VISUAL DISTURBANCES IN KERATOCONUS
The irregular astigmatism caused by the corneal warpage results in a slight dispersion of the focusing rays. This explains the perception of small tails around bright lights and ghost images, which cannot be corrected by spectacles.
Topography combined with aberrometry can be used to characterize and quantify irregular astigmatism (« irregularity »). In this example, the columns refer to the topographic (top) and refractive (middle and bottom) status of an eye with mild keratoconus (left) and a healthy eye (right). These eyes have 20/20 uncorrected visual acuity. However, the patient with keratoconus complains about vertical monocular ghosting (where a ghost of a letter « E » is perceived to be displaced in the inferior left direction). The vergence map highlights the effect of the inferior corneal steepening; in the inferior part of the entrance pupil, there is a localized myopic shift of about 1.6 D. The rays travelling across this area are defocused, causing visual symptoms which result from the spread of the light at the retinal plane.
The optical difference between keratoconic and healthy eyes resides in the fact that in keratoconic eyes, there are larger variations of the local optical power of the eye throughout the pupil area. The light rays are not focused in the same plane, causing some retinal blur.
To comprehend in more depth the effect of keratoconus on vision, it may be helpful for the reader to move from the domain of geometrical optics (light rays) to wavefront optics (light waves) – read more about wavefront sensing
Light rays do not exist but allow one to conveniently represent the assumed path of light, which travels in straight lines and can be refracted at each ocular interface. Light rays can also be conceived as the path taken by photons, which are energetic particles without mass. Photons can only be « seen » once they have interacted with a photosensitive membrane. Since they are of little help in our explanations here, we will consider geometric (ray) or physical (wave) optics whenever appropriate. There is not much in the way of duality: light rays represent direction, whereas “light waves” interfere in a constructive manner. Light waves represent the oscillation of the electromagnetic field. The latter can be simplified and represented as a longitudinal sinewave, where crests and troughs alternate regularly, with the distance between two consecutive crests (or troughs) being the wavelength of the emitted light.
Most natural light sources are polychromatic. In contrary, laser light is very (though not completely) monochromatic. Wavefront sensing is performed in infrared light, and the ensuing discussion will assume a monochromatic source of light. Infrared is invisible to the human eye but can travel through ocular media and be reflected by the retina, therefore making wavefront sensing possible without inducing any discomfort to the observer.
A wavefront is an abstract construct formed by joining all the points which are « in phase » at the same time amongst a set of light waves. A wavefront is also defined by its domain. Along the way from the star to the eye, the envelope joining the points which are « in phase » and which will be captured by the eye within its pupil corresponds to a flat disc (the figure depicts the envelope of all of the points located at the top of the light wave crests).
Light slows when travelling in a «more dense» transparent material such as the corneal tissue. Because of the gross geometry of the eyeball and the fact that light waves shorten (the speed of light is reduced) in the ocular media, the phase relations are modified; the convexity of the corneal dome and the variable thickness of the crystalline lens causes peripheral light waves to be less retarded than the central ones. It can be easily concluded that peripheral waves travel slightly more in the air than central ones, which hit first the corneal apex, and are thus retarded relative to the peripheral ones.
The formation of the image of a light point source
Light waves are guided towards a point where they arrive in phase, where the oscillations will add up to increase the amplitude of the electromagnetic field oscillations. The intensity of light (perceived brightness) is proportional to the square of the amplitude of the oscillations.
To form a bright image of a star, all that is needed is enabling the emitted light waves to interfere constructively at a point and make that point located on a photosensitive membrane (such as a screen, or a photoreceptor layer of the retina).
Intuitively, the proper refraction of the incident lightwaves requires that the refractive surfaces have a smooth and regular curvature, and posess a symmetrical geometry around the optical axis.
If the eye is a « perfect eye », then the location where the light waves are directed to interfere constructively after their travel through the anterior segment is the fovea . In the vitreous cavity (between the crystalline lens and the retina), the envelope of the points which are in phase form an exact portion of a sphere centered on the fovea (larger concentric spherical envelopes are represented by the pink mesh).
From the star to the fovea along the path of each « light ray » captured by the perfect eye, the number of oscillations (the number of light waves) is equal. This condition ensures that all of the light waves interfere constructively at each end of the path.
This total number of light waves represents the optical path. Although the wavelength shortens in the eye media, the optical path is equal to the physical distance that light would have traveled if there had been no shortening of the light waves, for the same number of electromagnetic field oscillations which were accomplished along the whole path.
To comprehend the concept of wavefront error and “irregular astigmatism” (where HOA: higher order aberrations), let us consider two optical systems.
In geometrical optics, a perfect system brings into the same focal point all the rays of an incident parallel bundle. When the system is free of optical aberrations, all the incident rays are refracted in a single focal point, which is called the « Point Spread Function (PSF) ». In the case of a non-aberrated system, the PSF is a point (again we have neglected the effect of diffraction) and the envelope of the refracted wavefront (in green) is a portion of a sphere (a circle in cross section). Rays can be visualized as pointing to the local direction of the propagation of the wavefront envelope.
In the case of a spherical wavefront, all the rays point toward the center of the sphere, and the center of that sphere coincides with the focal point. If the optical system 1 corresponds to the refractive lenses of the eye (corneal and lens), and if the retina is a plane which contains the PSF, the eye is said to be “emmetropic”. If the eye is too short, or too long, the imaged formed on the retina is a blurry disc. However, a spectacle glass can be used to refocus the rays in the retinal plane. The spherical wavefront can serve as a « reference surface », since it materializes the wavefront formed by a perfect optical imaging system.
The surface of the optical system 2 is slightly irregular (as is the corneal surface in keratoconic eyes); hence, some of the incident rays are no longer focused in the same location. This is what is referred to as optical aberration, where the refracted wavefront is no longer perfectly spherical. This cannot be fully corrected by spectacle glasses. The departure between the shape of this aberrated wavefront and the « perfect spherical » wavefront corresponds to what is called “the wavefront error”. The altered geometry of the optical system 2 therefore cannot bring all the light waves to interfere constructively within a compact location.
If the light waves interfere in an enlarged location, the image of a point is no longer a point but a blur patch. If the retina is in a different plane, the eye will suffer from added defocus. Spectacles glasses can selectively modulate the optical path between central and peripheral rays to bring most of the constructive interference back at the foveal plane. However, even when some “best spectacle power” is selected, the remaining non-spectacle correctable imperfections will alter the optical path along some rays (located at the periphery of the entrance pupil). These imperfections correspond to what is called the « higher order aberrations component » (the total of which corresponds to the « irregular astigmatism »).
Typical aberrations in keratoconic eyes
Using outgoing aberrometry, i.e for a wavefront leaving the eye, the reference wavefront is a flat disc. Regular astigmatism corresponds to a wavefront distortion which has a shape of a saddle. It can be corrected by spectacles. Irregular astigmatism corresponds to « coma-like » aberrations, which are also depicted above. Irregular astigmatism cannot be corrected by spectacles, but part of it can be neutralized by rigid contact lenses.
Regular astigmatism is present in many human eyes. In most cases it is due to the cornea, whose curvature varies progressively between two perpendicular axes. The schematic representation of an emerging wavefront by an eye affected by « mixed » regular astigmatism is shown.
Irregular astigmatism is the hallmark of the optical properties of keratoconic corneas. It can be broken down in specific aberrations which are labeled « higher-order aberrations » since they cannot be corrected by spectacles. Special mathematical functions called « Zernike polynomials » are employed to describe these aberrations (read more about Zernike polynomials). The corneal deformation generates higher-order aberrations such as coma, trefoil, negative spherical aberrations, etc.
Patients with keratoconus often complain of ghost images, light tails around bright lights and other annoying visual disturbances. These perturbations persist despite using corrective glasses but can be significantly reduced by rigid gas permeable contact lenses.
This is an example of « naked » keratoconic topographic and aberrometric data:
After fitting with a rigid or scleral contact lens, the optical quality of the keratoconus eye is dramatically improved