Patent Publication Number: US-2023161180-A1

Title: Progressive addition lenses without narrow progressive corridor

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present disclosure relates to an addition lens, and particularly relates to a progressive addition lens that greatly reduces the peripheral astigmatism zones and does not have progressive corridor areas. 
     2. The Prior Arts 
     As shown in  FIG.  1   , the distant vision zone  1  of the prior art progressive addition lens is positioned on the wide area of the upper half of the lens, and is sued to observe distant objects. The human eyes have the ability to correct distant vision when they are in a relaxed head-up state, and provide a clear and wide field of vision. The near vision zone  3  is positioned on the lower half of the lens, and is used to observe near objects with a small clear range of vision. The progressive corridor zone  5  is positioned on the middle area between the distant vision zone and the near vision zone. The progressive corridor zone  5  is used to observe objects at an intermediate distance, and has a narrow range of visual clarity. The peripheral astigmatism zone  7  (also known as a blind zone) is positioned on both sides of the lens, and cannot be provided for a wearer to observe. At the same time, it can be expressly seen from the contour diagram shown in  FIG.  2    that the contour lines of the peripheral astigmatism zone  7  are densely spaced such that the visual blur and shaking sensation caused by the peripheral astigmatism zone  7  will be obvious, and makes the wearer feel dizzy and uncomfortable. 
     In addition, taking the long distance as the design core will make the long-distance field of view wider, and the intermediate-distance and short-distance breath must be sacrificed, resulting in a narrower intermediate-range and short-range field of view. If the wearer wears the lenses for a long time, since the near vision zone  3  is too narrow, it is necessary to turn the head frequently to align with the area to be viewed, and it is easy to tilt the head for a long time, resulting in shoulder and neck compression and fatigue and pain. If the eyes look at the target through the near vision zone of a small area for a long time, it is also easy to cause eyes fatigue and feel sore. 
     Therefore, how to provide a better progressive addition lens is one of the current important issues. That is, a lens that has no progressive corridor zone, and can greatly reduce the peripheral astigmatism on both sides of the center of the lens (i.e., the middle area). The better progressive addition lens can be manufactured directly from the freeform machine, while overcoming the aforementioned shortcomings. 
     SUMMARY OF THE INVENTION 
     In order to achieve the above objective, according to a preferred embodiment, the present disclosure provides progressive addition lenses without narrow progressive corridor. 
     According to an embodiment of the present disclosure, the progressive addition lens without narrow progressive corridor takes the side facing the wearer&#39;s face as the back surface, and the outer side as the front surface. A preset three-dimensional free-form surface is formed by machining on the back surface of the lens, which includes a distant vision zone on an upper part of a lens; a near vision zone on a lower part of the lens; and an intermediate vision zone on a middle part of the lens and between the distant vision zone and the near vision zone, wherein an astigmatism zone is on both sides of the intermediate vision zone. The intermediate vision zone increases a field of view by the freeform surface, which forms an area that does not have a progressive corridor area and reduces the astigmatism zone, and a ratio of the astigmatism zone and the intermediate vision zone is between 5% and 20%. 
     Preferably, a front surface of the lens is a spherical surface or an aspherical surface. 
     Preferably, the spherical surface or the aspherical surface is determined according to the following formula: 
         x   2   +y   2 +(1+ Q ) z   2 −2 zR= 0
 
     where x is the x axis of a coordinate system on a surface of the lens, y is the y axis of the coordinate system of the surface of the lens, z is a surface height, R is a radius of curvature of an apex of the lens, and Q is the spherical surface or the aspherical surface (Q=0 represents the spherical surface, and Q≠0 represent the aspherical surface). 
     Preferably, the rear surface of the lens is composed of a combination of a primary structure height function and a secondary structure height function. 
     Preferably, the primary structure height function is determined by all of or part of the combination of shape functions that control a variation of a vertical power in a Zernike function, and the shape functions include Z 3  to Z 27 . 
     Preferably, the Zernike function is determined according to the following formula: 
     
       
         
           
             
               
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     where k is the k-th polynomial (integer of k≥0), x is a horizontal coordinate, y is a vertical coordinate, m is an angular frequency, n is the n-th order aberration, and a, b and c are all integers greater than or equal to 0. 
     Preferably, the secondary structure height function includes Z 6  to Z 27  in addition to the Zernike function used in the primary structure height function. 
     Preferably, the freeform surface includes spherocylindrical power and progressive addition power. The spherocylindrical power is determined according to the following formula: 
         F (θ)= S+C  sin 2 (θ−α),
 
     and 
         R (θ)=( n   2   −n   1 )/ F (θ),
 
     where s is the degree of the spherical surface, c is the degree of the cylindrical surface, α is the cylindrical axis, F(θ) is the degree at an angle θ, R(θ) is the radius of curvature at the angle θ, n 1  is the refractive index of air (n 1 =1.0), and n 2  is the refractive index of the lens. 
     Preferably, the rear surface of the lens is manufactured by a freeform machining process. 
     Preferably, the rear surface of the lens is manufactured by a freeform machining and a polishing process. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
         FIG.  1    is a schematic diagram of a prior art progressive addition lens. 
         FIG.  2    is a contour map of astigmatism of a prior art progressive addition lens. 
         FIG.  3    shows a schematic diagram of a progressive addition lens without narrow progressive corridor according to the present disclosure. 
         FIG.  4    shows a simulated contour diagram of equivalent spherical power (M) of the progressive addition lens (ϕ=67 mm) according to the first embodiment of the present disclosure. 
         FIG.  5    shows a simulated contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the first embodiment of the present disclosure. 
         FIG.  6    shows a measured contour diagram of equivalent spherical power (M) of the progressive addition lens (ϕ=67 mm) according to the second embodiment of the present disclosure (where only the progressive addition lens (ϕ=40 mm) is shown). 
         FIG.  7    shows a measured contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the second embodiment of the present disclosure (where only the progressive addition lens (ϕ=40 mm) is shown). 
         FIG.  8    shows a simulated contour diagram of equivalent spherical power (M) of the progressive addition lens according to the third embodiment of the present application. 
         FIG.  9    shows a simulated contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the third embodiment of the present disclosure. 
         FIG.  10    shows a schematic diagram of a freeform machining of the progressive addition lens according to the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The detailed description of the present disclosure is provided in combination with the accompanying drawings. 
     In general, in the case of ignoring the thickness of the lens (thin lens), the total power of the lens can be determined by the sum of the surface powers of the two surfaces of the lens (i.e., the front surface and the rear surface), and the surface power of the lens is calculated from the refractive index (n) and radius of curvature (R) of the lens. Consequently, the refractive index of the lens can be determined when the material of the lens is known. In addition, as long as the shapes of the front and rear surfaces of the lens are determined, the surface power of lens can be known. 
     The front surface of the lens of the present disclosure may be a spherical surface or an aspherical surface, and the rear surface of the lens is a freeform surface, but not limited thereto. Therefore, as shown in  FIG.  3   , a progressive addition lens proposed by the present disclosure includes a distant vision zone  10 , a near vision zone  20  and an intermediate vision zone  30 . The distant vision zone  10  is arranged at the upper part of the lens, and used to see distant objects clearly. The near vision zone  20  is provided at the lower part of the lens, and used to see objects at close range clearly. The intermediate vision zone  30  is provided at the middle part of the lens and between the distant vision zone and the near vision zone, and used to see object in the middle distance. In addition, the manufacturing method can be a freeform machining or polishing after freeform machining. 
     It is worth noting that the intermediate vision zone of the present disclosure does not have progressive corridor areas, and the peripheral astigmatism areas on both sides of the intermediate vision zone are greatly eliminated such that the progressive addition lens of the present disclosure has a wide field of view and high definition that greatly eliminates peripheral astigmatism from interfering with vision. That is, the ratio of the peripheral astigmatism zone to the intermediate vision is about 5%˜20%, and the best is about 5%˜10%. 
     If the front surface of the present disclosure is spherical or aspherical, it is determined according to the following formula: 
         x   2   +y   2 +(1+ Q ) z   2 −2 zR= 0,  (1)
 
     where x is the x axis of a coordinate system on a surface of the lens, y is the y axis of the coordinate system of the surface of the lens, z is a surface height, R is a radius of curvature of an apex of the lens, and Q is the spherical surface or the aspherical surface (Q=0 represents the spherical surface, and Q≠0 represent the aspherical surface). 
     The rear surface of the present disclosure is a freeform surface made by a freeform machining process includes spherocylindrical power and progressive addition power. The spherocylindrical power is determined according to the following formula: 
         F (θ)= S+C  sin 2 (θ−α), and  (2)
 
         R (θ)=( n   2   −n   1 )/ F (θ),  (3)
 
     where s is the degree of the spherical surface, c is the degree of the cylindrical surface, α is the cylindrical axis, F(θ) is the degree at an angle θ, R(θ) is the radius of curvature at the angle θ, n 1  is the refractive index of air (n 1 =1.0), and n 2  is the refractive index of the lens. 
     The progressive addition power is designed on the rear surface of the lens of the present disclosure. Accordingly, the full surface height function of the present disclosure can be obtained by combining both a primary structure height function and a secondary structure height function. 
     The primary structure height function is mainly used to design the magnitude and rate of change of the distant vision power and the near vision addition power, and is composed of all or partial combinations of the shape functions that control the vertical power changes in the Zernike polynomial. The shape functions include Z 3  to Z 27  (please refer to the Zernike polynomial below and Table 1 below). 
     The height function (Z k (x, y)) of the lens surface geometry can be described by the combination of Zernike polynomials representing the shape of the aberration surface: 
     
       
         
           
             
                 
               
                 
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                                               1 
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                     × 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     n 
                                     - 
                                     b 
                                   
                                   ) 
                                 
                                 ! 
                               
                               
                                 
                                   
                                     
                                       
                                         
                                           b 
                                           ! 
                                         
                                         [ 
                                         
                                           
                                             
                                               ( 
                                               
                                                 n 
                                                 + 
                                                 m 
                                               
                                               ) 
                                             
                                             / 
                                             2 
                                           
                                           - 
                                           b 
                                         
                                         ] 
                                       
                                       ! 
                                     
                                     [ 
                                     
                                       
                                         
                                           ( 
                                           
                                             n 
                                             - 
                                             m 
                                           
                                           ) 
                                         
                                         / 
                                         2 
                                       
                                       - 
                                       b 
                                       - 
                                       c 
                                     
                                     ] 
                                   
                                   ! 
                                 
                                 ⁢ 
                                 
                                   c 
                                   ! 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 n 
                                 - 
                                   
                                 
                                   2 
                                   ⁢ 
                                   a 
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   b 
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   c 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               y 
                               
                                 
                                   2 
                                   ⁢ 
                                   a 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   c 
                                 
                                 + 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         if 
                         ⁢ 
                             
                         m 
                       
                       ≠ 
                       
                         0 
                         ⁢ 
                             
                         and 
                         ⁢ 
                             
                         k 
                         ⁢ 
                             
                         odd 
                       
                     
                   
                 
               
             
           
         
       
     
     where k is the k-th polynomial (integer of k≥0), x is a horizontal coordinate, y is a vertical coordinate, m is an angular frequency, n is the n-th order aberration, and a, b and c are all integers greater than or equal to 0. 
     Moreover, under the condition that the secondary structure height function does not affect the equivalent spherical power (M) distribution presented by the primary structure height function, the added high-order Zernike function is mainly used to design the distribution, reduction and removal of the peripheral astigmatism power. In addition to the above-mentioned Zernike function used in the primary structure height function. The secondary structure height function includes Z 6  to Z 27  (please refer to the following Zernike polynomials and Table 1). 
     Using the aforesaid full surface height function of the lens of the present disclosure, the combination of Zernike polynomials up to sixth order and the Zernike coefficients thereof can be derived. The Zernike coefficients are variable. After that, the equivalent spherical power and astigmatism power of the lens can be calculated according to the coefficients brought into the polynomials according to the following formula: 
     
       
         
           
             
               
                 
                   M 
                   = 
                   
                     
                       
                         
                           - 
                           4 
                         
                         ⁢ 
                         
                           3 
                         
                         ⁢ 
                         
                           c 
                           2 
                           0 
                         
                       
                       + 
                       
                         1 
                         ⁢ 
                         2 
                         ⁢ 
                         
                           5 
                         
                         ⁢ 
                         
                           c 
                           4 
                           0 
                         
                       
                       - 
                       
                         2 
                         ⁢ 
                         4 
                         ⁢ 
                         
                           7 
                         
                         ⁢ 
                         
                           c 
                           6 
                           0 
                         
                       
                       + 
                       ⋯ 
                     
                     
                       r 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     J 
                     0 
                   
                   = 
                   
                     
                       
                         
                           - 
                           2 
                         
                         ⁢ 
                         
                           6 
                         
                         ⁢ 
                         
                           c 
                           2 
                           2 
                         
                       
                       + 
                       
                         6 
                         ⁢ 
                         
                           
                             1 
                             ⁢ 
                             0 
                           
                         
                         ⁢ 
                         
                           c 
                           4 
                           2 
                         
                       
                       - 
                       
                         1 
                         ⁢ 
                         2 
                         ⁢ 
                         
                           
                             1 
                             ⁢ 
                             4 
                           
                         
                         ⁢ 
                         
                           c 
                           6 
                           2 
                         
                       
                       + 
                       ⋯ 
                     
                     
                       r 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     J 
                     
                       4 
                       ⁢ 
                       5 
                     
                   
                   = 
                   
                     
                       
                         
                           - 
                           2 
                         
                         ⁢ 
                         
                           6 
                         
                         ⁢ 
                         
                           c 
                           2 
                           
                             - 
                             2 
                           
                         
                       
                       + 
                       
                         6 
                         ⁢ 
                         
                           
                             1 
                             ⁢ 
                             0 
                           
                         
                         ⁢ 
                         
                           c 
                           4 
                           
                             - 
                             2 
                           
                         
                       
                       - 
                       
                         1 
                         ⁢ 
                         2 
                         ⁢ 
                         
                           
                             1 
                             ⁢ 
                             4 
                           
                         
                         ⁢ 
                         
                           c 
                           6 
                           
                             - 
                             2 
                           
                         
                       
                       + 
                       ⋯ 
                     
                     
                       r 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   J 
                   = 
                   
                     
                       
                         J 
                         0 
                         2 
                       
                       + 
                       
                         J 
                         
                           4 
                           ⁢ 
                           5 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where c n   m  is the Zernike coefficient of the nth-order aberration angular frequency m, r is the simulated pupil radius (here set to 2.25 mm), M is the equivalent spherical power, Jo is the power of orthogonal astigmatism, J 45  is the power of oblique astigmatism, and J is the power of astigmatism. 
     In order to facilitate the understanding of the design of the progressive addition lenses without narrow progressive corridor of the present disclosure, the present disclosure provides the following specific embodiments, which are described as follows. 
     First Embodiment 
     In the first embodiment of the present disclosure, the material thereof is PC (n−1.586), the prescription thereof is plano/+2.00 Add, the diameter thereof is 67 mm, the front surface shape of the progressive addition lenses without narrow progressive corridor is designed to be Q=0 (spherical), and the base curve is +4.50 D. Therefore, the design of the rear surface shape of the progressive addition lens of the present disclosure is as follows. 
     In the first embodiment of the present disclosure, the primary structure height function is determined according to the following formula: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             Z 
                             
                               k 
                                 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               x 
                               , 
                               y 
                             
                             ) 
                           
                         
                         = 
                           
                         
                           
                             
                               
                                 
                                   
                                     C 
                                     4 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     4 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     C 
                                     7 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     7 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     C 
                                     12 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       12 
                                         
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     C 
                                     17 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     17 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     C 
                                     25 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     25 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               C 
                               4 
                             
                             ⁢ 
                             
                               3 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     x 
                                     
                                       2 
                                         
                                     
                                   
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   
                                     y 
                                     2 
                                   
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               C 
                               7 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                               2 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   3 
                                   ⁢ 
                                   
                                     x 
                                     2 
                                   
                                   ⁢ 
                                   y 
                                 
                                 + 
                                 
                                   3 
                                   ⁢ 
                                   
                                     y 
                                     3 
                                   
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   y 
                                 
                               
                               ) 
                             
                           
                           + 
                           
 
                           
                             
                               
                                 
                                   
                                     
                                       C 
                                       12 
                                     
                                     ⁢ 
                                     
                                       5 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           6 
                                           ⁢ 
                                           
                                             x 
                                             4 
                                           
                                         
                                         + 
                                         
                                           12 
                                           ⁢ 
                                           
                                             x 
                                             2 
                                           
                                           ⁢ 
                                           
                                             y 
                                             2 
                                           
                                         
                                         + 
                                         
                                           6 
                                           ⁢ 
                                           
                                             y 
                                             4 
                                           
                                         
                                         - 
                                         
                                           6 
                                           ⁢ 
                                           
                                             x 
                                             2 
                                           
                                         
                                         - 
                                         
                                           6 
                                           ⁢ 
                                           
                                             y 
                                             2 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       C 
                                       17 
                                     
                                     ⁢ 
                                     
                                       12 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           10 
                                           ⁢ 
                                           
                                             x 
                                             4 
                                           
                                           ⁢ 
                                           y 
                                         
                                         + 
                                         
                                           20 
                                           ⁢ 
                                           
                                             x 
                                             2 
                                           
                                           ⁢ 
                                           
                                             y 
                                             3 
                                           
                                         
                                         + 
                                         
                                           10 
                                           ⁢ 
                                           
                                             y 
                                             5 
                                           
                                         
                                         - 
                                         
                                           12 
                                           ⁢ 
                                           
                                             x 
                                             2 
                                           
                                           ⁢ 
                                           y 
                                         
                                         - 
                                         
                                           12 
                                           ⁢ 
                                           
                                             y 
                                             3 
                                           
                                         
                                         + 
                                         
                                           3 
                                           ⁢ 
                                           y 
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   
                                     C 
                                     
                                       25 
                                         
                                     
                                   
                                   ⁢ 
                                   
                                     14 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         15 
                                         ⁢ 
                                         
                                           x 
                                           6 
                                         
                                       
                                       + 
                                       
                                         15 
                                         ⁢ 
                                         
                                           x 
                                           4 
                                         
                                         ⁢ 
                                         
                                           y 
                                           2 
                                         
                                       
                                       - 
                                       
                                         15 
                                         ⁢ 
                                         
                                           x 
                                           2 
                                         
                                         ⁢ 
                                         
                                           y 
                                           4 
                                         
                                       
                                       - 
                                       
                                         20 
                                         ⁢ 
                                         
                                           x 
                                           4 
                                         
                                       
                                       + 
                                       
                                         6 
                                         ⁢ 
                                         
                                           x 
                                           2 
                                         
                                       
                                       - 
                                       
                                         15 
                                         ⁢ 
                                         
                                           y 
                                           6 
                                         
                                       
                                       + 
                                       
                                         20 
                                         ⁢ 
                                         
                                           y 
                                           4 
                                         
                                       
                                       - 
                                       
                                         6 
                                         ⁢ 
                                         
                                           y 
                                           2 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     In the first embodiment of the present disclosure, the secondary structure height function is determined according to the following formula: 
         Z   k ( x,y )=0  (10)
 
     The three-dimensional space data (x, y, z) obtained from the above formula is further converted into a computer numerical control program and input into a freeform machine, and the rear surface shape of the progressive addition lenses without narrow progressive corridor is formed through the freeform machining process.  FIG.  4    shows a simulated contour diagram of equivalent spherical power (M) of the progressive addition lens (ϕ=67 mm) according to the first embodiment of the present disclosure, and  FIG.  5    shows a simulated contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the first embodiment of the present disclosure. It can be explicitly seen from  FIGS.  4  and  5    that the progress addition lens of the present disclosure has a wide field of view and high visual clarity since the present disclosure does not have progressive corridor areas and has an extremely small peripheral astigmatism area (the area of J≤=0.50 D defined as the acceptable intermediate vision zone). 
     Second Embodiment 
     In the second embodiment of the present disclosure, the material thereof is PC (n−1.586), the prescription thereof is −2.50/+2.00 Add, the diameter thereof is 67 mm, the front surface shape of the progressive addition lens is designed to be Q=0 (spherical), and the base curve is +2.25 D.  FIG.  6    shows a measured contour diagram of equivalent spherical power (M) of the progressive addition lens (ϕ=67 mm) according to the second embodiment of the present disclosure (where only the progressive addition lens (ϕ=40 mm) is shown).  FIG.  7    shows a measured contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the second embodiment of the present disclosure (where only the progressive addition lens (ϕ=40 mm) is shown). It can be explicitly seen from  FIGS.  6  and  7    that the progress addition lens of the present disclosure has a wide field of view and significantly reduces the interference of peripheral astigmatism with high clear vision since the present disclosure does not have progressive corridor areas and has greatly reduces peripheral astigmatism (the area of J≤+0.50 D defined as the acceptable intermediate vision zone). 
     In light of the above, the detection methods of lens power distribution can be divided into optical and non-optical methods. The optical methods can be divided into Moire optical interference technology and wavefront aberration detection technology. The non-optical methods are mainly to scan the height change on the lens with a three-dimensional coordinate measuring machine, and then convert it into a power distribution diagram. 
     The measured diagram of the second embodiment of the present disclosure is that after the previous wavefront aberration detector measures the power of the entire surface of the lens to obtain data, the contour diagram is drawn with MATLAB software. The actual mass-produced lens of the second embodiment is tested by the instrument. The detection is mainly based on the center of the lens, and the lens area with a diameter of 40 mm is the actual measurement range. The lens area within this range is sufficient to cover all important optical areas of current progressive lenses. The actual measurement diagrams are shown in  FIGS.  6  and  7   . The second embodiment of the present disclosure does not have progressive corridor areas, and the peripheral astigmatism zone (the area of J≤+0.50 D as the acceptable intermediate vision zone) of the lens of the second embodiment only occupy a relatively small area of the lens. As such, the progressive addition lens of the present disclosure has a wide field of view and high visual clarity. 
     Third Embodiment 
     In the third embodiment of the present disclosure, the material thereof is PC (n−1.586), the prescription thereof is plano/+2.00 Add, the diameter thereof is 67 mm, the front surface shape of the progressive addition lens is designed to be Q=0 (spherical), and the base curve is +4.50 D. Therefore, the design of the rear surface shape of the progressive addition lens of the present disclosure is as follows. 
     In the third embodiment of the present disclosure, the primary structure height function is also determined according to the above formula, while the secondary structure height function is determined according to the following formula: 
         Z   k ( x,y )= C   15   Z   15 ( x,y )= C   15 √12(5 x   4   y   3 −10 x   2   y   3   +y   5 )  (11)
 
     With the design of the rear surface shape of the progressive addition lens mentioned above,  FIG.  8    shows a simulated contour diagram of equivalent spherical power (M) of the progressive addition lens according to the third embodiment of the present application, and  FIG.  9    shows a simulated contour diagram of astigmatism (J) of the progressive addition lens (ϕ=67 mm) according to the third embodiment of the present disclosure. It can be explicitly seen from  FIGS.  8  and  9    that the progress addition lens of the present disclosure has a wide field of view and high visual clarity since the present disclosure does not have progressive corridor areas and has an extremely small peripheral astigmatism area (the area of J≤+0.50 D defined as the acceptable intermediate vision zone). 
     It is worth mentioning that the Zernike coefficients of the above specific embodiments of the present disclosure are shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Zernike coefficients of the surface height function of 
               
               
                 the progressive addition lens of the present disclosure 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Coefficient 
                 Coefficient 
                 Coefficient 
               
               
                 k of Z k (x, y) 
                   
                 of front 
                 of rear 
                 of sum of two 
               
               
                 and C k   
                 C n   m (x, y) 
                 surface (μm) 
                 surface (μm) 
                 surfaces (μm) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 3 
                 C 2   −2   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 4 
                 C 2   0   
                 −1262.8 
                 975.5 
                 −287.2 
               
               
                 5 
                 C 2   +2   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 6 
                 C 3   −3   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 7 
                 C 3   −1   
                 0.1 
                 79.9 
                 80.0 
               
               
                 8 
                 C 3   +1   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 9 
                 C 3   +3   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 10 
                 C 4   −4   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 11 
                 C 4   −2   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 12 
                 C 4   0   
                 −5.4 
                 2.5 
                 −3.0 
               
               
                 13 
                 C 4   +2   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 14 
                 C 4   +4   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 15 
                 C 5   −5   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 16 
                 C 5   −3   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 17 
                 C 5   −1   
                 0.1 
                 −10.1 
                 −10.0 
               
               
                 18 
                 C 5   +1   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 19 
                 C 5   +3   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 20 
                 C 5   +5   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 21 
                 C 6   −6   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 22 
                 C 6   −4   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 23 
                 C 6   −2   
                 0.1 
                 −0.1 
                 0.2 
               
               
                 24 
                 C 6   0   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 25 
                 C 6   +2   
                 0.1 
                 3.2 
                 3.4 
               
               
                 26 
                 C 6   +4   
                 0.1 
                 −0.1 
                 0.0 
               
               
                 27 
                 C 6   +6   
                 0.1 
                 −0.1 
                 0.0 
               
               
                   
               
            
           
         
       
     
     In addition, please note that, as shown in  FIG.  10   , the progressive addition lens of the present disclosure is directly machined on the rear surface of the lens. Hence, the upper part of the lens can be used to see objects at a long distance, the lower part of the lens can be used to see objects at a close distance, and the middle part of the lens can be used to see objects at an intermediate distance. Moreover, the front surface of the lens of the present disclosure is spherical or aspherical P 2 , and the rear surface of the lens of the present disclosure is processed by the lens blank P with rear spherical or aspherical surface as the base curve to form a three-dimensional freeform surface P 1 . The processing method can be freeform machining or finishing after free from machining. The cutting tool T in  FIG.  10    is only an illustration of the processing method, but not limited thereto. As a result, the progressive addition lens of the present disclosure can have the advantages of a wide field of view and a small peripheral astigmatism area that interferes with vision and high visual clarity. 
     In light of the above, the present disclosure can directly use commercially available lens blanks to process the rear surface of the lens by a freeform machine according to the different needs of users to form the freeform surface. It can also be processed according to various needs, such as coatings including anti-scratch, anti-reflection, anti-fog, photochromic, etc., which can not only reduce mold development costs, but also reduce inventory costs. 
     The lens blank mentioned in the present disclosure generally refers to a blank made from a mold with a predetermined power curvature on the front surface of the lens, or made from a mold with basic power on the front and back surfaces of the lens. Then, the rear surface of the lens blank is freeform machined and polished to achieve the desired prescription of the consumer. 
     Although the present disclosure has been described with reference to the preferred exemplary preferred embodiments thereof, it is apparent to those skilled in the art that a variety of modifications and changes may be made without departing from the scope of the present disclosure which is intended to be defined by the appended claims.