Aberrations of the eye

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The eye, like any other optical system, suffers from a number of specific optical aberrations. The optical quality of the eye is limited by optical aberrations, diffraction and scatter. [1] Correction of spherocylindrical refractive errors has been possible for nearly two centuries following Airy's development of methods to measure and correct ocular astigmatism. It has only recently[ when? ] become possible to measure the aberrations of the eye and with the advent of refractive surgery it might be possible to correct certain types of irregular astigmatism.

Contents

The appearance of visual complaints such as halos, glare and monocular diplopia after corneal refractive surgery has long been correlated with the induction of optical aberrations. Several mechanisms may explain the increase in the amount of higher-order aberrations with conventional excimer laser refractive procedures: a change in corneal shape toward oblateness or prolateness (after myopic and hyperopic ablations respectively), insufficient optical zone size and imperfect centration. These adverse effects are particularly noticeable when the pupil is large. [2]

Wavefront approach to aberrations of the eye

The flat wavefronts change to spherical wavefronts as they pass through a pinhole Diffraction through Pinhole.svg
The flat wavefronts change to spherical wavefronts as they pass through a pinhole

A wavefront is a surface over which an optical disturbance has a constant phase. Rays and wavefronts are two mutually complementary approaches to light propagation. Wavefronts are always normal (perpendicular) to the rays.

For light to converge to a perfect point, the wavefront emerging from the optical system must be a perfect sphere centered on the image point. The distance in micrometers between the actual wavefront and the ideal wavefront is the wavefront aberration, which is the standard method of showing the aberrations of the eye. Therefore, aberrations of the eye are the difference between two surfaces: the ideal and the actual wavefront.

Aberration of normal eyes

In normal population the dominant aberrations are the ordinary second-order spherocylindrical focus errors, which are called refractive errors. Higher order aberrations are a relatively small component, comprising about 10% of the eye's total aberrations. [3] High order aberrations increase with age and mirror symmetry exists between the right and the left eyes. [4]

Several studies have reported a compensation of the aberration of the cornea by the aberration of the crystalline lens. The spherical aberration of the cornea is usually positive whereas the young crystalline lens exhibits a negative spherical aberration. Besides, there is strong evidence of compensation for aberrations between the cornea and intraocular optics in cases of astigmatism (horizontal/vertical) and horizontal coma. The balance of corneal and internal aberrations is a typical example of creating two coupling optical systems. [5]

The accommodative response of the eye results in changes to the lens shape and substantially affects the wavefront aberration pattern. Most eyes show positive spherical aberration when unaccommodated with a trend toward negative spherical aberration on accommodation. [1]

Low order aberrations

Low order aberrations include Myopia (positive defocus), hyperopia (negative defocus), and regular astigmatism. Other lower-order aberrations are non- visually significant aberrations known as first order aberrations, such as prisms and zero-order aberrations (piston). Low order aberrations account for approximately 90% of the overall wave aberration in the eye. [5] [6]

High order aberrations

Spherical aberration. A perfect lens (top) focuses all incoming rays to a point on the Optical axis. In spherical aberration (Bottom) peripheral rays are focused more tightly than central rays. Spherical aberration 2.svg
Spherical aberration. A perfect lens (top) focuses all incoming rays to a point on the Optical axis. In spherical aberration (Bottom) peripheral rays are focused more tightly than central rays.

There are numerous higher-order aberrations, of which only spherical aberration, coma and trefoil are of clinical interest.

Spherical aberration is a term used clinically to refer to a fourth-order spherical aberrations. This term is not to be confused with spherical Zernike polynomials, which are simply Zernike polynomials with an azimuthal degree of zero; in fact, one can mathematically describe defocus, a lower (second) order aberration as a spherical second order aberration. In this clinical context, however, spherical aberration refers to fourth-order spherical aberrations. Spherical aberration is the cause of night myopia and is commonly increased after myopic LASIK and surface ablation. It results in halos around point images. Spherical aberration exacerbates myopia in low light (night myopia). In brighter conditions, the pupil constricts, blocking the more peripheral rays and minimizing the effect of spherical aberration. As the pupil enlarges, more peripheral rays enter the eye and the focus shifts anteriorly, making the patient slightly more myopic in low-light conditions. The effect of spherical aberration (a fourth-order aberration) increases as the fourth power of the pupil diameter. Doubling pupil diameter increases the spherical aberration component by a factor of 16. [7] Thus, a small change in pupil size can cause a significant change in spherical aberration. This possibility should be considered in patients who have fluctuating vision despite well-healed corneas following keratorefractive surgery.

Coma (a third-order aberration) is common in patients with decentred corneal grafts, keratoconus, and decentred laser ablations.

Trefoil (a third-order aberration) produces less degradation in image quality compared with coma of similar RMS magnitude. [6]

In general, the increase in overall wave aberration with pupil size has been reported to increase to approximately the second power of the pupil radius. This is because most wave aberration is due to 2nd order aberrations, which have a square radius dependency. [5]

Assessment and quantitative expression of ocular aberrations

Assessment

Illustration of Shack-Hartmann system Shack hartmann.jpg
Illustration of Shack-Hartmann system

Many techniques for measuring the eye's aberrations have been described, The most common technique is Shack-Hartmann aberrometry. Other methods include Tscherning systems, ray tracing and Skiascopy methods. [2] [8]

Quantitative expression

RMS

Quantitative comparisons between different eyes and conditions are usually made using RMS (root mean square). To measure RMS for each type of aberration involves squaring the difference between the aberration and mean value and averaging it across the pupil area. Different kinds of aberrations may have equal RMS across the pupil but have different effects on vision, therefore, RMS error is unrelated to visual performance. The majority of eyes have total RMS values less than 0.3 μm. [6]

Zernike polynomials

The most common method of classifying the shapes of aberration maps is to consider each map as the sum of fundamental shapes or basis functions. One popular set of basis functions are the Zernike polynomials. [2] Each aberration may be positive or negative in value and induces predictable alterations in the image quality. [9] Because there is no limit to the number of terms that may be used by Zernike polynomials, vision scientists use the first 15 polynomials, based on the fact that they are enough to obtain a highly accurate description of the most common aberrations found in human eye. [10] Among these the most important Zernike coefficients affecting visual quality are coma, spherical aberration, and trefoil. [6]

Zernike polynomials are usually expressed in terms of polar coordinates (ρ,θ), where ρ is radial coordinate and θ is the angle. The advantage of expressing the aberrations in terms of these polynomials includes the fact that the polynomials are independent of one another. For each polynomial the mean value of the aberration across the pupil is zero and the value of the coefficient gives the RMS error for that particular aberration (i.e. the coefficients show the relative contribution of each Zernike mode to the total wavefront error in the eye). [4] However these polynomials have the disadvantage that their coefficients are only valid for the particular pupil diameter they are determined for.

In each Zernike polynomial , the subscript n is the order of aberration, all the Zernike polynomials in which n=3 are called third-order aberrations and all the polynomials with n=4, fourth order aberrations and so on. and are usually called secondary Astigmatism and should not cause confusion. The superscript m is called the angular frequency and denotes the number of times the Wavefront pattern repeats itself. [4]

List of Zernike modes and their common names: [11]

Plots of Zernike polynomials in the unit disk Zernike polynomials2.png
Plots of Zernike polynomials in the unit disk
Zernike TermName
Piston
, Tilt (Prism)
Defocus
, Astigmatism
, Secondary Astigmatism
Spherical aberration
, Coma
, Trefoil
, Quadrafoil

Management

Low order aberrations (hyperopia, Myopia and regular astigmatism), are correctable by eyeglasses, soft contact lenses and refractive surgery. Neither spectacles nor soft contact lenses nor routine keratorefractive surgery adequately corrects high order aberrations. Significant high order aberration usually requires a rigid gas-permeable contact lens for optimal visual rehabilitation. [6]

Customized Wavefront-guided refractive corneal laser treatments are designed to reduce existing aberrations and to help prevent the creation of new aberrations. [6] The wavefront map of the eye may be transferred to a Lasik system and enable the surgeon to treat the aberration. Perfect alignment of the treatment and the pupil on which the Wavefront is measured is required, which is usually achieved through iris feature detection. An efficient eye tracking system and small spot size laser is necessary for treatment. Wavefront customization of ablation increases the depth of ablation because additional corneal tissue must be ablated to compensate for the high order aberrations. [2] Actual results with Wavefront guided LASIK showed that not only it cannot remove HOA but also the optical aberrations are increased. However, the amount of increase in aberrations are less than conventional Lasik. [12] Corneal optical aberrations after photorefractive keratectomy with a larger ablation zone and a transition zone are less pronounced and more physiologic than those associated with first-generation (5 mm) ablations with no transition zone. [13] An upcoming systematic review will seek to compare the safety and effectiveness of wavefront excimer laser refractive surgery with conventional excimer laser refractive surgery, and will measure differences in residual higher order aberrations between the two procedures. [14]

Aspherical intraocular lenses (IOLs) have been used clinically to compensate for positive corneal spherical aberrations. Although Aspherical IOLs may give better contrast sensitivity, it is doubtful, whether they have a beneficial effect on distance visual acuity. Conventional (not Aspherical) IOLs give better depth of focus and better near vision. The reason for improved depth of focus in conventional lenses is linked to residual spherical aberration. The small improvement in depth of focus with the conventional IOLs enhances uncorrected near vision and contribute to reading ability. [15]

Wavefront customized lenses can be used in eyeglasses. Based on Wavefront map of the eye and with the use of laser a lens is shaped to compensate for the aberrations of the eye and then put in the eyeglasses. Ultraviolet Laser can alter the refractive index of curtain lens materials such as epoxy polymer on a point by point basis in order to generate the desired refractive profile. [1]

Wavefront customized contact lenses can theoretically correct HOA. The rotation and decentration reduces the predictability of this method. [1]

See also

Related Research Articles

<span class="mw-page-title-main">Optical aberration</span> Deviation from perfect paraxial optical behavior

In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

<span class="mw-page-title-main">Myopia</span> Problem with distance vision

Myopia, also known as near-sightedness and short-sightedness, is an eye disease where light from distant objects focuses in front of, instead of on, the retina. As a result, distant objects appear blurry while close objects appear normal. Other symptoms may include headaches and eye strain. Severe myopia is associated with an increased risk of macular degeneration, retinal detachment, cataracts, and glaucoma.

<span class="mw-page-title-main">Farsightedness</span> Eye condition in which light is focused behind instead of on the retina

Far-sightedness, also known as long-sightedness, hypermetropia, and hyperopia, is a condition of the eye where distant objects are seen clearly but near objects appear blurred. This blur is due to incoming light being focused behind, instead of on, the retina due to insufficient accommodation by the lens. Minor hypermetropia in young patients is usually corrected by their accommodation, without any defects in vision. But, due to this accommodative effort for distant vision, people may complain of eye strain during prolonged reading. If the hypermetropia is high, there will be defective vision for both distance and near. People may also experience accommodative dysfunction, binocular dysfunction, amblyopia, and strabismus. Newborns are almost invariably hypermetropic, but it gradually decreases as the newborn gets older.

<span class="mw-page-title-main">LASIK</span> Corrective ophthalmological surgery

Laser-Assisted in Situ Keratomileusis (LASIK), commonly referred to as laser eye surgery or laser vision correction, is a type of refractive surgery for the correction of myopia, hyperopia, and an actual cure for astigmatism, since it is in the cornea. LASIK surgery is performed by an ophthalmologist who uses a laser or microkeratome to reshape the eye's cornea in order to improve visual acuity.

<span class="mw-page-title-main">Photorefractive keratectomy</span> Refractive eye surgery procrdure

Photorefractive keratectomy (PRK) and laser-assisted sub-epithelial keratectomy (LASEK) are laser eye surgery procedures intended to correct a person's vision, reducing dependency on glasses or contact lenses. LASEK and PRK permanently change the shape of the anterior central cornea using an excimer laser to ablate a small amount of tissue from the corneal stroma at the front of the eye, just under the corneal epithelium. The outer layer of the cornea is removed prior to the ablation.

<span class="mw-page-title-main">Coma (optics)</span> Aberration inherent to certain optical designs or due to imperfection in the lens

In optics, the coma, or comatic aberration, in an optical system refers to aberration inherent to certain optical designs or due to imperfection in the lens or other components that results in off-axis point sources such as stars appearing distorted, appearing to have a tail (coma) like a comet. Specifically, coma is defined as a variation in magnification over the entrance pupil. In refractive or diffractive optical systems, especially those imaging a wide spectral range, coma can be a function of wavelength, in which case it is a form of chromatic aberration.

<span class="mw-page-title-main">Astigmatism (optical systems)</span> Optical aberration

An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning "without" and στίγμα (stigma), "a mark, spot, puncture".

<span class="mw-page-title-main">Radial keratotomy</span> Refractive surgical procedure to correct myopia (nearsightedness

Radial keratotomy (RK) is a refractive surgical procedure to correct myopia (nearsightedness). It was developed in 1974 by Svyatoslav Fyodorov, a Russian ophthalmologist. It has been largely supplanted by newer, more accurate operations, such as photorefractive keratectomy, LASIK, Epi-LASIK and the phakic intraocular lens.

<span class="mw-page-title-main">Refractive surgery</span> Surgery to treat common vision disorders

Refractive surgery is optional eye surgery used to improve the refractive state of the eye and decrease or eliminate dependency on glasses or contact lenses. This can include various methods of surgical remodeling of the cornea (keratomileusis), lens implantation or lens replacement. The most common methods today use excimer lasers to reshape the curvature of the cornea. Refractive eye surgeries are used to treat common vision disorders such as myopia, hyperopia, presbyopia and astigmatism.

<span class="mw-page-title-main">Intraocular lens</span> Lens implanted in the eye to treat cataracts or myopia

An Intraocular lens (IOL) is a lens implanted in the eye usually as part of a treatment for cataracts or for correcting other vision problems such as short sightedness and long sightedness; a form of refractive surgery. If the natural lens is left in the eye, the IOL is known as phakic, otherwise it is a pseudophakic lens. Both kinds of IOLs are designed to provide the same light-focusing function as the natural crystalline lens. This can be an alternative to LASIK, but LASIK is not an alternative to an IOL for treatment of cataracts.

<span class="mw-page-title-main">Refractive error</span> Problem with focusing light accurately on the retina due to the shape of the eye

Refractive error is a problem with focusing light accurately on the retina due to the shape of the eye and/or cornea. The most common types of refractive error are near-sightedness, far-sightedness, astigmatism, and presbyopia. Near-sightedness results in far away objects being blurry, far-sightedness and presbyopia result in close objects being blurry, and astigmatism causes objects to appear stretched out or blurry. Other symptoms may include double vision, headaches, and eye strain.

<span class="mw-page-title-main">Phakic intraocular lens</span> Lens implanted in eye in addition to the natural lens

A phakic intraocular lens (PIOL) is an intraocular lens that is implanted surgically into the eye to correct refractive errors without removing the natural lens. Intraocular lenses that are implanted into eyes after the eye's natural lens has been removed during cataract surgery are known as pseudophakic.

<span class="mw-page-title-main">Astigmatism</span> Type of eye defect

Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at night. Astigmatism often occurs at birth and can change or develop later in life. If it occurs in early life and is left untreated, it may result in amblyopia.

ReLExSmall incision lenticule extraction (SMILE), second generation of ReLEx Femtosecond lenticule extraction (FLEx), is a form of laser based refractive eye surgery developed by Carl Zeiss Meditec used to correct myopia, and cure astigmatism. Although similar to LASIK laser surgery, the intrastromal procedure uses a single femtosecond laser referenced to the corneal surface to cleave a thin lenticule from the corneal stroma for manual extraction.

<span class="mw-page-title-main">Emmetropia</span> State of vision

Emmetropia is the state of vision in which a faraway object at infinity is in sharp focus with the ciliary muscle in a relaxed state. That condition of the normal eye is achieved when the refractive power of the cornea and eye lens and the axial length of the eye balance out, which focuses rays exactly on the retina, resulting in perfectly sharp distance vision. A human eye in a state of emmetropia requires no corrective lenses for distance; the vision scores well on a visual acuity test.

Stephen Updegraff, M.D., FACS is an American refractive surgeon best known for his early involvement in, and contributions to, LASIK. He is a Fellow of the American College of Surgeons, a board-certified member of the American Board of Ophthalmology, a founding member of the American College of Ophthalmic Surgeons, and a member of the International Society of Refractive Surgery, the American Academy of Ophthalmology, the American Society of Cataract and Refractive Surgery, and the Pine Ridge Eye Study Society. Updegraff currently serves as the medical director of Updegraff Vision in St. Petersburg, Florida.

Laser blended vision is a laser eye treatment which is used to treat presbyopia or other age-related eye conditions. It can be used to help people that simply need reading glasses, and also those who have started to need bifocal or varifocal spectacle correction due to ageing changes in the eye. It can be used for people who are also short-sighted (myopia) or long-sighted (hyperopia) and who also may have astigmatism.

The Alpins Method is a system to plan and analyze the results of refractive surgical procedures, such as laser in-situ keratomileus (LASIK). The Alpins Method is also used to plan cataract/toric intraocular lens (IOL) surgical procedures.

Peter S. Hersh is an American ophthalmologist, researcher, and specialist in LASIK eye surgery, keratoconus, and diseases of the cornea. He co-authored the article in the journal Ophthalmology that presented the results of the study that led to the first approval by the U.S. Food and Drug Administration (FDA) of the excimer laser for the correction of nearsightedness in the United States. Hersh was also medical monitor of the study that led to approval of corneal collagen crosslinking for the treatment of keratoconus. He was the originator, in 2015, of CTAK for keratoconus, patent holder, and co-developer.

Post-LASIK ectasia is a condition similar to keratoconus where the cornea starts to bulge forwards at a variable time after LASIK, PRK, or SMILE corneal laser eye surgery. However, the physiological processes of post-LASIK ectasia seem to be different from keratoconus. The visible changes in the basal epithelial cell and anterior and posterior keratocytes linked with keratoconus were not observed in post-LASIK ectasia.

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