Abstract:
A method and system are provided for eroding or ablating a shaped volume of an eye&#39;s corneal tissue in accordance with the treatment of a specified eye condition. To determine the laser beam shot pattern, a plurality of laser beam shots of uniform intensity are first selected to form a uniform shot pattern of uniform shot density. The laser beam shots applied in accordance with the uniform shot pattern of uniform shot density would be capable of eroding a volume of the corneal tissue of uniform height. The volume of uniform height is approximately equivalent to that of the shaped volume. The laser beam shots are applied to the corneal tissue in a spatially distributed pattern spread over an area approximately equivalent to the surface area of the shaped volume to be eroded. The spatially distributed pattern extends the uniform shot pattern in fixed angles from a reference position on the shaped volume representative of the shaped volume&#39;s axis of symmetry. Shot density for the laser beam shots changes in correspondence with distance from the reference position.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. Ser. No. 08/232,956, filed Apr. 25, 1994, now U.S. Pat. No. 5,849,006 commonly owned and assigned with the present invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to ophthalmic laser surgery, and more particularly to a method and system for arranging a pattern of laser shots to erode a shaped volume of corneal tissue in accordance with the treatment of a specified eye condition. 
     BACKGROUND OF THE INVENTION 
     Photorefractive keratectomy (PRK) is a procedure for laser correction of focusing deficiencies of the eye by modification of corneal curvature. PRK is distinct from the use of laser-based devices for more traditional ophthalmic surgical purposes, such as tissue cutting or thermal coagulation. PRK is generally accomplished by use of a 193 nanometer wavelength excimer laser beam that ablates away corneal tissue in a photo decomposition process. Most clinical work to this point has been done with a laser operating at a fluence level of 120-195 mJ/cm 2  and a pulse-repetition rate of approximately 5-10 Hz. The procedure has been referred to as “corneal sculpting.” 
     Before sculpting of the cornea takes place, the epithelium or outer layer of the cornea is mechanically removed to expose Bowman&#39;s membrane on the anterior surface of the stroma. At this point, laser ablation at Bowman&#39;s layer can begin. An excimer laser beam is preferred for this procedure. The beam may be variably masked during the ablation to remove corneal tissue to varying depths as necessary for recontouring the anterior stroma. Afterward, the epithelium rapidly regrows and resurfaces the contoured area, resulting in an optically correct (or much more nearly so) cornea. 
     For ablation to occur, the energy density of the laser beam must be above some threshold value, which is currently accepted as being approximately 60 mJ/cm 2 . Such energy densities can be produced by a wide variety of commercially available lasers. For example, a laser could be used that is capable of generating a laser beam of diameter large enough to cover the surface to be ablated, i.e., on the order of 4.5-7.0 millimeters in diameter. However, such laser beams are typically not regular in intensity thereby causing a rough surface ablation. Further, lasers capable of producing such laser beams are typically, large, expensive and prone to failure. 
     Alternatively, a laser could be used that produces a much smaller diameter laser beam, i.e., on the order of 0.5-1.0 millimeters in diameter. There are several advantages afforded by the smaller diameter laser beam. They can be generated to meet the above noted threshold requirement with a lower energy pulse than that of the larger diameter beam. Further, such smaller diameter laser beams can be produced with a regular intensity while minimizing the variance in pulse-to-pulse energy levels. Finally, lasers producing the smaller diameter laser beam are physically smaller, less expensive and, frequently, more reliable. However, this requires that the position of the small pulses be precisely controlled so that the resulting ablated surface is smoother than that which is produced by the larger laser beam. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the present invention to provide a method and system of laser sculpting suitable for the recontouring of corneal tissue. 
     Another object of the present invention is to provide a method and system for arranging a pattern of small diameter, regular intensity laser pulses or shots to erode or ablate a shaped volume of corneal tissue in accordance with the treatment of a specific eye condition. 
     Still another object of the present invention is to provide a method and system of laser sculpting that is designed to use small inexpensive lasers. 
     Other objects and advantages of the present invention will become more obvious hereinafter in the specification and drawings. 
     In accordance with the present invention, a method and system are provided for eroding or ablating a shaped volume of an eye&#39;s corneal tissue in accordance with the treatment of a specified eye condition. A plurality of laser beam shots of uniform intensity are selected to form a uniform shot pattern of uniform shot density. If the laser beam shots were applied in accordance with the uniform shot pattern of uniform shot density, they would be capable of eroding a volume of the corneal tissue of uniform height. The volume of uniform height is approximately equivalent to that of the shaped volume. The laser beam shots are actually applied to the corneal tissue in a spatially distributed pattern spread over an area approximately equivalent to the surface area of the shaped volume to be eroded. The spatially distributed pattern is obtained by distorting the uniform shot pattern in a fixed manner from a reference position on the shaped volume representative of the shaped volume&#39;s axis of symmetry. Shot density for the laser beam shots changes in correspondence with distance from the reference position. The particular spatial distribution and change in shot density is adjusted to treat the eye conditions of myopia, hyperopia and astigmatism. 
     This patent application is copending with related patent applications entitled “Laser Beam Delivery and Eye Tracking System” filed on the same date and owned by a common assignee as subject patent application. The disclosures of these two applications are incorporated herein by reference. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a diagrammatic view of an eye showing a meniscus shape of corneal tissue associated with the condition of myopia that is to be ablated volumetrically in accordance with the present invention; 
     FIG. 1B is an enlarged isolated view of the meniscus of FIG. 1A; 
     FIG. 2 is an isolated view of the meniscus of FIG. 1A shown in comparison to a cross-section of a uniform cylinder dimensioned to have the same volume as that of the meniscus in accordance with the operation of the present invention; 
     FIG. 3 is a diagrammatic view of an eye showing a shape of corneal tissue associated with the condition of hyperopia that is to be ablated volumetrically in accordance with the present invention along with a cross-section of a uniform cylinder dimensioned to have the same volume as that of the volume represented by the shape; 
     FIG. 4 is a diagrammatic perspective view of the treatment zone of an eye showing a shape of corneal tissue associated with the condition of astigmatism that is to be ablated volumetrically in accordance with the present invention along with a uniform rectangular prism dimensioned to have the same volume as that of the volume represented by the shape; 
     FIG. 5 is a block diagram of the laser sculpting system in accordance with the present invention; 
     FIG. 6 depicts diagrammatically an arrangement for the projection optics of the present invention; and 
     FIG. 7 illustrates diagrammatically an optical arrangement of mirrors used to produce translational shifts in a light beam along one axis of translation. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the drawings, and more particularly to FIG. 1A, a diagrammatic view is shown of an eye designated generally by reference numeral  10 . Eye  10  has a meniscus of surface material, i.e., corneal tissue, as indicated by hatched area  11 , that is to be eroded by a small diameter laser beam (e.g., on the order of 0.5-1.0 millimeters in diameter) in accordance with the present invention. By way of example, meniscus  11  represents a shaped volume of corneal tissue, symmetrical about visual axis  12 , that is to be eroded to correct the condition of myopia. Accordingly, the thickness T(r) of meniscus  11  is maximum at visual axis  12 , i.e., r=0, of eye  10  and decreases to zero at the outside edge, i.e., r=r A , of meniscus  11 . However, it is to be understood that the method and system of the present invention are applicable for other eye conditions such as hyperopia and astigmatism as will be explained further below. 
     As is known in the art, either direct or indirect measurements can be made to determine the radius curvature R i . of outside surface  11   i  of meniscus  11  (i.e., the corneal surface of eye  10  prior to laser treatment). The radius of curvature R D  of inside surface  11   D  of meniscus  11  (i.e., the corneal surface of eye  10  after laser treatment) is known based on the desired refractive correction. The radius of aperture r A  of meniscus  11  (i.e., the treatment or optical zone) is defined by the doctor. Given these values, it is possible to determine the volume of meniscus  11  as follows for any radius of aperture r, 0≦r≦r A . 
     The meniscus volume out to a radius r is the algebraic sum of the volume of cylinder  110  of radius r and thickness T(r), plus the volume of spherical cap  112  of center thickness t ci , minus the volume of spherical cap  114  of center thickness t cD  (which is included in cylinder  110 ). This is best seen in FIG. 1B where meniscus  11  is enlarged and shown in isolation. The volumes V ci  and V cD  of caps  112  and  114 , respectively, are                v   ci     =     π   *     t   ci   2     *     (       R   i     -       t   ci     3       )               (   1   )                                
     and                v   cD     =     π   *     t   cD   2     *     (       R   D     -       t   c     3       )               (   2   )                                
     and the thickness T(r) of cylinder  110  is 
      T(r)=(h i −B i )−(h D −B D )  (3) 
     where 
     
       
         h i ={square root over ((R i   2 +L −r 2 +L ))}  (4) 
       
     
     
       
         h D ={square root over ((R D   2 +L −r 2 +L ))}  (5) 
       
     
     
       
         B i ={square root over ((R i   2 +L −r A   2 +L ))}  (6) 
       
     
     and 
     
       
         B D ={square root over ((R D   2 +L −r A   2 +L ))}  (7) 
       
     
     Substituting equations (4)-(7) into equation (3), T(r) becomes a function of r, r A , R i  and R D . The volume V cl  of cylinder  110  is thus 
     
       
         V cl =π*r 2 *T(r,r A ,R i ,R D )  (8) 
       
     
     and the volume of meniscus  11  at a radius r is 
     
       
         V r =V cl +V ci −V cD .  (9) 
       
     
     Since the volume of material ablated by each laser beam shot is known in advance, the number of laser beam shots N required to ablate meniscus  11  is easily calculated using the volume of meniscus  11 . Further, the local shot density at visual axis  12 , where r=0 to yield thickness T(0), is easily calculated. 
     The method of the present invention begins by selecting a uniform pattern such that if the N laser beam shots were applied with a uniform shot density over the uniform pattern, a cylinder of height T(0) would be ablated. The volume of such a cylinder would be equal to the volume of meniscus  11  and its radius would be r D  where r D &lt;r A . This is depicted in FIG. 2 where a cross-section of cylinder  20  of radius r D  and height T(0) is shown in comparison to meniscus  11 . 
     To achieve the desired ablation of meniscus  11 , the N laser beam shots must be spatially distributed to obtain smooth transitions between the resulting surface ablations. Conceptually, the present invention first fixes the local area density of laser beam shots at the axis of symmetry of meniscus  11 , i.e., visual axis  12 , to be equal to that of the uniform shot density represented by cylinder  20 . The shot density represented by cylinder  20  is then stretched or extended radially from visual axis  12  over the surface area formed by surface  11   i  out to r A  while steadily decreasing the laser beam shot density. The angles between each shot position in the uniform pattern of cylinder  20  and the actual pattern incident on eye  10  remain the same. In other words, the extension of shot positions occurs only in the radial direction. 
     The thickness of meniscus  11  at any radius r or T(r) is proportional to its local area density of laser beam shots. The center value of T(r) at r=0 is equal to the height of cylinder  20 . As the positions of the shot pattern on cylinder are extended radially, the center height or shot density remains unchanged and the local area density at other points must be determined. The relationship between any radius r of meniscus  11  and r D  is                  ∫   r   0            V        (   u   )                          u         =       T        (   0   )       *   π   *     r   D   2               (   10   )                                
     where du is the differential volume of the meniscus as a function of r which is the integration variable. This relationship may be digitized for ease of processing as follows. 
     Take a series of values r j , j=1, 2, . . . j max  where r j max =r A , and dr=(r j+1 −r j ). Further, let the corresponding values of r D  be called r Dj . Then                  ∑   0     (     j   -   1     )                         V        (     r   k     )          dr       =         T        (   0   )       *   π   *     r   Dj   2       =     π   *     T        (   0   )       *       ∑   0     (     j   -   1     )                       r   Dk   2                   (   11   )                                
     If r is extended over n equal steps, where n is selected to be as large as possible to minimize error, then dr=r A /n and r j =j*dr. Then, 
     
       
         π*T(0)*r Dk   2 =V(k*dr)=V(k*r A /n)  (12) 
       
     
     where k=0, 1, 2, . . . , n. 
     Since the volume meniscus  11  at any radius r can be determined using equation (9), equation (12) can be solved for r Dk  and the radius of cylinder  20  is extended to r k . Thus, the ratio r K /r Dk  is the desired stretch factor. The effect of the “stretch” is to decrease the density of the laser beam shots as the radial distance from the center of the eye increases. The gradually changing laser beam shot density, combined with a small ablation volume brought about by the use of a small diameter laser, provides for smooth transition from the thick portion of meniscus  11  to the thin portion of meniscus  11 . At a wavelength of 193 nanometers and a fluence of 160 mJ/cm 2 , each pulse ablates the corneal surface to a depth of about 0.25 μm. By distributing laser shot density in accordance with the above described procedure, the resulting ablated corneal surface is very smooth. 
     For the eye condition known as hyperopia, the present invention determines and applies the required laser beam shot pattern in a fashion very similar to that just described for the case of myopia. In the case of hyperopia, the surface of the eye&#39;s cornea is too flat and needs to be made steeper, i.e., the corneal radius of curvature must be decreased. Referring to FIG. 3, a diagrammatic view is shown of hatched shape  31  which is representative of a volumetrically symmetric shape about visual axis  12 . The volume represented by shape  31  must be ablated from eye  10  (which has been shown in dotted line form in order to highlight shape  31 ) in order to correct the condition of hyperopia. The total volume of shape  31  and number of laser beam shots N required to ablate same is first determined. Then, a uniform shot pattern of uniform shot density is selected such that cylinder  40  (shown in cross-section) of uniform height and a radius equal to that of shape  31  would be formed if the uniform shot pattern were applied to corneal tissue. 
     To achieve the desired ablation of shape  31 , the N laser beam shots must be spatially distributed to obtain smooth transitions between the resulting surface ablations. Conceptually, this is achieved by redistributing the uniform shot density represented by cylinder  40 . The local area density of laser beam shots at the axis of symmetry, i.e. visual axis  12 , is decreased to zero while shot density is steadily increased in a fixed angle radial fashion out to the perimeter of shape  31 . Thus, the final shot density profile will closely approximate that of shape  31  which is to be ablated. Depending on the amount of correction required, it may also be necessary to apply additional laser beam shots to eye  10  just beyond the treatment zone represented by shape  31  in order to provide a smooth transition between the treated and untreated portions of eye  10 . 
     Both the myopia and hyperopia conditions require that a volume of corneal tissue be removed which is radially symmetric about the eye&#39;s visual axis. However, the condition known as astigmatism is different in that it has an axis of symmetry in the plane perpendicular to the eye&#39;s visual axis. Further, the correction for astigmatism assumes that the surface of the eye is flat. This is shown diagrammatically in the perspective view of FIG. 4 where the flat surface of the eye that is to be treated, i.e., the treatment zone, is represented by dotted line  14 . The correction requires that portion  51  of a cylinder be removed from the cornea. Portion  51  has a thickness that is T 0  along its central axis  52  and decreasing out to its perimeter. Once again, the volume of corneal tissue to be removed and number of laser beam shots N required to do so is first determined. Then, a uniform shot pattern of uniform shot density is selected such that rectangular prism  60  having central longitudinal axis  62  would be generated by the N laser beam shots. Rectangular prism  60  has a uniform height H that is equivalent to the thickness T 0  along the central axis of portion  51 . The length L of rectangular prism  60  should be sufficient to span the diameter of treatment zone  14 . 
     To achieve the desired ablation of portion  51 , the N laser beam shots must be spatially distributed to obtain smooth transitions between the resulting surface ablations. Conceptually, this is achieved by redistributing the uniform shot density represented by rectangular prism  60 . The local area density of laser beam shots at the axis of symmetry, i.e., central axis  52  of portion  51 , is set to be equal to the uniform shot density of rectangular prism  60 . Shot density is then gradually decreased to zero as the uniform shot pattern represented by rectangular prism  60  is stretched outward in opposite directions from center axis  62  in the plane perpendicular to visual axis  12 . Thus, the final shot density profile will closely approximate that of portion  51  which is to be ablated. Note that not all of the N laser beam shots are applied. In particular, the laser beam shots associated with portion  51  lying outside of treatment zone  14  are truncated. 
     The present invention may be further extended to the case of irregular astigmatism which is described by a generalized corneal shape having no overall axis of symmetry. In this case, the overall volume to be eroded may be approximated by a multiplicity of locally symmetric volumes that are summed together. Each of the symmetric volumes is selected so that ablation thereof may be carried out in accordance with one of the above described methods. 
     To implement the above described procedures, a system  5  is shown in FIG. 5 in block diagram form. System  5  includes treatment laser  500  producing laser beam  502 , projection optics  510 , X-Y translation mirror optics  520  and beam translation controller  530 . Treatment laser  500  is typically a pulsed output laser. By way of example, it will be assumed that treatment laser  500  is a  193  nanometer wavelength pulsed excimer laser used in an ophthalmic PRK procedure performed on eye  10 . However, it is to be understood that the method and system of the present invention will apply equally as well to workpieces other than an eye, and further to other wavelength surface treatment or surface eroding lasers where it is desirable to erode a shaped volume of surface material. 
     Laser beam  502  is incident upon projection optics  510 . Projection optics  510  adjusts the diameter and distance-to-focus of beam  502  depending on the requirements of the particular procedure being performed. For the illustrative example of an excimer laser used in the PRK procedure, projection optics  510  includes planar concave lens  512 , and fixed focus lenses  514  and  516  as shown in the diagrammatic arrangement of FIG.  6 . Lenses  512  and  514  act together to form an A-focal telescope that expands the diameter of beam  502 . Fixed focus lens  516  focuses the expanded beam  502  at. the workpiece, i.e., eye  10 , and provides sufficient depth, indicated by arrow  518 , in the plane of focus of lens  516 . This provides flexibility in the placement of projection optics  510  relative to the surface of the workpiece. An alternative implementation is to eliminate lens  514  when less flexibility can be tolerated. 
     After exiting projection optics  510 , beam  502  impinges on X-Y translation mirror optics  520  where beam  502  is translated or shifted independently along each of two orthogonal translation axes as governed by beam translation controller  530 . Controller  530  is typically a processor programmed with a predetermined set of two-dimensional translations or shifts of beam  502  depending on the particular ophthalmic procedure being performed. Thus, controller  530  is programmed in accordance with one of the above described shot pattern distribution methods depending on the eye condition being treated. The programmed shifts of beam  502  are implemented by X-Y translation mirror optics  520 . 
     Each X and Y axis of translation is independently controlled by a translating mirror. As shown diagrammatically in FIG. 7, the Y-translation operation of X-Y translation mirror optics  520  is implemented using translating mirror  522 . Translating mirror  522  is movable between the position shown and the position indicated by dotted line  526 . Movement of translating mirror  522  is such that the angle of the output beam with respect to the input beam remains constant. Such movement is brought about by translating mirror motor and control  525  driven by inputs received from beam translation controller  530 . By way of example, motor and control  525  can be realized with a motor from Trilogy Systems Corporation (e.g., model T050) and a control board from Delta Tau Systems (e.g., model 400-602276 PMAC). 
     With translating mirror  522  positioned as shown, beam  502  travels the path traced by solid line  528   a . With translating mirror  522  positioned along dotted line  526 , beam  502  travels the path traced by dotted line  528   b . A similar translating mirror (not shown) would be used for the X-translation operation. The X-translation operation is accomplished in the same fashion but is orthogonal to the Y-translation. The X-translation may be implemented prior or subsequent to the Y-translation operation. 
     Although the invention has been described relative to a specific embodiment thereof, there are numerous variations and modifications that will be readily apparent to those skilled in the art in the light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced other than as specifically described.