In a perfect optical system, the light rays that emerge from the eye would be parallel and an undistorted plane wavefront would be formed. Ocular aberrations, as mentioned above, are deviations of the wavefront exiting the eye from a chosen unaberrrated reference wavefront 3 and can be affected by many variables that would influence the measurement taken.
Such variables for a particular eye can include tear film stability, 5 lid position, 6 pupil size, accommodation 7 and fixational eye movements, 8 to name a few. The tear film is composed of three layers i. Prolonged lid pressure has the ability to induce topography changes to the corneal surface.
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During reading, it was noted that a small defocus shift in the hyperopic direction occurred most frequently. The pupil size of healthy patients generally fluctuates with light and accommodation near triad throughout the day. The pupil diameter therefore influences the retinal image in terms of luminance and depth of focus and field.
Pupil constriction causes a decrease in retinal luminance; however, a smaller pupil affords an increase in depth of field and focus. The diameter of the pupil also influences diffraction and thus image quality. Higher order aberrations are often affected by pupil size. When performing measurements for laboratory use, the iris sphincter and ciliary muscle are often paralysed using cycloplegics, to inactivate pupillary oscillations and accommodation 9 to ensure the validity of measurements.
The eye houses the crystalline lens as well as the muscle that controls accommodation. The above-mentioned muscle action allows the clear viewing of proximal objects.
The change that the lens undergoes is roughly spherical in the absence of other variables. However, it remains imperative that the accommodative system is fully relaxed as active accommodation can hinder the accuracy of the refractive error or lower order aberration measurement. Fixational eye movements, being both voluntary and involuntary, can influence the measurements of ocular aberrations.
When a patient fixates an object, small eye movements occur of which the patient is unaware including drifts, tremors and microsaccades. As aberrations are measured with reference to a chosen or reference plane wavefront, that is undistorted, any eye movement would further shift the measured wavefront error closer to or further away from the reference wavefront and thus change the value of the Zernike coefficients. Polynomials are mathematical equations that usually involve multiple terms and variables.
Rho can further be defined as the distance from the chosen point to the center of the pupil r divided by the radius of the exit pupil a or r max. Zernike polynomials are advantageous when describing the wavefront error as their notation is specific to the aberrations they are classifying and can be expressed using either a single Z j or double indexing method system. The single index usually as j is perhaps simpler but the double indexing method allows the representation of more information in one term. The double indexing system displays both the order n and frequency m of the wavefront error.
For example, to convert the double indexing system to a single indexing, the following equation is used: The use of Zernike polynomials is beneficial as they possess a certain set of properties that allows them to be used somewhat universally. Mathematically, the calculation of means is important. With the exception of piston a lower and zero order aberration , all Zernike polynomials have an average of zero and the average of the entire ocular wavefront should equal the Zernike coefficient of piston. Both the lower and higher order ocular aberrations affect the visual performance of an individual.
Lower order aberrations LOA are sub-categorised as zero, first and second order aberrations. The zero order aberration is singular in nature and is termed piston. It can be described as the forward or backward shift of the entire wavefront; piston does not have an impact on the shape of the wavefront and is often not measured by typical wavefront sensors. The classification of refractive error is needed in the clinical practice of all eye care practitioners as well as a baseline for many research studies that involve different methods of determining refractive errors.
Refractive error can be described as the target vergence required at the corneal plane to ensure a clear and focused image on the retina. In relation to wavefront abberometry, refractive error can be determined through the second order aberrations, 16 these aberrations being spherical defocus, x-astigmatism and y -astigmatism 16 Spherical defocus is related to the spherical ametropia found in the refractive error, either the hyperopic or myopic entity in the clinical representation of the prescription.
Spherical defocus describes the position of the image formation in a purely spherical manner in relation to the retina. The x - and y -astigmatism, commonly known solely as astigmatism, is the refractive condition whereby the eye cannot produce a point image and the astigmatic refractive error varies in the different meridians. Therefore one can combine the x- and y- Zernike polynomials into a single term, 18 which can be achieved using two equations: one to determine a new angle whilst the other is used to determine the combined Zernike coefficient of the x- and y -astigmatism.
Second order aberrations, since they are related to refractive error, usually can be easily alleviated by prescribing compensatory spectacles or contact lenses, or by refractive surgery. In optometric practice, second order aberrations are the most important and the most clinically significant of the lower order aberrations.
There are several ways to represent second order aberrations in terms of refractive error, either clinically clinical prescription, in terms of sphere and cylinder power with a corresponding axis or mathematically using matrices and symmetric dioptric power spaces. The wavefront aberrometer has the ability to display the second order aberrations as the above-mentioned Zernike coefficients.
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These aberrations can negatively affect the vision of seemingly healthy eyes and typically cannot be easily corrected with non-invasive procedures or devices such as spectacles and contact lenses. The cornea is the primary refracting surface of the ocular system.
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As the cornea contributes to most of the refracting power of the eye, it stands to reason that aberrations will be more severe if the cornea is distorted. Third order aberrations include x- and y- trefoil as well as x - and y - coma. Trefoil and coma are both classified as a form of irregular astigmatism which results in an irregular or distorted wavefront.
The number of aberrations per order increases as the order of the Zernike polynomials increases.
In the fourth order there are five types of aberrations namely: x - and y- quatrefoil , x- and y - secondary astigmatism and spherical aberration. Spherical aberration is often caused by the difference in refracting power of the lenticular annular rings of the internal crystalline lens as well as the pupil size. Peripheral light is refracted to a greater or lesser extent and is therefore focused off the retina, causing visual disturbances.
Pupillary miosis can cause a decrease in the effects of spherical aberration as less of the peripheral lenticular rings are exposed to incident light.
It has been reported that Zernike coefficients can vary from Ocular higher order aberrations can be expanded as far as the instrument will allow in terms of order. However, those of main interest are the third and fourth orders, as the fifth and sixth order aberrations are usually very small in magnitude and therefore negligible. Coma, as mentioned above, is a form of irregular astigmatism. The wavefront produced when coma is present is asymmetrical and the image created on the retina has a comet-like or flare-like appearance.
The presence of a large amount of coma during aberration measurements has been seen to relate to progressive corneal eye diseases, such as keratoconus. Spherical aberration presents as complaints of halos and night vision disturbances owing to the lenticular annular zones and enlarged pupil diameter during dim lighting conditions.
While the ocular accommodation system is relaxed, spherical aberration is usually positive. As accommodation increases between two and three diopters, 23 spherical aberration decreases and becomes less positive or even negative. The change in spherical aberration as accommodation increases can be explained as resulting from the shape and position variation of the ocular lens.
Wavefront aberrations represented with Zernike polynomials and coefficients can be difficult to understand and interpret, and therefore the root mean square RMS can be valuable when assessing the wavefront error. RMS wfe can be calculated using the information given by the aberrometer once a measurement has been taken.
As seen in the above equation, piston is not included in the calculation as it has no effect on the quality of the retinal image. Refractive surgery has become increasingly popular for the correction of unwanted refractive errors. The surgery aims to eliminate the presence of lower order aberrations, namely defocus and x - and y -astigmatism. Whilst most surgical interventions are successful in reducing or eradicating refractive errors, patients still present with visual disturbances. The development of wavefront aberrometers has allowed the thinking that higher order aberrations can also be corrected in time with refractive surgery via custom ablation or custom contact lenses.
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There are, however, already limitations to this notion. With current wavefront analysers, the ability to reproduce wavefront measurements that are reliable has not yet been done successfully. Wavefront aberrations are seen to be dynamic which poses a problem for correction. Refractive surgery, however, has been shown to increase higher order aberrations, often because of the induced corneal changes 20 and particularly causes an increase in coma and spherical aberration. The symptoms that can present after refractive surgery include glare, halos, poor scotopic night vision, decreased contrast sensitivity and poor subjective refraction results.
The increase in scattered light usually results from the size of the ablation zone chosen during surgery. Light will strike the cornea as well as the edge of the ablation zone, and this causes increased scattering of light and therefore becomes the source of the visual disturbance.
Constriction of the pupil should in theory decrease the amount of light scattered. Spherical aberration has also been seen to increase after ablation refractive surgery.
Age-related changes in corneal and ocular higher-order wavefront aberrations.
As mentioned above, spherical aberration is responsible for the presence of glare and halos, and therefore the increase in spherical aberration after refractive surgery would result in a heightening of these visual disturbances. Myopic ablation patterns tend towards positive spherical aberrations whilst hyperopic ablation patterns are more negative. Refractive surgery causes changes to the corneal surface and can therefore induce unwanted aberrations. Striae or folds within the cornea can add to the increase in experienced glare and halos. Pre-operative higher order RMS wfe values provide surgeons with an indication as to which aberrations may increase after surgery.
The smaller the higher order RMS wfe before surgery, the more likely that the procedure will increase aberrations post-operatively. The discovery of an increase in higher order aberrations after refractive surgery has contributed to the development and advancements in laser ablation technology during refractive surgery. Rangefinders Night vision devices.
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