Introduction

The visual system is an exceptional combination of different physiological elements that constitute our main window onto the world. Although its study within the context of different disciplines tends to separate its various elements, the exceptional aspect lies in its extremely delicate integration. The objective of the visual system is to analyse appropriately the images received from the outside world. The first step is the formation of these images on the retinal film. This is an optical image obtained passively, the concept of which is very simple. As an optical system, the task of the eye is to project onto the retina images of an acceptable optical quality under various conditions, which will then be processed and analysed. For physicists this is the most important stage in the visual system. If the eye, as an optical instrument that forms the retinal image, does not work correctly, the entire visual system will not be operational. Despite the optical simplicity of the eye, its relative importance derives from the fact that it is the first element in the chain of visual process. If this first link is incorrect, the following stages will not provide more and vision will be of poor quality. The images projected onto the retina appear (that is to say are digitalised) in the photoreceptors and other retinal cells at different levels: spatial (in terms of the position), chromatic (according to the spectral composition of light) and temporal. This range of signals is then sent to be processed and interpreted in the visual cortex. Of course, all the links in this chain must work correctly. In fact, we know that the capacities of each phase in the visual system appear to be well adjusted between themselves. This is an example of economy in the design of the system, which has no doubt been optimised over the course of evolution.

In this article, my main interest, as a physicist who has devoted many years to research into visual optics, is to demonstrate that the eye, although a simple optical system, places fundamental limits on our visual capacity. After a brief note on some of its optical characteristics and its intrinsic robustness, I will concentrate more particularly on the relationship between optics and visual quality. I believe that this journey will provide us with a better understanding of this relationship, about which we have been aware for only a short while (less than ten years) and, specifically, thanks to new experiments that have been performed using the latest technologies available, such as wave front measurement systems or adaptive optics, combined with visual quality assessments undertaken under rigorous control.

The eye as a solid optical system

The human eye is a very simple optical system compared to most artificial optical instruments. It is made up solely of two converging lenses (the cornea and the crystalline), a diaphragm (the iris) and a screen (the retina). Ideally, in emmetropic eyes, for distant objects images must form on a perfect focal point on the retina. If objects are close, young eyes will continue to maintain the focus of images, thanks to a change in the power of the crystalline, known as capacity of accommodation. Even when the image is formed at the right focal point, the eye, just like every other optical system, is not perfect. That is to say that the image of a particular object will not correspond to another perfect point on the retina. The image of a point on the retina is known in English as the PSF ("point-spread function") and corresponds to a point of light with specific characteristics for each eye. An eye with high optical quality will form a very small and compact image, whilst in the opposite case the point will be blurred and spread. A quantification of the eye's aberrations results in characterisation of its optical properties. A system that is highly affected by aberrations has poor optical quality and produces spread retinal images. It has been well known, since the time of Helmholtz in the mid-19th century, that the eye is not a perfect optical system, even when it does not suffer from any so-called refractive error (defocusing and astigmatism). The type and quantity of aberrations depend on the person and on a variety of factors, such as the size of the pupil, the entry angle or the accommodation state. On average, in young people with normal eyes, aberrations of a 5mm diameter pupil are of a magnitude of 0.25 μm RMS spread on the spherical wave. This is equivalent to defocusing of approximately 0.25 dioptres. As readers working in the field of optometry and clinical ophthalmology will know, 0.25 dioptres is a very low reading that can often be considered to be an error of measurement. The biggest aberrations in a normal eye are spherical aberration (slightly positive) and coma aberration (the value and orientation of which are variable). Curiously, the values of these two aberrations are below expectations due to a compensation mechanism between the cornea and the crystalline. The shape of the crystalline is certainly optimised in order to compensate in part for corneal aberrations. Thus, the eye acts like an aplanatic optical system, that is to say that it corrects spherical and coma aberrations reasonably well [1, 5, 6]. With age the crystalline changes shape and compensation disappears in part, which leads to an increase in the eye's aberrations [2]. Figure 1 shows a diagram of the eye's compensation phenomenon with examples of aberrations of the cornea, the crystalline and the complete eye. The image of an object is a point of light (PSF) which is all the more spread out when the eye has numerous aberrations.

Fig. 1: Example of a schematised eye, showing tables of aberration for the various components and the image of a point on the retina (PSF).

From optics to vision

If, in a group of observers, one measures the optical properties of each eye and one makes various visual assessments, it is possible to define the way in which optics influence visual quality. The experiment is simple and, in one way or another, has been used as a basis for numerous studies since the study of physiological optics began. Figure 2 shows a diagram of the relations that can exist between the optical and visual parameters.

Fig. 2: Diagram of the relationship between purely optical parameters and visual quality parameters.

I would mention, for example, a study that we carried out in my own laboratory a few years ago, in collaboration with research workers from the Essilor Centre, Saint- Maur, France, during which we concentrated on the effect produced by defocusing on visual acuity and sensitivity to contrast [15]. This is an important point because it is defocusing that has the greatest impact on vision, which no doubt readers suffering from myopia or hypermetropia will easily understand. We proceeded in the following way: we recorded retinal images by double pass of a point [14] for various cases of defocus in a small group of normal observers. These images are directly linked to ocular PSF [3]. On this same instrument, and using exactly the same optics, subjects took various visual tests, including a test of visual acuity. Figure 3 presents typical results.

Fig. 3: Development in optical quality (Strehl ratio) and visual quality (acuity) according to defocus caused. The upper section of the figure shows double pass images for the various cases of defocus. For more information, see the article and reference documents of Villegas et al., 2002.

Based on double pass images on the same focal points and for additional defocus (included between -2 and 2 dioptres), a parameter of optical quality (in this case the Strehl ratio) was defined. Visual acuity was measured under these same conditions, as well as the minimal discernable size of a letter. The two panels in the figure show how optical quality and acuity follow a very similar model according to the added defocus. This demonstrates that when defocus reduces the quality of the image on the retina, visual acuity is reduced too. Optics and vision are therefore details that are indeed clearly linked. This correlation is minor for small defocus values, where their magnitude is similar to the other aberrations present in the eye. Various researchers have attempted to define the most appropriate optical quality parameters, that is to say those that best predict visual quality. There exists a general agreement according to which parameters calculated based on measurements of the plane of the retina (such as PSF for example) are more efficient that those estimated based on measurements of the plane of the pupil (such as, for example, aberration variation) [12].

The following stage, during the numerous studies, consisted of understanding the exact effect of aberrations on visual quality. This phenomenon is more subtle than the impact of defocus because the relative impact of aberrations is generally much smaller. In terms of quantity, it would appear clear that if an eye is affected by more aberrations, the visual quality of the person concerned will be less. And this is indeed the case where the aberrations are above normal (more than a difference of 0.3 μm RMS on the spherical wave surface, for a 5mm pupil). On the other hand, in eyes with normal aberration values, the impact of the latter on visual acuity has to be explained according to a variety of scenarios. A purely “physical” option would suppose that eyes with less aberrations and even eyes that are perfect from an optical point of view, offer better vision. Another alternative could suggest that the best option for good vision would be an eye with specific optics affected by a given type of aberration (for example a vertical coma model). The final option developed by recent studies on neuronal adaptation [4] would have it that optimal optics are optics specific to each individual (to which each of us adapts over time). To make the distinction between these various options and to find out more about the puzzle of the relation between optics and vision, we performed the following experiment [16]. We identified a certain number of subjects with good or very good visual quality. In practice this was a group of young students with decimal visual acuities of between 1 and 2. The optical quality of each of them was measured precisely. Quite surprisingly, as shown on figure 4, no link was found between optical quality and visual acuity in this group of subjects.

Fig. 4: Relation between optical quality (expressed in the form of an algorithm of the Strehl ratio) and visual acuity in a group of subjects with good to excellent spatial vision. See the reference documents of Villegas et al. 2008, for further information on the study.

It may be concluded, therefore, that people with high visual acuity are not specifically those whose eyes benefit from the best optical quality. This phenomenon is represented (the best acuity shown in the lower area). Note that the eye of a person with normal, but not excellent, visual acuity (marked by a red circle), obtains a near clear point retinal image, which demonstrates very strong optical quality for the eye. On the other hand, one of the subjects with excellent visual acuity (close to 2) benefits from just normal optical quality shown by an enlarged, deformed PSF (image marked by a blue circle). This result demonstrates that it is not necessary to have exceptional optical quality to benefit from exceptional visual quality. It should be noted, however, and we will return to this point later, that this does not mean that it is impossible to improve the visual acuity of a given individual by correcting aberrations in the laboratory. An analysis of the various aberrations present in the eyes according to acuity was also undertaken, but this did not reveal any specific trend in the model, liable to offer preferential visual quality. Even though this is still the object of further research and studies, I would at least like to mention here the fact that it is important to take into account the combination of different types of aberrations which occur normally together in the eye. The combinations of spherical aberration with defocus and trefoil shaped coma, are respectively particular cases. This means that it is not correct to consider separately and independently those aberrations that may be present in an eye, without taking into account the balance and the final contribution made by the latter to the quality of the image on the retina.

Fig. 5: Images of a point (PSF) for a group of subjects, ranked according to visual acuity. A subject with an excellent optical quality (red circle) has normal visual acuity, whereas one of the subjects in the group with the best visual acuity (blue circle) has poor optical quality.

The reason why optical aberrations and visual acuity are not linked is due to the fact that other restriction factors exist, which we have not yet taken into account. It is right to say that the optics of the eye are not only affected by aberrations but also by intraocular scatter. In young, normal eyes, its effect may only be small, even though it is acknowledged that it increases gradually with age and may completely dominate the deterioration of images in case of cataracts [8]. One will understand that, in view of the fact that the mechanisms that produce aberrations and scatter and their effect on the image are different, any of the eyes in the study with very little aberration and less than excellent acuity, may have been affected by a higher degree of scatter. Although these are different phenomena, they produce their effects together and it is acknowledged that in the presence of a certain amount of scatter, a combination with aberrations may also occur. We have actually recently shown [13] that sensitivity to contrast could improve in eyes with high scatter, where certain quantities of spherical aberrations are added. In this result, one notes an interesting mechanism of compensation with age, because it is recognised that intraocular scatter and spherical aberration tend to increase with normal ageing, such that contrast in the images is reduced less than expected.

Without going into detail, estimates of the eye's optical quality are normally done using monochrome light, that is to say using a single colour. On the other hand, our natural vision conditions are clearly under polychromatic white light. Curiously the eye, as an optical system, is particularly affected by what are known as chromatic aberrations. Just like any other system, and in view of the fact that the refractive indices of the material depend on the wavelength of light, the eye concentrates images on various points depending on the colours. The chromatic scatter produces a difference in the position of the focal points on the eye of almost 2 dioptres between objects formed with red light and with blue light. This means, neither more nor less, that an eye with a blue object in its focal point will by hypermetropic by 2 dioptres for a red object. In addition to these relative differences in the power of the eye for each colour, the lateral increase of the eye also depends on the colour. An object under white light will appear to be coloured round the edges because the image of each colour will form with a different enlargement, spreading the images over the retina and potentially impacting visual quality. However, what is certain is that our visual system is very well equipped to minimise these chromatic errors, which explains why few people can imagine that their eyes present these 2 dioptres difference in focal point between the colours. The main reason is that the visual system is above all sensitive to the central light of the spectrum (yellow-green) and less to the colours located at the extremities (red and violet), which are those that present a higher relative defocus. We are therefore still questioning the effect of correction of the eye's chromatic aberration on visual quality. This is possible thanks to the use of so-called achromatic lenses. The experiment we performed [7] consisted of measuring the visual acuity of various subject before and after correction of their chromatic aberration. We systematically obtained an improvement in acuity of around 40% when the chromatic and spherical aberrations were corrected. In all cases, the practical possibilities of correcting chromatic errors are not very extensive, due to the precision necessary at the centre of the achromatic lenses.

After the factors related purely to ocular optics, sampling of the images on the retina requires the following fundamental limit on the vision of details. In the centre of the fovea is concentrated a large quantity of photoreceptors (cones), resulting in maximum accessible resolution. Within the limit set by the mathematical theorem of the sampling, a true representation of a letter E, for example, should possess at least one cone on each stroke of the letter. If they are separated by 30 seconds of arc, the minimum size of the letter that would appear will correspond to a decimal acuity of 2. This is actually the maximum visual acuity achieved for the group of subjects, within the context of our experiment. One can understand that the anatomical differences in the quantity of cones will limit acuity differently. This is a simplified explanation, however, because, in reality, various phases in the sampling or digitalisation of images in cascade occur in the various layers of retinal cells. And, finally, the images are represented in the visual cortex in an even more complicated way. Transmission of the signal in the cortex is also different in each individual subject, which in turn leads to another limitation of accessible acuity. But this remains entirely within the context of neuronal factors.

Neuronal adaptation to aberrations

If neuronal adaptation to the aberrations of a particular individual's eye existed, his vision would be clearer with normal aberrations than with different optics. It is well known that the adaptation and plasticity of the visual system play a very important role in numerous visual tasks. In fact, over the centuries of clinical practice, some properties of neuronal adaptation have been discovered. One of the most impressive examples of adaptation in the visual system is perhaps that demonstrated by an experiment carried out in the fifties. A volunteer was given a pair of spectacles on which inversion prisms were mounted. Initially, as was to be expected, he saw the world around upside down. However, after a period of adaptation, he perceived his environment normally, even though the optical inversion was still present on the retina. When the volunteer was asked to remove his spectacles he was very surprised to perceive images of the real world upside down. Luckily, his normal vision returned after a time. I must confess that I myself would never have volunteered to take part in an experiment like that!

The visual system presents many other less fantastic and more common cases of adaptation, for example adaptation to the blurring of images [17], to colour or distortions of field. In clinical practice, these are relatively common phenomena with progressive lenses, which are used very frequently to correct presbyopia. Initially the subject notices the image distortion caused by the lenses very clearly. However, after a few days, these problems tend to disappear and most people adapt to them over time.

With all of the above, we are seeking to determine whether the visual system also adapts to aberrations of the eye. To do this we have planned an experiment in collaboration with David Williams of Rochester University, USA, using an adaptive optical system [4]. This technology has proved to be very useful in obtaining high resolution retinal images, and it is also useful in other applications to create different models of aberrations in the eye, whilst the subject carries out different visual tasks. We call these types of instrument adaptive optics visual simulators or evaluators [9]. The situation that we want to show in this experiment is illustrated in the diagram given in figure 6.

Fig. 6: Example illustrating the underlying hypothesis of neuronal adaptation to optical aberrations.

If the visual system truly adapts to aberrations of the eye, visual quality will be better with normal aberrations than with a different optical system. Using an adaptive optical system, we control aberrations of the eye of the subject, so as to be able to perform visual tests such as, for example, measurement of visual acuity, with its normal aberrations or those oriented to an angle of 45°. In this case the magnitude of aberrations was the same but their orientation was different. Figure 7 illustrates visual acuity in a subject (in this case, the author) expressed in the form of a minimum resolution angle in minutes of arc, with corrected aberrations, normal aberrations and aberrations oriented to an angle of 45 degrees. As was to be expected, the greatest acuity is obtained when the aberrations are corrected, but the most important point here is that acuity is considerably lower with the aberrations reversed compared to his own aberrations. This result shows that the visual system adapts to the optical characteristics of the eye. We do not yet know properly the time required to achieve or re-establishthis adaptation, nor the magnitude of the aberrations that can be partially compensated. The mechanisms for adaptation to aberrations can have a certain importance in clinical practice and in the design of new corrective systems in the field of ophthalmic optics.

Fig. 7: Visual acuity of the author, with his normal aberrations (orange), then with corrected aberrations (red) and oriented aberrations (green). Even if the
magnitude of aberrations is the same, acuity falls significantly when the aberrations model is oriented in another direction. This suggests that the visual
system can adapt to the eye's optical characteristics.

Other aspects and prospects

In addition to what has been mentioned so far, the presence of aberrations in the eye affects other aspects of vision that I cannot address in detail here, due to lack of space. However, I cannot end without mentioning them briefly, in this final section. As with any kind of optical system, the eye forms less good images of objects situated off-axis. On the other hand, this is not a major limitation for the peripheral vision of detail because in these areas of the retina, it is the density of photoreceptors (much less than in the fovea) which sets the greatest limits on resolution. We demonstrated this phenomenon in an experiment in which, when aberrations were corrected, visual quality in the various retinal eccentricities did not show any improvement compared to the normal situation without correction [11].

The effect of aberrations during vision in conditions of low luminosity has been only very rarely studied. Although with very little light the visual system functions at the limit from a neuronal point of view, it is possible that a correction of aberrations could improve vision. And finally, we should not forget that our visual system is binocular. The combination of aberrations from both eyes affects the end visual quality in a way that can be complicated. We have recently used a binocular adaptive optics system to evaluate the impact that different aberrations of each eye have on binocular vision [10].

Over these past ten years we have made considerable progress in knowledge of the relationship between optical and visual quality. Today, the impact of retinal image quality on vision is understood much better. In addition to the pure advances made in knowledge that this represents, this progress will have a beneficial effect in the near future on the development of new strategies and solutions for more sophisticated and, above all, more efficient visual correction.

Acknowledgements

Most of the results summarised in this article have been obtained thanks to experiments carried out in the author's laboratory. Every member of the team has participated in one way or another and I would like to thank them all for their help and cooperation. Over all these years of my research work, my laboratory has been financed by various bodies, by the Spanish Ministry of Science and Technology, the Fundación Séneca of the Murcia region and the sixth framework programme of the European Union.