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Measuring Higher Order Optical Aberrations of the Human Eye: Techniques and Applications

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Measuring Higher Order Optical Aberrations of the Human Eye: Techniques and Applications Brazilian Journal of Medical and Biological Research (2002) 35: 1395-1406 Optical aberrations of the human eye 1395 ISSN 0100-879X Measuring higher order optical aberrations of the human eye: techniques and applications L. Alberto V. Carvalho1, 1Grupo de Óptica, Instituto de Física de São Carlos, Universidade de São Paulo, J.C. Castro1 and São Carlos, SP, Brasil L. Antonio V. Carvalho2 2Departamento de Matemática, Universidade Estadual de Maringá, Maringá, PR, Brasil Abstract Correspondence In the present paper we discuss the development of wave-front, an Key words L. Alberto V. Carvalho instrument for determining the lower and higher optical aberrations of · Optical aberrations Grupo de Óptica, IFSC, USP the human eye. We also discuss the advantages that such instrumenta- · Corneal topography 13560-900 São Carlos, SP tion and techniques might bring to the ophthalmology professional of · Zernike polynomials Brasil the 21st century. By shining a small light spot on the retina of subjects · Refractive surgery E-mail: [email protected] and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberra- Research partially supported by FAPESP (Nos. 01/03132-8 and tions (astigmatism, myopia, hyperopia) and higher order aberrations 00/06810-4). L. Antonio V. Carvalho (coma, spherical aberration, etc.). We have measured artificial eyes is partially supported by CNPq with calibrated ametropia ranging from +5 to -5 D, with and without (No. 304041/85-8). 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information Received June 28, 2001 Accepted June 10, 2002 to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this tech- nique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications. Introduction human eye (2). Scheiner in 1619 (3), pub- lished the work Oculus, sive fundamentum The ophthalmology professional of the opticum where he announced the invention 21st century is living a silent revolution, one of a disc with a centered and a peripheral which started at the University of Heidelberg pinhole that was placed before the eyes of a (1994) with the Ph.D. thesis of Liang (1). subject to view a distant light source (Figure Many scientists throughout the history of 1). If the subject saw a single spot he was an physiological optics have attempted to pre- emmetrope, if he saw two inverted spots, he cisely measure the optical aberrations of the was a myope and if he saw two upright spots, Braz J Med Biol Res 35(11) 2002 1396 L. Alberto V. Carvalho et al. a hyperope. This device was the first qualita- oped the technique still used nowadays more tive refractor and became known as Schei- than a century ago other devices with magni- ners disc. After Scheiner, many scientists fying optics and photographic cameras were attempted to construct more precise refrac- only possible later in the 20th century. These tors. Tscherning (4) in 1894 used a four- improvements culminated in the develop- dimensional spherical lens with a grid pat- ment of well-known keratometers and the tern on its surface to project a regular pattern photokeratoscope. But these were still lim- on the retina (Figure 2). He would then ask ited techniques. The keratometer is still used the patient to sketch drawings of the pattern. today, but it only measures the steepest and Depending on the patterns distortion, the flattest meridians at the central 3 mm of Tscherning was able to obtain a semiquanti- the cornea; the photokeratoscope photo- tative measurement of the patients aberra- graphs had to be developed and analyzed tions. It was only at the beginning of the manually, a process that could take hours, if 1960s that Howland (5) devised a quantita- not days. And even after a careful analysis, tive version of the Tscherning aberroscope few techniques were available for displaying by attaching an imaging system and imple- these results in a comprehensive and com- menting rigorous mathematical analysis of pact fashion. There were no fast methods for the collected data. Of course, low resolution Scientific Visualization (11) (a term refer- quantitative systems (autorefractors) have ring to a relatively new field in computer been developed in parallel throughout the graphics, initiated in the mid-1980s, with the last quarter of the last century. We will not objective of developing more didactic tech- discuss the principle of these instruments niques for visual presentation and analysis here, which has been recently reported else- of scientific data). Since the mid-1980s, with where (6-9), but we will compare the preci- the microcomputer revolution, computer sion of our results with those of autorefractors power became accessible enough so as to be in general. incorporated into traditional photokerato- The instruments devised by Scheiner, scopes. Thus, the photokeratoscope became Tscherning and later by Howland, all had a the modern computerized videokeratoscope, specific disadvantage. They were developed which is an example of the improvement in a non-computerized age. Although there allowed by the integration of computers and were computers back in the 1960s, the mi- medical devices. The photographic cameras crocomputer revolution started only in the were replaced by modern semiconductor mid-1980s. The same occurred with the de- charge coupling devices (CCD) and the tire- vices for measuring corneal curvature (video- some analysis of the Plácido images was keratoscopes). Although Plácido (10) devel- replaced by fast and semiautomated image processing algorithms (12,13) and sophisti- cated mathematical models of the human Figure 1. The principle of Schei- ner’s disc. cornea (14,15). Nowadays the whole pro- Two retinal cess of corneal analysis takes only a few Paraxial points seconds and at the end the eye-care profes- Eye with aberration sional may have a multitude of visualization options at a click of the mouse, with the aid of special tools, such as indexes for kerato- Figure 2. The Tscherning aber- conus screening (16,17), contact lens fitting roscope. modules (18) and special displays of corneal parameters (19). These displays may go from Light bundle Grid mask simple corneal slices, difference maps for Braz J Med Biol Res 35(11) 2002 Optical aberrations of the human eye 1397 pre- and postsurgical analysis, up to rotating tions, which cause considerable image deg- three-dimensional corneal maps. radation, preventing astronomers from per- It is our very strong belief that the refrac- forming a thorough analysis of these images. tion techniques available nowadays have In order to diminish or eliminate these ef- many limitations, analogous to the photo- fects, a field of optics, called Adaptive Op- keratoscopes back in the 1950s. Although tics (22), studies methods for measuring and the conventional autorefractors available to- compensating for these aberrations. The sen- day have sophisticated accommodation de- sor used to measure these aberrations was vices and electronics, like linear CCD for first developed by Hartmann in 1900 (23) signal processing and microprocessors for and later improved by Shack in 1971 (24). dedicated tasks, they still measure refractive This sensor became known as the Hartmann- errors in only three meridians. The output is Shack sensor, abbreviated HS sensor. usually on a sheet of paper with two lines or We present here the development and a few more, indicating the ametropia in the preliminary results obtained with an HS sen- conventional spherocylindrical form: sphere sor constructed at the Instituto de Física de + cylinder at axis. Until today, the auto- São Carlos, USP (25), that was used to refraction and the conventional trial lens measure artificial eyes with different ab- procedure have been sufficiently precise to errations. Our claim is that the HS sensor prescribe spectacles and contact lenses, and may be applied to the human eye with patients have been reasonably satisfied. With more precision than traditional refraction the advent of refractive surgery and the pos- techniques. sibility of contact lenses with customized anterior shapes, the conventional refraction Material and Methods instrumentation is no longer precise enough. And this precision has no relation to how Optical configuration precisely these instruments can measure the best spherocylinder surface that approximates The diagram in Figure 3 shows a simpli- the eyes ametropia; it is the lack of resolu- fied scheme of the instrument. tion that makes these instruments obsolete A fiber optic infrared light source gener- for modern applications. For customized ates a non-coherent bundle of rays which are corneal ablation there is an intrinsic need to collimated by a system of lenses and a dia- know the refractive errors at several points phragm. This small diameter (0.5 mm) bundle over the entrance pupil. This happens be- of rays enters the eye through the optical cause the modern laser beams (20) have center of the entrance pupil. This bundle of enough resolution to independently ablate rays focuses a small spot over the retina specific regions of the cornea. because of very little refraction and negli- In fact, although there have been low gible aberration. The diffuse reflection at the priced computers since the mid-1980s, no eye fundus generates a cone of light rays that quantitative technique for measuring eye leaves the retina in the direction of the lens aberrations with high resolution was applied and pupil.
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