Abstract:
Methods and apparatus are disclosed for diagnosing vision and improving vision, for example by reducing or eliminating the effects of macular degeneration, in a manner which does not interfere with the natural shape of the cornea or its orientation relative to the remainder of the eye, but which changes its surface curvature appropriately to achieve the required correction of vision. The focus of sub-regions of the cornea is adjusted so that different regions focus at a controlled distance about a reference axis. This can be accomplished by shaping the cornea (e.g. through ablation) or by applying an appropriate contact lens or other optical lens.

Description:
[0001]    The present patent application is a continuation of International Application No. PCT/US2011/026941 filed Mar. 3, 2011, which was published in English under Publication No. WO 2011/109571 on Sep. 9, 2011, and which claimed the priority of U.S. Provisional Application No. 61/310,073. Each of the preceding documents is hereby incorporated by reference in its entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates generally to a method and system for diagnosing and improving the vision of an eye and, more particularly, to improvement of the vision of an eye with macular degeneration. 
         [0003]    Macular degeneration is a progressive disease of the retina of the eye in which the light-sensing cells in the central area of vision (the macula) cease to function properly. The most common form of macular degeneration is age-related macular degeneration, and it is most common in people who are age 60 and over. In the early stages of the disease, there may be a slight loss of central vision, including a dark or blurry central spot (a central scotoma). As the disease progresses, central vision is increasingly lost, until it disappears entirely in the advanced stages. This disease is the leading cause of blindness in senior citizens. Approximately 15 million people in the United States have it, and approximately 2 million new cases are diagnosed annually. 
         [0004]    The present invention provides for the improvement of vision in an eye with macular degeneration. It contemplates ablation procedures of the cornea and the provision of various types of corrective lenses, including contact lenses and spectacles. 
         [0005]    Ophthalmologists model the cornea as a portion of an ellipsoid defined by orthogonal major and minor axes. Current surgical procedures for correcting visual acuity are typically directed at increasing or decreasing the surface curvature of the cornea, while making its shape more spherical, or conforming it to an “average” ellipse, or making corrections based on wavefront analysis. 
         [0006]    In conjunction with modern corneal procedures, such as corneal ablation surgery, for clinical applications, and for contact lens design and manufacture, high resolution cameras are used to obtain a digitized array of discrete data points on the corneal surface. One system and camera which have been available for mapping the cornea is the PAR Corneal Topography System (PAR CTS) of PAR Vision Systems. The PAR CTS maps the corneal surface topology in three-dimensional Cartesian space, i.e., along x- and y-coordinates, as well as a depth (z) coordinate. 
         [0007]    The “line-of-sight” is a straight line segment from a fixation point to the center of the entrance pupil. As described more fully in Mandell, “Locating the Corneal Sighting Center From Videokeratography,” J. Refractive Surgery, V. 11, pp. 253-259, July/August 1995), a light ray which is directed toward a point on the entrance pupil from a point of fixation will be refracted by the cornea and aqueous humor and pass through a corresponding point on the real pupil to eventually reach the retina. 
         [0008]    The point on the cornea at which the line-of-sight intersects the corneal surface is the “optical center” or “sighting center” of the cornea. It is the primary reference point for refractive surgery in that it usually represents the center of the area to be ablated in photorefractive keratectomy. The line-of-sight has conventionally been programmed into a laser control system to govern corneal ablation surgery. However, some surgeons prefer to use the pupillary axis as a reference line. Experienced practitioners have employed various techniques for locating the sighting center. In one technique, the angle lambda is used to calculate the position of the sighting center relative to the pupillary (“optic”) axis. See Mandell, supra, which includes a detailed discussion of the angles kappa and lambda, the disclosure of which incorporated herein by reference as if set forth in its entirety herein. 
         [0009]    In current LASIK corneal ablation procedures, a portion of the corneal surface or a surface under a flap is ablated. Gathered elevational data is used to direct an ablation device, such as a laser, so that the corneal surface can be selectively ablated to more closely approximate a spherical surface of appropriate radius about the line-of-sight, (or an “average” ellipse, or a wavefront fingerprint) within the ablation zone. The use of the line-of-sight as a reference line for the procedures may reduce myopia or otherwise correct a pre-surgical dysfunction or a visual abnormality. However, a more irregularly shaped cornea may result, which may exacerbate existing astigmatism or introduce astigmatism or spherical aberration in the treated eye. This will complicate any subsequent vision correction measures that need be taken. Also, any substantial surface irregularities which are produced can cause development of scar tissue or the local accumulation of tear deposits, either of which can adversely affect vision. 
         [0010]    Implicit in the use of the-line-of sight or the pupillary axis as a reference axis for surgical procedures is the assumption that the cornea is symmetric about an axis extending along a radius of the eye. The cornea, however, is an “asymmetrically aspheric” surface. “Aspheric” means that the radius of curvature along any corneal “meridian” is not a constant (a “meridian” could be thought of as the curve formed by the intersection of the corneal surface and a plane containing a reference axis, such as the pupillary axis). Indeed, the corneal curvature tends to flatten progressively from the geometric center to the periphery. “Asymmetric” means that the corneal meridians do not exhibit symmetry about their centers. The degree to which the cornea is aspheric and/or asymmetrical varies from patient to patient and from eye to eye within the same person. 
         [0011]    Analysis of clinical measurements in accordance with surface modeling techniques disclosed in U.S. Pat. No. 5,807,381 assigned to the assignee of the present patent application, reveals that the cornea exhibits a tilt, typically a forward and downward tilt, relative to the eye. This tilt may be as great as 6° and, on the average, is between 1° and 3°. Hence, a corneal ablation procedure which utilizes the line-of-sight or pupillary axis as a reference axis tends to over-ablate some portions of the cornea and under-ablate other potions of the cornea. At the same time, it changes the geometric relationship between the ablated cornea and the remainder of the eye. Thus, any ablation procedure which does not take into account the tilt of the cornea is not likely to achieve the desired shaping of the cornea and may therefore be unpredictable in its effect. Similarly, a contact lens design (or any other lens used to improve vision) which does not take into account the tilt cannot achieve optimum results. 
         [0012]    Analysis of clinical measurements in accordance with the surface modeling techniques of U.S. Pat. No. 5,807,381 also reveals that the point on the surface of the cornea which is most distant from the reference plane of the PAR CTS (hereafter referred to as the HIGH point) is a far more effective reference point for corneal ablation and lens design than the center of the cornea or the pupillary center. Specifically, as demonstrated in U.S. Pat. No. 5,807,381 laser ablation about an axis passing through the HIGH point produces a much more regularly shaped cornea and removes less corneal material than the same operation performed about an axis close to the center of the eye, such as the pupillary axis. 
         [0013]    Although incorporating corneal tilt and utilizing the HIGH point produce improved and more consistent results with corneal ablation surgery, there is still an excessively high degree of unpredictability. For example, analyses of clinical measurements have revealed that, in some eyes, the postoperative cornea begins to change shape a short time after corneal ablation surgery. Thus, a nearly perfectly spherical post-operative cornea of the type most commonly produced by conventional surgery will, over time, return to an aspheric, asymmetric shape. 
         [0014]    Analysis of clinical measurements in accordance with the methods of U.S. Pat. No. 5,807,381, and International Application No. PCT/US03/1763 (published as W003/101341), the disclosures both of which are incorporated herein by reference in their entirety, raises questions about assumptions that have been made about the structure of the human cornea which are inherent in such well-known corneal analysis technologies as wave-front analysis and placido disc technology. In particular, it was found that, unlike other optical systems, the central portion of the cornea (for example, out to a 3 mm diameter) is not necessarily optically superior to substantially greater portions of the cornea (for example, out to a 7 mm diameter) in its ability to focus. The central portion of the cornea exhibits a great deal of focus scattering. That is, different regions on the cornea do not focus to the same point on a focal axis. Indeed, they do not even focus on the axis. This focus difference is most pronounced in the central portion of the cornea and decreases substantially at increasing diameters from the center. 
         [0015]    As disclosed in PCT/US03/1763, vision can be improved by adjusting the focus of the cornea, referred to as “orthogonalizing”, so that different regions focus substantially to the same axis. This can be accomplished by shaping the cornea (e.g. through ablation) or by applying an appropriate corrective lens, effectively reducing radial and axial focus scatter. An additional benefit of orthogonalization was that presbyopia (defective near vision) was substantially reduced. That is, presbyopic patients fitted with orthogonalized contact lenses that did not have components that focused at different distances had improved near vision to the extent of not requiring reading glasses. 
         [0016]    Subsequent experimentation has revealed that the symptoms of macular degeneration can be reduced through orthogonalization, but by doing so less than perfectly. In accordance with the present invention, orthogonalization is performed so as to produce a predetermined amount of imperfection in the orthogonalization. This will be referred to as “decentered orthogonalization.” The invention contemplates that light be delivered to the macula in patterns designed to avoid areas of the macula with “dead” light receptors. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]    The foregoing brief description, as well as other objects, features and advantages of the present invention will be understood more completely from the following detailed description of presently preferred embodiments, with reference being had to the accompanying drawings in which: 
           [0018]      FIG. 1  is a block diagram illustrating a method for achieving vision correction in accordance with the present invention through either laser ablation of the cornea or an appropriately shaped lens; 
           [0019]      FIG. 2  is a schematic diagram illustrating a plan view of a point cloud as obtained with a corneal image capture system; 
           [0020]      FIG. 3  is a schematic plan view similar to  FIG. 2  illustrating a plurality of splines and how they are connected through the data points of the point cloud; 
           [0021]      FIG. 4  is a perspective view of a cornea matching surface illustrating how characterizing curves are constructed; 
           [0022]      FIG. 5  is a diagram exemplifying the axial focus scatter of a cornea at a 3 millimeter diameter. 
           [0023]      FIG. 6  illustrates the radial focus scatter corresponding to  FIG. 5 ; 
           [0024]      FIG. 7  is a diagram exemplifying the axial focus scatter of a cornea at a 5 millimeter diameter; 
           [0025]      FIG. 8  illustrates the radial focus scatter corresponding to  FIG. 7 ; 
           [0026]      FIG. 9  is a diagram exemplifying the axial focus scatter of a cornea at a 7 millimeter diameter; 
           [0027]      FIG. 10  illustrates the radial focus scatter corresponding to  FIG. 9 ; 
           [0028]      FIG. 11  illustrates a method for modifying the corneal model by orthogonalizing to the central axis; 
           [0029]      FIG. 12  illustrates the concept of decentered orthogonalization; and 
           [0030]      FIGS. 13-15  are plan views of the macula showing the 72 focus points P distributed in spiral, rose and dual rose patterns, respectively, on the anterior surface of the macula. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0031]    A process for achieving laser ablation of the cornea and contact lens shaping in accordance the present invention is illustrated in block diagram form in  FIG. 1 . The process makes use of a Corneal Image Capture System  610 , an Elevation Analysis Program  620 , a Computer Aided Design System  630 , a Command Processor  640  and a Cornea Shaping System  650 . The Corneal Image Capture System  610 , in conjunction with the Elevation Analysis Program  620 , generates a three dimensional topographic map of the cornea of the patient. The Computer Aided Design System  630  is used as an aid in editing or modifying the corneal topographic data, to create a surface model, and data relating to the model is sent to a Cornea Shaping System  650  via the Command Processor  640 . The Command Processor  640  uses the topographic data describing the surface of the cornea to be shaped from the Computer Aided Design System  630  to generate a sequence of commands/control signals required by the Cornea/Lens Shaping System  650 . The Cornea/Lens Shaping System  650  accepts, from the Command Processor  640 , a sequence of commands that describe the three dimensional movements of the Cornea/Lens Shaping System (any coordinate system may be used; e.g., Cartesian, radial or spherical coordinates) to shape the cornea or machine (e.g. a lathe) manufacturing a contact lens. 
         [0032]    The Corneal Image Capturing System  610  and the Elevation Analysis Program  620  are preferably components of the PAR® Corneal Topography System (“the PAR® System”), which is available from PAR Vision Systems. The Elevation Analysis Program  620  is a software program executed by a processor, for example an IBM™ compatible PC. Program  620  generates a third dimension element (a Z coordinate representing distance away from a reference plane inside the eye) for each of a plurality of sample points on the surface of the cornea measured by system  610 . Each point is defined by its X-Y coordinates as mapped into the reference plane, and its Z coordinate is determined from brightness of the point. One method of calculating the elevation of each point, i.e., the Z coordinate, is by comparing the X-Y and brightness values measured from the patient&#39;s cornea  14  with the coordinates and brightness of some reference surface with known elevation, e.g., a sphere of a known radius. The reference values can be pre-stored. 
         [0033]    The final output of the Elevation Analysis Program  620  is the X-Y-Z coordinates for a multiplicity of sample points, commonly known as a point cloud, on the surface of the cornea  14 . It will be apparent to those skilled in the art that any method can be used that can generate X, Y, Z corneal data providing both location and elevation information for points on the corneal surface with the required accuracy. In the preferred embodiment about 1200 points are spaced in a grid pattern, as viewed in the X-Y plane, so the projections of the points into the X-Y plane are about 200 microns apart. 
         [0034]    The X-Y-Z data output from the Elevation Analysis Program  620  can be formatted in any number of well-known machine-specific formats. In the preferred embodiment, the data are formatted in Data Exchange File (DXF) format, an industry standard format which is typically used for the inter-application transfer of data. A DXF file is an ASCII data file, which can be read by most computer aided design systems. 
         [0035]    Referring now to  FIGS. 2 and 3 , a point cloud  100  is depicted as it would appear when viewing the reference plane along the Z-axis (i.e., as projected into the X-Y plane). Each point corresponds to a particular location on the patient&#39;s cornea. The data are usually generated from an approximately 10 mm×10 mm bounded area of the cornea, the working area. Thus, there may be as many as 50 rows of data points. A surface  108  (see  FIG. 4 ) that models or matches the topography of the surface of the patient&#39;s cornea is generated by the computer aided design system  630  from the data points generated by the Elevation Analysis Program. In a preferred embodiment, Computer Aided Design System  630  is the Anvil 5000™ program which is available from Manufacturing Consulting Services of Scottsdale, Ariz. 
         [0036]    Cornea matching surface  108  is preferably produced by first generating a plurality of splines  102 , each defined by a plurality of the data points of the point cloud  100 . The generation of a spline that intersects a plurality of data points (i.e., knot points) is, per se, known to those skilled in the art and can be accomplished by the Anvil 5QQQ™ program once the input data have been entered. For more information regarding the generation of a surface model, see U.S. Pat. No. 5,807,381, the disclosure of which is incorporated herein by reference in its entirety. In a preferred embodiment, the known non-uniform rational B-spline formula is used to generate the splines, but they could be generated by other well-known mathematical formulas for splines, such as the cubic spline formula or the rational uniform B-spline formula. As illustrated in  FIG. 3 , in a preferred embodiment, each of the splines  102  lies in a plane that is parallel to the X and Z axes and includes a row of points from the cloud  100  in  FIG. 3 . 
         [0037]    Surface  108 , which matches the corneal surface of the scanned eye, is then generated from splines  102 . There are a number of well-known mathematical formulas that may be used to generate a surface from a plurality of splines  102 . In the preferred embodiment, the well known nurb surface equation is used to generate a corneal surface from splines  102 . In the embodiment, because the scanned area of the eye is approximately 10 mm×10 mm, approximately 50 splines  102  are created. As illustrated in  FIG. 3 , a skinned surface segment  104  is created for a small number (e.g., five) of the adjacent splines. Adjacent skinned surface segments  104  share a common border spline. Thus, about ten skinned surface segments are generated from the point cloud and are then merged together by the Anvil 5000™ program in a manner known to those skilled in the art, to produce one composite surface  108 . 
         [0038]    Neither the original data points, nor the knot points of splines  102  necessarily lie on-surface  108 , owing to the mathematical generation of the surface when using the nurb surface equation formula. However, the surface  108  estimates those points within a predefined tolerance. 
         [0039]    The HIGH point on the generated corneal matching surface  108  (i.e., the point having the greatest Z value) is determined. A cylinder  106  of a predetermined diameter is then projected onto the corneal matching surface  108  along an axis which is parallel to the Z-axis and passes through the HIGH point. Cylinder  106  preferably has a diameter of about 3 mm to about 8 mm, typically about 7 mm, and the closed contour formed by the intersection of cylinder  106  with surface  108  projects as a circle  106 ′ in the X-Y plane. On the matching surface  108 , this contour defines the outer margin  26  of the working area of the cornea. The cornea is the most symmetric and spherical about the HIGH point and, therefore, provides the best optics at this point. 
         [0040]    The outer margin  26  must fit within the point cloud, so that the surfaces of the cornea can be formed based on the measured corneal data. The computer aided design system  630  can then illustrate a default circle  106 ′ (in the X-Y plane) with respect to the point cloud, for example on a monitor screen, so that the operator can be assured that circle  106 ′ falls within the point cloud. Additionally, system  630  can be set up to determine if circle  106 ′ falls within point cloud  100  and, if it does not fall completely within point cloud  100 , to alert the user to manipulate the circle (i.e., move the center point and/or change the radius of the circle) so that circle  106 ′ lies within the corneal data point cloud  100 . In a worst case scenario, the eye should be rescanned if insufficient data is available from the scanned eye to ensure that the working area of the cornea will fit properly within the point cloud. Alternatively, the area of the point cloud can be made larger. 
         [0041]    It is to be understood that circle  106 ′ is only a circle when viewed in the X-Y plane (i.e., looking along the Z-axis). Actually, the periphery  26  is approximately elliptical and lies in a plane which is tilted relative to the reference plane. A line Perpendicular to this tilted plane which passes through the HIGH point will be referred to as the “LOCAL Z-AXIS” or “tilted axis”, and the tilt of the tilted plane relative to the reference plane will be considered the tilt angle of the working area of the cornea. 
         [0042]    The cornea is about 600 pm thick. In most corneal ablation procedures, less than 100 pm depth of cornea is ablated because there is virtually no risk of scarring with the type of lasers that are typically used. Beyond the 100 pm depth, there is a risk of scar-like imperfections. For example, 120 pm depth ablation is known to cause scarring. However, there exists the possibility that the risk of scarring for surface ablations may be reduced by drug therapy prior to or contemporaneous with the laser treatment. However, most of today&#39;s laser surgery does not cause scarring, as most procedures are under the LASIK flap. The fear in LASIK is ablating too deep wherein the residual bed is less than −250 pm. If the bed is less than this amount, structural failure can occur. The magnitude of the corneal undulations is typically about fifteen to twenty microns from the crest of a hill to the trough of a valley and may be as great as about thirty microns. 
         [0043]    Surgical procedures performed in accordance with the present invention and optical lenses manufactured in accordance with the invention, in addition to relieving macular degeneration, will seek to correct the patient&#39;s vision in accordance with the required corrections established in a “refraction test.” When this test is performed, the patient sits in chair which is fitted with a special device called a “phoropter”, through which the patient looks at an eye chart approximately 20 feet away. As the patient looks into the phoropter, the doctor manipulates lenses of different strengths into view and, each time, asks the patient whether the chart appears more or less clear with the particular lenses in place. In practice, the doctor is able to vary the power or diopter correction about two orthogonal axes, as well as the degree of rotation of those axes about a Z-axis along the line-of-sight. The doctor continues to modify these three parameters until he achieves the optimum vision. The results of the refraction test are usually given in the form “a, b, c”, where “a” is the diopter correction at the first axis, “b” is the additional diopter correction required at the second, orthogonal axis, and “c” is the angle of rotation of the first axis relative to the horizontal. This form of information is given for each eye and is immediately useful in grinding a pair of lenses for eyeglasses. 
         [0044]    For the purposes of the present invention, it is preferred to perform a modified form of refraction test. For this modified form of refraction test, the eye doctor adjusts the phoropter at a series of equally spaced angles, say every 15° from the horizontal, and obtains the optimum refraction at each angle. Typically, the more angles that are measured, the better the results. The manner of using the modified refraction test will be described in detail below. 
         [0045]    There will now be described a technique for generating characterizing curves on surface  108 , which will be useful below. A plane  110  is constructed which contains the LOCAL Z-AXIS (See  FIG. 4 ). The intersection between plane  110  and surface  108  defines a first characterizing curve  112 . Plane  110  is then rotated about the LOCAL Z-AXIS, for example by a 5° increment counterclockwise, as represented by line  114 , where its intersection with surface  108  defines a second characterizing curve  116 , which is illustrated as a dashed line in  FIG. 4 . This process continues at fixed rotational increments about the LOCAL Z-AXIS, for example every 5°, until plane  110  has swept 360°, to produce a complete set of characterizing curves (meridians), in this case seventy-two (360° % 5°). 
         [0046]    Each of these characterizing curves is then estimated by a best-fit spherical (circular) arc. One manner of doing this is simply to select a circular arc which passes through three known points for each curve (e.g. the point at which it touches the contour  106 ′, the HIGH point, and that point which is halfway between those two points when viewed in projection along the local Z axis). Once the spherical arcs are generated, the focal point of a portion of the cornea represented by a circular arc can be estimated by the center of that arc. Techniques for locating the center of a spherical arc are well-known. The resulting set of arc centers then provides a representation of focus scattering. 
         [0047]    For purposes of illustration, the preceding procedure was performed on the corneal model of a patient having 20/15 uncorrected visual acuity. 
         [0048]      FIG. 5  is a focus scatter diagram along the LOCAL Z-AXIS for that portion of the cornea extending out to a 3.0 mm diameter. In this case, the focal points start at 7.06 mm along the LOCAL Z-AXIS and extend out an additional 6.91 mm.  FIG. 6  illustrates that the radial scatter within a 3 mm diameter is 1.2 mm. Similarly,  FIG. 7  illustrates that the axial focus scatter of a 5 mm diameter portion of the cornea begins at 8.99 mm and extends for an additional 1.69 mm. As shown in  FIG. 8 , the radial scatter of the same portion of the cornea is 0.49 mm.  FIG. 9  illustrates that the axial focus scatter at 7 mm begins at 8.68 mm and extends axially for an additional 0.47 mm, whereas  FIG. 10  illustrates that the corresponding radial scatter is 0.33 mm. Clearly, focus scatter is most severe in the central portion of the cornea, and decreases significantly as larger portions of the cornea are considered. 
         [0049]    Therefore, it would clearly be desirable to reduce or eliminate the focus scatter at least in central portions of the cornea. However, for the purpose of relieving macular degeneration, it must not be eliminated entirely, but must be closely controlled. 
         [0050]    In accordance with the present invention, this is accomplished by “orthogonalizing” at least a portion of the cornea. The term “orthogonalizing” refers to a re-shaping of the surface model so as to piecewise re-focus the cornea towards the LOCAL Z-AXIS. The re-shaped surface model can then be applied to the cornea (e.g. through ablation) or to shape the posterior surface of a contact lens (or another type of optical lens) so as to achieve the required focus scatter correction. It has been found that orthogonalizing the cornea not only reduces radial focus scatter, but simultaneously reduces axial focus scatter substantially and produces more uniformity in the radius of curvature of the orthogonalized portion of the cornea. 
         [0051]      FIG. 11  illustrates the process of orthogonalization. The process is carried out on each of the arcs which represent characteristic curves, in the manner explained below. After this piecewise refocusing, the modified arcs are reassembled into a modified surface model having the refocused characteristics. 
         [0052]    In  FIG. 11 ,  130  represents one of the half-meridian arcs corresponding to a characterizing curve. Arc  130  has a center point C, the location of which has been exaggerated to demonstrate focus which is radially spaced from the LOCAL Z-AXIS. Orthogonalization of arc  130  begins with creating a chord  132  between the two ends of the arc. A perpendicular bisector  134  of chord  132  may be constructed, and it will pass through point C and intersect the LOCAL Z-AXIS at a point X. Using the distance of point X from point H (the HIGH point) as a radius, a new arc  130 ′ can now be drawn between the two end points of arc  130 . Arc  130 ′ will be focused on the LOCAL Z-AXIS and will have a larger radius of curvature than arc  130 . 
         [0053]    At this point, arc  130 ′ could be accepted as an arc defining the modified surface model  108 ′. However, it would be desirable to avoid too great a change in the thickness of the cornea. Accordingly, a certain threshold is defined (for example 0.0075 mm), and if any portion of arc  130 ′ is more than a distance inside or outside the surface  108 , arch  130 ′ is not accepted for use in the modified surface model. Instead, point x can be moved up or down on the LOCAL Z-AXIS (depending upon which direction arch  130 ′ needs to be moved) by half the excess over. Arc  130 ′ can then be re-drawn and re-tested against the threshold. This readjustment and testing continues until an acceptable arc  130 ′ has been found. Then, the next arc is orthogonalized. After all of the arcs are orthogonalized, a new surface model  108 ′ is created based upon all of the arcs. 
         [0054]    As has been explained above, the orthogonalization process is applicable to corneal ablation procedures. Prior to the procedure, a corrected corneal surface model is generated, which is shaped to provide relief from macular degeneration and correction of refraction established by an eye test (as described in the patents cited above), and all the arcs are orthogonalized. The corrected corneal surface model is then registered with the unmodified corneal surface model, and it is moved towards the unmodified surface until the corrected surface just contacts the unmodified surface. If the point of initial contact is at the center of the corrected surface, it is moved toward the uncorrected surface until the periphery of the corrected surface just contacts the uncorrected surface. If the point of initial contact is at the periphery of the corrected surface, it is moved toward the uncorrected surface until the center of the corrected surface just contacts the uncorrected surface. The corrected surface will then be displaced so that it is, at least partially, inside the cornea, and the cornea is ablated until the displaced corrected surface becomes its new surface. 
         [0055]    This procedure can be expected to reduce substantially the amount of material removed from the cornea, in comparison to all prior ablation techniques. 
         [0056]    The central region of the retina is called the macula, and the very center of the macula, called the foveola, is the most sensitive. The macula typically has a diameter in the range of 6 to 7 millimeters, and the foveola typically has a diameter of about 0.35 mm. With perfect orthogonalization, all sub-portions of the cornea are refocused to the center of the macula, the foveola. However, this is the area usually affected by macular degeneration first, so it becomes necessary to spread the focus points away from the foveola while still controlling them. When orthogonalization is performed by refocusing all of the sub-regions onto the LOCAL Z-AXIS, orthogonalization is not perfect. The sub-portions of the cornea still focus on different points of the macula; some relief from macular degeneration is achieved. However, further adjustment of orthogonalization appears to be necessary in order to compensate effectively for macular degeneration. 
         [0057]    In accordance with the present invention, sub-portions of the cornea are refocused so as to place their focal points outside the foveola yet still within the macula at a controlled distance from the LOCAL Z-AXIS. The macula has approximately the shape of a cap-shaped segment of a sphere, is usually between 6 millimeter and 7 millimeters in diameter and is approximately 0.88 millimeters deep. Optimum correction for macular degeneration is achieved when all sub-portions of the cornea are focused so as to make use of portions of the macula which are not affected by macular degeneration. 
         [0058]    The difference should be kept in mind between introducing de-focus and the decentered focus of the invention. Ophthalmologists have long known that, in prescribing corrective lenses, distance focus can be reduced through de-focus, and a benefit in near vision can result. In accordance with the present invention, there is no de-focus. All sub-portions of the cornea are fully focused, but the focus point is moved away from an axis passing through the foveola, thereby achieving correction for macular degeneration. 
         [0059]      FIG. 12  illustrates the concept of decentered orthogonalization. The arc  130  is a sub-portion of the cornea which has a scattered focal point X. Ordinary orthogonalization as shown in  FIG. 11  would move the focal point X to the LOCAL Z-AXIS, LZ. Perfect orthogonalization would move it to the foveola F on the macula M. Decentered orthogonalization creates a new arc  130 ′″ which focuses at a point X′, which is at a predefined radius r from the foveola. The axis Z′ is parallel to the LOCAL Z-AXIS and passes through the point X. For purposes of estimation, the macula can be considered flat in the region between the axes LZ and Z′. 
         [0060]    The preferred manner of performing decentered orthogonalization utilizes the technique discussed with respect to  FIG. 4 . Specifically, the anterior surface of the cornea is broken down into 72 arcs spaced 5° apart rotationally, and each arc is subjected to decentered orthogonalization. In order to achieve effective correction for macular degeneration, the  72  resulting focus points should be well distributed in a working region W′ of the foveola which preferably has a diameter less than 0.07 millimeters.  FIG. 13  is a top plan view of the foveola showing the 72 points P distributed in a spiral pattern on the surface of the foveola. 
         [0061]    A more preferred configuration for the points is illustrated in  FIG. 14 . This pattern is described by the polar equation R=a·cos 2e, where R is the two-dimensional radius of the point from the foveola, a is a constant selected to spread the points well over the entire working area M′, and e is the rotational angle of the particular arc on the cornea. This pattern is preferred to the spiral, because every quadrant of the working area M′ has focus points at a full range of distances from the foveola. 
         [0062]    Another preferred pattern for the focus point is illustrated in  FIG. 14 . In this case, the pattern is formed from two overlaid rose patterns, a large one  150  and a small one  150 ′, which is offset by 45° from the pattern  150 . Only one petal of each rose pattern is shown to have points, but it will be understood that each of the other petals is similarly provided with points. The points are shared evenly between the patterns  150  and  150 ′. However, the pattern  150  provides the outermost points and has points distributed at over its outermost two-thirds. Pattern  150 ′ provides the innermost points and has them evenly distributed. As a result, the pattern in  FIG. 14  provides a good distribution of points near to and distant from the foveola. 
         [0063]    It should be appreciated that, in all the focus point patterns that have been shown, in most instances the points are equally spaced along a curve. However, those skilled in the art will appreciate that unequal spacing could be provided for the points so as to concentrate them more in a specific region (e.g. the center or the outermost area of the working region. 
         [0064]    A further method, defining a further embodiment of the invention, has been developed for decentered orthogonalization which is preferred over all those described previously for dealing with the effects of macular degeneration. The method proceeds exactly as in the  FIG. 11 , except that once arc  130 ′ has been reshaped, it is tilted clockwise so as to move the point X, the endpoint of the arc&#39;s axis, to the left, across the local z-axis so that it lies at a preselected distance from the local z-axis. At present, the preferred distance is approximately 0.01 mm. However, distances in the range of approximately 0.0025 mm to approximately 0.01 mm would still be effective to overcome the effects of macular degeneration. 
         [0065]    In accordance with yet a further embodiment, the lens may be constructed as explained with respect to any of  FIGS. 11-15 , and so that its position relative to the cornea is rotated circumferentially so as to tilt the local z-axis relative to the position shown and  FIGS. 11 and 12 . Preferably, the tilt of this axis is less than approximately 5°. Modern analysis methods permit an ophthalmologist to determine those areas of the macula which remain functional. After making such a determination, the lens construction orientation is modified, as explained above, so that local z-axis is tilted sufficiently to move the image produced by the lens off-center and onto a functional portion of the macula. The computer aided design system  630  ( FIG. 1 ) can achieve such rotation of the entire structure by methods that are well-known. 
         [0066]    Although preferred embodiments of the invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that many additions, modifications, and substitutions are possible without departing from the scope and spirit of the invention. For example, the present invention is applicable not only to corneal ablation and contact lenses, but to any other kind of lens, including cataract, phakic, intraocular, intracorneal and spectacle lenses.