Ординатура / Офтальмология / Английские материалы / LASIK and Beyond LASIK Wavefront Analysis and Customized Ablation_Boyd_2001

Chapter 33

Principles for the Study and Diagnosis of Aberrations

The present methods of diagnosis to determine the different types of aberrations function according to the following principles:

a.Outgoing reflective aberrometry (Figure 29-3)

b.Ingoing adjustable aberrometry (Figures 29-4 and 29-5)

c.Ingoing retinal imaging aberrometry (Figures 29-4 and 29-5)

Aberrometers are an important conceptual development in the investigation of Physiological Optics. Nevertheless, at present they are of medium practical interest to the clinician that performs surgery on ametropias because the instruments available are still somewhat “crude,” not 100% exact for the precision required for the determination of an aberration (Figure 33-2). With the equipment now

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Figure 34-2. Sensing Mirrors and Adaptive Optic Deformable Mirror. Lower right of slide reveals a chip detector microlens array for obtaining the wavefront and the upper right of slide reveals a deformable chip mirror to perfect the imperfect wavefront.

Josef Bille, Ph.D., professor and physicist at the University of Heidelberg, Germany, is considered by many to be the “father” of wavefront technology. 1 Dr. Bille who is the Director of the Institute of Applied Physics at the University of Heidelberg first began work in this field while developing this specific technology for astronomy applications in the mid-1970’s. He issued and received the first German patents in 1982 and 1986, respectively. In 1997 he co-founded 20/10 Perfect Vision. Since that time he and his co-workers have designed and brought to market a stand-alone desktop-sized testing device which includes: image acquisition device, monitor, computer processing unit and keyboard (See Figure 34-3 ).

Definition of Important Terms 2,3

Spherical Aberration - Spherical lenses do not bring all rays to a perfect point focus. For a plus spherical lens there is increasing converging power as the lateral distance from the central ray is increased. Thus, spherical aberration causes rays at the edge of the lens to be focused anterior to the focus of the central ray. Instead of all of the rays of light coming to a concise point of focus, they are distributed over a small region of the image and there is no single sharp point of focus for all of the light rays passing

Figure 34-3. Patient being examined by technician. Note desktop CPU, monitor, keyboard and acquisition device.

through the pupil. Spherical aberration in humans is due to the anterior surface of the cornea and the anterior and posterior surfaces of the crystalline lens. Spherical aberration increases as the fourth power of the pupil size. At night, pupil dilation increases spherical aberration, which causes a slight (0.5 to 1.0 diopter) increase in myopia, due to the shift in image location which defines the condition of night myopia.

Chromatic Aberration - The ocular media have a different refractive index for each wavelength of light. Hence, blue light which has a short wavelength is brought to a focus in front of longer wavelength red light resulting in an imperfect point of focus. In the human eye chromatic aberration is the result of this differential refraction by the cornea and crystalline lens. As with spherical aberration, chromatic aberration increases as the size of the pupil increases and both are accentuated the further one moves from the optical center of the cornea or crystalline lens. In consideration of spherical and chromatic aberration, the sharpest retinal image is produced when the pupil is 2-3 millimeters in diameter. A smaller pupil will degrade the sharpness of the retinal image by diffraction effects about the edge of the papillary aperture.

Coma and off-axis astigmatism cause rays to be distributed over a small area of the image rather

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than to converge to a single point. Coma derives its name from the fact that the rays are distributed in a pattern reminiscent of a comet. Coma and off-axis astigmatism increase as the object moves away from or lateral to the optical axis.

Point-spread-function is explained by directing a normal emmetropic eye toward a tiny single point source of light such as a star. The resulting image on the retina will not be a point but a small circle of finite size. This effect is called point-spread- function and results from diffraction effects about the margin of the pupil.

Modular transfer function is an optical bench measurement used by engineers to evaluate the performance of a lens, or lens systems. The MTF is a method to describe the contrast sensitivity of a lens. Modulation transfer is the ability of a lens system to transfer an object’s contrast to its image. Modulation is therefore a ratio of image contrast to object contrast. Ideally, it would be one, or 100%. Modulation transfer plots describe the modulation of a lens system as the object increases in complexity. The Y-axis is modulation and the X-axis is spatial frequency, measured in line pairs per millimeter. As the spatial frequency increases, the modulation of any lens system decreases. ( Definition courtesy of Warren Hill, M.D., Mesa, Arizona )

CURRENT OCULAR REFRACTION EVALUATION SYSTEMS

Phoroptor and Autorefractors

Manual refraction with the time-tested phoropter incorporates both objective retinoscopy by trained examiner and subjective refinement with patient input. Autorefraction obtains objective measurement followed by subjective input from the patient. With either of these formats, only sphere, cylinder and axis of cylinder are quantifiable. Irregular astigmatism and other higher order aberrations are not measurable. Minimal measurement is 0.12 diopters.

Corneal Topography

Placido-disc or slit-light systems supply corneal curvature and elevation data with an accuracy

Figure A: The CustomCornea System to be used with the

LADARVision excimer laser

light charge couple device (CCD) linked to a computer, and these patterns are used to compute wavefront aberrations in the form of Zernike polynomials. When compared to and integrated with preoperative corneal topography, an ablation profile is computed and used to feed the excimer laser to correct for all of the eye’s aberrations. The device uses a frequency-doubled Nd:YAG laser at 532 nM and mask system to create 168 equidistant and parallel light rays for projection onto the cornea. The overall exposure time is 40 ms. The precision of the device allows for an objective measurement of spherical and cylindrical refractive error with an accuracy of better than +/- 0.25 diopters. By definition this is an ingoing testing device in that the image formed on the retina is observed and evaluated. No informa-

tion on outgoing light is necessary.

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C.Bausch & Lomb Surgical (Claremont, CA) Aberrometer/Wavefront Analyzer (designed by Technolas GmbH of Munich, Germany) which is to be incorporated into the Bausch & Lomb Orbtek (Salt Lake City, Utah) Orbscan topography device. This system appears to be a Shack-Hartmann type system operating in a similar fashion to Visx 20/10 Perfect Vision and Autonomous systems.

D.Tracy Technologies ( Bellaire, TX ) Electro-optical Ray-Tracing Analyzer. Unlike the Shack-Hartmann-type devices the Tracy ray-tracing device uses the fundamental thin-beam principle of optical ray tracing to measure the refractive power of the eye on a point-by-point basis. The device measures one point in the entrance pupil at a time rather than measuring the entire entrance pupil at once, like the aberroscopes and Shack-Hartmann devices which supposedly have the possibility of data points criss crossing with a highly aberrated eye leading to erroneous information and subsequent conclusions. The ray tracer is designed to fire a rapid series of parallel light beams into the eye one at a time, passing through the entrance pupil in an infinite selection of software-selectable patterns. With this technique, the Tracy system can probe particular areas of the aperture of the eye. By design, the Tracey system can register where each “ bullet “ of light strikes the retina as the fovea is represented by the conjugate focal point of the system from the patient’s fixation. Semiconductor photodetectors are able to detect the location of where each light ray strikes the retina and provide raw data measuring the error distance from the ideal conjugate focus point, giving

Figure 34-4. Schematic diagram of a SH type aberrometer. The key component is the ShackHartmann wavefront sensor shown in the gray box. Dashed rays show the conjugacy relationship between the eye’s entrance pupil and the lenslet array. Solid lines show the conjugacy relationship between the retina and the CCD video sensor. F is the fixation target. For calibration purposes the light trap T is replaced by a mirror that reflects the collimated laser beam into the Shack-Hartmann wavefront sensor. ( Figure courtesy American Academy of Optometry - Thibos LN, Hong X. Clinical applications of the Shack-Hartmann Aberrometer. Optom Vis Sci 1999;76:817-825. ) 7

lected by a CCD video camera within the acquisition module. If the optical system is without aberration, the wavefront exits the eye as parallel flat sheets

just as they entered (Figures 34-5 A, 34-6A). If the optical system has aberrations the flat sheets entering will exit as irregular curved sheets ( Figures 34- 5 B, 34-6 B ).

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Figure 34-6A. Incident plane wave resulting in a square grid of spots.

Figure 34-6B. Distorted wavefront causes lateral displacement of spots.

The returning wavefront after being captured by the CCD video camera is converted to a color coded Acuity Map for points over the pupil area. Some prefer the term “Phase Map” or “Spatially Resolved Refractometer Map”. Nevertheless, the map is a translation of 100,000 data point numbers for a 6 mm pupil. Measurements are taken every 20 microns over a 6 mm pupil area and thus describe the refractive properties of the eye from tear film to retina.

The technique of adaptive optics can then be employed on the irregular wavefront to correct for all aberrations above sphere and regular astigmatism. What physicians call irregular astigmatism (any re-

fractive error which can not be corrected by spherocylinder lens combinations) physicists call higher

order aberrations (comma, spherical aberration, chro- Help ? matic aberration).

Wavefront data can determine abnormalities within the ocular system, as depicted on the wavefront map, but it can not tell the clinician at what level the abnormality is located, i.e. cornea, lens, vitreous, or retina. Therefore, complete ocular examination (retinoscopy, slit lamp examination, fundus biomicroscopy, and ophthalmoscopy) in combination with data from keratometry and corneal topography will define the locale of pathology.

How to Read a Wavefront Map

Visx 20/10 has called their maps “ Acuity Maps“. Acuity maps are color coded and separated into 20 shades of color which are autoformated in micron scale for the given eye. The total interval of measurement of the individual map is determined by the actual microns of difference in the most advanced (maximum) and most latent or trailing (minimum) of the wavefronts for the individual eye.

Figure 34-7 A (above right) - Visx 20/10 Perfect Vision Acuity Map of an unoperated “ normal “ eye. Upper left gives patient name, presumed refraction and eye of regard. Upper right provides CCD picture of cornea and pupil (In future formats, the raw Shack-Hartmann data image will be placed here). Lower Right provides the measured refraction via the wavefront reading for first order – sphere and second order – regular astigmatism and axis. The lower left provides the acuity map with sphere, astigmatism and higher order aberrations on the left and the acuity map with sphere and regular astigmatism removed. The second map only describes the higher order aberrations. Note the left map is scaled from –1.5 microns to +1.5 microns with most values from 0 (baseline reference plane) to +1.5 microns and the second map is scaled from –0.5 microns to + 0.5 microns. In this example there are essentially no higher order aberrations. These maps should be looked upon as contour maps. After taking the scale range in microns into account, if there are widely spaced contours this would indicate an eye relatively free of optical aberrations whereas if the contours are tightly spaced there is a greater degree of aberration.

Figure 34-7B (below right) - Humphrey corneal topography provided at right for comparison.

WAVEFRONT ANALYSIS

The acuity map is purely an objective reading of the wavefront. The “ loop “ per se for an individual eye is “closed “ by enlisting the patient to provide subjective feedback when the adaptive optics technology of deformable mirrors which correct the aberrations and project a Snellen-like acuity chart onto the patient’s fovea. The patient is asked to read as far down on the “chart” as possible and this will be the best acuity the treating physician could hope to achieve after surgical intervention. In theory, this

Visx 20/10 Perfect Vision

Acuity Map (Figs. 34-7 A-B)

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Chapter 34

should create the optimal ablation with laser vision correction for each eye and correctly treat the irregular corneal optic. According to Dr. Bille, in the population undergoing surgery 99.9% have retinas capable of seeing 20/10 but their corneal shape does not permit this to happen and programming the laser to reshape the cornea to compensate for these imperfections and allow the patient to realize their best possible acuity.

A very helpful image for the clinician to evaluate with each visual acuity map, phase map or spatial map, as used by Thibon and Hong 7 ,(color coded map in the lower left of figure 34-7) is the ShackHartmann data map. The SH data map is the raw light image impinging on the CCD camera. It appears as a grid of light dots as seen in Figure 34-8A.

If the eye is without aberration the pattern will be extremely uniform with the dots perfectly aligned horizontally and vertically. In addition the image of each dot will be very precise without blurring of the edges or “trailing” of the edges in “comet like “ fashion. (Figure 34-8A). If the eye has significant aberration the image will show a distorted pattern with individual qualitative abnormalities of the dots and overall irregularity of the group pattern. (Figure 34-8B )

Data from the wavefront map is explained mathematically in three dimensions with polynomial functions. It turns out that most investigators have chosen the Zernike method for this analysis although Taylor series can be used. 8 The ray points described by Zernike Polynomials are used to obtain a best-fit

toric to compensate for the refractive error of the eye. The points are described in the x and y coordinates and the third dimension, height, is described in the z-axis. The first order polynomial describes the spherical error or power of the eye. The second order polynomial describes the regular astigmatic component and its orientation or axis of the standard refraction clinicians are accustomed to obtaining. Third order aberrations are considered to be coma and fourth order aberrations are considered to be spherical aberration. Zernike polynomial descriptions for wavefront analysis typically go up to the tenth order of expression. A normal straight curve would have two orders, first and second, to describe its morphology. As one adds more local maximum and minimum points more or higher orders of the polynomial series are required to describe the surface. The power of wavefront analysis is the fact that it can describe these other aberrations within the optical system that to date have only been explained as “ irregular astigmatism “ and treated with a rigid contact lens.

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