Patent Publication Number: US-2006001830-A1

Title: Method for designing aspheric spectacle lens

Description:
FIELD OF THE INVENTION  
      The present invention relates to spectacle lens design methods, and particularly to a method for designing an aspheric spectacle lens.  
     BACKGROUND  
      Most conventional spectacle lenses are produced with an emphasis on ease of manufacture. Accordingly, in general, both of first and second surfaces of a typical spectacle lens have spherical shapes. Theoretically, for an infinitely thin lens, a spherical curvature is ideal for sharply focusing light passing through the lens. However, the curvatures and thickness of a normal lens produce well-known optical aberrations, which include spherical aberration, coma, distortion, and astigmatism. That is, light from a point source passing through different areas of the lens does not focus at a single point. This causes a certain amount of blurring. In addition, in the case of a spherical spectacle lens for correcting hyperopia, the thickness of the lens, particularly the central thickness of the lens, increases rapidly with an increase in the lens power of the lens. Similarly, in the case of a spherical spectacle lens for correcting myopia, the thickness of the lens, particularly the edge thickness of the lens, increases rapidly with an increase in the lens power of the lens. This is undesirable from the viewpoint of the external aesthetic appearance of such spherical spectacle lenses.  
      To solve the above-described problems, some aspheric spectacle lenses have been developed. At least one surface of such an aspheric spectacle lens is formed to have an aspheric shape. The aspheric spectacle lens has a thickness less than that of a spherical spectacle lens having the same lens power, and has reduced optical aberrations. However, a conventional aspheric lens almost invariably has inflection points, which cause much difficulty in manufacturing.  
      What is needed, therefore, is an aspheric spectacle lens design method which yields an aspheric spectacle lens without inflection points.  
     SUMMARY  
      A method for designing an aspheric spectacle lens includes the following steps: designing a spherical spectacle lens, the spherical spectacle lens having a first surface being substantially flat, and a second surface being spherical and having a predetermined lens power; and correcting aberration of the spherical spectacle lens by changing the second surface into an aspheric surface. The second step includes: defining an aspheric surface by an aspheric-surface function, parameters of the function including a conic constant and at least one aspheric-surface coefficient; defining a merit function, the merit function having a parameter of inflection point, the parameter of inflection point being described with the conic constant and the aspheric-surface coefficient of the aspheric-surface function; and calculating a resolution of the merit function by a damped least square method.  
      Other advantages and novel features will become more apparent from the following detailed description. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENT  
      An aspheric spectacle lens design method of a preferred embodiment according to the present invention is used with software simulation techniques. The method includes the following steps: A. Designing a spherical spectacle lens; and B. Correcting aberration of the spherical spectacle lens by changing the second surface into an aspheric surface.  
      In step A., the spherical spectacle lens has two surfaces: a first surface which is farthest from the wearer&#39;s eye, and a second surface which is nearest to the wearer&#39;s eye. The first surface is substantially flat; i.e., a radius of curvature R 1  of the first surface is infinite. The spectacle lens is made of PC (polycarbonate), which has a refractive index n designated as n=1.586. The spectacle lens has a lens power F v  designated as F v =−6D (Diopter), a diameter D A  designated as D A =75 mm, and a central thickness t designated as t=1 mm. A radius of curvature R 2  of the second surface is determined by the following equations:  
               F   1     =       (     n   -   1     )     /     R   1                     F   2     =       (     1   -   n     )     /     R   2                     F   V     =         F   1     +     F   2     -       t   n     ⁢     F   1     ⁢     F   2           1   -       t   n     ⁢     F   1                     
 
 where F 1  is a refractive power of the first surface, and F 2  is a refractive power of the second surface. 
 
      Step B. includes the following steps:  
      1. Defining an aspheric surface by an aspheric-surface function. The aspheric-surface function in the present embodiment is:  
       Z   =           c   v     ⁢     r   2         1   +       1   -       Pc   v   2     ⁢     r   2               +     Br   4     +     Cr   6     +     Dr   8     +     Er   10           
 
 where Z is a length of a perpendicular dropped or drawn from a point, which is positioned on the aspheric surface and is located at a distance r from an optical axis, to a meridian plane, which contacts the aspheric surface at a vertex thereof; c v  is a curvature at the vertex of the aspheric surface; P is the conic constant, and B, C, D and E are aspheric-surface coefficients. 
 
      2. Defining a merit function. The merit function in the present embodiment is:  
             Φ   =         ∑     i   =   1     m     ⁢           ⁢       [       W   i     ⁡     (       e   i     -     t   i       )       ]     2       =       ∑     i   =   1     m     ⁢           ⁢     f   i   2                       f   i     =       W   i     ⁡     (       e   i     -     t   i       )                 
 
 where W i  is a weighted factor, whose value is related to e i ; e i  is one of the aberrations of the aspheric spectacle lens; t i  is a target value of e i ; and m is a number of the aberrations. 
 
      In the present embodiment, an astigmatism in 0.5 field of view is designated as e 1 , an astigmatism in 0.7 field of view is designated as e 2 , an astigmatism in 1.0 field of view is designated as e 3 , a distortion is designated as e 4 , and an inflection point is designated as e 5 . The 1.0 field of view is defined as a field of view where input light beams irradiate to the wearer&#39;s eye over an angle of 30 degrees. Similarly, the 0.5 field of view is defined as a field of view where input light beams irradiate to the eye over an angle of 0.5*30=15 degrees, and the 0.7 field of view is defined as a field of view where input light beams irradiate to the eye over an angle of 0.7*30=21 degrees. Φ is now represented as the following function: 
 
 ΦW   1   2 ( e   1   −t   1 ) 2   +W   2   2 ( e   2   −t   2 ) 2   +W   3   2 ( e   3   −t   3 ) 2   +W   4   2 ( e   4   −t   4 ) 2   +W   5   2 ( e   5   −t   5 ) 2  
 
 wherein e 1 , e 2  , e 3  , e 4  and e 5  can be described with the conic constant P, and with the aspheric-surface coefficients B, C, D and E, so Φ can be described with parameters (P, B, C, D, E). 
 
      3. Calculating the solution of the merit function by a damped least square method. The solution of the damped least square method is according to the following equation:  
             X   =       -       (         A   T     ⁢   A     +   QI     )       -   1         ⁢     A   T     ⁢     f   0                     A   ij     =       ∂     f   i         ∂     x   j                     x   =       x   0     +   X               
 
 where A T  is a transpose matrix of A; Q is a damped factor; I is a unitary matrix; and (A T A+QI) −1  is an inverse matrix of (A T A+QI). In the present embodiment, i and j are integers from 1 to 5; A is a 5*5 matrix; W 1 =W 2 =W 3 =W 4 =W 5 =1, and t 1 =t 2 =t 3 =t 4 =t 5 =0. The original values of P, B, C, D and E are represented as x 0 =(x 10 , x 20 , x 30 , x 40 , x 50 ) and are determined by the second spherical surface of the spherical spectacle lens. The solutions of P, B, C, D and E are represented as x=(x 1 , x 2 , x 3 , x 4 , x 5 ). The original values of e 1 , e 2 , e 3 , e 4  and e 5  are represented as f 0 =(f 10 , f 20 , f 30 , f 40 , f 50 ). 
 
      TABLE 1 shows parameters of a typical aspheric spectacle lens obtained according to the present embodiment, when the lens powers is −6D. TABLES 2-4 show parameters of other aspheric spectacle lenses obtained according to the present embodiment, when the lens powers are −5D, −7D and −8D respectively. Further, each of TABLES 1-4 show differences between the aspheric spectacle lens obtained according to the present embodiment and a conventional spherical spectacle lens having the same lens power, diameter and central thickness.  
      Referring to TABLE 1, compared to the spherical spectacle lens, the edge thickness of the aspheric spectacle lens is reduced by 32%, the axial height of the aspheric spectacle lens is reduced by 59%, and the mass of the aspheric spectacle lens is reduced by 20%.  
                       TABLE 1                           Aspheric Spectacle   Spherical Spectacle       Parameter   Lens   Lens                                        Lens Power:   −6D       Diameter:   75 mm                                 First Curvature   10 8     mm   122.878   mm       Radius:       Second Curvature   97.6667   mm   54.343   mm       Radius:                             Conic Constant P:   −2.8777               Aspheric-surface   B: −4.0545 × 10 −7         Coefficient:   C: 1.6837 × 10 −10             D: −9.4327 × 10 −14             E: 1.572 × 10 −18                                   Central thickness:   1   mm   1   mm       Edge Thickness:   6.948   mm   10.150   mm       Axial Height:   6.948   mm   16.012   mm       Astigmatism:   0       0       Refractive Power   0.269       0.245       Error:       Distortion:   −7.500%       −6.047%       Mass:   23.023   g   28.705   g                  
 
      Referring to TABLE 2, compared to the spherical spectacle lens, the edge thickness of the aspheric spectacle lens is reduced by 32%, the axial height of the aspheric spectacle lens is reduced by 62%, and the mass of the aspheric spectacle lens is reduced by 20%.  
                       TABLE 2                           Aspheric Spectacle   Spherical Spectacle       Parameter   Lens   Lens                                        Lens Power:   −5D       Diameter:   75 mm                                 First Curvature   10 8     mm   108.936   mm       Radius:       Second Curvature   117.2   mm   56.359   mm       Radius:                             Conic Constant P:   −4.7315               Aspheric-surface   B: −4.2120 × 10 −7         Coefficient:   C: 1.7608 × 10 −10             D: −7.0909 × 10 −14             E: 8.4856 × 10 −18                                   Central thickness:   1   mm   1   mm       Edge Thickness:   5.834   mm   8.629   mm       Axial Height:   5.834   mm   15.287   mm       Astigmatism:   0       0       Refractive Power   0.235       0.212       Error:       Distortion:   −6.224%       −4.863%       Mass:   19.826   g   24.871   g                  
 
      Referring to TABLE 3, compared to the spherical spectacle lens, the edge thickness of the aspheric spectacle lens is reduced by 30%, the axial height of the aspheric spectacle lens is reduced by 51 %, and the mass of the aspheric spectacle lens is reduced by 19%.  
                       TABLE 3                           Aspheric Spectacle   Spherical Spectacle       Parameter   Lens   Lens                                        Lens Power:   −7D       Diameter:   75 mm                                 First Curvature   10 8     mm   139.425   mm       Radius:       Second Curvature   83.7143   mm   52.255   mm       Radius:                             Conic Constant P:   −1.1445               Aspheric-surface   B: −4.829 × 10 −7         Coefficient:   C: 1.2762 × 10 −10             D: −2.767 × 10 −14             E: −1.098 × 10 −18                                   Central thickness:   1   mm   1   mm       Edge Thickness:   8.196   mm   11.726   mm       Axial Height:   8.196   mm   16.863   mm       Astigmatism:   0       0       Refractive Power   0.296       0.275       Error:       Distortion:   −8.793%       −7.282%       Mass:   26.502   g   32.614   g                  
 
      Referring to TABLE 4, compared to the spherical spectacle lens, the edge thickness of the aspheric spectacle lens is reduced by 29%, the axial height of the aspheric spectacle lens is reduced by 50%, and the mass of the aspheric spectacle lens is reduced by 18%.  
                       TABLE 4                           Aspheric Spectacle   Spherical Spectacle       Parameter   Lens   Lens                                        Lens Power:   −8D       Diameter:   75 mm                                 First Curvature   10 8     mm   159.388   mm       Radius:       Second Curvature   73.25   mm   50.149   mm       Radius:                             Conic Constant P:   −0.3882               Aspheric-surface   B: −4.9137 × 10 −7         Coefficient:   C: 9.089 × 10 −10             D: −4.8032 × 10 −14             E: −2.3177 × 10 −18                                   Central thickness:   1   mm   1   mm       Edge Thickness:   9.501   mm   13.378   mm       Axial Height:   9.501   mm   17.852   mm       Astigmatism:   0       0       Refractive Power   0.319       0.300       Error:       Distortion:   −10.096%       −8.565%       Mass:   30.016   g   36.626   g                  
 
      It is to be understood, however, that even though numerous characteristics and advantages of the preferred embodiment have been set forth in the foregoing description, together with details of the structure and function of the preferred embodiment, the disclosure is illustrative only, and changes may be made in detail, especially in matters of shape, size, and arrangement of parts within the principles of the invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed.