Ординатура / Офтальмология / Английские материалы / Wavefront Analysis Aberrometers and Corneal Topography_Boyd_2003

22.H. Herloski. "Strehl ratio for untruncated aberrated Gaussian beams", J. Opt. Soc. Am. A 1985;2:1027-1030.

23.D. Schröder. Astronomical Optics, 2/E, Academic Press. 2000.

24.H. Hamam. "Simplified linear formulation of diffraction", Optics communications, 144, 89-98, 1997

25.A. Papoulis, "Pulse compression, fiber communications, and diffraction: a unified approach", J. Opt.

Soc. Am. A 11, 3-13, 1994.

26.H. Hamam and J. L. de Bougrenet de la Tocnaye "An Efficient Fresnel Transform Algorithm based on fractional Fresnel diffraction" J. of the Optical Society of America A. 12, 1920-1931, 1995.

27.E. Hecht (1987) Optics. 2/E Addison-Wesley Publishing Company.

28.J. W. Goodman, Introduction to Fourier optics, MacGraw-Hill Edition, 1968.

29.D. Malacara and Z. Malacara, Handbook of lens design, Ed. Marcel Dekker INC., New York, 1994.

30.A. Papoulis, The Fourier Integral and Its Applications. McGraw-Hill Edition, 1962.

31.H. Hamam. An interactive pedagogical method simplifying complex optical aspects – Wavefront decompositions and representations, Various Pedagogical Strategies, University of Montreal, May 2002.

Applet : http://www.umoncton.ca/genie/electrique/Cours/Hamamh /Optics/Aber/Aber.htm.

32.FM. Grimaldi. Physico-mathesis de Lumine, coloribus et irride, (published just after his death), Bologne, 1665.

33.O. Bryngdahl and F. Wyrowski. "Digital holography : computer-generated holograms", Prog.Optics 28, 1-85, 1990.

34.H. Hamam and JL. de Bougrenet. "Efficiency of programmable quantized diffractive phase elements", Pure and Applied Optics 5, 389-403, 1996.

35.J. Fienup, "Iterative method applied to image reconstruction and computer generated holograms", Opt. Eng. 19, 297-305, 1980.

36.J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization", IBM J. Res. & Develop. 14, 478-484, 1970.

37.W. N. Charman, "Wavefront aberration of the eye : A review", Optometry & Vision Science 68, 574-583 (1991).

38.J. Liang, B. Grimm, S. Goelz and J. F. Bille, "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor", JOSA A 11, 1949-1957, (1994).

39.A. Ivanoff, "Les Aberrations de l'oeil", Editions de la revue d'Optique, Théorie et Instrumentale, Paris, 1953.

40.M. Campbell, E. Harrison, and P. Simonet, "Psychophysical measurement of blur on the retina due to optical aberrations of the eye", Vision Res. 30, 1587-1602, (1990).

41.F. Berny, and S, Slansky, "Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments", in Optical instruments and Techniques , H. Dickson, ed. Oriel Press, London, 375-386, (1970).

42.H. Howland and B. Howland, "A subjective method for the measurement of monochromatic aberrations of the eye", J. Opt. Soc. Am. 67, 1508-1518 (1977).

43.G. Walsh, W. N. Charman, and H. Howland, "Objective technology for the determination of monochromatic aberrations of the human eye", J. Opt. Soc. Am. A 1, 987-992 (1984).

44.B. Platt and R. V. Shack, "Lenticular Hartmann-screen", Opt. Sci. Center Newsl. 5, 15-16, (1971).

45.H. Hamam, "An apparatus for the objective measurement of ocular image quality in clinical conditions" Optics communications 173, 23-36 (2000).

46.J. Liang and D. Williams, "Aberrations and retinal image quality of the normal human eye " , JOSA A 14, 2873-2883, (1997).

47.W.H. Press, B. Flannery, S.A. Teukolsky and W.T. Vetterling. Numerical recipes in C, the art of scientific computing, Chapter 14, Cambridge University Press, 1988.

48.R. Cubalchini, "Modal wave-front estimation from derivative measurements" J. Opt. Soc. Am. 69, 972977 (1979).

49.R. Applegate. Monochromatic wavefront aberrations in myopia. In Non-Invasive Assessment of Visual System. Optical Society of America 1, 234-237, (1991).

50. M. Collins, C. Wildsoet, D. Atchison. Monochromatic aberration and myopia. Vision Res 35, 1157-1163, (1995).

51.M.P. Paquin, H. Hamam and P. Simonet, "The Julius F. NEUMUELLER Award in Optics -Objective measurement of the optical aberrations for myopic eyes", Opt. and Vis. Science 79, 285-291, (2002).

52.M. Campbell, H. Hamam, P. Simonet, I. Brunette. Optical image quality in eyes after Excimer laser photorefractive keratectomy (PRK). Invest Ophthalmol Vis Sci 1998; 39(4):S466.

John F. Doane, M.D.,

Scot Morris, O.D.,

Andrea D. Border, O.D.,

Lon S. EuDaly , O.D.,

James A. Denning, B.A., B.S.,

Louis E. Probst, M.D.

What is Wavefront Technology?

Just as you may or may not have become accustomed to understanding corneal topography maps the next evolution of refractive ocular imaging in the form of “Wavefront Analysis” has come on to the visual science scene. This technology is rooted in the astrophysics domain where astronomers hoped to perfect

the images impinging on their telescopes. To do this astrophysicists had to be able to measure, let alone, correct the imperfect higher-order aberrations or wavefront distortions that entered their telescopic lens system from the galaxy. Using a process called “ adaptive optics “ deformable mirrors were used to reform the distorted wavefront to allow clear visualization of celestial objects (See Figures 1 AB and 2).

Figure 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.

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

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-work- ers have designed and brought to market a standalone desktop-sized testing device which includes: image acquisition device, monitor, computer processing unit and keyboard (See Figure 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 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 than to converge to a single point. Coma derives its name from the fact that the rays are distributed in a

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 of 0.25 diopters or 2-3 microns. The excimer laser can remove tissue at 0.25 microns per pulse of ablation. The

20/10 Perfect Vision Wavefront System

This system describes the refraction of the eye within 0.05 microns. This is five times more accurate than the excimer laser beam and approximately 25-50 times more accurate than phoropter, autorefractor and topography based systems. It is important to understand that the Wavefront System is not a “ newer “ version of corneal topography but a visual acuity measuring device that takes all elements of the optical train into consideration which includes: tear film, anterior corneal surface, corneal stroma, posterior corneal surface, anterior crystalline lens surface, crystalline lens substance, posterior crystalline lens surface, vitreous and retina.

Other Wavefront Sensing Devices 5

A.Autonomous Technologies Custom Cornea / LadarVision Wavefront Measurement Device. This is a Shack-Hartmann style device. All ShackHartmann devices are outgoing testing devices in that they evaluate the light being bounced back out through optical system.

B.Dresden Wavefront Analyzer. Theo Seiler, M.D. and his colleagues from University Eye Clinic, Dresden, Germany have developed this system. It is to be distributed by Technomed GmbH of Baesweiler, Germany. The system will work in conjunction with the Wavelight ( Erlangen, Germany ) Allegretto scanning spot laser and the soon to be introduced scanning spot laser from Schwind Eye-Tech- Solutions GmbH (Kleinostheim, Germany ). This system is based upon the Tschernig aberroscope, first described in 1894. A bundle of equidistant light rays are projected onto the cornea and, due to optical imaging, become focused on the retina. In an aberration free eye, the retinal image pattern consists of equidistant light spots. The spot pattern of a normal eye is distorted due to ocular aberration. The deviation of all spots from the ideal pattern is measured by an indirect ophthalmoscope and directed to a low-light charge couple device (CCD) linked to a computer, and these patterns are used to compute wavefront aberrations in

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 softwareselectable 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 direct measurement of refractive

error for that point in the entrance pupil. 64 points of light within a 6 mm pupil can be measured five times each in just over 10 ms. This device like the Dresden system is an ingoing measuring device. When measuring a physiological system, such as the eye, with its range of refractive errors, this system in essence measures the point-spread function that can easily provide for full calculation of wavefront deformation and modulation transfer function of the eye. One major hurdle for this system is that it currently does not have adaptive optics possibilities ( see below ) which would seem to be imperative to assess preoperatively that the correct wavefront-augmented treatment will be performed.

E. Spatially Resolved Refractometer of Emory University (Atlanta, GA). This device is being designed, built and tested by the Emory Vision Correction Center. It takes a relatively lengthy 3-4 minutes to complete the test but does have direct patient involvement in the testing which adds important subjective value. 6

How the Visx 20/10 Wavefront System

Works

With the Visx 20/10 System a 785 nM nominal wavelength light is projected into the eye onto the macula (Figure 4). This light is not a laser, so there is a considerable spread about the center wavelength. The light is projected as flat sheets or “ wavefronts “. The wavefronts are projected through the entire optical system and reflected back and collected 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 5 A, 6A). If the optical system has aberra-

Section IV: Aberrations and Aberrometer Systems

tions the flat sheets entering will exit as irregular curved sheets (Figures 5 B, 6 B).

Figure 5A. Light reflecting from the retinal surface and travelling to the right exiting through the entrance pupil. The particular eye has no aberration and the wavefronts are straight and parallel to each other.

Figure -5B. Light emerging from an eye with significant aberration. The emerging wavefronts are not straight but are curved.

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 refrac-

tive error which can not be corrected by sphero-cylin- der lens combinations) physicists call higher order aberrations (comma, spherical aberration, chromatic 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 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 7B (below right) - Humphrey corneal topography provided at right for comparison.

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

Visx 20/10 Perfect Vision

Acuity Map (Figs. 7 A-B)

intervention. In theory, this 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 7) is the Shack-Hartmann 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 8A. If the eye is without

Section IV: Aberrations and Aberrometer Systems

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 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 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.