What is Zernike and how do I use it? What is RMS? What is the RMS of a "normal, healthy" eye? How are wavefronts used to measure accommodation? Why is this important? Why is wavefront aberrometry an essential part of modern ophthalmic practice? What should I look out for when selecting a SH wavefront aberrometer? A wavefront is a physical representation of the optical quality of a light beam's optical quality. The quality of a light beam can be degraded by any imperfect optical element, a lens, a piece of glass, and in the eye, a cornea for example. When the light beam is "perfect" in terms of optical quality, the wavefront is plane (flat). When light is degraded by an optical element, the corresponding wavefront is not plane anymore, but has a disrupted shape. A representation of this shape, by way of its variations and amplitude, gives a precise knowledge of the amount of perturbation that was introduced by the optical elements. Some ophthalmologists have described a wavefront in recent years as a measure of the total refractive errors of the eye, including myopia, hypermetropia, astigmatism, and other refractive errors that cannot be corrected with glasses or contacts. In ophthalmology, wavefronts are measured by devices called aberrometers. Aberrometers use wavefronts to objectively measure the overall refractive power error of the eye. They do this by mapping how light rays travel through the eye and by providing maps using color gradients to represent magnitudes of the refractive errors, which enables ophthalmologists to locate and possibly correct even obscure imperfections that cause vision defects. As the name indicates, an aberrometer measures aberrations, and an aberration is a vision defect that occurs when light rays are improperly bent (refracted) in the eye. An aberration may occur because of a flaw in the structure of the eye. There are lower order aberrations, sphere and cylinder, and there are higher order aberrations such as coma, trefoil and spherical aberration. Patients who complain of glare, halos, starbursts and poor night driving often have increased higher-order aberrations.
Shack Hartmann is the wavefront measuring technology chosen by the majority of aberrometer manufacturers. A Shack-Hartmann-based system measures a wavefront in one shot, which makes it quicker compared to other technologies that use consecutive measurements. This gives it a high repeatability, because the longer the measurement takes, the more negative effect eye movements will have on the repeatability. Shack-Hartmann can have a very high resolution which is directly related to the number of measuring points. Ray tracing is the main alternative technique. This is a fine method to measure wavefront but it needs more time to measure since it is not a one-shot but a consecutive measurement. It has also fewer measuring points, thus reducing the precision. But most damaging is the fact that ray tracing incurs the aberrations twice because it passes light through the eye to create a wavefront and then retrieves it from the retina to measure it. This fundamentally hampers both the repeatability and precision. Adaptive Optics consists of 3 elements: - Wavefront sensor
- Algorithms
- Deformable mirror
A Shack-Hartmann wavefront sensor uses the first two elements of Adaptive Optics, but not the third.
Aberrometers differ from auto refractometers because they measure more optical parameters than auto-refractometers do. Auto refractometers measure the average optical quality of the eye. Aberrometers measure this same average quality and also detailed local differences in optical quality. This is important because the optical quality in an eye is not homogeneous. Auto refractometers measure sphere and astigmatism. Aberrometers measure sphere, astigmatism, and also what is known as irregular astigmatism. Irregular astigmatism is a group name for those optical defects that were near impossible to measure before the introduction of the aberrometer. The optics of the eye are mostly determined by 2 elements: the cornea and the crystalline lens. Aberrometers differ from corneal topographers in that corneal topographers are only able to measure the optical quality of the eye linked to the cornea. Aberrometers measure the global optical quality of the eye, due to both cornea and crystalline lens.
Lower order aberrations (LOAs): - 1st Order Aberration - tilt (prism)
- 2nd Order Aberration - defocus (sphere) and cylinder (astigmatism)
Some of the most important higher order aberrations (HOAs): - 3rd Order Aberration - coma and trefoil
- 4th Order Aberration - spherical aberration and quadrefoil
- 5th Order and higher – pentafoil etc.
Approximately 90% of the eye’s optical imperfections are due to lower order aberrations with the rest being made up of higher order aberrations. Everyone has a certain degree of higher order aberration in their visual system that may affect the way they see. People with significant higher order aberrations may not see perfectly, even with the best glasses or contact lenses possible. Two common and potentially disruptive higher order aberrations are spherical aberration and coma. Spherical aberration creates halos around points of light while coma makes points of light appear comet-like with a blurry tail-like smudge to them. Irregular astigmatism was a term used before the aberrometer arrived to better identify unknown causes for lack of visual acuity due to the optical quality of the eye. The aberrometer has now opened our eyes to much higher detail. Another example to show the influence of higher order aberrations is sphere. Sphere can be seen on a wavefront as a spherical shape all along the pupil of the eye, that means that the optical defect, myopia for example, is the same in all parts of the pupil of the eye. If only sphere is considered, the myopia will be the same for any pupil size of the patient. When looking at higher order aberrations, it is possible to identify wavefront shapes that vary in the pupil area. For example spherical aberration is a higher order aberration, which is characterized by a variable power over the pupil. This means that if also this higher order aberration is taken into account , the myopia of the patient will vary with his pupil size. This could explain why someone with high spherical aberration can see halos at low light conditions, when the pupil is big.
Fritz Zernike was a Nobel Prize winning physicist who developed a set of mathematical functions (polynomials) to very precisely describe very complex shapes like wavefronts. He introduced that a set of pre-determined known shapes, of growing complexity, can be combined to precisely describe a surface that fits as well as possible to a measured wavefront. Zernike analysis describes the wavefront mathematically as the weighted sum of Zernike basis functions or modes. The weight which must be applied to each mode when computing the sum is called an Zernike coefficient and is usually expressed in microns. Each mode describes a certain three-dimensional surface and corresponds with ocular aberrations. For instance, second-order Zernike polynomials represent the conventional aberrations such as defocus and astigmatism. Zernike polynomials above the second order represent the higher-order aberrations that are suspected of causing night glare and halos. Zernike polynomials help to simplify the wavefront technology by combining all aberrations into one single map. This is called a wavefront map and is usually a two-dimensional map using colour gradients representing powers of the aberrations. These Zernike polynomials can also be displayed as a pyramid starting from 0 (no aberrations or piston) to, theoretically, as high as you want to go.
RMS stands for Root Mean Square, a term that is used in relation with Zernike polynomials. It is a quadratic sum of the Zernike coefficients that give the power of the aberrations for the terms that have been summed. For example higher order RMS is the total of all the higher order aberrations. You can also come across “Total RMS”, which is the overall magnitude of all the eye’s refractive errors (sphere, cylinder and HOAs) In a Zernike polynomial, the correct way to combine the aberration coefficients is to take the root mean square of them. Aberrometers use the RMS to record and measure optical aberrations as detailed as 0.01 microns. Thanks to this kind of accuracy, aberrometers can express lower and higher order aberrations in terms far more accurate than ever seen in clinical eye care. With the RMS system, we can reconstruct the mathematical calculations of an aberration into Zernike polynomials.
The way to measure accommodation with an aberrometer is to make the internal fixation target start from the far point of a subject and then make the target approach over a custom defined distance and in a custom defined number of steps. At each step a wavefront measurement will be taken and by measuring the defocus, we get also a measure of the patient’s ability to accommodate. It is then possible to analyse the evolution of all the components of the optical quality of the eye with accommodation: sphere (with a direct link to presbyopia), cylinder and also higher-order aberrations. With a rapidly aging population in the West, presbyopia is a problem for more and more people. Having a tool that can measure this is an important step forward in eye care. Having a tool that also allows to measure any related aberrations to accommodation can provide valuable insight into a patient’s evolution of visual quality.
SH wavefront aberrometry is not difficult to learn because the measurements are very easy to do (comparable to that of an auto-refractometer), and because there is more and more literature available and an increasing number of practitioners with experience. Doing a measurement can be learnt in minutes and having a good working knowledge of exploiting the information is a question of practice and can take some weeks, depending on the intended application and previous experience of the user.
Eye care has known a number of major technological innovations in recent years. Aberrometers have made it possible for the first time to measure higher order aberrations in the clinic. This breakthrough has been a runaway success with refractive surgeons from the outset, and now there is a growing realisation in the market that the type of precision and detail offered by aberrometers is increasingly needed in the general practice as well. There is a growing number of new correcting elements based on information coming from aberrometry. Best known are Lasik and IOLs; aberrometers can help making a sharper prescription. Contact and spectacle lens manufacturers are under tremendous pressure to offer custom correction solutions. Aberrometers have been the key enablers for this trend. It is clear that aberrometers are an essential part of the forward-looking ophthalmic practice.
Not all Shack-Hartmann wavefront aberrometers are alike. Different manufacturers offer products with varying degrees of accuracy, dynamic range, max./min. pupil diameters, analysis features and compatibility with other devices. Two of the key factors when choosing a Shack-Hartmann aberrometer are accuracy and dynamic range. Accuracy, is directly linked to the number of points measured and the spread of these measuring points. The higher the number of points the better, but some aberrometers underachieve because of an uneven spread of the points, even though they have a high number of them. Sometimes manufacturers use software algorithms to enhance the optical resolution of their wavefront sensors; this is called software interpolation. This process takes data from nearby points to calculate, by approximation, what the desired added data points would be if they could be measured physically. The inherent room for error with this type of technology is evident because the device is not providing a true, physical measurement of each point, but an approximation calculated by the software. As for Dynamic range, the quality of the design of the wavefront sensor directly impacts its ability to detect the higher and lower ranges as well as the subtleties in the wavefront’s variations. A good way to gauge an aberrometer’s overall dynamic range is to look at the cylinder range. Aberrometers built around less precise wavefront sensors do not enable users to detect disorders including keratoconus, corneal scarring and severe higher-order aberrations. |