolution of receptor spectral sensitivities are less well understood. This paper examines how chromatic aberration affects image quality in the middle-wavelength sensitive (M-) cones, viewing broad-band spectra, over a range of spatial frequencies and focal planes. We also model the effects on M-cone contrast of moving the M-cone fundamental relative to the long- and middle-wavelength (L- and M-cone) fundamentals, while the eye is accommodated at different focal planes or at a focal plane that maximizes luminance contrast. When the focal plane shifts towards longer (650nm) or shorter wavelengths (420nm) the effects on M-cone contrast are large: longitudinal chromatic aberration causes total loss of M-cone contrast above 10-20c/d. In comparison, the shift of the M-cone fundamental causes smaller effects on M-cone contrast. At 10c/d a shift in the peak of the M-cone spectrum from 560 to 460nm decreases M-cone contrast by 30%, while a 10nm blue-shift causes only a minor loss of contrast. However, a noticeable loss of contrast may be seen if the eye is focused at focal planes other than that which maximizes luminance contrast. The presence of separate long- and middle-wavelength sensitive cones therefore has a small, but not insignificant cost to the retinal image via longitudinal chromatic aberration. This aberration may therefore be a factor limiting evolution of visual pigments and trichromatic color vision.     

The influence of age on the chromatic aberration of the eye

Summary The axial chromatic aberration of the eye was measured in 58 persons varying from 10 to 80 years of age. It was found that the chromatic aberration diminished significantly after the onset of presbyopia. It is suggested that this decrease in axial chromatic aberration may be due to increase in the index of refraction of the vitreous thereby producing a negative optical surface in the eye which more or less cancels the chromatic aberration of the cornea and anterior surface of the lens. This supposition is supported by measurements of chromatic aberration made on 10 aphakic patients. It is also observed that at near, older eyes who exhibit very little chromatic aberration, cannot make use of this aberration to spare some of the required accommodation (simulated by ophthalmic lenses in older eyes) as is the case in younger eyes.

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Zusammenfassung Die axiale chromatische Aberration des Auges wurde bei 58 Probanden im Alter von 10 bis 80 Jahren bestimmt. Hierbei zeigte sich, daß sie sich signifikant nach dem Einsetzen der Presbyopie verminderte. Es ist zu vermuten, daß dies auf eine Zunahme des Berechnungsindex im Glaskörper zurückgeht, wobei eine negative optische Fläche im Auge entsteht, welche die chromatische Aberration der Cornea und der Linsenvorderfläche mehr oder minder ausgleicht. Hierfür sprechen auch Messungen der chromatischen Aberration bei 10 aphaken Patienten. Hinsichtlich des Nahesehens wurde beobachtet, daß Augen älterer Menschen, welche nur sehr geringe chromatische Aberrationen zeigen, diese zum Ausgleich der benötigten Akkommodation nicht mehr nutzen können als jene junger Individuen.

     

Variation in ocular modulation and phase transfer functions with grating orientation

For circular pupils of diameters < or = 2 mm the optical performance of the eye in monochromatic light is effectively diffraction-limited, so that its modulation transfer function (MTF) is essentially independent of grating orientation and its phase transfer function (PTF) is close to zero. For larger pupils, however, the wave aberration of the eye usually exceeds the Rayleigh quarter-wavelength limit. It is shown that the monochromatic MTF may then display marked variation with orientation and the associated PTFs can be non-zero. The exact effects vary markedly with the individual subject. In white light additional asymmetries may occur due to transverse chromatic aberration.     

Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye

We provide a simple model for calculating the chromatic difference of magnification for the human eye. Spectral differences in image size are proportional to the eye's longitudinal chromatic aberration and the axial distance between the entrance pupil and nodal point. We verify that the model provides magnification estimates equal to previously published predictions, and we show the significant increase in this aberration produced by experimental use of artificial pupils.     

Longitudinal chromatic aberration of the vertebrate eye

A recent study involving Abbe and Pulfrich refractometry analyses the dispersion of the human lens and the ocular media of a number of vertebrates. In general, the lens and, to a lesser extent, the cornea, are more dispersive than expected at wavelengths below 500 nm. The dispersion findings of this study were used in conjunction with reduced eye parameters of a number of vertebrates to calculate the longitudinal chromatic aberration of rock bass, frog, chicken, rat, cat, pig, cow, and human eyes. The calculated chromatic aberration of the human eye is greater than values reported earlier, because of the exaggerated dispersion of the lens at short wavelengths. While the values calculated for the additional species studied may be larger in some instances than expected, presumably due to lens dispersion as well, chromatic aberration is not large enough to account for the hyperopia found by retinoscopic study of small eyes.