Patent Publication Number: US-8982312-B2

Title: 2D and 3D switchable display device and liquid crystal lenticular lens thereof

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a two-dimensional and three-dimensional stereoscopic switchable display device and a liquid crystal lenticular lens, and more particularly, to the two-dimensional and three-dimensional stereoscopic switchable display device and the liquid crystal lenticular lens with electrode pattern design of different pitches, thereby decreasing the amount of power sources. 
     2. Description of the Prior Art 
     The principle of the stereoscopic display technology includes delivering different images respectively to a left eye and a right eye of a viewer to give to the viewer a feeling of gradation and depth in the images, thereby generating the stereoscopic effect in the cerebrum of the viewer by analyzing and overlapping the images received separately by the left eye and the right eye. 
     To prevent the parallax barrier of a parallax barrier spatial multiplexing three-dimensional stereoscopic display device from blocking light, a liquid crystal lenticular lens stereoscopic display device is developed to overcome the drawbacks of the conventional three-dimensional stereoscopic display device. Please refer to  FIG. 1 .  FIG. 1  is a schematic diagram illustrating the conventional liquid crystal lenticular lens stereoscopic display device. As shown in  FIG. 1 , the conventional liquid crystal lenticular lens stereoscopic display device includes a display panel  20  and a liquid crystal lenticular lens  30  disposed on the display panel  20 . The liquid crystal lenticular lens  30  includes a first substrate  32 , a second substrate  34 , an electrode unit  36 , a liquid crystal layer  38  and a planar electrode  40 . The first substrate  32  is disposed opposite to the second substrate  34 . The electrode units  36  are disposed on the side of the first substrate  32  facing the second substrate  34 . The electrode unit  36  includes thirteen electrodes  36   a . The thirteen electrodes  36   a  are arranged on the first substrate  32  along a direction in sequence. The liquid crystal layer  38  is disposed between the electrode units  36  and the second substrate  34 . The planar electrode  40  is disposed between the liquid crystal layer  38  and the second substrate  34 . Moreover, there is a gap between any two of the electrodes  36   a  adjacent to each other. The ratio of each gap to the width of each of the electrodes is 1:1. Therefore, under a three-dimensional stereoscopic display mode, different voltages are necessary to be applied to the electrodes  36   a  of the electrode unit respectively. Common voltage is applied to the planar electrode  40 . Since voltage varies in different horizontal surface of the liquid crystal layer  38 , the liquid crystal molecules in different horizontal surface tend to orient differently—rotate and orient themselves following the electric-field lines—so as to achieve lens effect. However, the conventional liquid crystal lenticular lens  30  requires thirteen power sources to achieve the lens effect similar to that of an ideal lens, and therefore burdens the power source and limits design possibilities. 
     SUMMARY OF THE INVENTION 
     It is one of the objectives of the invention to provide a method of fabricating a display device so as to overcome the drawbacks of the conventional techniques. 
     To achieve the purposes described above, an embodiment of the invention provides a liquid crystal lenticular lens including a first substrate, a second substrate, a liquid crystal layer, two first electrodes, two second electrodes, and a common electrode. The second substrate and the first substrate are disposed opposite to each other. The liquid crystal layer is disposed between the first substrate and the second substrate, and the liquid crystal layer has an ordinary refractive index and an extraordinary refractive index. The first electrodes and the second electrodes are disposed between the first substrate and the liquid crystal layer. The common electrode is disposed between the second substrate and the liquid crystal layer. Each of the first electrodes has a first inner side and a first outer side disposed opposite to the first inner side. The first inner sides face each other. There is a first distance between the first outer sides. There is a first center point between the first outer sides, and the first outer sides are equidistant from the first center point. There is a second distance G 2  between the first center point and each of the first inner sides, and second distance G 2  satisfies a following relation: 
                   [     Formula   ⁢           ⁢   1     ]                                   ⁢         G   2     =       [     2   ⁢     df   ⁡     (       n   e     -     n   o       )       ⁢       a   -   1     a       ]       1   2         ,             (   1   )               
where d denotes a maximum thickness of the liquid crystal layer, f denotes a focus of the liquid crystal lenticular lens, n e  denotes the extraordinary refractive index of the liquid crystal layer, n o  denotes the ordinary refractive index of the liquid crystal layer, a denotes a number of equal parts of a whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer, and the number of the equal parts is greater than or equal to 3. The second electrodes are disposed between the first electrodes. Each of the second electrodes has a second inner side and a second outer side disposed opposite to the second inner side. The second inner sides face each other. There is a fourth distance between the second inner sides, and the fourth distance equals one-fourth of the first distance. There is a fifth distance G 5  between the first center point and each of the second outer sides, and the fifth distance G 5  satisfies a following relation:
 
     
       
         
           
             
               
                 
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     To achieve the purposes described above, another embodiment of the invention provides a two-dimensional and three-dimensional stereoscopic switchable display device including a display panel and a liquid crystal lenticular lens. The liquid crystal lenticular lens disposed on display panel includes a first substrate, a second substrate, a liquid crystal layer, a plurality of electrode units, and a common electrode. The second substrate and the first substrate are disposed opposite to each other. The liquid crystal layer is disposed between the first substrate and the second substrate, and the liquid crystal layer has an ordinary refractive index and an extraordinary refractive index. The electrode units are disposed between the first substrate and the liquid crystal layer. The common electrode is disposed between the second substrate and the liquid crystal layer. Each of the electrode units includes two first electrodes and two second electrodes. Each of the first electrodes has a first inner side and a first outer side disposed opposite to the first inner side. The first inner sides face each other. There is a first distance between the first outer sides. There is a first center point between the first outer sides, and the first outer sides are equidistant from the first center point. There is a second distance G 2  between the first center point and each of the first inner sides, and second distance G 2  satisfies a following relation: 
                   [     Formula   ⁢           ⁢   1     ]                                   ⁢         G   2     =       [     2   ⁢     df   ⁡     (       n   e     -     n   o       )       ⁢       a   -   1     a       ]       1   2         ,             (   1   )               
where d denotes a maximum thickness of the liquid crystal layer, f denotes a focus of the liquid crystal lenticular lens, n e  denotes the extraordinary refractive index of the liquid crystal layer, n o  denotes the ordinary refractive index of the liquid crystal layer, a denotes a number of equal parts of a whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer, and the number of the equal parts is greater than or equal to 3. The second electrodes are disposed between the first electrodes. Each of the second electrodes has a second inner side and a second outer side disposed opposite to the second inner side. The second inner sides face each other. There is a fourth distance between the second inner sides, and the fourth distance equals one-fourth of the first distance. There is a fifth distance G 5  between the first center point and each of the second outer sides, and the fifth distance G 5  satisfies a following relation:
 
     
       
         
           
             
               
                 
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     These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating a conventional liquid crystal lenticular lens stereoscopic display device. 
         FIG. 2  is a schematic diagram illustrating a two-dimensional and three-dimensional stereoscopic switchable display device according to a first embodiment of the present invention. 
         FIG. 3  is a schematic diagram of the refractive index of an ideal lens versus the position in an electrode unit according to the first embodiment of the present invention. 
         FIG. 4  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the first embodiment of the present invention. 
         FIG. 5  is a schematic diagram of the refractive index versus the position in a liquid crystal lenticular lens of a conventional approach with thirteen electrodes. 
         FIG. 6  is a schematic diagram of the refractive index versus the position in a liquid crystal lenticular lens of a conventional approach with seven electrodes. 
         FIG. 7  is a schematic diagram illustrating a liquid crystal lenticular lens according to a second embodiment of the present invention. 
         FIG. 8  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the second embodiment of the present invention. 
         FIG. 9  is a schematic diagram illustrating a liquid crystal lenticular lens according to a third embodiment of the present invention. 
         FIG. 10  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the third embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     To provide a better understanding of the present invention, features of the embodiments will be made in detail. The embodiments of the present invention are illustrated in the accompanying drawings with numbered elements. In addition, the terms such as “first” and “second” described in the present invention are used to distinguish different components or processes, which do not limit the sequence of the components or processes. 
     Please refer to  FIG. 2 .  FIG. 2  is a schematic diagram illustrating a two-dimensional and three-dimensional stereoscopic switchable display device according to a first embodiment of the present invention. As shown in  FIG. 2 , the two-dimensional and three-dimensional stereoscopic switchable display device  100  in this embodiment includes a display panel  102  and a liquid crystal lenticular lens  104 . The display panel  102  and the liquid crystal lenticular lens  104  are disposed on the display panel  102 . The display panel  102  in this embodiment may include a liquid crystal display (LCD) panel, an organic electroluminescent display panel, a plasma display panel, an electro-phoretic display panel, a field emission display (FED) panel or other kinds of suitable display panels. The display panel  102  includes a plurality of sub-pixel regions  103 . The liquid crystal lenticular lens  104  includes a first substrate  106 , a second substrate  108 , a liquid crystal layer  110 , a plurality of electrode units  112  and a common electrode  114 . The first substrate  106  and the second substrate  108  are disposed opposite to each other. The second substrate  108  is disposed between the display panel  102  and the first substrate  106 . The liquid crystal layer  110  is disposed between the first substrate  106  and the second substrate  108 . The liquid crystal layer  110  has an ordinary refractive index and an extraordinary refractive index. The liquid crystal layer  110  includes a plurality of liquid crystal molecules  110   a . Each of the liquid crystal molecules  110   a  has a long axis  116  and a short axis  118 . When light propagates along the long axis  116  of the liquid crystal molecules  110   a , the light will experience the ordinary refractive index of the liquid crystal molecules  110   a . On the other hand, when light propagates along the short axis  118  of the liquid crystal molecules  110   a , the light will experience the extraordinary refractive index of the liquid crystal molecules  110   a . The electrode units  112  are disposed on the first substrate  106  and beneath the liquid crystal layer  110 . The common electrode  114  is disposed between the second substrate  108  and the liquid crystal layer  110  and disposed on the second substrate  108 . Under a three-dimensional stereoscopic display mode, the electric field between the common electrode  114  and each of the electrode units  112  causes the liquid crystal molecules  110   a  to rotate and orient themselves along the direction of the field, and thus a liquid crystal lens is formed in the liquid crystal layer  110  corresponding to each of the electrode units  112 . In addition, each of the electrode units  112  is disposed correspondingly to two of the sub-pixel regions  103  adjacent to each other so that the sub-pixel regions  103  can be divided into a left eye sub-pixel  103   a  and a right eye sub-pixel  103   b . The liquid crystal lenticular lens  104 , moreover, can be employed to alter the directions of light rays emitted from the left eye sub-pixels  103   a  and the right eye sub-pixels  103   b  adjacent to the left eye sub-pixels  103   a  so as to display a three-dimensional stereoscopic image. 
     To provide a better understanding of the structure of the liquid crystal lenticular lens, the following illustration and descriptions will only focus on a single electrode unit, but not limited thereto. Please refer to  FIG. 3  and also refer to  FIG. 2 .  FIG. 3  is a schematic diagram of the refractive index of an ideal lens versus the position in an electrode unit according to the first embodiment of the present invention. As shown in  FIGS. 2-3 , the first curve U 1  presents significant information about a relation between the refractive index of an ideal lens and the position in an electrode unit. In this embodiment, the number of equal parts of the whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer equals 5. The quantity of each equal part is the same as that of the others. Each of the electrode units  112 , in this embodiment, includes two first electrodes  120 , two second electrodes  122 , two third electrodes  124  and two fourth electrodes  126 . The first electrodes  120  are electrically connected to the first voltage source V 1 . The second electrodes  122  are respectively electrically connected to the second voltage source V 2  and the third voltage source V 3 . The third electrodes  124  are respectively electrically connected to the sixth voltage source V 6  and the seventh voltage source V 7 . The fourth electrodes  126  are respectively electrically connected to the fourth voltage source V 4  and the fifth voltage source V 5 . In each of the electrode units  112 , each of the first electrodes  120  has a first inner side S 11  and a first outer side S 12  disposed opposite to the first inner side S 11 . The first inner sides S 11  of the first electrodes  120  face each other. There is a first distance G 1  between the first outer sides S 12  of the first electrodes  120 , and the first distance G 1  is the unit width of the liquid crystal lenticular lens  104 . For example, if the width of the display panel  102  is 15.6 inch, the unit width of the liquid crystal lenticular lens  104  may be 257 micrometers, but not limited thereto. There is a first center point C 1  between the first outer sides S 12  of the first electrodes  120 , and the first center point C 1  is equidistant from each of the first outer sides S 12 . In other words, the first electrodes  120  are symmetric with respect to the first center point C 1 . The second electrodes  122 , the third electrodes  124  and the fourth electrodes  126  are respectively symmetric with respect to the first center point C 1 . Moreover, there is a second distance G 2  between the first center point C 1  and each of the first inner sides S 11 . The second distance G 2  satisfies the following relation: 
                   [     Formula   ⁢           ⁢   1     ]                                   ⁢         G   2     =       [     2   ⁢     df   ⁡     (       n   e     -     n   o       )       ⁢       a   -   1     a       ]       1   2         ,             (   1   )               
where d denotes the maximum thickness of the liquid crystal layer  110 . For example, the third distance G 3  between the common electrode  114  and the first substrate  106  is the cell gap of the liquid crystal layer  110  of the liquid crystal lenticular lens  104 . f denotes a focal length of the liquid crystal lenticular lens  104 . n e  denotes the extraordinary refractive index of the liquid crystal layer  110 . n o  denotes the ordinary refractive index of the liquid crystal layer  110 . a denotes the number of the equal parts of the whole difference between the extraordinary refractive index of the liquid crystal layer  110  and the ordinary refractive index of the liquid crystal layer  110 . The quantity of each equal part is the same as that of the others. In this embodiment, the number of the equal parts equals 5. Therefore, the second distance G 2  of this embodiment is
 
                 [       8   5     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
The number of the equal parts in the present invention is not limited to this, and may be greater than or equal to 3. Because the first distance G 1  between the first outer sides S 12  of the first electrodes  120  is the unit width of the liquid crystal lenticular lens  104 , the exact location of each of the first electrodes  120  in the liquid crystal lenticular lens  104  can be determined. Moreover, the distance between the first inner side S 11  and the first outer side S 12  of each of the first electrodes  120 , which is the width of each of the first electrodes  120 , can be determined with the second distance G 2 . The width of each of the first electrodes  120  may be, for example, in a range between 13 micrometers and 15 micrometers. In the liquid crystal lenticular lens  104  of this embodiment, one of the first electrodes  120  of each of the electrode units  112  and one of the first electrodes  120  of another one of the electrode units  112  adjacent to each other are in contact with each other. In other words, any two of the first electrodes  120  adjacent to each other in any two of the electrode units  112  adjacent to each other respectively is in contact with each other, and there is no gap between the adjacent electrode units  112 . In this way, the same voltage can be applied to the first electrodes  120 . In this embodiment, the first curve U 1 , which presents the relation between the refractive index and the position in one electrode unit, satisfies the following relation:
 
                   [     Formula   ⁢           ⁢   5     ]                                   ⁢         n   ⁡     (   r   )       =       n   e     -       r   2       2   ⁢   df           ,             (   5   )               
where r denotes the distance between the position and the first center point C 1 . For example, the third distance G 3  between the common electrode  114  and the first substrate  106  may be 30.5 micrometers. The focal length of the liquid crystal lenticular lens  104  may be 1344.3 micrometers. The extraordinary refractive index of the liquid crystal layer  110  may be 1.712. The ordinary refractive index of the liquid crystal layer  110  may be 1.511. However, the present invention is not limited to this.
 
     In each of the electrode units  112 , both the second electrodes  122  are disposed between the two first electrodes  120 , and each of the second electrodes  122  has the first width W 1 . Each of the second electrodes  122  has a second inner side S 21  and a second outer side S 22 . The second inner side S 21  and the second outer side S 22  are disposed opposite to each other. The second inner sides S 21  face each other. There is a fourth distance G 4  between the second inner sides S 21 , and the fourth distance G 4  equals one-fourth of the first distance G 1 . In other words, the fourth distance G 4  between the second inner sides S 21  of the second electrodes  122  is designed as one-fourth of the unit width of the liquid crystal lenticular lens  104 . For example, if the unit width of the liquid crystal lenticular lens  104  is 257 micrometers, the fourth distance G 4  may be in a range between 64 micrometers and 65 micrometers, but not limited thereto. Because the second electrodes  122  are symmetric with respect to the first center point C 1 , the exact location of each of the second electrodes  122  in the liquid crystal lenticular lens  104  can be determined. Moreover, there is a fifth distance G 5  between the first center point C 1  and each of the second outer sides S 22 , and the fifth distance G 5  satisfies the following relation: 
     
       
         
           
             
               
                 
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     In this embodiment, because the number of the equal parts equals 5, the fifth distance G 5  of this embodiment is 
                 [       2   5     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
Accordingly, the first width W 1  of the second electrodes  122  can be determined with both the fourth distance G 4  and the fifth distance G 5 . The first width W 1 , for example, is in a range between 20 micrometers and 25 micrometers.
 
     In each of the electrode units  112 , each of the third electrodes  124  is respectively disposed between each of the first electrodes  120  and each of the second electrodes  122  adjacent to each other. Each of the third electrodes  124  has a second center point C 2 . Moreover, there is a sixth distance G 6  between the first center point C 1  and each of the second center points C 2 , and the sixth distance G 6  satisfies the following relation: 
     
       
         
           
             
               
                 
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     In this embodiment, because the number of the equal parts equals 5, the sixth distance G 6  of this embodiment is 
                 [       6   5     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
Accordingly, the exact location of each of the third electrodes  124  in the liquid crystal lenticular lens  104  can be determined.
 
     In addition, in each of the electrode units  112 , each of the fourth electrodes  126  is respectively disposed between each of the third electrodes  124  and each of the second electrodes  122  adjacent to each other. Each of the fourth electrodes  126  has a third center point C 3 . Moreover, there is a ninth distance G 9  between the first center point C 1  and each of the third center points C 3 , and the ninth distance G 9  satisfies the following relation: 
     
       
         
           
             
               
                 
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     In this embodiment, because the number of the equal parts equals 5, the ninth distance G 9  of this embodiment is 
                 [       4   5     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
Accordingly, the exact location of each of the fourth electrodes  126  in the liquid crystal lenticular lens  104  can be determined.
 
     In this embodiment, each of the third electrodes  124  has a second width W 2 . Each of the fourth electrodes  126  has a third width W 3 . Each of the first widths W 1 , each of the second widths W 2  and each of the third widths W 3  are in the ratio of 5:3:2. For example, the second width W 2  is in a range between 12 micrometers and 15 micrometers, and the third width W 3  is in a range between 8 micrometers and 10 micrometers, but not limited thereto. Furthermore, there is a tenth distance G 10  between each of the second electrodes  122  and each of the fourth electrodes  126  adjacent to each other. There is an eleventh distance G 11  between each of the fourth electrodes  126  and each of the third electrodes  124  adjacent to each other. There is a twelfth distance G 12  between each of the third electrodes  124  and each of the first electrodes  120  adjacent to each other. Each of the tenth distances G 10 , each of the eleventh distances G 11  and each of the twelfth distances G 12  in the ratio of 2:1:1. For example, the tenth distance G 10  is in a range between 19 micrometers and 21 micrometers, the eleventh distance G 11  is in a range between 8 micrometers and 12 micrometers, and the twelfth distance G 12  is in a range between 8 micrometers and 12 micrometers, but not limited thereto. 
     Please refer to  FIGS. 4-6 .  FIG. 4  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the first embodiment of the present invention. In  FIG. 4 , the first curve U 1  presents the relation between the refractive index of an ideal lens and the position in an electrode unit. The second curve U 2  presents the relation between the refractive index of the liquid crystal lenticular lens in this embodiment and the position in the electrode unit.  FIG. 5  is a schematic diagram of the refractive index versus the position in a liquid crystal lenticular lens of a conventional approach with thirteen electrodes. In  FIG. 5 , the third curve U 3  presents the relation between the refractive index of the liquid crystal lenticular lens and the position in the conventional approach with thirteen electrodes.  FIG. 6  is a schematic diagram of the refractive index versus the position in a liquid crystal lenticular lens of a conventional approach with seven electrodes. In  FIG. 6 , the fourth curve U 4  presents the relation between the refractive index of the liquid crystal lenticular lens and the position in the conventional approach with seven electrodes. As shown in  FIGS. 4-6 , the lens effect of the liquid crystal lenticular lens of this embodiment is an acceptable approximation of the lens effect of an ideal lens, and therefore the liquid crystal lenticular lens of this embodiment can offer a vivid three-dimensional stereoscopic image effectively. Compared with the liquid crystal lenticular lens in the conventional approach with thirteen electrodes, which requires thirteen power sources, the liquid crystal lenticular lens in this embodiment only requires seven power sources to match the lens effect of the liquid crystal lenticular lens in the conventional approach with thirteen electrodes. Accordingly, the liquid crystal lenticular lens in this embodiment can effectively lighten the loads of a power source, decrease the amount of electrodes in each of the electrode units, and broaden design possibilities. Moreover, compared with the liquid crystal lenticular lens in the conventional approach with seven electrodes, which requires seven power sources, the liquid crystal lenticular lens in this embodiment requires the same amount of power sources but more accurately match the lens effect similar to that of an ideal lens. 
     Please refer to  FIGS. 7-8 .  FIG. 7  is a schematic diagram illustrating a liquid crystal lenticular lens according to a second embodiment of the present invention.  FIG. 8  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the second embodiment of the present invention. In order to simplify and show the differences or modifications between the following embodiments and the above-mentioned embodiment, the same numerals denote the same components in the following description, and the similar parts are not detailed redundantly. As shown in  FIG. 7 , the difference between the first embodiment and this embodiment is that the number of the equal parts of the whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer equals 4. In addition, each of the electrode units  112  only includes the first electrodes  120 , the second electrodes  122  and the third electrodes  124  and excludes the fourth electrodes. Therefore, the liquid crystal lenticular lens  200  only requires the first voltage source V 1  applied to the first electrodes  120 , the second voltage source V 2  applied to one of the second electrodes  122 , the third voltage source V 3  applied to the other of the second electrodes  122 , the fourth voltage source V 4  applied to one of the third electrodes  124  and the fifth voltage source V 5  applied to the other of the third electrodes  124 . Accordingly, the second distance G 2  becomes 
                 [       6   4     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
The fifth distance G 5  becomes
 
                 [       2   4     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
The sixth distance G 6  becomes
 
                 [     df   ⁡     (       n   e     -     n   0       )       ]       1   2       .         
In this embodiment, the ratio of each of the first widths W 1  to each of the second widths W 2  is 2:1. There is a seventh distance G 7  between each of the second electrodes  122  and each of the third electrodes  124  adjacent to each other. There is an eighth distance G 8  between each of the third electrodes  124  and each of the first electrodes  120  adjacent to each other. The ratio of each of the seventh distances G 7  to each of the eighth distances G 8  is 1:1. As shown in  FIG. 8 , the first curve U 1  presents the relation between the refractive index of an ideal lens and the position in an electrode unit. The fifth curve U 5  presents the relation between the refractive index of the liquid crystal lenticular lens in the second embodiment and the position in the electrode unit. Moreover, the liquid crystal lenticular lens in this embodiment only requires five power sources to achieve the lens effect similar to that of an ideal lens, and therefore the liquid crystal lenticular lens of this embodiment can offer a vivid three-dimensional stereoscopic image effectively.
 
     Please refer to  FIGS. 9-10 .  FIG. 9  is a schematic diagram illustrating a liquid crystal lenticular lens according to a third embodiment of the present invention.  FIG. 10  is a schematic diagram of the refractive index versus the position in the liquid crystal lenticular lens according to the third embodiment of the present invention. In order to simplify and show the differences or modifications between the following embodiments and the above-mentioned embodiment, the same numerals denote the same components in the following description, and the similar parts are not detailed redundantly. As shown in  FIG. 9 , the difference between the first embodiment and this embodiment is that the number of the equal parts of the whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer equals 3. In addition, each of the electrode units  112  only includes the first electrodes  120  and the second electrodes  122  and excludes the fourth electrodes and the third electrodes. Therefore, the liquid crystal lenticular lens  300  only requires the first voltage source V 1  applied to the first electrodes  120 , the second voltage source V 2  applied to one of the second electrodes  122  and the third voltage source V 3  applied to the other of the second electrodes  122 . Accordingly, the second distance G 2  becomes 
                 [       4   3     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
The fifth distance G 5  becomes
 
                 [       2   3     ⁢     df   ⁡     (       n   e     -     n   0       )         ]       1   2       .         
As shown in  FIG. 10 , the first curve U 1  presents the relation between the refractive index of an ideal lens and the position in an electrode unit. The sixth curve U 6  presents the relation between the refractive index of the liquid crystal lenticular lens in the third embodiment and the position in the electrode unit. Moreover, the liquid crystal lenticular lens in this embodiment only requires three power sources to achieve the lens effect similar to that of an ideal lens, and therefore the liquid crystal lenticular lens of this embodiment can offer a vivid three-dimensional stereoscopic image effectively.
 
     In other variant embodiments of the present invention, the number of the equal parts of the whole difference between the extraordinary refractive index of the liquid crystal layer and the ordinary refractive index of the liquid crystal layer may be greater than 5. In this case, crystal lenticular lens may require more than seven power sources. Moreover, the quantity of electrodes in each of the electrode units may be greater than four pairs. 
     To sum up, in the liquid crystal lenticular lenses of the present invention, the refractive index of an ideal lens is divided into a plurality of equal parts. Electrodes with different widths and different pitches are disposed according to the equal parts so as to achieve the lens effect similar to that of an ideal lens. In this way, the loads of a power source can be effectively lightened, the amount of electrodes in each of the electrode units decreases, and design possibilities are broadened. 
     Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above invention should be construed as limited only by the metes and bounds of the appended claims.