Abstract:
An intraocular lens, with equal conic surfaces, is intended to replace the crystalline lens in the posterior chamber of a patient&#39;s eye, in particular after a cataract extraction. The lens provides optical power to focus objects onto a patient&#39;s retina. In addition the lens surfaces are shaped to reduce optical aberrations at the retina and are tolerant to lens tilt and decentration within the eye. The lens is designed to have zero longitudinal ray aberrations at a specific ray height.

Description:
This application claims the benefit of U.S. Provisional Application No. 60/690,664 filed Jun. 14, 2005. 
    
    
     BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The present invention pertains to intraocular lenses within the posterior chamber, and more particularly, to aspheric, conic, or prolate intraocular lenses within the posterior chamber.  
         [0003]     2. Description of Related Art  
         [0004]     It is often the case that an elderly patient will develop a condition called a cataract in the eye&#39;s crystalline lens. The cataract can develop to such a state that vision quality is significantly diminished to the point where surgical intervention is required to restore clear vision. In this surgical intervention, the crystalline lens containing the cataract is removed and an artificial lens is implanted. This artificial lens is called an intraocular lens (IOL). The IOL can be made of various materials, and its optical surfaces can be very simple such as planes, spheres, or torics, or the surfaces can be quite complex and even designed for a specific eye. The goal of the IOL design is, of course, to provide the patient with good vision quality. This means that the optical aberrations (deviation from a perfect focus) should be small. Over the last few decades the goal has been to provide the patient with a lens that significantly removes defocus and astigmatism. More recently, there has been an effort to remove other (higher-order) aberrations, such as spherical aberrations, through the IOL design.  
         [0005]     The eye can be considered as an optical system with its specific set of ocular aberrations. Since the normal cornea adds positive spherical aberration, it is possible to design an IOL with negative spherical aberration to reduce the normal eye&#39;s total spherical aberrations. If the lens is placed in the correct position and orientation in a normal eye, the spherical aberrations will be reduced as desired. This is the ideal situation. However, it is often the case that a patient&#39;s eye will have a cornea that has had refractive surgery such as LASIK, PRK, or RK. In addition, the lens may be decentered or tilted within the eye. In these non-ideal situations, the patient&#39;s vision will no longer have the desired improvement over the traditional spherical lenses. If the situation is far enough from the ideal, the patient&#39;s vision would have been better with a traditional spherical IOL rather than the “improved” IOL designed for reduction of spherical aberration.  
         [0006]     It is possible to consider a reasonable amount of IOL decentration and tilts during the design process and so develop an IOL that is more tolerant to these types of situations. Such considerations can lead to an IOL design where very little positive spherical aberrations are added to the positive spherical aberrations generated by the typical cornea. However, the IOL would not necessarily have the benefit of being an equal surface (both surfaces are the same) optic. Also, the amount of spherical aberration for the IOL should be the same for each lens power provided so that postoperative results are more predictable. This can be measured using the longitudinal ray aberrations for the IOL. It is the objective of the present invention to provide a foldable IOL design that retains the benefits of an aspheric IOL that reduces spherical aberrations and additionally, is an equal surface design and has the same longitudinal ray aberrations characteristic for each IOL power.  
       SUMMARY OF INVENTION  
       [0007]     In this section we describe how a foldable IOL can be designed with powers from −10 to +35 D (or larger range) with the characteristics that (1) the surfaces are equal, (2) provide the same longitudinal ray aberration characteristic for each lens power, and (3) add essentially zero spherical aberrations to the eye&#39;s ocular aberrations. In the preferred embodiment, parameters common to all powers of IOLs are: optical lens diameter of 5.75 mm, lens edge thickness of 0.35 mm, and material index of refraction of 1.4585 (polyhema). We refer to our lens design as the balanced aspheric IOL (B-IOL). 
     
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0008]      FIG. 1A  illustrates longitudinal aberrations for a marginal ray that intersects paraxial focus;  
         [0009]      FIG. 1B  illustrates longitudinal aberrations for a marginal ray height of 0.7071 times clear aperture radius;  
         [0010]      FIG. 2  illustrates the eye in cross section showing intersection of ray; and  
         [0011]      FIG. 3  illustrates geometry for ray tracing of marginal ray and calculation of longitudinal ray aberrations. 
     
    
     DETAILED DESCRIPTION  
       [0012]     Given that the B-IOL must have symmetric surfaces (design requirement) and the paraxial power of the lens is the labeled power, the only true design parameter is the conic coefficient K. It is possible to set the conic constant so that the marginal ray (which just clears the edge of the clear aperture of the lens) for a distant object intersects the paraxial focus. The distance between the intersection of the off-axis ray with the optical axis and the paraxial focus is called the longitudinal aberration of the ray. For the case of zero longitudinal aberration at the marginal ray, the longitudinal aberration across the semi-diameter is graphed in  FIG. 1 .A. Note that in  FIG. 1 .A, the aberration at ray height of zero (the chief ray) is zero as is the ray at the edge of the lens. To reduce the overall sum of the longitudinal aberration, we can alternatively select the conic coefficient so that a ray at a height equal to 0.7071 of the clear aperture radius intersects the paraxial focus. This is illustrated in  FIG. 1 .B. The Seidel spherical aberration corresponding to  FIG. 1 .B is about half that represented in  FIG. 1 .A. Thus, the longitudinal aberrations are approximately “balanced”. Our strategy is: select the conic coefficient that causes the parallel incident ray at a height of 0.7071 of the clear aperture radius to intersect the paraxial focus. This strategy is illustrated in  FIG. 2 , which shows eye  20  having lens  22 . Parallel incident ray  24  enters the eye  20  at a height of 0.7071 times the radius of lens  22 . Ray  24  is shown to be not focused on paraxial focus  26 , which then requires an adjustment to K to cause ray  24  to focus at  26  and satisfy the strategy.  
         [0013]     The conic constant K is well known in the optics field and is given by the surface equation for a conic:  
             z   =         s   2     R       1   +       1   -       (     1   +   K     )     ⁢       s   2       R   2                         (   1   )             
 
 where R is the apical radius, K is the conic constant (K=−e 2 ), and s 2 =x 2 +y 2 . We are now ready to describe the method in which the lens parameters: apical radius, conic constant, and center thickness are computed. 
 
         [0014]     Determining conic constant K for a given IOL power: As noted above the preferred embodiment has lens parameters: optical lens diameter of 5.75 mm, lens edge thickness of 0.35 mm, and material index of refraction of 1.4585. A sphere has a conic constant K=0. In our calculation of K to control the longitudinal ray aberrations, we use a starting value of K=0 and iterate over K until we have a longitudinal ray aberration of zero for an incident ray height of 0.7071 times the lens optical zone radius. This incident ray is referred to as the marginal ray. This iterative optimization is performed using a well known algorithm called Newton-Raphson iteration. The method requires two starting values for the parameter being optimized. Here we use K=0 and K=0.1. The method also requires two “error values” corresponding to the K values. The error value is this signed distance of where the final ray from the marginal ray crosses the optical axis minus the paraxial focus for the desired IOL power.  
         [0015]     This is illustrated in  FIG. 3  wherein the geometry for ray tracing of marginal ray and calculation of longitudinal ray aberrations is shown. The IOL  31  is centered on optical axis  32 . The paraxial focus  33  is located a distance equal to the back focal length  34  from the back of the IOL  31 . The marginal ray  35  intersects the optical axis at intersection point  36 . The signed distance from the paraxial focus  33  to the marginal ray intersection point  36  is referred to as the longitudinal ray aberration  37 .  
         [0016]     In  FIG. 3 , the longitudinal ray aberration is denoted by item  37 . To compute the location of the intersection point  36 , we first need a complete description of the lens  31 . Given the power Pe of the IOL and the current conic constant K, we need to compute the center thickness CT of the lens so that the edge thickness ET is the desired value (ET=0. 35 for the preferred embodiment). Since the IOL has equal surfaces, the paraxial powers P of the anterior and posterior surfaces are equal. The apical radius R for the anterior surface is given by:  
             R   =           n   ⁢   1     -     n   ⁢   0       P     ⁢   1000             (   2   )             
 
 where n 1  is the index of refraction of the IOL (1.4585), n 0  is the index of refraction of the medium inside the eye (commonly taken as 1.336), P is the power of the anterior surface in diopters, and the apical radius R is given in mm. The sag Z for the anterior conic surface of the lens can be found using equation (1). Since we know the optical zone diameter OZ (OZ=5.75 mm in the preferred embodiment) and the edge thickness ET, we can compute the center thickness CT using (3).  
               CT   =     ET   +     2   ×         s   2     R       1   +       1   -       (     1   +   K     )     ⁢       s   2       R   2                       ⁢     
     ⁢     s   =     OZ   2               (   3   )             
 
         [0017]     The surface power (either surface since they are equal) can be computed from the desired IOL power Pe, the IOL index of refraction n 1 , and the center thickness CT using (4).  
               P   =       n   -       n   ⁡     (     n   -     CT   ×   Pe       )           CT       ⁢     
     ⁢     n   =     n   ⁢           ⁢   1   ×   1000               (   4   )             
 
         [0018]     It is evident that there is a dependence of the variables in equations (2), (3), and (4) on each other. Thus, we use an iteration loop over these equations until the apical radius R and the center thickness CT converge. We have empirically determined that a loop of 20 iterations is sufficient for all lens powers Pe in the range of −20 to 50 D. To start the iteration, we set P=Pe/2.  
         [0019]     The back focal length bfl identified as item  34  in  FIG. 3 , can be computed from the paraxial relations given in equation (5).  
               Pv   =     P   +       1000   ×   n   ⁢           ⁢   1         -   CT     +       1000   ×   n   ⁢           ⁢   1     P             ⁢     
     ⁢     bfl   =       n   ⁢           ⁢   0   ×   1000     Pv               (   5   )             
 
 Returning to the ray tracing illustrated in  FIG. 3 , for a given IOL power Pe and conic constant K, we can now describe how the longitudinal aberration is computed. An incident ray (left side of item  5  of  FIG. 3 ) is parallel to the optical axis  32  at a height h=0.7071×OZ/2. We intersect the incident ray with the anterior surface of the IOL using a ray/conic intersection routine. Once the intersection is found, we compute the surface normal for the anterior surface and then refract the ray to determine its new direction. This refracted ray is then intersected and refracted with the posterior surface of the lens (separated by a distance CT from the anterior surface). The resulting refracted ray is then intersected with the optical axis to find the intersection point identified by item  36  in  FIG. 3 . These ray refraction and intersection calculations are well known to those familiar to the art. This intersection point  36  and the paraxial focus  33  found using equation (5) are subtracted to find the error used in the Newton-Raphson iteration described above. Thus, to find the error for a given conic constant K, we perform the following steps: 
 
         [0020]     Error calculation: 
        1. Iterate over equations (2), (3), and (4) to find R and CT for a given Pe and K.     2. Find the paraxial focus point using equation (5)     3. Trace a marginal ray using the procedure described above and compute the ray intersection point item  36      4. Compute the error E=signed distance from point  36  to point  33 .        
 
         [0025]     In summary, to compute the apical radius R, conic constant K, and center thickness CT for an IOL of equivalent power Pe, we perform the following steps: Lens parameters calculation: 
        1. Initialize 
 
a. Set K0=0 and K1=0.1 
 
b. Set E0 and E1=errors found using algorithm above 
 
c. NumIterations=0 
 
d. Set tol=1.0e−9 
    2. While NumIterations&lt;10 and | E 0 −E 1|&gt;tol do the following steps 
 
a. NumIterations=NumIterations+1 
 
b.  K=K 0 −E 0×( K 0− K 1)/( E 0 −E 1) 
 
c. K0=K1 
 
d. E0=E1 
 
e. K1=K 
 
f. E1=(error computed using algorithm for K1) 
    3. Compute R and CT by iteration over equations (2)-(4) using the final value of K        
 
         [0029]     Using this calculation approach we arrive at the example IOL design table shown below:  
                                         Aspheric IOL Table       Surrounding medium index = 1.3360       Material index = 1.4585       Edge thickness = 0.35       Lens diameter = 5.75                                    Lens_Power, R1 = −R2, K1 = K2, CT           4.00, 61.229627, −1.232115, 0.484977           4.50, 54.423361, −1.232072, 0.501852           5.00, 48.978206, −1.232028, 0.518728           5.50, 44.522950, −1.231983, 0.535604           6.00, 40.810119, −1.231937, 0.552480           6.50, 37.668382, −1.231889, 0.569357           7.00, 34.975364, −1.231841, 0.586235           7.50, 32.641319, −1.231791, 0.603112           8.00, 30.598941, −1.231740, 0.619990           8.50, 28.796759, −1.231688, 0.636868           9.00, 27.194740, −1.231634, 0.653746           9.50, 25.761280, −1.231580, 0.670624           10.00, 24.471094, −1.231524, 0.687502           10.50, 23.303715, −1.231467, 0.704379           11.00, 22.242397, −1.231409, 0.721257           11.50, 21.273304, −1.231350, 0.738135           12.00, 20.384910, −1.231290, 0.755012           12.50, 19.567531, −1.231228, 0.771890           13.00, 18.812971, −1.231165, 0.788766           13.50, 18.114252, −1.231101, 0.805643           14.00, 17.465390, −1.231036, 0.822519           14.50, 16.861227, −1.230970, 0.839395           15.00, 16.297295, −1.230902, 0.856270           15.50, 15.769698, −1.230834, 0.873145           16.00, 15.275032, −1.230764, 0.890019           16.50, 14.810302, −1.230693, 0.906892           17.00, 14.372866, −1.230621, 0.923765           17.50, 13.960386, −1.230547, 0.940637           18.00, 13.570781, −1.230473, 0.957508           18.50, 13.202197, −1.230397, 0.974379           19.00, 12.852974, −1.230320, 0.991248           19.50, 12.521623, −1.230242, 1.008117           20.00, 12.206803, −1.230163, 1.024985           20.50, 11.907305, −1.230082, 1.041852           21.00, 11.622035, −1.230001, 1.058718           21.50, 11.349999, −1.229918, 1.075583           22.00, 11.090296, −1.229834, 1.092447           22.50, 10.842102, −1.229749, 1.109309           23.00, 10.604668, −1.229662, 1.126171           23.50, 10.377307, −1.229574, 1.143031           24.00, 10.159389, −1.229486, 1.159891           24.50, 9.950336, −1.229396, 1.176749           25.00, 9.749615, −1.229304, 1.193605           25.50, 9.556738, −1.229212, 1.210461           26.00, 9.371251, −1.229119, 1.227315           26.50, 9.192735, −1.229024, 1.244168           27.00, 9.020805, −1.228928, 1.261019           27.50, 8.855099, −1.228831, 1.277869           28.00, 8.695286, −1.228732, 1.294718           28.50, 8.541054, −1.228633, 1.311565           29.00, 8.392116, −1.228532, 1.328410           29.50, 8.248201, −1.228430, 1.345254           30.00, 8.109059, −1.228327, 1.362097           30.50, 7.974455, −1.228222, 1.378938           31.00, 7.844169, −1.228117, 1.395777           31.50, 7.717995, −1.228010, 1.412615           32.00, 7.595742, −1.227902, 1.429452           32.50, 7.477227, −1.227793, 1.446286           33.00, 7.362281, −1.227683, 1.463119           33.50, 7.250745, −1.227571, 1.479951           34.00, 7.142467, −1.227458, 1.496781           34.50, 7.037306, −1.227344, 1.513609           35.00, 6.935128, −1.227229, 1.530435