Patent Publication Number: US-2015070607-A1

Title: Stereoscopic display apparatus

Description:
TECHNICAL FIELD 
     The present invention relates to a stereoscopic display apparatus. More particularly, the present invention relates to a stereoscopic display apparatus including a liquid crystal lens. 
     Priority is claimed on Japanese Patent Applications No. 2012-087600 filed Apr. 6, 2012, No. 2012-087579 filed Apr. 6, 2012, and No. 2012-088704 filed Apr. 9, 2012, the content of which are incorporated herein by reference. 
     BACKGROUND ART 
     Multiview stereoscopic display apparatuses regularly arrange and display images captured from multiple directions. For this reason, a resolution decreases as the number of points of view increases. Accordingly, a preferable configuration is such that a two-dimensional display mode and a three-dimensional display mode are switchable, and a resolution can be maintained in the two-dimensional display mode. 
     As such a stereoscopic display apparatus, stereoscopic display apparatuses using liquid crystal lenses are known. Regarding liquid crystal lenses, orientation of the liquid crystal is controlled based on a potential difference between an electrode pattern and a common electrode, thus forming a refractive index distribution. 
     Japanese Unexamined Patent Application, First Publication No. 2010-282090 discloses a stereoscopic display apparatus including a variable lens array element. The stereoscopic display apparatus includes a display panel and a variable lens array element. The variable lens array element includes a first electrode and a second electrode opposing the first electrode. The second electrode is formed smaller in width than a sub-pixel of the display panel. The second electrode is provided at least at the position of each of sub-pixels arranged in the horizontal direction. Regarding the variable lens array element, the voltages to be applied to a plurality of second electrodes are independently controlled, thus changing, for each sub-pixel, at least the horizontal position and the shape of the cylindrical lens. 
     DISCLOSURE OF THE INVENTION 
     Problems to be Solved by the Invention 
     In the liquid crystal lens, however, in a case where the distance between the electrode patterns is larger than the distance between the electrode pattern and the common electrode, there is a problem that an electric field is not applied to a central portion between the electrode patterns. In this case, a potential gradient is not formed in the central portion. Accordingly, an effective refractive index distribution cannot be obtained, and thus a function as the lens cannot be obtained. 
     Regarding a variable lens array element disclosed in Japanese Unexamined Patent Application, First Publication No. 2010-282090, an electrode pattern is formed for each sub-pixel, and the voltage to be applied to each electrode pattern is independently controlled. Thus, the horizontal position and the shape of the cylindrical lens are changed for each sub-pixel. However, in order to form an electrode pattern for each sub-pixel and independently control the voltage to be applied to the electrode pattern, a complex manufacturing process is required. Additionally, a signal generating circuit for generating various types of voltages is required. 
     An object of the present invention is to provide a stereoscopic display apparatus including a liquid crystal lens that can achieve an effective refractive index distribution even in a case where the distance between the electrode patterns is larger than the distance between the electrode pattern and the common electrode. 
     A three-dimensional display apparatus disclosed here includes a display device capable of displaying an image, and a liquid crystal lens disposed so as to overlap the display device. The liquid crystal lens includes an insulating substrate, a first electrode formed extending in a first direction, a second electrode formed substantially parallel to the first electrode, a high resistance portion electrically connecting the first electrode and the second electrode, an opposing substrate, a common electrode, a liquid crystal layer, and a controller. The sheet resistance of the high resistance portion is in 100 GΩ/sq or less. The controller controls, in one of the modes, the first electrode and the second electrode to be at different potentials. 
     According to the stereoscopic display apparatus of the present invention, even in a case where the distance between the electrode patterns is larger than the distance between the electrode pattern and the common electrode, it is possible to achieve an effective refractive index distribution. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an exploded perspective view showing a schematic configuration of a stereoscopic display apparatus according to one embodiment of the present invention. 
         FIG. 2  is a cross-sectional view taken along a line II-II shown in  FIG. 1  and schematically showing a configuration of a liquid crystal lens according to a first embodiment of the present invention. 
         FIG. 3  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the first embodiment, a part of a pattern substrate. 
         FIG. 4  is a schematic cross-sectional view showing the liquid crystal lens in one mode according to the first embodiment. 
         FIG. 5  is a schematic cross-sectional view showing the liquid crystal lens in another mode according to the first embodiment. 
         FIG. 6  is a schematic cross-sectional view showing a liquid crystal lens according to a hypothetical comparative example. 
         FIG. 7  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens according to the first embodiment. 
         FIG. 8  is a schematic sectional view showing a schematic configuration of a liquid crystal lens according to a second embodiment of the present invention. 
         FIG. 9  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the second embodiment, a part of a pattern substrate. 
         FIG. 10  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens according to the second embodiment. 
         FIG. 11  is a perspective view showing by extracting from the configuration of a liquid crystal lens according to a third embodiment, a part of a pattern substrate. 
         FIG. 12  is a plan view showing, by extracting from the configuration of the pattern substrate of the liquid crystal lens according to the third embodiment, a first electrode, a second electrode, an auxiliary electrode, and a high resistance portion. 
         FIG. 13  is a perspective view showing, by extracting from a configuration of a liquid crystal lens according to a fourth embodiment, a part of the pattern substrate. 
         FIG. 14  is a perspective view showing, by extracting from a configuration of a liquid crystal lens according to a fifth embodiment, a part of a pattern substrate. 
         FIG. 15  is a perspective view showing by extracting from a configuration of a liquid crystal lens according to a sixth embodiment, a part of a pattern substrate. 
         FIG. 16  is a schematic cross-sectional view illustrating a schematic configuration of a liquid crystal lens according to a seventh embodiment of the present invention. 
         FIG. 17  is a schematic cross-sectional view illustrating operation of the liquid crystal lens according to the seventh embodiment. 
         FIG. 18  is a schematic sectional view showing a schematic configuration of a liquid crystal lens according to an eighth embodiment of the present invention. 
         FIG. 19  is a schematic cross-sectional view illustrating operation of the liquid crystal lens according to the eighth embodiment. 
         FIG. 20  is a diagram showing an arrangement of components in a simulation performed to illustrate the effects of the embodiment. 
         FIG. 21  is a graph showing a result of the simulation and a theoretical curve in a case where liquid crystal molecules are subject to horizontal orientation when no voltage is applied. 
         FIG. 22  is a graph showing a result of the simulation and a theoretical curve in a case where liquid crystal molecules are subject to TN orientation when no voltage is applied. 
         FIG. 23  is a cross-sectional view taken along a line II-II shown in  FIG. 1  and schematically showing a configuration of a liquid crystal lens according to a ninth embodiment of the present invention. 
         FIG. 24  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the ninth embodiment, a part of a first substrate and a second substrate. 
         FIG. 25  is a schematic cross-sectional view showing the liquid crystal lens in one mode according to the ninth embodiment. 
         FIG. 26  is a schematic cross-sectional view showing the liquid crystal lens in another mode according to the ninth embodiment. 
         FIG. 27  is a schematic cross-sectional view showing a liquid crystal lens according to a hypothetical comparative example. 
         FIG. 28  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens according to a tenth embodiment of the present invention. 
         FIG. 29  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens according to the tenth embodiment. 
         FIG. 30  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens according to an eleventh embodiment of the present invention. 
         FIG. 31  is a schematic cross-sectional view illustrating operation of the liquid crystal lens according to the eleventh embodiment. 
         FIG. 32  is a schematic sectional view showing a schematic configuration of a liquid crystal lens according to a twelfth embodiment of the present invention. 
         FIG. 33  is a schematic cross-sectional view illustrating operation of the liquid crystal lens according to the twelfth embodiment. 
         FIG. 34  is a diagram and chart showing arrangement and potential of each component in a simulation performed to illustrate the effects of the embodiment. 
         FIG. 35  is a graph showing a result of the simulation and a theoretical curve in the case of the arrangement and potential shown in  FIG. 34 . 
         FIG. 36  is a diagram and chart showing arrangement and potential of each component in a simulation performed to illustrate the effects of the embodiment. 
         FIG. 37  is a graph showing a result of the simulation and a theoretical curve in the case of the arrangement and potential shown in  FIG. 36 . 
         FIG. 38  is a diagram and chart showing arrangement and potential of each component in a simulation performed to illustrate the effects of the embodiment. 
         FIG. 39  is a graph showing a result of the simulation and a theoretical curve in the case of the arrangement and potential shown in  FIG. 38 . 
         FIG. 40  is a diagram and chart showing arrangement and potential of each component in a simulation performed to illustrate the effects of the embodiment. 
         FIG. 41  is a graph illustrating a result of the simulation and a theoretical curve in the case of the arrangement and potential shown in  FIG. 40 . 
         FIG. 42  is a graph showing a relationship between the number of potentials on the horizontal axis and a root mean square of the difference from the theoretical curve on the vertical axis. 
         FIG. 43  is an exploded perspective view showing a schematic configuration of a stereoscopic display apparatus according to a thirteenth embodiment. 
         FIG. 44  is a diagram showing a cross section of the liquid crystal lens of the thirteenth embodiment, which is taken along II-II shown in  FIG. 43 . 
         FIG. 45  is a schematic diagram showing a state of the liquid crystal lens when a voltage is applied in the thirteenth embodiment. 
         FIG. 46  is a schematic diagram showing a state of the liquid crystal lens when no voltage is applied in the thirteenth embodiment. 
         FIG. 47  is a diagram showing a relationship between crosstalk and the ratio of the distance between the common electrode and the electrode pattern to the distance between electrode patterns. 
         FIG. 48  is a diagram showing parameters of a theoretical expression indicating the lens characteristics. 
         FIG. 49A  is a diagram showing conditions of the simulation of the lens characteristics. 
         FIG. 49B  is a diagram showing results of the simulations under the respective conditions shown in  FIG. 49A . 
         FIG. 49C  is a diagram showing a difference between the results of the simulations shown in  FIG. 49B  and theoretical values. 
         FIG. 50  is a schematic view showing a cross section of a liquid crystal lens according to a fourteenth embodiment. 
         FIG. 51  is a schematic view showing electrodes of the liquid crystal lens shown in  FIG. 50 , viewed from a positive direction of a z-axis. 
         FIG. 52  is a schematic view showing a cross section of the liquid crystal lens according to a fifteenth embodiment. 
         FIG. 53A  is a diagram showing a relationship between the luminance and the presence or absence of a polarizing plate in a modified example (2). 
         FIG. 53B  is a diagram showing a relationship between crosstalk and the presence or absence of the polarizing plate in the modified example (2). 
         FIG. 54A  is a schematic view showing a cross section of a liquid crystal lens according to a modified example (3). 
         FIG. 54B  is a schematic view showing a cross section of the liquid crystal lens according to the modified example (3). 
         FIG. 55A  is a schematic view showing an electrode pattern in a modified example (4). 
         FIG. 55B  is a schematic view showing the electrode pattern in the modified example (4). 
         FIG. 56  is a schematic view showing a cross section of a liquid crystal lens according to a modified example (5). 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     A three-dimensional display apparatus according to one embodiment of the present invention includes: a display device capable of displaying an image; and a liquid crystal lens disposed so as to overlap the display device. The liquid crystal lens includes: an insulating substrate; a first electrode formed on the substrate and extending in a first direction; a second electrode formed on the substrate and being substantially parallel to the first electrode; a high resistance portion formed on the substrate and electrically connecting the first electrode and the second electrode; an opposing substrate disposed opposing the substrate; a common electrode formed on the opposing substrate; a liquid crystal layer sandwiched between the substrate and the opposing substrate; and a controller configured to control potentials of the first electrode, the second electrode, and the common electrode, and switch two or more modes. The sheet resistance of the high resistance portion is in 100 GΩ/sq or less. The controller is configured to, in one of the modes, control the first electrode and the second electrode to be at different potentials (the first configuration of the three-dimensional display apparatus). 
     According to the above configuration, in one mode, the first and second electrodes are controlled to be at different potentials. The first and second electrodes are electrically connected by the high resistance portion. By the high resistance portion, the potential of the region between the first electrode and the second electrode continuously changes from the potential of the first electrode to the potential of the second electrode. For this reason, even when the distance between two adjacent first electrodes is long, it is possible to form a potential gradient up to a center portion between two adjacent first electrodes. The liquid crystal molecules of the liquid crystal layer are oriented according to the potential gradient, thus forming a refractive index distribution. It is possible to obtain excellent lens characteristics by forming the potential gradient up to the center portion between the two adjacent first electrodes. 
     In the above first configuration of the stereoscopic display apparatus, the high resistance portion may be formed to cover a region between the first electrode and the second electrode. In this case, it is preferable that the sheet resistance is 100 kΩ/sq or more (the second configuration of the stereoscopic display apparatus). 
     In the above first configuration of the stereoscopic display apparatus, the stereoscopic display apparatus may further includes an auxiliary electrode formed substantially parallel to the first electrode and the second electrode, the auxiliary electrode being electrically connected to the high resistance portion (the third configuration of the stereoscopic display device). 
     According to the above configuration, it is possible to form a potential difference between the auxiliary electrode and the common electrode. Thus, it is possible to form the high resistance portion in, for example, a region not overlapping the display area of the display apparatus. 
     In the above third configuration of the stereoscopic display apparatus, it is preferable that a resistance per unit length of the high resistance portion is 10 −4  to 2MΩ/μm (the fourth configuration of the stereoscopic display apparatus). 
     In the above fourth configuration of the stereoscopic display apparatus, it is preferable that the high resistance portion is formed close to one end of the first electrode (the fifth configuration of the stereoscopic display apparatus). 
     In the above fourth or fifth configuration of the of the stereoscopic display apparatus, it is preferable that the resistance per unit length of the high resistance portion changes along a direction perpendicular to the first direction (the sixth configuration of the stereoscopic display apparatus). 
     According to the above configuration, it is possible to change a slope of the potential gradient by changing the resistance of the high resistance portion. 
     In any one of the above first to sixth configurations of the stereoscopic display apparatus, it is preferable that the controller is configured to control two or less types of potentials of electrodes on a side of the substrate (the seventh configuration of the stereoscopic display apparatus). 
     According to the above configuration, it is possible to simplify a circuit for generating a potential. 
     In any one of the above first to the seventh configurations of the stereoscopic display apparatus, in a case that no potential difference is generated between the substrate and the opposing substrate, liquid crystal molecules of the liquid crystal layer may be oriented in a direction substantially parallel to the substrate (the eighth configuration of the stereoscopic display apparatus). 
     In any one of the first to the seventh configurations of the stereoscopic display apparatus, in a case that no potential difference is generated between the substrate and the opposing substrate, liquid crystal molecules of the liquid crystal layer may be oriented in a direction substantially vertical to the substrate (the ninth configuration of the stereoscopic display apparatus). 
     In the above eighth configuration of the stereoscopic display apparatus, in the case that no potential difference is generated between the substrate and the opposing substrate, an orientation direction of the liquid crystal molecules on a side of the substrate may be substantially perpendicular to an orientation direction of the liquid crystal molecules on a side of the opposing substrate (the tenth configuration of the stereoscopic display apparatus). 
     In the above tenth configuration of the stereoscopic display apparatus, the orientation direction of the liquid crystal molecules on the side of the substrate and the first direction form an angle of approximately 45 degrees (the eleventh configuration of the stereoscopic display apparatus). 
     In the above tenth or eleventh configuration of the stereoscopic display apparatus, it is preferable that the stereoscopic display apparatus further includes a polarizer disposed on the side of the substrate and having a polarization axis that is substantially parallel to the orientation direction of the liquid crystal molecules on the side of the substrate (the twelfth configuration of the stereoscopic display apparatus). 
     In the above tenth or eleventh configuration of the stereoscopic display apparatus, it is preferable that the stereoscopic display apparatus further includes a polarizer disposed on the side of the opposing substrate and having a polarization axis that is substantially parallel to the orientation direction of the liquid crystal molecules on the side of the opposing substrate (the thirteenth configuration of the stereoscopic display apparatus). 
     According to the above twelfth or thirteenth configuration of the stereoscopic display apparatus, when no potential difference is generated between the substrate and the opposing substrate, the orientation direction of the liquid crystal molecules is rotated by approximately 90° in a plane substantially perpendicular to the substrate. The polarization axis of the light incident on the liquid crystal layer rotates accordingly and passes through the polarizing plate. On the other hand, when the liquid crystal molecules are oriented substantially perpendicular to the substrate by the potential difference between the substrate and the opposing substrate, the polarization axis of the light incident on the liquid crystal layer does not rotate. For this reason, this light cannot pass through the polarizing plate. Thus, it is possible to form a hypothetical parallax barrier (parallax barrier) that blocks light at regular intervals. It is possible to reduce crosstalk by the parallax barrier. 
     In any one of the above first to thirteenth configuration of the stereoscopic display apparatus, the substrate may be disposed on a side of the display device (the fourteenth configuration of the stereoscopic display apparatus). 
     In any one of the above first to thirteenth configuration of the stereoscopic display apparatus, the opposing substrate may be disposed on a side of the display device (the fifteenth configuration of the stereoscopic display apparatus). 
     A liquid crystal lens according to one embodiment of the present invention includes: a first insulating substrate; a first electrode pattern on the first substrate, the first electrode pattern including a conductive portion and a non-conductive portion which are repeated in stripes along a first direction; a second insulating substrate opposing the first substrate; a second electrode pattern on the second substrate, the second electrode pattern including a conductive portion and a non-conductive portion which are repeated in stripes along the first direction; a liquid crystal layer sandwiched between the first substrate and the second substrate; and a controller configured to control potentials of the first electrode pattern and the second electrode pattern to switch between two or more modes (the first configuration of the liquid crystal lens). 
     According to the above configuration, the first electrode pattern and the second electrode pattern each including the conductive portion and the non-conductive portion which are repeated in stripes are formed on both the first substrate and the second substrate. Thus, it can become easier to apply an electric field to the in-plane direction in comparison with a case where an electrode pattern is formed on any one of the first substrate and the second substrate, and a uniform common electrode is formed on the other one. The liquid crystal molecules of the liquid crystal layer are oriented according to the electric field, thus forming a refractive index distribution. By the electric field being applied to the in-plane direction, a continuous refractive index distribution can be obtained. Thus, excellent lens characteristics can be obtained. 
     In the above first configuration of the liquid crystal lens, it is preferred that the non-conductive portion of the first electrode pattern and the non-conductive portion of the second electrode pattern are not opposed to each other (the second configuration of the liquid crystal lens). 
     According to the above configuration, over substantially the entire region on which the first electrode pattern and the second electrode pattern are formed, the conductive portion is formed on at least one of the first electrode pattern and the second electrode pattern. Thus, a potential gradient becomes easily formed in both the non-conductive portion of the first electrode pattern and the non-conductive portion of the second electrode pattern. Thus, it is possible to more effectively apply an electric field to the in-plane direction. 
     In the above first or second configuration of the liquid crystal lens, a width of the conductive portion of the first electrode pattern in a portion having a large potential difference between the first electrode pattern and the second electrode pattern is formed narrower in comparison with a portion having a small potential difference between the first electrode pattern and the second electrode pattern (the third configuration of the liquid crystal lens). 
     A refractive index distribution of the ideal GRIN (gradient index lens) lens becomes a quadratic curve. For this reason, a change in refractive index of the end portion of the lens is steeper than a change in refractive index of the center of the lens. Accordingly, in order to obtain lens characteristics close to those of the ideal GRIN lens, it is preferable to make the potential gradient in the end portion of the lens be steeper than the potential gradient at the center of the lens. The width of the first electrode pattern is formed narrower in a portion having a relatively large potential difference between the first electrode pattern and the second electrode pattern, in comparison with a portion having a relatively small potential difference between the first electrode pattern and the second electrode pattern. Thus, it is possible to make the potential gradient in the end portion of the lens be steeper. 
     In any one of the above first to third configurations of the liquid crystal lens, it is preferable that the controller is configured to control the potentials of the first electrode pattern and the second electrode pattern to be four or more potential levels in total (the fourth configuration of the liquid crystal lens). 
     In any one of the above first to fourth configurations of the liquid crystal lens, liquid crystal molecules of the liquid crystal layer may be oriented substantially parallel to the first substrate, in a case that no potential difference is generated between the first substrate and the second substrate (the fifth configuration of the liquid crystal lens). 
     In any one of the above first to fourth configurations of the liquid crystal lens, liquid crystal molecules of the liquid crystal layer may be oriented substantially vertical to the first substrate, in a case that no potential difference is generated between the first substrate and the second substrate (the sixth configuration of the liquid crystal lens). 
     In the above fifth configuration of the liquid crystal lens, in a case that no potential difference is generated between the first substrate and the second substrate, an orientation direction of the liquid crystal molecules on a side of the first substrate may be substantially perpendicular to an orientation direction of the liquid crystal molecules on a side of the second substrate (the seventh configuration of the liquid crystal lens). 
     In the above seventh configuration of the liquid crystal lens, an angle formed by the orientation direction of the liquid crystal molecules on the side of the first substrate and the second direction may be approximately 45 degrees (the eighth configuration of the liquid crystal lens). 
     In the above seventh or eighth configuration of the liquid crystal lens, the liquid crystal lens may further include a polarizer disposed on the first substrate side, the polarizer having a polarization axis substantially parallel to the orientation direction of the liquid crystal molecules on the side of the first substrate (the ninth construction of the liquid crystal lens). 
     In the above seventh or eighth configuration of the liquid crystal lens, the liquid crystal lens may further includes a polarizer disposed on the second substrate side, the a polarizer having a polarization axis substantially parallel to the orientation direction of the liquid crystal molecules on the side of the second substrate (the tenth construction of the liquid crystal lens). 
     According to the above ninth or tenth configuration of the liquid crystal lens, when no potential difference is generated between the first substrate and the second substrate, the orientation direction of the liquid crystal molecules is rotated by approximately 90° in a plane substantially perpendicular to the first substrate. The polarization axis of the light incident on the liquid crystal layer rotates accordingly and passes through the polarizing plate. On the other hand, when the liquid crystal molecules are oriented substantially perpendicular to the first substrate by the potential difference between the first substrate and the second substrate, the polarization axis of the light incident on the liquid crystal layer does not rotate. For this reason, this light cannot pass through the polarizing plate. Thus, it is possible to form a hypothetical parallax barrier (parallax barrier) that blocks light at regular intervals. It is possible to reduce crosstalk by the parallax barrier. 
     A stereoscopic display apparatus according to one embodiment of the present invention includes: a display device configured to display an image; and the liquid crystal lens according to any one of the above first to tenth configurations (the sixteenth construction of the liquid crystal lens). 
     In the above sixteenth configuration of the stereoscopic display apparatus, the first substrate of the liquid crystal lens may be disposed on a side of the display device (the seventeenth construction of the liquid crystal lens). 
     In the above sixteenth configuration of the stereoscopic display apparatus, the second substrate of the liquid crystal lens may be disposed on a side of the display device. 
     Embodiment 
     Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The same symbols will be appended to the same or corresponding portions in the drawings, and description thereof will not be repeated. In order to simplify the description, in the drawings referenced in the following, the illustrated configuration has been schematically simplified, or a part of components has been omitted. The dimensional ratio between components shown in each drawing does not necessarily indicate the actual dimension ratio. 
     [Entire Configuration] 
       FIG. 1  is an exploded perspective view showing a schematic configuration of a stereoscopic display apparatus  1  according to an embodiment of the present invention. The stereoscopic display apparatus  1  includes a liquid crystal lens  11 , a phase difference plate  12 , a spacer  13 , a liquid crystal display  14 , and a backlight  15 . 
     The liquid crystal lens  11  and the liquid crystal display  14  have plate-like shapes which are substantially rectangular in plan view, and are formed such that the sizes of main surfaces (surfaces with the largest area) are substantially equal to each other. 
     The liquid crystal display  14  has a display region D1 for displaying an image, and a non-display region P1 in which wires and the like are arranged. In  FIG. 1 , the non-display region P1 is formed in a frame-like shape surrounding the display region D1, but the arrangement of the non-display region P1 is not limited thereto. The liquid crystal lens  11  has a display region D schematically corresponding to the display region D1, and a non-display region P schematically corresponding to the non-display area P1. 
     Although a detailed configuration of the liquid crystal lens  11  will be described later, the liquid crystal lens  11  includes a pair of substrates and a liquid crystal layer sandwiched therebetween. The liquid crystal lens  11  changes orientation of liquid crystal molecules included in the liquid crystal layer, thereby changing behavior of light passing through the liquid crystal layer. 
     The phase difference plate  12  is disposed on the back of the liquid crystal lens  11 . The phase difference plate  12  adjusts the polarization direction of the light emitted from the liquid crystal display  14 . Here, it is not necessary to provide the phase difference plate  12 , depending on the polarization direction of the light emitted from the liquid crystal display  14 . 
     The liquid crystal display  14  is disposed on the back of the phase difference plate  12  through the spacer  13 . The liquid crystal display  14  includes an active matrix substrate, a color filter substrate disposed opposite thereto, and a liquid crystal layer sandwiched between both the substrates. TFTs (thin film transistors) and pixel electrodes are formed in a matrix on the active matrix substrate. The liquid crystal display  14  controls the TFTs, thereby changing orientation of the liquid crystal molecules included in the liquid crystal layer on any pixel electrode. Thus, the liquid crystal display  14  can display any image. 
     The backlight  15  is disposed on the back of the liquid crystal display  14 . The backlight  15  emits light to the liquid crystal display  14 . 
     The stereoscopic display apparatus  1  conjunctively controls the liquid crystal lens  11  and the liquid crystal display  14 , thereby switching between a two-dimensional display mode and a three-dimensional display mode. 
     In the two-dimensional display mode, the liquid crystal display  14  displays a normal two-dimensional image. At this time, the liquid crystal molecules included in the liquid crystal layer of the liquid crystal lens  11  are oriented uniformly, and most of the light passing through the liquid crystal lens  11  proceeds as it is. As a result, a normal two-dimensional image is displayed on the three-dimensional display device  1 . 
     In the three-dimensional display mode, the liquid crystal display  14  regularly arranges and displays images captured from multiple directions. Correspondingly with this, the liquid crystal lens  11  regularly changes orientation of the liquid crystal molecules included in the liquid crystal layer. Thus, when observing the stereoscopic display apparatus  1  at the optimum position, different images can reach the left and right eyes. In other words, in the three-dimensional display mode, the stereoscopic display apparatus  1  performs a stereoscopic display by a so-called parallax method. 
     The schematic configuration of the three-dimensional display device  1  has been described above. Here, the stereoscopic display apparatus  1  may include any display device other than the liquid crystal display  14 . 
     Embodiment 1 
     Hereinafter, the configuration of the liquid crystal lens  11  will be described in detail. Hereinafter, as shown in  FIG. 1 , a long-side direction, a short side direction, and a thickness direction of the liquid crystal lens  11  are respectively referred to as an x-direction, a y-direction, and a z-direction. 
       FIG. 2  is a cross-sectional view taken along a line II-II shown in  FIG. 1 , and schematically illustrates the configuration of the liquid crystal lens  11 . The liquid crystal lens  11  includes a patterned substrate S1, an opposing substrate C1, a liquid crystal layer  115 , and a controller  119 . 
     In the present embodiment, as liquid crystal molecules  115   a  constituting the liquid crystal layer  115 , liquid crystal molecules with positive dielectric anisotropy are used. The liquid crystal molecules  115   a  have birefringence. In other words, a refractive index n e  with respect to the light vibrating in a direction parallel to the optical axis is different from a refractive index n o  with respect to light vibrating in a direction perpendicular to the optical axis. Regarding the liquid crystal molecules  115   a , the liquid crystal molecules having a large value of Δn=n e −n o  are preferred. 
     The controller  119  controls the patterned substrate S1 and the opposing substrate C1, and applies an electric field to the liquid crystal layer  115 , thus changing the orientation of the liquid crystal molecules  115   a . The controller  119  is disposed in, for example, the non-display region P of the patterned substrate S1 or the opposing substrate C1. The controller  119  may be monolithically formed on these substrates by a semiconductor process. Alternatively, the controller  119  may be mounted on these substrates by the COG (chip on glass) technology. The controller  119  may be disposed on a place other than the non-patterned substrate S1 and the opposing substrate C1. In this case, the controller  119  is connected to those substrates via, for example, an FPC (flexible printed circuit). 
       FIG. 3  is a perspective view showing, by extracting from the configuration of the liquid crystal lens  11 , a part of the patterned substrate S1. As shown in  FIGS. 2 and 3 , the patterned substrate S1 includes a substrate  111 , a high resistance portion  112 , a first electrode  113 A, a second electrode  113 B, and an alignment film  114 . 
     The substrate  111  has light-transmissive and insulating properties. The sheet resistance of the substrate  111  is higher than 100 GΩ/sq. An example of the substrate  111  is a glass substrate. A surface of the substrate  111  may be coated with a passivation film, or the like. 
     The high resistance portion  112  is formed of a transparent material as a uniform film on the substrate  111 . A sheet resistance of the high resistance portion  112  is a 100 k to 100 GΩ/sq. An example of the high resistance portion  112  is IGZO (indium gallium zinc oxide). The high resistance portion  112  is deposited on the substrate  111  by, for example, a CVD (chemical vapor deposition). In this case, the sheet resistance can be controlled by, for example, varying the amount of impurities. 
     Preferably, the high resistance portion  112  is formed as a film covering the entire display region D and having a uniform thickness. 
     The first electrode  113 A and the second electrode  113 B are formed of a light transmissive material, in contact with the high resistance film  112 . As shown in  FIGS. 2 and 3 , the first electrode  113 A and the second electrode  113 B are alternately disposed at predetermined intervals along the x-direction. As shown in  FIG. 3 , each of the first electrode  113 A and the second electrode  113 B is formed elongated so as to extend in the y-direction. 
     The sheet resistances of the first electrode  113 A and the second electrode  113 B are, for example, 20 to 100 Ω/sq, and a lower resistance is preferred. An example of the first electrode  113 A and the second electrode  113 B is ITO (indium tin oxide) or IZO (indium zinc oxide). The first electrode  113 A and the second electrode  113 B are deposited by, for example, sputtering or CVD, and are patterned by photolithography. 
     The first electrode  113 A and the second electrode  113 B are connected to the controller  119  via wires (not shown). The controller  119  independently controls the potentials of the first electrode  113 A and the second electrode  113 B. In  FIG. 3 , as an example of applied voltages, the first electrode  113 A and the second electrode  113 B are respectively controlled to be at the potential V1 and the ground potential (GND). 
     The alignment film  114  is formed so as to cover the high resistance portion  112 , the first electrode  113 A, and the second electrode  113 B. An example of the alignment layer  114  is polyimide, which is formed by a printing method. 
     The opposing substrate C1 includes a substrate  116 , a common electrode  117 , and an alignment film  118 . 
     Similar to the substrate  111 , the substrate  116  has light-transmissive and insulating properties. An example of the substrate  116  is a glass substrate. 
     The common electrode  117  is uniformly formed of a light-transmissive material on the substrate  111 . Similarly to the first electrode  113 A and the second electrode  113 B, a sheet resistance of the common electrode  117  is, for example, 20 to 100 Ω/sq, and a lower value is preferred. An example of the common electrode  117  is ITO or IZO, and is deposited by sputtering or CVD. 
     The common electrode  117  is connected to the controller  119  via wires (not shown). The controller  119  controls the potential of the common electrode. 
     The alignment film  118  is formed so as to cover the common electrode  117 . Similar to the alignment film  114 , an example of the alignment film  118  is polyimide, and is formed by a printing method. 
     In the present embodiment, the alignment film  114  and the alignment film  118  have been rubbed (rubbing) in a direction substantially parallel to the x-direction. As a result, when no potential difference is generated between the patterned substrate  51  and the opposing substrate C1, the liquid crystal molecules  115   a  are oriented in the x-direction. 
     The liquid crystal lens  11  is manufactured by superimposing the patterned substrate S1 and the opposing substrate C1, sealing a periphery portion, and injecting liquid crystal into the gap. 
     Next, operation of the liquid crystal lens  11  will be described with reference to  FIGS. 4 and 5 . 
       FIG. 4  is a schematic cross-sectional view of the liquid crystal lens  11  in one mode. In  FIG. 4 , the controller  119  controls the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  to be the potentials V1, GND, and GND, respectively. 
     The liquid crystal molecules  115   a  are oriented so that molecular long axes thereof becomes parallel to the electric field generated by the potential difference between the patterned substrate S1 and the opposing substrate C1. The potential difference V1 is being generated between the first electrode  113 A and the common electrode  117 . Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the first electrode  113 A are oriented parallel to the z-direction. 
     In the present embodiment, the high resistance portion  112  is formed so as to cover a region between the first electrode  113 A and the second electrode  113 B. In other words, the first electrode  113 A and the second electrode  113 B are electrically connected to each other by the high resistance portion  112 . Therefore, the potential of the region between the first electrode  113 A and the second electrode  113 B is continuously changing from the potential V1 to GND. The potential of the common electrode  117  is constant at GND. For this reason, the potential difference between the patterned substrate S1 and the opposing substrate C1 is continuously changing from V1 to GND along the x-direction. Thus, the orientation direction of the liquid crystal molecules  115   a  is continuously changing from the z-direction to the x direction. 
     According to the change in the orientation direction of the liquid crystal molecules  115   a , a refractive index of the liquid crystal layer  115  changes. For this reason, the liquid crystal layer  115  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  115  can condense the light incident on the liquid crystal layer  115 , as indicated by dashed arrows shown in  FIG. 4 . In other words, the liquid crystal lens  11  in this mode functions as a gradient index lens (GRIN lenses). 
       FIG. 5  is a schematic cross-sectional view of the liquid crystal lens  11  in another mode. In  FIG. 5 , the controller  119  controls the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode to be GND. For this reason, no potential difference is generated between the patterned substrate S1 and the opposing substrate C1. The liquid crystal molecules  115   a  are oriented by the alignment films  114  and  118  so that the molecular long axes thereof become parallel to the x-direction. 
     Since the liquid crystal molecules  115   a  are aligned uniformly, the refractive index of the liquid crystal layer  115  also becomes uniform. As indicated by dashed arrows shown in  FIG. 5 , most of the light incident on the liquid crystal layer  115  passes as it is. In other words, the liquid crystal lens  11  is not functioning as a GRIN lens in this operation mode. 
     Thus, the liquid crystal lens  11  can switch the functions of the GRIN lens by the controller  119  controlling the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117 . 
     Comparative Example 
       FIG. 6  is a schematic cross-sectional view of a liquid crystal lens  91  according to a hypothetical comparative example to describe the effects of the present embodiment. The liquid crystal lens  91  includes a patterned substrate S9, in lieu of the patterned substrate S1. The patterned substrate S9 is one obtained by excluding the high resistance portion  112  and the second electrode  113 B from the configuration of the patterned substrate S1.  FIG. 6  also shows a manner of a change along the x-direction in potential difference between the patterned substrate S9 and the opposing substrate C1. 
     In  FIG. 6 , the controller  119  has controlled the potentials of the first electrode  113 A and the common electrode  117  to be the potential V1 and GND, respectively. Similar to the liquid crystal lens  11 , a potential difference V1 is generated between the first electrode  113 A and the common electrode  117 . Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the first electrode  113 A are oriented parallel to the z-direction. 
     However, in the liquid crystal lens  91 , a potential gradient is not formed in an intermediate region between two adjacent first electrodes  113 A. In this region, the orientation direction of the liquid crystal molecules  115   a  has not almost changed. For this reason, an effective refractive index distribution cannot be obtained, and therefore excellent lens characteristics cannot be obtained. 
     Such a problem arises when a value of the interval a between two adjacent first electrodes  113 A is larger than the distance d between the first electrode  113 A and the common electrode  117 . When the ratio a/d is approximately 7 or more, the liquid crystal lens  91  does not function as a GRIN lens. 
       FIG. 7  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens  11  according to the present embodiment.  FIG. 7  also shows a manner of a change along the x-direction in potential difference between the patterned substrate S1 and the opposing substrate C1. 
     In the present embodiment, the high resistance portion  112  electrically connects the first electrode  113 A and the second electrode  113 B. Thus, the potential difference between the patterned substrate S1 and the opposing substrate C1 is continuously changing from V1 to GND along the x-direction. In other words, a potential gradient is formed also in the intermediate region between two adjacent first electrodes  113 A. Thus, the orientation direction of the liquid crystal molecules  115   a  also changes continuously, and thus excellent lens characteristics can be obtained. 
     The sheet resistance of the high-resistance film  112  is 100 k to 100 GΩ/sq. This is due to the following reasons. 
     It is necessary that a potential drop from one end of the first electrode  113 A to the other end (the potential drop in the y-direction) be sufficiently small in comparison with a potential drop in the x-direction. Assuming that the sheet resistance of the high resistance portion  112  is ρ s , it is necessary to satisfy, for example, the relation ρ s ×0.5&gt;&gt;100×400 where the sheet resistance of the first electrode  113 A is 100 Ω/sq, the length in the y-direction of the first electrode  113 A is 400 mm, and the distance between the first electrode  113 A and the second electrode  113 B is 0.5 mm. Accordingly, the sheet resistance of the high resistance portion  112  should be 100 kΩ/sq or more. More preferably, the sheet resistance of the high resistance portion  112  is 500 kΩ/sq or more. Much more preferably, the sheet resistance of the high resistance portion  112  is 1 MΩ/sq or more. 
     On the other hand, a potential gradient cannot be formed when the sheet resistance of the high resistance portion  112  is too high. Accordingly, the sheet resistance of the high resistance portion  112  should be 100 GΩ/sq or less. More preferably, the sheet resistance of the high resistance portion  112  is 1 GΩ/sq or less. Much more preferably, the sheet resistance of the high resistance portion  112  is 100 MΩ/sq or less. 
     The configurations and effects of the liquid crystal lens  11  according to the first embodiment have been described above. According to the present embodiment, it is possible to obtain excellent lens characteristics even when the ratio a/d is large. 
     The liquid crystal lens  11  may be configured in the stereoscopic display apparatus  1  ( FIG. 1 ) such that the patterned substrate S1 is disposed on the liquid crystal display  14  side, or the opposing substrate C1 is disposed on the liquid crystal display  14  side. 
     The alignment films  114  and  118  of the liquid crystal lens  11  have been rubbed in a direction (x-direction) substantially perpendicular to the extending direction (y-direction) of the first electrode  113 A and the second electrode  113 B. However, the rubbing direction of the alignment films is optional. For example, the alignment films  114  and  118  may be rubbed parallel to the y-direction. 
     The description has been given above with respect to the example where in one mode of the liquid crystal lens  11 , the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  are respectively controlled to be V1, GND, and GND. Further, the description has been given above with respect to the example where in the other mode of the liquid crystal lens  11 , the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  are controlled to be GND. However, values of the potentials are all optional. For example, the potentials of the second electrode  113 B and the common electrode  117  need not be the same. Additionally, the potentials of the second electrode  113 B and the common electrode  117  may take any value other than GND. 
     The liquid crystal lens  11  can independently control, using the controller  119 , the first electrode  113 A and the second electrode  113 B. In other words, the liquid crystal lens  11  can simultaneously input two types of potentials to the patterned substrate S1. The liquid crystal lens  11  may be configured to be able to further input multiple types of potentials to the patterned substrate S1. In other words, a configuration may be such that the patterned substrate S1 further includes multiple kinds of electrodes, which are independently controlled by the controller  119 . 
     However, in order to increase the types of potentials, a signal generating circuit therefor is required. Further, if electrodes are densely formed, there is a concern about a reduction in yield. According to the present embodiment, even when the number of types of potentials is small, it is possible to obtain excellent lens characteristics with use of the high resistance portion  112 . 
     Second Embodiment 
     The stereoscopic display apparatus  1  may include, in lieu of the liquid crystal lens  11 , any one of liquid crystal lenses that will be described below. 
       FIG. 8  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens  21  according to a second embodiment of the present invention. The liquid crystal lens  21  includes a patterned substrate S2, in lieu of the patterned substrate S1.  FIG. 9  is a perspective view showing, by extracting from the configuration of the liquid crystal lens  21 , a part of the patterned substrate S2. As shown in  FIG. 9 , the patterned substrate S2 includes a high resistance portion  212 , in lieu of the high resistance portion  112  of the patterned substrate  51 . The patterned substrate S2 further includes an auxiliary electrode  213 . 
     The high resistance portion  212  is formed close to one ends of the first electrode  113 A and the second electrode  113 B. In other words, the high resistance portion  212  is formed close to the one end of the first electrode  113 A and the one end of the second electrode  113 B adjacent to the first electrode  113 A. Thus, the high resistance portion  212  is formed in the non-display region P of the substrate  111 . For this reason, the high resistance portion  212  may not have a light-transmissive property. Additionally, in the present embodiment, a signal is input from one ends of the first electrode  113 A and the second electrode  113 B. For this reason, a voltage drop is less likely to occur in the xy-plane. Accordingly, as the high resistance portion  212 , a material having a low resistivity can also be used in comparison with a high resistance portion  112  of the first embodiment. 
     The high resistance portion  212  is formed in a linear shape that is substantially parallel to the x-direction. The high resistance section  212  connects the first electrode  113 A and the second electrode  113 B. A resistance per unit length of the high resistance portion  212  is 10 −4  to 2 MΩ/μm. The resistance per unit length of the high resistance portion  212  may be controlled based on a material, a thickness, or a line width. 
     The auxiliary electrodes  213  are formed of a light-transmissive material on the substrate  111 . Each auxiliary electrode  213  is formed between the first electrode  113 A and the second electrode  113 B. Similar to the first electrode  113 A and the second electrode  113 B, the auxiliary electrodes  213  are disposed at predetermined intervals along the x-direction, and are formed elongated so as to extend in the y-direction. In other words, the auxiliary electrodes  213  are formed in a strip shape extending in the y-direction. A sheet resistance of the auxiliary electrode  213  is, for example, 20 to 100 Ω/sq, and a lower value is preferred. 
     The auxiliary electrode  213  is formed in contact with the high resistance portion  212 . Thus, the first electrode  113 A, the second electrode  113 B, and the auxiliary electrode  213  are electrically connected through the high resistance portion  212 . Here, the auxiliary electrode  213  is not controlled directly by the controller  119 . 
     Any two or more of the first electrode  113 A, the second electrode  113 B, the high resistance portion  212 , and the auxiliary electrode  213  can be formed of the same material and by the same process. In this case, these elements are, for example, ITO or IZO, which are deposited by CVD or sputtering and patterned by photolithography. 
       FIG. 10  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens  21 .  FIG. 10  also shows a manner of a change along the x-direction in potential difference between the patterned substrate S2 and the opposing substrate C1. 
     In  FIG. 10 , the controller  119  has controlled potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  to the potentials V1, GND, and GND, respectively. 
     In the present embodiment, the first electrode  113 A, the second electrode  113 B, and the auxiliary electrode  213  are electrically connected through the high resistance portion  212 . For this reason, the potential is changing continuously from the first electrode  113 A to the auxiliary electrode  213 , and from the auxiliary electrode  213  to the second electrode  113 B. Thus, the potential difference between the patterned substrate S2 and the opposing substrate C1 is continuously changing from V1 to GND along the x-direction. In other words, a potential gradient is formed even in an intermediate region between two adjacent first electrodes  113 A. Thus, the orientation direction of the liquid crystal molecules  115   a  also changes continuously, and therefore excellent lens characteristics can be obtained. 
     Considering a voltage drop between the power supplies, when a resistance value of the high resistance portion  212  is too low, it becomes necessary to increase the voltage to be applied. For this reason, a resistance per unit length of the high resistance portion  212  should be 10 −4  Ω/μm or more. More preferably, the resistance per unit length of the high resistance portion  212  is 1 Ω/μm or more. Much more preferably, the high resistance portion  212  is 100 Ω/μm or more. 
     On the other hand, when the resistance per unit length of the high resistance portion  212  is too high, a potential gradient cannot be formed. Accordingly, the resistance per unit length of the high resistance portion  212  should be 2MΩ/μm or less. More preferably, the resistance per unit length of the high resistance portion  212  is 20 kΩ/μm or less. Much more preferably, the resistance per unit length of the high resistance portion  212  is 2 kΩ/μm or less. 
     In  FIGS. 8 to 10 , two auxiliary electrodes  213  are formed between the first electrode  113 A and the second electrode  113 B, but the number of the auxiliary electrodes  213  is optional. The auxiliary electrode  213  is formed so as to extend from the high resistance portion  212  in the case of  FIG. 9 . However, the auxiliary electrode  213  and the high resistance portion  212  may be connected in any manner. For example, the auxiliary electrodes  212  may be formed so as to intersect the high resistance portion  212 . 
     Additionally, in  FIG. 9 , the high resistance portion  212  is formed in a straight line parallel to the x-direction. However, the high resistance portion  212  may not be parallel to the x-direction, nor be straight. 
     Also in the present embodiment, a configuration may be such that the patterned substrate S2 further includes multiple types of electrodes, and the controller  119  independently controls those electrodes. However, according to the present embodiment, even when the number of types of potentials is small, it is possible to obtain excellent lens characteristics by use of the high resistance portion  212 . 
     Third Embodiment 
     A liquid crystal lens according to a third embodiment of the present invention includes a patterned substrate S3, in lieu of the patterned substrate S2 of the liquid crystal lens  21 .  FIG. 11  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the third embodiment, a part of the patterned substrate S3. The patterned substrate S3 includes a high resistance portion  312 , in lieu of the high resistance portion  212  of the patterned substrate S2. 
       FIG. 12  is a plan view showing, by extracting from the configuration of the patterned substrate S3, the first electrode  113 A, the second electrode  113 B, the auxiliary electrode  213 , and the high resistance portion  312 .  FIG. 12  also shows a manner of a change along the x-direction in potential difference between the patterned substrate S3 and the common electrode C1. 
     In  FIG. 12 , the controller  119  has controlled potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  to be the potentials V1, GND, and GND, respectively. 
     The high resistance portion  312  has different line widths w1, w2, and w3. The line width w1 is a width of a portion connecting the first electrode  113 A and the auxiliary electrode  213 . The line width w2 is a width of a portion connecting two adjacent auxiliary electrodes  213 . The line width w3 is a width of a portion connecting the auxiliary electrode  213  and the second electrode  113 B. Thus, the resistance of the high resistance portion  312  differs among those electrodes. For this reason, the amounts of potential drops among those electrodes differ from one another. In the examples shown in  FIGS. 11 and 12 , the high resistance portion  312  is formed such that the line width w1&gt;the line width w2&gt;the line width w3. Thus, the amount of the potential drop between the first electrode  113 A and the auxiliary electrode  213  is smaller than the amount of a potential drop between two adjacent auxiliary electrodes  213 . Similarly, the amount of a potential drop between the two adjacent auxiliary electrodes  213  is smaller than the amount of a potential drop between the auxiliary electrode  213  and the second electrode  113 B. 
     Thus, it is possible to freely design a potential gradient by varying the resistance per unit length of the high resistance portion  312  along the x-direction. 
     In the present embodiment, the resistance of the high resistance portion  312  is changed by changing the line width of the high resistance portion  312 . However, a material or thickness of the high resistance portion  312  may be changed in order to change the resistance of the high resistance portion  312 . 
     Fourth Embodiment 
     A liquid crystal lens according to a fourth embodiment of the present invention includes a patterned substrate S4, in lieu of the patterned substrate S2 of the liquid crystal lens  21 .  FIG. 13  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the fourth embodiment, a part of the patterned substrate S4. The patterned substrate S4 includes high resistance portions  412 , in lieu of the high resistance portion  212  of the patterned substrate S2. 
     The high resistance portions  412  are formed close to both ends of both the first electrode  113 A and the second electrode  113 B. Thus, the high resistance portions  412  are formed on two opposing non-display regions P of the substrate  111 . 
     Further, in the patterned substrate S4, the controller  119  inputs signals from both sides in the y-direction to the first electrode  113 A and the second electrode  113 B. 
     It is possible to increase the redundancy of the signals by inputting signals from both sides in the y-direction. In other words, it is possible to form a strong structure for defects such as breakage. Additionally, by inputting signals from both sides in the y-direction, it is possible to reduce the potential difference between one end and the other end of the first electrode  113 A and the second electrode  113 B. 
     Fifth Embodiment 
     A liquid crystal lens according to a fifth embodiment of the present invention includes a patterned substrate S5, in lieu of the patterned substrate S2 of the liquid crystal lens  21 .  FIG. 14  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the fifth embodiment, a part of the patterned substrate S5. The patterned substrate S5 includes a high resistance portion  512 , in lieu of the high resistance portion  212  of the patterned substrate S2. 
     The high resistance portion  512  is formed in the display region D. For this reason, it is preferable that the high resistance portion  512  be formed of a light-transmissive material or with the sufficiently-thin line width. 
     Also in patterned substrate  55 , the controller  119  inputs signals from both sides of the y-direction to the first electrode  113 A and the second electrode  113 B. 
     Also in the present embodiment, similar effects to those in the fourth embodiment can be obtained. 
     Sixth Embodiment 
     A liquid crystal lens according to a sixth embodiment of the present invention includes a patterned substrate S6, in lieu of the patterned substrate S2 of the liquid crystal lens  21 .  FIG. 15  is a perspective view showing, by extracting from the configuration of the liquid crystal lens according to the sixth embodiment, a part of the patterned substrate S6. The patterned substrate S6 includes high resistance portions  612   a  to  612   e , in lieu of the high resistance portion  212  of the patterned substrate S2. 
     The high resistance portions  612   a  and  612   e  are formed close to both ends of the first electrode  113 A and the second electrode  113 B. Thus, the high resistance portions  612   a  and  612   e  are formed in the two opposing non-display regions P. On the other hand, the high resistance portions  612   b ,  612   c , and  612   d  are formed in the display region D. For this reason, it is preferable that the high resistance portions  612   b ,  612   c , and  612   d  be formed of a light-transmissive material or with sufficiently-thin line widths. The high resistance portions  612   a  to  612   e  may have different resistances per unit length and be formed of different materials. 
     Also in the patterned substrate S6, the controller  119  inputs signals from both sides of the y-direction to the first electrode  113 A and the second electrode  113 B. 
     In some cases, the high resistance portions  612   a  to  612   e  are formed thin or narrow in order to increase the resistance per unit length. It is possible to increase the redundancy by forming a plurality of high resistance portions. In other words, it is possible to form a strong structure for defects such as breakage. 
     Additionally, it is possible to control the amount of potential drops in the y-direction by changing the resistance per unit length of each of the high resistance portions  612   a  to  612   e . Thus, it is possible to equalize the potential in the y-direction of the first electrode  113 A and the like. 
     Seventh Embodiment 
       FIG. 16  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens  71  according to a seventh embodiment of the present invention. The liquid crystal lens  71  includes a patterned substrate S7, an opposing substrate C2, a liquid crystal layer  715 , and a controller  119 . 
     In the present embodiment, as liquid crystal molecules  715   a  constituting the liquid crystal layer  715 , liquid crystal molecules with negative dielectric anisotropy are used. 
     The patterned substrate S7 is one obtained by replacing the alignment film  114  of the patterned substrate S1 with an alignment film  714  for vertical alignment. The opposing substrate C2 is one obtained by replacing the alignment film  118  of the opposing substrate C1 with an alignment film  718  for vertical alignment. 
     When no potential difference is generated between the patterned substrate S7 and the opposing substrate C2, the liquid crystal molecules  715   a  are oriented by the alignment films  714  and  718  such that molecular long axes thereof are parallel to the z-axis direction. Since the liquid crystal molecules  715   a  are aligned uniformly, a refractive index of the liquid crystal layer  715  also becomes uniform. Accordingly, in this case, the liquid crystal lens  71  is not functioning as a GRIN lens. 
       FIG. 17  is a schematic cross-sectional view illustrating operation of the liquid crystal lens  71 . In  FIG. 17 , the controller  119  has controlled potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  to be the potentials V1, GND, and GND, respectively. 
     The liquid crystal molecules  715   a  with the negative dielectric anisotropy are oriented so that the molecular long axes thereof becomes vertical to the electric field generated by the potential difference between the patterned substrate S7 and the opposing substrate C2. A potential difference V1 has been generated between the first electrode  113 A and the common electrode  117 . Thus, the molecular long axes of the liquid crystal molecules  715   a  close to the first electrode  113 A are oriented perpendicular to the z-direction. 
     Also in the present embodiment, the high resistance portion  112  electrically connects the first electrode  113 A and the second electrode  113 B. Accordingly, the potential of the region between the first electrode  113 A and the second electrode  113 B is changing continuously from the potential V1 to GND. Thus, a potential gradient is formed along the x-direction between the patterned substrate S7 and the opposing substrate C2. According to this potential gradient, the orientation direction of the liquid crystal molecules  715   a  is also changing. For this reason, the liquid crystal layer  715  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  715  can condense the light incident on the liquid crystal layer  715 , as indicated by dashed arrows shown in  FIG. 19 . In other words, the liquid crystal lens  71  is functioning as a GRIN lens. 
     Thus, similarly to the liquid crystal lens  11 , the liquid crystal lens  71  can switch the functions of the GRIN lens by the controller  119  controlling the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117 . 
     Additionally, similarly to the liquid crystal lens  11 , it is possible to obtain excellent lens characteristics even when the ratio a/d is large by the presence of the second electrode  113 B and the high resistance portion  112 . 
     In the present embodiment, the alignment films  714  and  718  for vertical alignment are used. For this reason, there is no need to perform a rubbing treatment. Thus, it is possible to eliminate the influence of asymmetry due to a rubbing treatment. 
     Eighth Embodiment 
       FIG. 18  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens  81  according to an eighth embodiment of the present invention. The liquid crystal lens  81  includes a patterned substrate S8, an opposing substrate C3, a liquid crystal layer  115 , a controller  119 , and a polarizing plate  86 . 
     The patterned substrate S8 is one obtained by replacing the alignment film  114  of the patterned substrate S1 with an alignment film  814 . The direction of the rubbing treatment is different between the alignment film  114  and the alignment film  814 . Similarly, the opposing substrate C3 is one obtained by replacing the alignment film  118  of the opposing substrate C1 with an alignment film  818 . The direction of the rubbing treatment is different between the alignment film  118  and the alignment film  818 . 
     The alignment film  814  has been rubbed in a direction that forms an angle of approximately 45° with the extending direction of the first electrode  113 A (y-direction). The alignment film  818  has been rubbed in a direction substantially perpendicular to the rubbing direction of the alignment film  814 . 
     Thus, when no potential difference is generated between the patterned substrate S8 and the opposing substrate C3, the liquid crystal molecules  115   a  of the liquid crystal layer  115  are oriented as follows. In other words, the liquid crystal molecules  115   a  are oriented along the rubbing direction of the alignment layer  814  on the patterned substrate S8 side, and are oriented along the rubbing direction of the alignment layer  818  on the opposing substrate C3 side. Thus, the orientation direction of the liquid crystal molecules  115   a  is rotated by 90° between the opposing substrate C3 side and the patterned substrate S8 side. In other words, the liquid crystal layer  115  is TN (twisted nematic) liquid crystal. 
     The liquid crystal lens  71  further includes a polarizing plate  86 . The polarizing plate  86  is disposed on a main surface opposite to the liquid crystal layer  115  of the patterned substrate S8. The polarization axis of the polarizing plate  86  is substantially identical to the rubbing direction of the alignment film  814 . 
     Next, operation of the liquid crystal lens  81  will be described. First, by the phase difference plate  12  ( FIG. 1 ), the polarization direction of light emitted from the liquid crystal display  14  is aligned to the rubbing direction of the alignment film  818 . Here, it is not necessary to provide the phase difference plate  12 , depending on the polarization direction of the light emitted from the liquid crystal display  14 . 
     When no potential difference is generated between the patterned substrate S8 and the opposing substrate C3, the orientation direction of the liquid crystal molecules  115   a  is rotated as the level in the z-direction increases, as described above. On the other hand, the orientation direction of the liquid crystal molecules  115   a  is uniform in the xy-plane. 
     The orientation direction of liquid crystal molecules  115   a  is uniform in the xy-plane, a refractive index distribution thereof is also uniform in the xy-plane. Accordingly, when no potential difference is generated between the pattern substrate S8 and the opposing substrate C3, the liquid crystal lens  81  is not functioning as a GRIN lens. 
     As shown in  FIG. 18 , according to a change in orientation direction of the liquid crystal molecules  115   a , the polarization axis of the light incident on the liquid crystal layer  115  changes by 90°. The polarization axis of the polarizing plate  86  is substantially identical to the rubbing direction of the alignment film  814 . For this reason, light passing through the liquid crystal layer  115  can pass through the polarizing plate  86 . 
       FIG. 19  is a schematic cross-sectional view illustrating operation of the liquid crystal lens  81 . In  FIG. 19 , the controller  119  has controlled potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  to be the potentials V1, GND, and GND, respectively. 
     A potential difference V1 is generated between the first electrode  113 A and the common electrode  117 . Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the first electrode  113 A are oriented parallel to the z-direction. 
     Also in the present embodiment, the high resistance portion  112  electrically connects the first electrode  113 A and the second electrode  113 B. Accordingly, the potential of the region between the first electrode  113 A and the second electrode  113 B is changing continuously from the potential V1 to GND. Thus, a potential gradient is formed along the x-direction between the patterned substrate S8 and the common electrode C3. According to this potential gradient, the orientation direction of the liquid crystal molecules  115   a  is also changing. For this reason, the liquid crystal layer  115  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  115  can condense the light incident on the liquid crystal layer  115 , as indicated by dashed arrows shown in  FIG. 19 . In other words, the liquid crystal lens  81  is functioning as a GRIN lens. 
     At this time, the light passing through the vicinity of the first electrode  113 A passes through the liquid crystal layer  115  without the polarization axis being rotated. For this reason, the light cannot pass through the polarizing plate  86 , as indicated by solid arrows shown in  FIG. 19 . Thus, in the liquid crystal lens  81 , a virtual parallax barrier is formed in the boundary region of the virtual lens. 
     According to the present embodiment, the liquid crystal lens  81  has a function as a parallax barrier, in addition to the function as a GRIN lens. Thus, it is possible to reduce crosstalk in the stereoscopic display. 
     Thus, the liquid crystal lens  81  can switch between the function as a parallax barrier and the function as a GRIN lens by the controller  119  controlling the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  117 . 
     Similar to the liquid crystal lens  11 , it is possible to obtain excellent lens characteristics even when the ratio a/d is large by the presence of the high resistance portion  112  and the second electrode  113 B. 
     In the present embodiment, the polarizing plate  86  is disposed on the patterned substrate S8 side. In this case, in the stereoscopic display apparatus  1  ( FIG. 1 ), the opposing substrate C3 is disposed on the liquid crystal display  14  side. Here, the polarizing plate  86  may be disposed on the opposing substrate C3 side. In this case, in the stereoscopic display apparatus  1 , the patterned substrate S8 is disposed on the liquid crystal display  14  side. 
     The alignment film  814  of the liquid crystal lens  81  has been rubbed in a direction that forms an angle of 45° with the extending direction of the first electrode  113 A (y-direction). Additionally, the alignment film  818  has been rubbed in a direction perpendicular to the rubbing direction of the alignment film  814 . However, the rubbing directions of the alignment films  814  and  818  are optional as long as those rubbing directions intersect each other. 
     [Calculation Example of Lens Characteristics] 
     A simulation was performed using the configurations of the liquid crystal lens  11  and  81 .  FIG. 20  is a view showing the arrangement of each component in this simulation. A calculation was performed assuming that an interval a between two adjacent first electrodes  113 A is 2.0, the width w1 of the first electrode  113 A is 0.1, and the width w2 of the second electrode  113 B is 0.6. The calculation was performed assuming that the sheet resistances of the first electrode  113 A, the second electrode  113 B, and the common electrode  117  are 40 Ω/sq. The calculation was performed assuming that the sheet resistance of the high resistance portion  112  is 40MΩ/sq. The calculation was performed assuming that the refractive index difference Δn of the liquid crystal molecules of the liquid crystal layer  115  is 0.17. The calculation was performed assuming that the potentials of the first electrode  113 A, the second electrode  113 B, and the common electrode  17  are 2.0V, 0.5V, and 0.0V, respectively. 
       FIGS. 21 and 22  show the results. The horizontal axes shown in  FIGS. 21 and 22  represent the distance from the center of the lens. The vertical axes shown in  FIGS. 21 and 22  represent a phase difference (normalized value). 
       FIG. 21  is a graph showing a simulation result P1 and a theoretical curve P0 in the case of the liquid crystal lens  11 , that is, in a case where the liquid crystal molecules applied with no voltage were subject to horizontal orientation. A mean square of the difference between the simulation result P1 and the theoretical curve P0 were 0.046. 
       FIG. 22  is a graph showing a simulation result P2 and a theoretical curve P0 in the case of the liquid crystal lens  81 , that is, in a case where the liquid crystal molecules applied with the voltage were subject to TN orientation. A mean square of the difference between the simulation result P2 and the theoretical curve P0 were 0.055. 
     Thus, the lens characteristics close to the ideal one was obtained by the configuration of the liquid crystal lens  11  or the liquid crystal lens  81 . 
     Ninth Embodiment 
     The configuration of the liquid crystal lens  11  will be described in detail. Hereinafter, as shown in  FIG. 1 , a long-side direction, a short-side direction, and a thickness direction of the liquid crystal lens  11  are referred to as an x-direction, a y-direction, and a z-direction, respectively. 
       FIG. 23  is a cross-sectional view taken along a line II-II in  FIG. 1  and schematically showing the configuration of the liquid crystal lens  11 . The liquid crystal lens  11  includes a first substrate S11, a second substrate C11, a liquid crystal layer  115 , and a controller  119 . 
     In the present embodiment, as the liquid crystal molecules  115   a  constituting the liquid crystal layer  115 , liquid crystal molecules with positive dielectric anisotropy are used. The liquid crystal molecules  115   a  have birefringence. In other words, a refractive index n e  with respect to the light vibrating parallel to the optical axis differs from the refractive index n o  with respect to light vibrating perpendicular to the optical axis. The liquid crystal molecules  115   a  having a large value of Δn n =n e −n o  is preferred. 
     As the liquid crystal molecules  115   a , a ferroelectric liquid crystal may be used. The ferroelectric liquid crystal has a memory effect. For this reason, once the ferroelectric liquid crystal is oriented by applying an electric field thereto, there is no need to continuously apply the electric field to maintain the orientation. Therefore, it is possible to reduce the power consumption. 
     The controller  119  controls the first substrate S11 and the second substrate C11, applies the electric field to the liquid crystal layer  115 , and thus changes the orientation of the liquid crystal molecules  115   a . The controller  119  is disposed in, for example, the non-display region P of the first substrate S11 or the second substrate C11. The controller  119  can be formed monolithically on these substrates by a semiconductor process. Alternatively, the controller  119  can be mounted on these substrates by the COG (chip on glass) technology. The controller  119  may be disposed on a place other than the first substrate S11 and the second substrate C11. In this case, the controller  119  is connected to those substrates via, for example, a FPC (flexible printed circuit). 
       FIG. 24  is a perspective view showing, by extracting from the configuration of the liquid crystal lens  11 , a part of the first substrate S11 and the second substrate C11. As shown in  FIGS. 23 and 24 , the first substrate S11 includes a substrate  111 , a first electrode pattern  1113 , and an alignment film  114 . The second substrate C11 includes a substrate  116 , a second electrode pattern  1117 , and an alignment film  118 . 
     The substrate  111  and the substrate  116  have light-transmissive and insulating properties. Examples of the substrate  111  and the substrate  116  are glass substrates. Surfaces of the substrate  111  and the substrate  116  may be coated with a passivation film, or the like. 
     The first electrode pattern  1113  is formed on the substrate  111  so as to include a conductive portion and a non-conductive portion which are repeated in stripes along the x-direction. More specifically, the first electrode pattern  1113  includes electrodes  1113 A and electrodes  1113 B which are formed at predetermined intervals along the x-direction. 
     The second electrode pattern  1117  is formed on the substrate  116  so as to include a conductive portion and a non-conductive portion which are repeated in stripes along the x-direction. More specifically, the first electrode pattern  1117  includes electrodes  1117 A and electrodes  1117 B which are formed at predetermined intervals along the x-direction. 
     As shown in  FIG. 24 , each of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B is formed elongated so as to extend in the y-direction. The electrodes  1113 A,  1113 B,  1117 A, and  1117 B are formed of a light-transmissive conductive material. An example of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B is ITO (indium tin oxide) or IZO (indium zinc oxide). The electrodes  1113 A,  1113 B,  1117 A, and  1117 B, are deposited by, for example, sputtering or CVD, and are patterned by photolithography. 
     The electrodes  1113 A,  1113 B,  1117 A, and  1117 B are connected to the controller  119  via wires (not shown). The controller  119  independently controls the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B. In  FIG. 24 , as an example of the applied voltages, the controller  119  has controlled the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B to be the potentials V10, V20, V30, and V40, respectively. 
     The alignment film  114  is formed so as to cover the substrate  111  and the electrodes  1113 A and  1113 B. The alignment film  118  is formed so as to cover the substrate  116  and the electrodes  1117 A and  1117 B. For example, the alignment films  114  and  118  are polyimide, which is formed by a printing method. 
     In the present embodiment, the alignment films  114  and  118  have been rubbed in a direction substantially parallel with the x-direction (rubbing treatment). As a result, the liquid crystal molecules  115   a  are oriented in the x-direction when no potential difference is generated between the first substrate S11 and the second substrate C11. 
     The liquid crystal lens  11  is manufactured by superimposing the first substrate S11 and the second substrate C11, sealing a periphery portion, and injecting liquid crystal into the gap. 
     In the present embodiment, the electrodes  1113 A and  1117 A are arranged by aligning the center positions in the x-direction thereof to each other. On the other hand, the electrodes  1113 B and  1117 B are arranged by shifting the center positions in the x-direction thereof from each other. 
     Next, operation of the liquid crystal lens  11  will be described with reference to  FIGS. 25 and 26 . 
       FIG. 25  is a schematic cross-sectional view showing the liquid crystal lens  11  in one mode. In  FIG. 25 , the controller  119  has controlled the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B to be V10, V20, V30, and V40, respectively. 
     In the present embodiment, the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B are controlled to meet the condition that V10&gt;V20&gt;V40&gt;V30. 
     The liquid crystal molecules  115   a  are oriented so that the molecular long axes thereof become parallel to the electric field generated by the potential difference between the first substrate S11 and the second substrate C11. A potential difference (V10-V30) is generated between the electrodes  1113 A and  1117 A. Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the first electrode  1113 A are oriented parallel to the z-direction. 
     In the present embodiment, the position and width of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B, and the respective potentials V10, V20, V30, and V40 thereof are adjusted so that the potential difference between the first substrate S11 and the second substrate C11 becomes smallest at a middle position between two adjacent electrodes  1113 A. 
     Thus, the orientation direction of the liquid crystal molecules  115   a  is continuously changing along the x-direction, from the z-direction to the x-direction. 
     According to a change in orientation direction of the liquid crystal molecules  115   a , a refractive index of the liquid crystal layer  115  changes. For this reason, the liquid crystal layer  115  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  115  can condense the light incident on the liquid crystal layer  115 , as indicated by dashed arrows shown in  FIG. 25 . In other words, the liquid crystal lens  11  in this mode is functioning as a GRIN lens. 
       FIG. 26  is a schematic cross-sectional view of the liquid crystal lens  11  in another mode. In  FIG. 26 , the controller  119  has controlled the potentials of the electrode  1113 A,  1113 B,  1117 A, and  1117 B to be V0. For this reason, no potential difference is generated between the first substrate S11 and the second substrate C11. The liquid crystal molecules  115   a  are oriented by the alignment films  114  and  118  so that the molecular long axes thereof become parallel to the x-direction. 
     Since the liquid crystal molecules  115   a  are aligned uniformly, a refractive index of the liquid crystal layer  115  has also become uniform. As indicated by the dashed arrows shown in  FIG. 26 , most of the light incident on the liquid crystal layer  115  passes through as it is. In other words, the liquid crystal lens  11  in this operation mode is not functioning as a GRIN lens. 
     Thus, the liquid crystal lens  11  can switch the functions of the GRIN lens by the controller  119  controlling the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B using. 
     Comparative Example 
       FIG. 27  is a schematic cross-sectional view showing a liquid crystal lens  191  according a hypothetical comparative example to explain the effects of the present embodiment. The liquid crystal lens  191  includes a first substrate S9 in lieu of the first substrate S11, and a second substrate C9 in lieu of the second substrate C11. 
     The first substrate S9 includes an electrode pattern  913 , in lieu of the first electrode pattern  1113  of the first substrate S11. The electrode pattern  913  is one obtained by excluding the electrode  1113 B from the configuration of the first electrode pattern  1113 . 
     The second substrate C9 includes a common electrode  917 , in lieu of the second electrode patterns  1117  of the second substrate C11. The common electrode  917  is formed on the substrate  116  as a uniform film. 
     In  FIG. 27 , the controller  119  has controlled the potentials of the electrode  1113 A and the common electrode  917  to be a potential V10 and a ground potential (GND), respectively. A potential difference V10 has been generated between the electrode  1113 A and the common electrode  917 . Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the electrode  1113 A are oriented parallel to the z-direction. 
     However, in the liquid crystal lens  191 , a potential gradient is not formed in an intermediate region between two adjacent electrodes  1113 A. In this region, the orientation direction of the liquid crystal molecules  115   a  have not almost changed. For this reason, an effective refractive index distribution cannot be obtained, and therefore excellent lens characteristics cannot be obtained. 
     Such a problem arises when a value of an interval a between two adjacent electrodes  1113 A is large in comparison with a distance d between the electrode  1113 A and the common electrode  917 . If the ratio a/d is approximately 7 or more, the liquid crystal lens  191  does not function as a GRIN lens. 
     With reference to  FIG. 25  again, the effects of the present embodiment will be described. In the present embodiment, electrode patterns are formed not only on the first substrate S11, but also on the second substrate C11. This, the electric field becomes easily applied to the xy-plane. 
     The configuration and effect of the liquid crystal lens  11  according to the ninth embodiment have been described above. According to the present embodiment, it is possible to obtain excellent lens characteristics even when the ratio a/d is large. 
     In the present embodiment, the first electrode pattern  1113  includes the electrodes  1113 A and  1113 B. Additionally, the second electrode pattern  1117  includes the electrodes  1117 A and  1117 B. Then, the electrodes  1113 A,  1113 B,  1117 A, and  1117 B are independently controlled by the controller  119 . However, it is optional how many types of independent electrodes each of the first electrode pattern  1113  and the second electrode pattern  1117  includes. For example, any one or both of the first electrode pattern  1113  and the second electrode pattern  1117  may be constituted by one type of electrodes. Additionally, the first electrode pattern  1113  and the second electrode pattern  1117  may include three or more types of independent electrodes. 
     However, as will be described later, it is preferable that the controller  119  controls, based on four or more potential levels in total, the potentials of electrodes on the first electrode substrate S11 side and the potentials of electrodes on the second electrode substrate C11 side. 
     In the present embodiment, the electrodes  1113 A and  1117 A are arranged by aligning the center positions in the x-direction thereof to one another. On the other hand, the electrodes  1113 B and  1117 B are arranged by shifting the center positions in the x-direction thereof from one another. However, this arrangement is illustrative. The electrodes  1113 B and  1117 B may be arranged by shifting the center positions in the x-direction thereof from one another. Alternatively, the electrodes  1113 B and  1117 B may be arranged by aligning the center positions in the x-direction thereof to one another. 
     However, it is possible to reduce the number of electrodes required to form an electric field in the in-plane direction by arranging the electrodes by shifting the center positions of at least one pair of electrodes from each other. 
     In the present embodiment, the potentials of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B are controlled so as to meet the condition that V10&gt;V20&gt;V40&gt;V30. However, this is illustrative. The values of V10, V20, V30, and V40, and the positions and widths of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B, are adjusted in accordance with the lens characteristics. This will be described later along with specific examples. 
     The liquid crystal lens  11  may be configured such that, in the stereoscopic display apparatus  1  ( FIG. 1 ), the first substrate S11 is disposed on the liquid crystal display  14  side, or the second substrate C11 is disposed on the liquid crystal display  14  side. 
     The alignment films  114  and  118  of the liquid crystal lens  11  has been rubbed in a direction (x-direction) substantially perpendicular to the extending direction (y direction) of the electrodes  1113 A,  1113 B,  1117 A, and  1117 B. However, the rubbing direction of the alignment film is optional. For example, the alignment films  114  and  118  may be rubbed in a direction parallel to the y-direction. 
     Embodiment 10 
     The stereoscopic display apparatus  1  may include, in lieu of the liquid crystal lens  11 , any one of liquid crystal lens  121 ,  131 , and  141  described below. 
       FIG. 28  is a schematic cross-sectional view showing a schematic configuration of the liquid crystal lens  121  according to a tenth embodiment of the present invention. The liquid crystal lens  121  includes a first substrate S12 in lieu of the first substrate S11, and a second substrate C12 in lieu of the second substrate C11. 
     The first substrate S12 includes a first electrode pattern  1213 , in lieu of the first electrode pattern  1113  on the first substrate S11. The second substrate C12 includes a second electrode pattern  217 , in lieu of the second electrode pattern  1117  on the second substrate C11. 
     Similar to the first electrode pattern  1113  and the second electrode pattern  1117 , the first electrode pattern  1213  and the second electrode patterns  217  are formed such that a conductive portion and a non-conductive portion are repeated in stripes along the x-direction. The first electrode pattern  1213  includes electrodes  1213 A and electrodes  1213 B. The second electrode pattern  217  includes electrodes  217 A and electrodes  217 B. 
     In the liquid crystal lens  121 , the electrodes  1213 A,  1213 B,  217 A, and  217 B are formed respectively with the different widths in the x-direction. 
     In the liquid crystal lens  121 , as indicated by one-dot chain lines shown in  FIG. 28 , a non-conductive portion of the first electrode pattern  1213  and a non-conductive portion of the second electrode pattern  217  are not opposed to each other. In other words, over substantially the entire display region D of the liquid crystal lens  121  ( FIG. 1 ), a conductive portion (at least one of electrodes  1213 A,  1213 B,  217 A, and  217 B) is formed on at least one of the first substrate S12 and the second substrate C12. 
     Next, the effects of the present embodiment will be described with reference to  FIG. 29 .  FIG. 29  is a schematic cross-sectional view illustrating the effects of the liquid crystal lens  121 .  FIG. 29  shows a case where the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B are controlled to be V10, V20, V30, and V40, respectively.  FIG. 29  also shows a schematic refractive index of the liquid crystal layer  115  along the x-direction. 
     Similar to the ninth embodiment, also in the present embodiment, it is possible to switch the functions of a GRIN lens by the controller  119  controlling the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B. Additionally, an electrode pattern is formed not only on the first substrate S12, but also on the second substrate C12. Thus, the electric field becomes easily applied to the xy-plane. Accordingly, it is possible to obtain excellent lens characteristics even when the ratio a/d is large. 
     In the present embodiment, the non-conductive portion of the first electrode pattern  1213  and the non-conductive portion of the second electrode pattern  217  are not opposed to each other. As a result, the electric field is more easily applied to the xy-plane. For this reason, it is possible to further reduce the number of potentials necessary to obtain an effective refractive index distribution. 
     A refractive index distribution of the ideal GRIN lens becomes a quadratic curve as shown in  FIG. 29 . For this reason, a change in refractive index of the end portion of the lens is steeper than a change in refractive index of the center of the lens. Accordingly, in order to obtain lens characteristics close to those of the ideal GRIN lens, it is preferable to make the potential gradient in the end portion of the lens be steeper than the potential gradient at the center of the lens. 
     For this reason, it is preferable that the width in the x-direction of the first electrode pattern  1213  or the second electrode pattern  217  is formed narrower in a portion having a relatively large potential difference between the first substrate S12 and the second substrate C12, in comparison with a portion having a relatively small potential difference between the first substrate S12 and the second substrate C12. For example, in the present embodiment, the width in the x-direction of the electrode  1213 A is formed narrower in comparison with the width in the x-direction of the electrodes  1213 B,  217 A, and  217 B. 
     In the present embodiment, it is optional how many types of independent electrodes each of the first electrode pattern  1213  and the second electrode pattern  217  includes. Additionally, the electrodes  1213 A and the electrodes  217 A may be arranged by shifting the center positions in the x-direction thereof from one another. Alternatively, the electrodes  1213 B and the electrodes  217 B may be arranged by aligning the center positions in the x-direction thereof to one another. 
     Embodiment 11 
       FIG. 30  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens  131  according to an eleventh embodiment of the present invention. The liquid crystal lens  131  includes a first substrate S13, a second substrate C13, a liquid crystal layer  315 , and a controller  119 . 
     In the present embodiment, as the liquid crystal molecules  315   a  constituting the liquid crystal layer  315 , liquid crystal molecules with negative dielectric anisotropy are used. 
     The first substrate S13 is one obtained by replacing the alignment film  114  of the first substrate S12 with an alignment film  314  for vertical alignment. The second substrate C13 is one obtained by replacing the alignment film  118  of the second substrate C12 with an alignment film  318  for vertical alignment. 
     The liquid crystal molecules  315   a  are oriented by the alignment films  314  and  318  so that molecular long axes thereof become parallel to the z-axis direction when no potential difference is generated between the first substrate S13 and the second substrate C13. Since the liquid crystal molecules  315   a  are aligned uniformly, a refractive index of the liquid crystal layer  315  becomes uniform. Accordingly, in this case, the liquid crystal lens  131  is not functioning as a GRIN lens. 
       FIG. 31  is a schematic cross-sectional view illustrating operation of the liquid crystal lens  131 . In  FIG. 31 , the controller  119  has controlled the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B to V10, V20, V30, and V40, respectively. 
     The liquid crystal molecules  315   a  with the negative dielectric anisotropy are oriented so that the molecular long axes thereof become vertical to the electric field generated by the potential difference between the first substrate S13 and the second substrate C13. A potential difference (V10-V30) is being generated between the electrode  1213 A and the electrode  217 A. Thus, the molecular long axes of the liquid crystal molecules  315   a  close to the electrode  213 A are oriented in a direction perpendicular to the z-direction. 
     Also in the present embodiment, the positions and widths of electrodes  1213 A,  1213 B,  217 A, and  217 B, and the potentials V10, V20, V30, and V40 thereof are adjusted so that a potential difference between the first substrate S13 and the second substrate C13 becomes smallest at a middle position between two adjacent electrodes  1213 A. Thus, the orientation direction of the liquid crystal molecules  315   a  is continuously changing along the x-direction, from the x-direction to the z-direction. 
     For this reason, the liquid crystal layer  315  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  315  can condense the light incident on the liquid crystal layer  315 , as indicated by dashed arrows shown in  FIG. 31 . In other words, the liquid crystal lens  131  is functioning as a GRIN lens. 
     Thus, similar to the liquid crystal lens  11 , the liquid crystal lens  131  can switch the functions of the GRIN lens by the controller  119  controlling the potentials of electrodes  1213 A,  1213 B,  217 A, and  217 B. 
     Additionally, similarly to the liquid crystal lens  11 , electrode patterns are formed not only on the first substrate S13, but also on the second substrate C13. Thus, the electric field becomes easily applied to the xy-plane. Accordingly, it is possible to obtain excellent lens characteristics even when the ratio a/d is large. 
     In the present embodiment, the alignment films  314  and  318  for vertical alignment are used. For this reason, there is no need to perform a rubbing treatment. Thus, it is possible to eliminate the influence of asymmetry due to the rubbing treatment. 
     Twelfth Embodiment 
       FIG. 32  is a schematic cross-sectional view showing a schematic configuration of a liquid crystal lens  141  according to the twelfth embodiment of the present invention. The liquid crystal lens  141  includes a first substrate S14, a second substrate C14, a liquid crystal layer  115 , a controller  119 , and a polarizing plate  46 . 
     The first substrate S14 is one obtained by replacing the alignment film  114  of the first substrate S12 with an alignment film  414 . The directions of the rubbing treatments performed on the alignment film  114  and the alignment film  414  are different. Similarly, the second substrate C14 is one obtained by replacing the alignment film  118  of the second substrate C12 with an alignment film  418 . The directions of the rubbing treatments performed on the alignment film  118  and the alignment film  418  are different. 
     The alignment film  414  has been rubbed in a direction that forms an angle of approximately 45° with the extending direction (y-direction) of the electrodes  1113 A. The alignment film  418  has been rubbed in a direction substantially perpendicular to the rubbing direction of the alignment film  414 . 
     Thus, when no potential difference is generated between the first substrate S14 and the second substrate C14, the liquid crystal molecules  115   a  of the liquid crystal layer  115  are oriented as follows. In other words, the liquid crystal molecules  115   a  are oriented along the rubbing direction of the alignment layer  414  on the first substrate S14 side. Additionally, the liquid crystal molecules  115   a  are oriented along the rubbing direction of the alignment layer  418  on the second substrate C14 side. Thus, the orientation direction of the liquid crystal molecules  115   a  is rotated by 90° between the first substrate side S14 and the second substrate C14 side. In other words, the liquid crystal layer  115  is TN (twisted nematic) liquid crystal. 
     The liquid crystal lens  141  further includes a polarizing plate  46 . The polarizing plate  46  is disposed on a main surface of the first substrate S14 opposite to the liquid crystal layer  115 . The polarization axis of the polarizing plate  46  is substantially identical to the rubbing direction of the alignment film  414 . 
     Next, operation of the liquid crystal lens  141  will be described. First, by the phase difference plate  12  ( FIG. 1 ), a polarization direction of light emitted from the liquid crystal display  14  is aligned to the rubbing direction of the alignment film  418 . It is not necessary to provide the phase difference plate  12 , depending on the polarization direction of the light emitted from the liquid crystal display  14 . 
     When no potential difference is generated between the first substrate S14 and the second substrate C14, the orientation direction of the liquid crystal molecules  115   a  further rotates as the level in the z-direction increases, as described above. On the other hand, the orientation direction of the liquid crystal molecules  115   a  is uniform in the xy-plane. 
     Since the orientation direction of the liquid crystal molecules  115   a  is uniform in the xy-plane, a refractive index distribution thereof is also uniform in the xy-plane. Accordingly, when no potential difference is generated between the substrate S14 and the substrate C14, the liquid crystal lens  141  is not functioning as a GRIN lens. 
     As shown in  FIG. 32 , according to a change in the orientation direction of the liquid crystal molecules  115   a , the polarization axis of the light incident on the liquid crystal layer  115  changes by 90°. The polarization axis of the polarizing plate  46  is substantially identical to the rubbing direction of the alignment film  414 . For this reason, light passing through the liquid crystal layer  115  can pass through the polarizing plate  46 . 
       FIG. 33  is a schematic cross-sectional view illustrating operation of the liquid crystal lens  141 . In  FIG. 33 , the controller  119  has controlled the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B to V10, V20, V30, and V40, respectively. 
     A potential difference (V10-V30) is generated between the electrode  1213 A and the electrode  217 A. Thus, the molecular long axes of the liquid crystal molecules  115   a  close to the electrode  213 A are oriented parallel to the z-direction. 
     Also in the present embodiment, the positions and widths of the electrodes  1213 A,  1213 B,  217 A, and  217 B, and the potentials V10, V20, V30, and V40 thereof are adjusted so that the potential difference between the first electrode S14 and the second substrate C14 becomes smallest at a middle position between two adjacent electrodes  1213 A. Thus, the orientation direction of the liquid crystal molecules  115   a  is continuously changing along the x-direction, from the z-direction to the x-direction. 
     For this reason, the liquid crystal layer  115  has a refractive index distribution in the x-direction. By this refractive index distribution, the liquid crystal layer  115  can condense the light incident on the liquid crystal layer  115 , as indicated by dashed arrows shown in  FIG. 33 . In other words, the liquid crystal lens  141  is functioning as a GRIN lens. 
     At this time, the light passing through the vicinity of the electrode  213 A passes through the liquid crystal layer  115  without the polarization axis being rotated. For this reason, the light cannot pass through the polarizing plate  46 , as indicated by solid arrows shown in  FIG. 33 . Thus, the liquid crystal lens  141  forms a virtual parallax barrier in a boundary region of the virtual lens. 
     According to the present embodiment, the liquid crystal lens  141  has a function as a parallax barrier, in addition to the function as a GRIN lens. Thus, it is possible to reduce crosstalk in the stereoscopic display. 
     Thus, the liquid crystal lens  141  can switch the functions as the GRIN lens and the parallax barrier by the controller  119  controlling the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B. 
     Additionally, similarly to the liquid crystal lens  11 , electrode patterns are formed not only on the first substrate S14, but also on the second substrate C14. Thus, an electric field becomes easily applied to the xy-plane. Therefore, it is possible to obtain excellent lens characteristics even when the ratio a/d is large. 
     In the present embodiment, the polarizing plate  46  is disposed on the first substrate S14 side. In this case, in the stereoscopic display apparatus  1  ( FIG. 1 ), the second substrate C14 is disposed on the liquid crystal display  14  side. Here, the polarizing plate  46  may be disposed on the second substrate C14 side. In this case, in the stereoscopic display apparatus  1 , the first substrate S14 is disposed on the liquid crystal display  14  side. 
     The alignment film  414  of the liquid crystal lens  141  has been rubbed in a direction that forms an angle of 45° with the extending direction (y-direction) of the electrodes  1113 A. Additionally, the alignment film  418  has been rubbed in a direction perpendicular to the rubbing direction of the alignment film  414 . However, the rubbing directions of the alignment films  414  and  418  are optional as long as the rubbing directions intersect each other. 
     [Calculation Example of Lens Characteristics] 
     Hereinafter, a calculation example of lens characteristics will be described with reference to  FIGS. 34 to 41 . A simulation of the lens characteristics was performed while changing the number of potentials.  FIGS. 34 ,  36 ,  38 , and  40  are diagrams and charts showing the arrangement and potential of each component in the simulation.  FIGS. 35 ,  37 ,  39 , and  41  are graphs showing results of the simulation where a horizontal axis represents a distance (μm) from the center of the lens, and a vertical axis represents a phase difference (wave number). 
       FIGS. 34 ,  36 ,  38 , and  40  show, by extracting, only related configurations. The calculation was performed assuming that the liquid crystal molecules of the liquid crystal layer are subjected to TN orientation when no potential difference is generated between the first substrate  111  and the second substrate  116 . In any case, calculation was performed assuming that an interval between the electrodes (pitch) is 700 μm. Additionally, calculation was performed assuming that a distance d between the first substrate  111  and the second substrate  116  (approximately equal to the distance between the electrode on the first electrode substrate  111  and the electrode on the second substrate  116 ) is 60 μm. The ratio a/d was 11.66, thus exceeding 7.0. 
     In  FIG. 34 , the electrodes  213 A were arranged on the first substrate  111 , and the common electrode  917  was disposed on the second substrate  116 . Then, the potentials of the electrode  213 A and the common electrode  917  were respectively controlled to be two potential levels, V10 and V20, thus forming a potential gradient. Here, W10 is the half width of the electrode  213 A, and G11 is an interval between two adjacent electrodes  213 A. Thus, the electrode pattern including the conductive portion and the non-conductive portion which are repeated in stripes was disposed on the first substrate  111 , and the uniform common electrode  917  was disposed on the second substrate  116 , and then calculation was performed. 
       FIG. 35  is a graph showing a potential simulation result P2 in the case of two potential levels, and a theoretical curve P0. Since the ratio a/d exceeds 7.0, it can be found that an effective refractive index distribution cannot be obtained at a point close to the center between two adjacent electrodes  213 A. A mean square of the difference between the simulation result P2 and the theoretical curve P0 was 1.88. 
     In  FIG. 36 , the electrodes  1213 A and  1213 B were arranged on the first substrate  111 , and the electrodes  217 A and  217 B were arranged on the second substrate  116 . Then, the potentials of the electrodes  1213 A,  1213 B,  217 A, and  217 B were respectively controlled to be four potential levels, V10, V20, V30, and V40, thus forming a potential gradient. Here, W10 is the half width of the electrode  1213 A. W20 is the width of the electrode  1213 B. W30 is the half width of the electrode  217 A. W40 is the width of the electrode  217 B. G12 is a distance between the electrode  1213 A and the electrode  1213 B. G22 is an interval between two adjacent electrodes  1213 B. G34 is a distance between the electrode  217 A and the electrode  217 B. Thus, an electrode patterns including the conductive portion and the non-conductive portion which are repeated in stripes is disposed on both the first substrate  111  and the second substrate  116 , and then calculation was performed. 
       FIG. 37  is a graph showing a simulation result P4 in the case of four potential levels, and a theoretical curve P0. A mean square of the difference between the simulation result P4 and the theoretical curve P0 was 0.40. 
     In  FIG. 38 , the electrodes  1213 A,  1213 B, and  1213 C were arranged on the first substrate  111 , and the electrodes  217 A,  217 B, and  217 C were arranged on the second substrate  116 . Then, the potentials of the electrodes  1213 A,  1213 B,  1213 C,  217 A,  217 B, and  217 C were respectively controlled to be six potential levels, V10, V20, V30, V40, V50, and V60, thus forming a potential gradient. Here, W10 is the half width of the electrodes  1213 A. W20 is the width of the electrode  1213 B. W30 is the width of the electrode  1213 C. W40 is the half width of the electrode  217 A. W50 is the width of the electrode  217 B. W60 is the width of the electrode  217 C. G12 is the distance between the electrode  1213 A and the electrode  1213 B. G23 is the distance between the electrode  1213 B and the electrode  1213 C. G33 is the interval between two adjacent electrodes  1213 C. G45 is the distance between the electrode  217 A and the electrode  217 B. G56 is the distance between the electrode  217 B and the electrode  217 C. Thus, the electrode pattern including the non-conductive portion and the conductive portion which are repeated in stripes was disposed on both the first substrate  111  and the second substrate  116 , and then calculation was performed. 
       FIG. 39  is a graph showing a simulation result P6 in the case of the six potential levels, and a theoretical curve P0. A mean square of the difference between the simulation result P6 and the theoretical curve P0 was 0.21. 
     In  FIG. 40 , the electrode  1213 A,  1213 B,  1213 C, and  1213 D were on the first substrate  111 , and the electrodes  217 A,  217 B,  217 C, and  217 D were arranged on the second substrate  116 . Then, the potentials of the electrode  213 A,  213 B,  213 C,  213 D,  217 A,  217 B,  217 C, and  217 D were respectively controlled to be 8 potential levels, V10, V20, V30, V40, V50, V60, V70, and V8, thus forming a potential gradient. Here, W10 is the half width of the electrode  1213 A. W20 is the width of the electrode  1213 B. W30 is the width of the electrode  1213 C. W40 is the width of the electrode  1213 D. W50 is the half width of the electrode  217 A. W60 is the width of the electrode  217 B. W70 is the width of the electrode  217 C. W80 is the width of the electrode  217 D. G12 is the distance between the electrode  1213 A and the electrode  1213 B. G23 is the distance between the electrode  1213 B and the electrode  1213 C. G34 is the distance between the electrode  1213 C and the electrode  1214 D. G44 is the interval between two adjacent electrodes  1213 D. G56 is the distance between the electrode  217 A and the electrode  217 B. G67 is the distance between the electrode  217 B and the electrode  217 C. G78 is the distance between the electrode  217 C and the electrode  217 D. Thus, the electrode pattern including the conductive portion and the non-conductive portion which are repeated in stripes was disposed on both the first substrate  111  and the second substrate  116 , and then calculation was performed. 
       FIG. 41  is a graph showing a simulation result P8 in the case of the eight potential levels, and a theoretical curve P0. A mean square of the difference between the simulation result P8 and the theoretical curve P0 was 0.13. 
       FIG. 42  is a graph showing a relationship between the number of potentials on a horizontal axis and a mean square of the difference from the theoretical curve C0 on a vertical axis. As shown in  FIG. 42 , the difference from the theoretical curve C0 is abruptly small when the number of potential levels is four or more. Accordingly, the number of potentials is preferably four or more. 
     The configurations of the liquid crystal lens and the stereoscopic display apparatus according to one aspect of the present invention are described as the following notes. 
     [Note 1] 
     A liquid crystal lens comprising: 
     a first insulating substrate; 
     a first electrode pattern on the first substrate, the first electrode pattern including a conductive portion and a non-conductive portion which are repeated in stripes along a first direction; 
     a second insulating substrate opposing the first substrate; 
     a second electrode pattern on the second substrate, the second electrode pattern including a conductive portion and a non-conductive portion which are repeated in stripes along the first direction; 
     a liquid crystal layer sandwiched between the first substrate and the second substrate; and 
     a controller configured to control potentials of the first electrode pattern and the second electrode pattern to switch between two or more modes. 
     [Note 2] 
     The liquid crystal lens according to Note 1, wherein the non-conductive portion of the first electrode pattern and the non-conductive portion of the second electrode pattern are not opposed to each other. 
     [Note 3] 
     The liquid crystal lens according to Note 1 or 2, wherein a width of the conductive portion of the first electrode pattern in a portion having a large potential difference between the first electrode pattern and the second electrode pattern is formed narrower in comparison with a portion having a small potential difference between the first electrode pattern and the second electrode pattern. 
     [Note 4] 
     The liquid crystal lens according to any one of Notes 1 to 3, wherein the controller is configured to control the potentials of the first electrode pattern and the second electrode pattern to be four or more potential levels in total. 
     [Note 5] 
     The liquid crystal lenses according to any one of Notes 1 to 4, wherein liquid crystal molecules of the liquid crystal layer are oriented substantially parallel to the first substrate, in a case that no potential difference is generated between the first substrate and the second substrate. 
     [Note 6] 
     The liquid crystal lenses according to any one of Notes 1 to 4, wherein liquid crystal molecules of the liquid crystal layer are oriented substantially vertical to the first substrate, in a case that no potential difference is generated between the first substrate and the second substrate. 
     [Note 7] 
     The liquid crystal lens according to Note 5, wherein in a case that no potential difference is generated between the first substrate and the second substrate, an orientation direction of the liquid crystal molecules on a side of the first substrate is substantially perpendicular to an orientation direction of the liquid crystal molecules on a side of the second substrate. 
     [Note 8] 
     The liquid crystal lens according to Note 7, wherein the orientation direction of the liquid crystal molecules on the side of the first substrate and the second direction form approximately 45 degrees. 
     [Note 9] 
     The liquid crystal lens according to Note 7 or 8 further comprising: 
     a polarizer disposed on the first substrate side, the polarizer having a polarization axis substantially parallel to the orientation direction of the liquid crystal molecules on the side of the first substrate. 
     [Note 10] 
     The liquid crystal lens according to Note 7 or 8 further comprising: 
     a polarizer disposed on the second substrate side, the a polarizer having a polarization axis substantially parallel to the orientation direction of the liquid crystal molecules on the side of the second substrate. 
     [Note 11] 
     A stereoscopic display apparatus comprising: 
     a display device configured to display an image; and 
     the liquid crystal lens according to any one of Notes 1 to 10. 
     [Note 12] 
     The stereoscopic display apparatus according to Note 11, wherein the first substrate of the liquid crystal lens is disposed on a side of the display device. 
     [Note 13] 
     The stereoscopic display apparatus according to Note 11, wherein the second substrate of the liquid crystal lens is disposed on a side of the display device. 
     [Configuration According to Another Aspect of the Present Invention] 
     Hereinafter, a configuration according to another aspect of the present invention will be described. Specifically, Japanese Unexamined Patent Application, First Publication No. 2010-282090 described above discloses a configuration in which a variable lens array element based on the liquid crystal lens system switches between two dimensional display and three-dimensional display. This configuration includes a first electrode in a planar shape and a plurality of second electrodes provided for the arrangement position of each sub-pixel, the first and second electrodes sandwiching a liquid crystal layer of the variable lens array element. The second electrode is provided for each sub-pixel. With this configuration, the voltages applied to the second electrodes are independently controlled in accordance with the viewpoint of an observer, thus solving the problem of crosstalk such that a parallax image for the right or left eye of the observer in the 3-dimensional display includes a parallax image of the other eye. 
     However, in the configuration disclosed in Japanese Unexamined Patent Application, First Publication No. 2010-282090, at least the second electrode is required for each sub-pixel, and a plurality of voltages to be applied to the respective second electrodes are also required. For this reason, there is a problem that a wiring process becomes complicated, and the manufacturing cost increases. In another aspect of the present invention, embodiments disclosed below provide technique of reducing crosstalk in three-dimensional display without increasing the number of electrodes in a liquid crystal lens. 
     For this reason, a liquid crystal lens disclosed below includes: an electrode pattern unit configured to transmit light and including a first electrode, the first electrode including a conductive portion and a non-conductive portion which are repeated at predetermined intervals; a common electrode unit configured to transmit light and including a common electrode at a position opposing the first electrode; a controller configured to control potentials of the first electrode and the common electrode and to cause a potential difference to be generated between the electrode pattern unit and the common electrode unit; a light controller including a liquid crystal layer formed between the common electrode unit and the electrode pattern unit, the liquid crystal layer having a refractive index distribution of light that is variably controlled by an electric field according to the potential difference; and a non-conductive layer formed between the common electrode unit and the electrode pattern unit, the non-conductive layer being formed of a light-transmissive medium. A ratio a/d is greater than 3.0 and is less than 8.5 where a is a distance between two adjacent conductive portions on the first electrode, and d is a distance between the common electrode unit and the electrode pattern unit. 
     According to the above configuration, it is possible to reduce crosstalk in three-dimensional display without increasing the number of electrodes. 
     Hereinafter, specific embodiments will be described. A liquid crystal lens disclosed below includes: an electrode pattern unit configured to transmit light and including a first electrode, the first electrode including a conductive portion and a non-conductive portion which are repeated at predetermined intervals; a common electrode unit configured to transmit light and including a common electrode at a position opposing the first electrode; a controller configured to control potentials of the first electrode and the common electrode and to cause a potential difference to be generated between the electrode pattern unit and the common electrode unit; a light controller including a liquid crystal layer formed between the common electrode unit and the electrode pattern unit, the liquid crystal layer having a refractive index distribution of light that is variably controlled by an electric field according to the potential difference; and a non-conductive layer formed between the common electrode unit and the electrode pattern unit, the non-conductive layer being formed of a light-transmissive medium. A ratio a/d is greater than 3.0 and is less than 8.5 where a is a distance between two adjacent conductive portions on the first electrode, and d is a distance between the common electrode unit and the electrode pattern unit (the eleventh configuration of the liquid crystal lens). According to this configuration, by the provision of the non-conductive layer, the electric field becomes easily applied also to the non-conductive portion of the liquid crystal layer. As a result, it is possible to reduce crosstalk in three-dimensional display without increasing the number of electrodes. 
     Additionally, in the above eleventh configuration of the liquid crystal lens, the electrode pattern unit further includes a second electrode including a conductive portion and a non-conductive portion which are repeated at predetermined intervals. The controller may be configured to control the potentials of the electrode pattern unit and the common electrode unit so that the potential difference between the first electrode and the common electrode differs from the potential difference between the second electrode and the common electrode (twelfth configuration of the liquid crystal lens). According to the twelfth configuration, it is possible to more precisely control a change in orientation of the liquid crystal molecules included in the liquid crystal layer, compared to the case where the present configuration is not provided. 
     Further, in the above eleventh or twelfth configuration of the liquid crystal lens, the liquid crystal molecules in the liquid crystal layer may be oriented substantially parallel to one direction of the display region when no potential difference is generated between the electrode pattern unit and the common electrode portion (thirteenth configuration). According to the thirteenth configuration, in addition to the above effects of the eleventh and twelfth configurations, liquid crystal materials of the positive type can be used. Thus, a thickness of the liquid crystal layer can be reduced in comparison with the case of vertical orientation where liquid crystal materials of the negative type are used, thus enabling enhancement of the response speed. 
     Moreover, in the above eleventh or twelfth configuration, when no potential difference is generated between the electrode pattern unit and the common electrode unit, an orientation direction of the liquid crystal molecules included in the liquid crystal layer on a side of the common electrode unit may be substantially perpendicular to that on a side of the electrode pattern unit (fourteenth configuration of the liquid crystal lens). Additionally, in the fourteenth configuration, the orientation direction and a direction substantially perpendicular to the arrangement direction of the first electrode may form an angle of approximately 45 degrees (fifteenth configuration of the liquid crystal lens). 
     According to the fourteenth or fifteenth configuration, it is possible in addition to reduce the manufacturing cost of the liquid crystal lens, in addition to the effects of the eleventh and twelfth configurations. 
     Further, in the above fourteenth or fifteenth configuration of the liquid crystal lens, the liquid crystal lens includes a polarizing plate on a light emitting side of the light controller. A polarization axis of the polarizing plate may be substantially parallel to the orientation direction of the liquid crystal molecules on the side of the electrode pattern unit or the common electrode portion (sixteenth configuration of the liquid crystal lens). According to the sixteenth configuration, it is possible to further reduce crosstalk in comparison with a case where the present configuration is not included. 
     Moreover, in the above eleventh or twelfth configuration of the liquid crystal lens, when no potential difference is generated between the electrode pattern unit and the common electrode portion, the liquid crystal molecules included in the liquid crystal layer may be oriented substantially parallel to a thickness direction of the liquid crystal layer (seventeenth configuration of the liquid crystal lens). According to the seventeenth configuration, in addition to the effects of the eleventh and twelfth configurations, it is possible to simplify the manufacturing process because an orientation treatment is not required in comparison with the case where the present configuration is not included. 
     A stereoscopic display apparatus according to one embodiment of the present invention may be configured to include the liquid crystal lens having the above eleventh to seventeenth configuration, and a display panel configured to display an image. According to the stereoscopic display apparatus, by providing the non-conductive layer in the liquid crystal lens, an electric field becomes easily applied also to the non-conductive portion of the liquid crystal layer. As a result, it is possible to reduce crosstalk in three-dimensional display without increasing the number of electrodes in the liquid crystal lens. 
     Thirteenth Embodiment 
     Hereinafter, embodiments will be described in detail with reference to the drawings. The same symbols will be appended to the same or corresponding portions, and description thereof will not be repeated. In order to simplify the description, in the drawings referenced in the following, a configuration has been schematically simplified or, some components have been omitted. The dimensional ratios between components shown in each drawing do not necessarily indicate the actual dimension ratios. 
       FIG. 43  is an exploded perspective view showing a schematic configuration of a stereoscopic display apparatus  1  according to one embodiment of the present invention. The stereoscopic display apparatus  1  includes a liquid crystal lens  11 A, a phase difference plate  12 , a spacer  13 , a liquid crystal display  14  (an example of a display panel), and a backlight  15 . 
     In this drawing, the upper direction of the liquid crystal lens  11 A (the positive direction side of a z-axis) becomes the position where an image to be displayed on the liquid crystal display  14  is viewed. The stereoscopic display apparatus  1  transmits light emitted from the backlight  15  through the liquid crystal display  14 , the phase difference plate  12 , and the liquid crystal lens  11 A, in this order, thus switches an image to be displayed on the liquid crystal display  14  to a plane image or a stereoscopic image, and displays the image at the predetermined viewing position. 
     The liquid crystal lens  11 A and the liquid crystal display  14  are formed so as to have planes in a substantially-rectangular plate-like shape when viewed from the z-axis direction and in substantially equal size. 
     The liquid crystal lens  11 A includes a pair of substrates and a liquid crystal layer sandwiched therebetween. The liquid crystal lens  11 A changes orientation of liquid crystal molecules included in the liquid crystal layer, thereby changing behavior (gradient index) of light passing through the liquid crystal layer. The detailed configuration of the liquid crystal lens  11 A will be described later. 
     The phase difference plate  12  is disposed on the back side of the liquid crystal lens  11 A (the negative direction side of the z-axis), that is, the side where light emitted from the liquid crystal display  14  is incident on the liquid crystal lens  11 A. The phase difference plate  12  adjusts the polarization direction of the light emitted from the liquid crystal display  14 , thus aligning the polarization direction to the changing orientation direction of the liquid crystal molecules of the liquid crystal lens  11 A. 
     The liquid crystal display  14  is disposed on the back side of the phase difference plate  12  (the negative direction side of the z-axis) through a spacer  13 . The liquid crystal display  14  includes an active matrix substrate, a color filter substrate disposed opposite thereto, and a liquid crystal layer sandwiched between both the substrates. 
     TFTs (thin film transistors) and pixel electrodes are formed in a matrix on the active matrix substrate. The liquid crystal display  14  controls the TFTs, thereby changing the orientation of the liquid crystal molecules included in the liquid crystal layer above any pixel electrode. Light emitted from the backlight  15  provided on the rear surface of the liquid crystal display  14  (the negative direction side of the z-axis) passes through the liquid crystal layer, and thus any image is displayed on the display surface of the liquid crystal display  14 . 
     The backlight  15  includes a light source, such as a cold cathode tube or an LED (light emitting diode), and emits light from the rear surface of the liquid crystal display  14  (the negative direction side of the z-axis). 
     The stereoscopic display apparatus  1  conjunctively controls the liquid crystal lens  11 A and the liquid crystal display  14 , thereby switching the display modes of an image. The display modes include two modes, a two-dimensional display mode and a three-dimensional display mode. In the case of the two-dimensional display mode, the liquid crystal molecules included in the liquid crystal layer of the liquid crystal lens  11 A are in a state of being oriented uniformly, and most of the light emitted from the liquid crystal display  14  and incident on the liquid crystal layer passes without being refracted. As a result, a plane image projected by the liquid crystal display  14  is displayed. 
     In the three-dimensional display mode, the liquid crystal display  14  regularly arranges and displays images captured from multiple directions. Correspondingly with this, the liquid crystal lens  11 A regularly changes orientation of the liquid crystal molecules included in the liquid crystal layer. Thus, the light emitted from the liquid crystal display  14  and incident on the liquid crystal layer transmits while being refracted according to the refractive index distribution of the liquid crystal layer. When the stereoscopic display apparatus  1  is observed in the optimal viewing position, different images reach the left and right eyes. In other words, the stereoscopic display apparatus  1  in the three-dimensional display mode performs three-dimensional display using a so-called parallax method. 
     Next, a configuration of the liquid crystal lens  11 A according to the thirteenth embodiment will be described in detail. 
       FIG. 44  shows a schematic cross-sectional view of the liquid crystal lens  11 A, which is taken along a line II-II shown in  FIG. 43 . The liquid crystal lens  11 A includes, between an opposing substrate  2111   a  and a control substrate  2111   b , a common electrode  2112 , alignment films  2113   a  and  2113   b , a liquid crystal layer  2114 , a dielectric layer  2115 , and an electrode pattern  2116 . The liquid crystal lens  11 A further includes a controller  2117  that controls the voltage to be applied between the opposing substrate  2111   a  and the control substrate  2111   b . Here, the alignment films  2113   a  and  2113   b , and the liquid crystal layer  2114  are examples of an optical controller. Additionally, the common electrode  2112  is an example of a common electrode unit. Further, the electrode pattern  2116  is an example of an electrode pattern unit. Moreover, the dielectric layer  2115  is an example of a non-conductive layer. 
     The control substrate  2111   b  is formed of a light-transmissive glass. An electrode pattern  2116  that is a transparent electrode, such as ITO (Indium-tin-oxide), is formed on a surface of the dielectric layer  2115  side of the control substrate  2111   b.    
     The electrode pattern  2116  includes a plurality of electrodes (first electrodes)  2116 A. Each electrode  2116 A is formed elongated along the y-direction. The electrodes  2116 A are arranged at a constant pitch a that corresponds to the pitch of lenses so as to be parallel to one another along the x-direction. 
     The dielectric layer  2115  with a thickness d 2  (the height in the z-axis direction) is formed over the electrode pattern  2116 . The dielectric layer  2115  is formed of an insulating dielectric material. In the present embodiment, the dielectric layer  2115  is formed of, for example, acrylic resin, polyimide resin, or the like. 
     The liquid crystal layer  2114  with a thickness d 1  (the height in the z-axis direction) is formed over the dielectric layer  2115  through an alignment film  2113   b . In the present embodiment, as liquid crystal molecules  2114   a  constituting the liquid crystal layer  2114 , liquid crystal molecules with positive dielectric anisotropy are used. The liquid crystal molecules  2114   a  have the anisotropy of the refractive index such that a refractive index n e  with respect to light vibrating parallel to the optical axis is different from a refractive index n o  with respect to light vibrating perpendicular to the optical axis. The liquid crystal molecules  2114   a  having a large value of Δn=n e −n o  is preferred. 
     Alignment layers  2113   a  and  2113   b  are formed on the upper and lower surfaces of the liquid crystal layer  2114 . In the present embodiment, the alignment films  2113   a  and  2113   b  have a plurality of grooves formed in parallel to the x-direction by a rubbing treatment. In a state where no voltage is applied to the liquid crystal layer  2114 , the liquid crystal molecules  2114   a  are oriented by the alignment films  2113   a  and  2113   b  so that long axes thereof become parallel to the x-direction (horizontal orientation). 
     The common electrode  2112  is a transparent electrode, such as ITO, which is formed on the entire surface of the opposing substrate  2111   b . The controller  2117  applies different potentials to the common electrode  2112  and the electrode pattern  2116 , to cause a potential difference to be generated between the common electrode  2112  and the electrode pattern  2116 . 
     Here, a state of the liquid crystal lens  11 A in accordance with the potential difference between the common electrode  2112  and the electrode pattern  2116  will be described. 
       FIG. 45  is a schematic diagram showing a state of the liquid crystal lens  11 A in a case where a voltage is applied by the controller  2117 , and thus a predetermined potential difference is generated between the common electrode  2112  and the electrode pattern  2116 . In this drawing, a broken line represents part of light emitted from the liquid crystal display  14 . The liquid crystal molecules  2114   a  are oriented so that the molecular long axes thereof become parallel to the electric field generated by the voltage. The molecular long axes of the liquid crystal molecules  2114   a  close to the electrodes  2116 A are oriented parallel to the z-axis direction. However, the electric field decreases as the distance from the electrode  2116 A increases. Therefore, the orientation direction of the liquid crystal molecules  2114   a  will tilt from the z-axis direction to the x-axis direction. A refractive index of the liquid crystal layer  2114  changes according to the change in orientation direction of the liquid crystal molecules  2114   a . Thus, the liquid crystal layer  2114  has a refractive index distribution in the x-axis direction. 
     When light emitted from the liquid crystal display  14  transmits through the control substrate  2111   b  and enters the dielectric layer  2115 , the light transmits through the dielectric layer  2115  and the alignment film  2113   b  and enters the liquid crystal layer  2114 . The light incident on the liquid crystal layer  2114  is refracted according to the refractive index distribution of the liquid crystal layer  2114 , transmits through the alignment film  2113   a , the common electrode  2112 , and the opposing substrate  2111   a , and is condensed at the viewing position, as indicated by the dashed arrow. In other words, the liquid crystal lens  11 A functions as a gradient index lens (GRIN lens). The state of the liquid crystal layer  2114  shown in  FIG. 45  corresponds to the three-dimensional display mode. 
     On the other hand,  FIG. 46  is a schematic diagram showing a state of the liquid crystal lens  11 A in a case where no voltage is applied by the controller  2117 , and no predetermined potential difference is generated between the common electrode  2112  and the electrode pattern  2116 . In this state, an electric field is not generated in the liquid crystal layer  2114 , and the liquid crystal molecules  2114   a  are oriented by the alignment films  2113   a  and  2113   b  so that the molecular long axes thereof become parallel to the x-direction. Since the liquid crystal molecules  2114   a  are oriented uniformly, a refractive index distribution of the liquid crystal layer  2114  also becomes uniform. For this reason, as indicated by broken lines, light incident on the liquid crystal layer  2114  is refracted slightly due to the refractive index difference from the adjacent medium, most of the light proceeds as it is. In other words, in the state where no voltage is applied, the liquid crystal lens  11 A does not function as a GRIN lens, and a two-dimensional image displayed on the liquid crystal display  14  is displayed at the viewing position. The state of the liquid crystal layer  2114  shown in  FIG. 46  corresponds to the two-dimensional display mode. 
     The present inventors paid attention to a point that as the distance between the electrodes  2116 A becomes larger in comparison with the distance between the common electrode  2112  and the electrode pattern  2116 , an electric field is hardly applied between the electrodes  2116 A, in comparison with the vicinity of the electrode  2116 A, and crosstalk occurs in the three-dimensional display mode. Then, the distance between the common electrode  2112  and the electrode pattern  2116  was adjusted by providing the dielectric layer  2115 . Here, the crosstalk is a ratio L2/L1 (%) where a position that is a predetermined distance away from the liquid crystal lens  11  is defined as the center (reference position) of the left and right eyes of the observer, L1 represents a luminance value at the reference position, and L2 represents a luminance value with respect to the horizontal distance (for example, approximately 65 mm) or angle from the reference position corresponding to the positions of the left and right eyes of the observer. 
       FIG. 47  shows a relationship between crosstalk and a ratio (a/d) where d (d=d 1 +d 2 ) represents the distance between the common electrode  2112  and the electrode pattern  2116 , and a represents a pitch of the electrodes  2116 A. Generally, it is preferable that crosstalk is 3% or less. Additionally, as shown in  FIG. 48 , lens characteristics of an ideal liquid crystal lens that can achieve crosstalk that is 3% or less meet the following relation, where f represents the focal length of the lens, P represents the width of the lens, n c  represents the maximum effective refractive index, n b  represents the minimum effective refractive index of the liquid crystal, and d Lc  represents a thickness of the liquid crystal. 
         f=P   2 /8( n   c   −n   b ) d   Lc    
     Accordingly, in order to adjust the distance between the common electrode  2112  and the electrode pattern  2116  of the liquid crystal lens  11 A to achieve the ideal lens characteristics described above, the present inventors have conducted a simulation under the following condition. The condition was that the width of the electrode  2116 A: 15 μm, a pitch a of the electrodes  2116 A: 670 μm, a thickness d 1  of the liquid crystal layer  2114  including the alignment layers  2113   a  and  2113   b:  40 μm, a dielectric constant of the dielectric layer  2114 : 5%, and the voltage of the common electrode  2112 : 0V.  FIGS. 49B and 49C  show results of the simulation of the lens characteristics performed under this precondition with respect to the thickness d 2  of the dielectric layer  2115  indicated by conditions A to E shown in  FIG. 49A . 
     It was assumed in this simulation that a distance d which combined the thickness d 1  of the liquid crystal layer  2114  including the alignment films  2113   a  and  2113   b  and the thickness d 2  of the dielectric layer  2115  is the distance between the common electrode  2112  and the electrode pattern  2116 .  FIG. 49B  shows a theoretical curve and results of the simulation performed under the respective conditions (A to E) shown in  FIG. 49A . Additionally,  FIG. 49C  shows a root-mean-square value (deviation from the theoretical curve) of the theoretical curve shown in  FIG. 49B  and the results of the simulation performed under the respective conditions. 
     As shown in  FIGS. 49B and 49C , it was the condition D (a/d=3.7) that achieved the smallest deviation from the theoretical curve F. Additionally, it was the condition A (a/d=13.4) that achieved the greatest deviation from the theoretical curve F. From  FIG. 47  and the above results of the simulation, a/d that makes crosstalk approximately 3% is preferably 3.0&lt;a/d&lt;8.5 where a root mean square value with the theoretical value is less than 1.5, and more preferably, 3.5&lt;a/d&lt;5.5 where a mean square value with the theoretical value is less than 1.0. 
     In the embodiment described above, the dielectric layer  2115  is provided in contact with the electrode pattern  2116  to adjust the distance between the common electrode  2112  and the electrode pattern  2116 , thereby reducing crosstalk. By such a configuration, the cost for manufacturing the liquid crystal lens  11 A can be suppressed at low cost, compared to a case where the thickness of the liquid crystal layer  2114  including the alignment films  2113   a  and  2113   b  is increased in order to adjust the distance between the common electrode  2112  and the electrode pattern  2116 . Additionally, in the above-described embodiment, the dielectric layer  2115  is disposed on the electrode pattern  2116  side. An electric field is hardly applied to the portion of the dielectric layer  2115 . For this reason, compared to a case where the dielectric layer  2115  is provided on the common electrode  2112  side, the liquid crystal layer  2114  is less likely to be affected by a lateral electric field between the electrode patterns  2116 , and becomes likely to be affected by a vertical electric field between the common electrode  2112  and the electrode pattern  2116 . As a result, the lens characteristics of the liquid crystal lens  11 A are likely to approach the theoretical curve f. 
     Fourteenth Embodiment 
     The description has been given in the above thirteenth embodiment with respect to the case where one potential is applied to the electrode pattern  2116 . In the present embodiment, description will be given with respect to a case where two potentials are applied to the electrode pattern  2116 . 
       FIG. 50  is a schematic view showing a cross section of a liquid crystal lens  11 B according to the present embodiment. The same reference symbols are appended to the same configuration as that of the thirteenth embodiment described above. Hereinafter, a configuration different from that of the thirteenth embodiment will be described. 
     An electrode pattern  2116 ′ (electrode pattern unit) includes electrodes  2116 A 1  (first electrodes) and electrodes  2116 A 2  (second electrodes).  FIG. 51  is a schematic diagram showing the electrodes  2116 A 1  and the electrodes  2116 A 2  shown in  FIG. 50 , which are viewed from the positive direction of the z-axis. As shown in  FIG. 51 , the electrode  2116 A 1  includes an elongated electrode portion  1161  extending in the x-axis direction and an elongated electrode portion  1162  extending from the electrode portion  1161  in the negative direction of the y-axis. The electrode  2116 A 1  is formed by connecting the electrode portion  1161  and the electrode portions  1162  so that the electrode portions  1162  are arranged at regular intervals along the x-axis direction. 
     The electrode  2116 A 2  includes an elongated electrode portion  1163  extending in the x-axis direction, and an elongated electrode portion  1164  extending from the electrode portion  1163  in the positive direction of the y-axis. The electrode  2116 A 2  is formed by connecting the electrode portion  1164  and the electrode portion  1163  so that two electrode portions  1164  are arranged at regular intervals between two adjacent electrodes portions  1162  of the electrode  2116 A 1 . In other words, in the present embodiment, the two adjacent electrodes  2116 A 1  and the electrode  2116 A 2  disposed therebetween correspond to one GRIN lens. Additionally, the electrode  2116 A 1  and the electrode  2116 A 2  are symmetrically disposed in one GRIN lens. 
     Referring back to  FIG. 50 , the controller  2117  applies a voltage so that the potential of the electrode  2116 A 1  differs from the potential of the electrode  2116 A 2 . In the present embodiment, for example, a thickness d 1  of the liquid crystal layer  2114  including the alignment films  2113   a  and  2113   b  is set to be 50 μm. A thickness d 2  of the dielectric layer  2115  is set to be 60 μm. A pitch (lens pitch) of the electrodes  2116 A 1  is set to be 670 μm (a/d=670/110=6.1). In this case, the controller  2117  applies 12V and 4.5V respectively to the electrode  2116 A 1  and the electrode  2116 A 2  while regarding the potential of the common electrode  2112  as 0V (ground potential). When the voltages are applied, an electric field E1 is generated between the electrode  2116 A 1  and the common electrode  2112 , and an electric field E2 is generated between the electrode  2116 A 2  and the common electrode  2112  (E2&lt;E1). The thickness of the dielectric layer  2115  is different between the present embodiment and the thirteenth embodiment. As described in the thirteenth embodiment, the electric field applied to the liquid crystal layer  2114  between the electrodes at one potential is controlled, thereby making it easier to approach the theoretical curve F. In the present embodiment, since the two potentials are applied to the electrode pattern  2116 , it is possible to approach the theoretical curve F even if the dielectric layer is made thinner in comparison with the case of the thirteenth embodiment. 
     The orientation of liquid crystal molecules  2114   a  close to the electrode  2116 A 1  changes by the electric field E1 so that the molecular long axes thereof become parallel to the z-axis direction. The closer to the electrode  2116 A 2  from the electrode  2116 A 1 , the molecular long axes of the liquid crystal molecules  2114   a  further tilts in the x-axis direction due to the influence of the electric fields E1 and E2. Then, since the liquid crystal molecules  2114   a  are hardly affected by the electric fields E1 and E2 between the electrodes  2116 A 2  and  2116 A 2 , the molecular long axes of the liquid crystal molecules  2114   a  are oriented parallel to the x-axis direction. 
     In the fourteenth embodiment described above, two potentials are applied to the electrode pattern  2116 . For this reason, compared to the case of the thirteenth embodiment, it is possible to more precisely control the electric field applied to the liquid crystal layer  2114 , and improve the accuracy of controlling the optical path of the light transmitting through the liquid crystal layer  2114 . 
     Embodiment 15 
     The description has been given in the above thirteenth embodiment with respect to the case where the dielectric layer  2115  is provided at a position in contact with the electrode pattern  2116 . However, as shown in  FIG. 52 , the dielectric layer  2115  may be replaced with a liquid crystal lens  11 C provided at a position in contact with the common electrode  2112 . In this configuration, a considerable example of the configuration may be such that a thickness of the liquid crystal layer  2114  including the alignment films  2113   a  and  2113   b  is 40 μm, a thickness of the dielectric layer  2115  is 140 μm, a pitch of the electrodes  2116 A is 670 μm (a/d=3.7). In this configuration example, when the mode is switched to the three-dimensional display mode, the voltage  26   v  is applied to the electrode  2116 A by the controller  2117 , and thus a three-dimensional image is displayed at the viewing position. 
     Modified Example 
     Although the thirteenth to fifteenth embodiments have been described above, the above embodiments are merely examples for implementing the present invention. Thus, the present invention is not limited to the above embodiments, and the above embodiments can be appropriately modified and practiced without departing from the scope thereof. For example, regarding the thirteenth to fifteenth embodiments, the following modifications can be considered. 
     (1) The example taken in the above thirteenth and fourteenth embodiments is the example of the configuration that the electrodes  2116 A,  2116 A 1 , and  2116 A 2  of the electrode pattern  2116  are substantially perpendicular to the orientation direction of the liquid crystal molecules  2114   a . However, the configuration may be as follows. The alignment films  2113   a  and  2113   b  may be configured to have a plurality of grooves parallel to the y-axis direction, which are formed by a rubbing treatment, so that the electrodes  2116 A,  2116 A 1 , and  2116 A 2  of the electrode pattern  2116  become substantially parallel to the orientation direction of the liquid crystal molecules  2114   a . Additionally, in the above-described embodiments, the electrodes  2116 A,  2116 A 1 , and  2116 A 2  of the electrode pattern  2116  may be arranged at regular intervals along the y-axis direction. In this case, the electrodes  2116 A,  2116 A 1 , and  2116 A 2  of the electrode pattern  2116  become substantially parallel to the orientation direction of the liquid crystal molecules  2114   a.  
 
(2) The description has been given in the above thirteenth embodiment with respect to the configuration that the liquid crystal molecules  2114   a  of the liquid crystal layer  2114  are oriented in the x-axis direction when no voltage is applied. In the present modified example, a configuration may be such that when no voltage is not applied to the liquid crystal layer  2114 , the liquid crystal molecules  2114   a  are oriented so as to be twisted by approximately 90° in the liquid crystal layer  2114  (TN orientation (twisted nematic type)). In this case, the alignment films  2113   a  and  2113   b  have a plurality of grooves formed by a rubbing process so as to intersect each other at the angle of 90°. Alternatively, a configuration may be such that each rubbing direction and the longitudinal direction of the electrode patterns  2116 A (y-direction), that is, a direction substantially perpendicular to the arrangement direction of the electrode patterns  2116 A (x-direction), forms an angle of substantially 45°.
 
     Further, in this case, a configuration may be such that a polarizing plate is provided on a surface of the opposing substrate  2111   a  (the viewing position side). The polarization axis of the polarizing plate is configured to be the same direction as the rubbing direction of the alignment layer  2113   a .  FIG. 53A  shows the angle from the center position of the lens and a change in brightness in cases where a polarizing plate is provided and where the polarizing plate is not provided. In this drawing, P1 represents a change in brightness in the case where the polarizing plate is provided. P2 represents a change in brightness in the case where the polarizing plate is not provided. As shown in the drawing, a peak brightness is between −4° and −5° in both the cases where the polarizing plate is provided and where the polarizing plate is not provided. The brightness is larger in the case where the polarizing plate is not provided than in the case where the polarizing plate is provided. 
     Additionally,  FIG. 53B  shows the crosstalk at the angles shown in  FIG. 53A , in the cases where the polarizing plate is provided and where the polarizing plate is not provided. In this drawing, P1 represents the crosstalk at each angle in the case where the polarizing plate is provided. P2 represents the crosstalk at each angle in the case where the polarizing plate is not provided. As shown in this drawing, it can be understood that between 3° and 6.5°, the crosstalk is reduced in the case where the polarizing plate is provided, in comparison with the case where the polarizing plate is not provided. Accordingly, it is possible to further reduce the crosstalk in the three-dimensional display by providing a polarizing plate in the liquid crystal lens  11 . 
     (3) The description has been given in the above thirteenth embodiment with respect to the example of the horizontal orientation such that the liquid crystal molecules  2114   a  are oriented parallel to the x-axis direction. However, as shown in  FIG. 54A , vertical orientation may be employed such that when no voltage is applied, the liquid crystal molecules  2114   a  are oriented substantially parallel to the z-axis direction (the direction substantially vertical to the display surface of the liquid crystal display  14 ). In this case, negative type nematic liquid crystal with negative dielectric anisotropy is used, and a vertical alignment film is used as the alignment film  2113   a  and  2113   b . The voltage is applied by the controller  2117 , and thereby the orientation of the liquid crystal molecules  2114   a  changes in a direction vertical to the electric field, in accordance with the potential difference between the common electrode  2112  and the electrode pattern  2116 . Accordingly, in the case of vertical orientation, as shown in  FIG. 54B , the electric field close to the electrodes  2116 A of the electrode pattern  2116  becomes larger than the other positions, the molecular long axes of the liquid crystal molecules  2114   a  between the electrode  2116 A and the electrode  2116 A are oriented parallel to the z-axis direction, and the molecular long axes of the liquid crystal molecules  2114   a  close to the electrode  2116 A are oriented parallel to the x-axis direction.
 
(4) The description has been given in the above fourteenth embodiment with respect to the case where two potentials are applied to the electrode pattern  2116 . However, three or more potentials may be applied to the electrode pattern  2116 . As an example, a configuration of the electrode pattern  2116  in the case where three potentials are applied to the electrode pattern  2116  is shown below.  FIG. 55A  is a schematic view showing a cross section of the dielectric layer  2115  and the electrode pattern  2116  of a liquid crystal lens according to the present modified example. As shown in  FIG. 55A , the electrode pattern  2116  includes electrodes  2116 A 3 , in addition to electrodes  2116 A 1  and  2116 A 2  which are similar to those of the fourteenth embodiment. For example, the electrodes  2116 A 1  and  2116 A 2  are formed on the same layer, and the electrodes  2116 A 3  are formed on a higher layer above the electrodes  2116 A 1  and  2116 A 2 .  FIG. 55B  is a diagram showing the electrodes  2116 A 2  and  2116 A 3  when  FIG. 55A  is viewed from the x-axis direction. As shown in the drawing, a configuration may be such that an interlayer insulating film  1165  is formed between the layer on which the electrodes  2116 A 2  are provided and the layer on which the electrodes  2116 A 3  are provided, and a contact hole  1166  is formed in the interlayer insulating film  1165 , and an electrode  2116 A 3  is connected with wires.
 
(5) The description has been given in the above thirteenth embodiment with respect to the example where the electrode pattern  2116  is disposed on the liquid crystal display  14  side, and the common electrode  2112  is provided on the viewing position side (on the side where light is emitted from the liquid crystal lens). However, a configuration may be made as shown in  FIG. 56 . In other words, as shown in this figure, a configuration may be such that the electrode pattern  2116  is provided on the viewing position side.
 
(6) The description has been given in the above thirteenth embodiment using the liquid crystal display as an example of display panels. However, a display device, such as a PDP (plasma display panel) or an organic EL display (organic electroluminescence display), may be used.
 
(7) The example taken in the above thirteenth embodiment is the example where the phase difference plate  12  is used. However, it is not necessary to provide the phase difference plate  12 , depending on the polarization direction of light emitted from the liquid crystal display  14 .
 
     Here, configurations of the liquid crystal lens and the stereoscopic display apparatus according to another aspect of the present invention will be disclosed as the following Notes. 
     [Note 14] 
     A liquid crystal lens comprising: 
     an electrode pattern unit configured to transmit light and including a first electrode, the first electrode including a conductive portion and a non-conductive portion which are repeated at predetermined intervals; 
     a common electrode unit configured to transmit light and including a common electrode at a position opposing the first electrode; 
     a controller configured to control potentials of the first electrode and the common electrode and to cause a potential difference to be generated between the electrode pattern unit and the common electrode unit; 
     a light controller including a liquid crystal layer formed between the common electrode unit and the electrode pattern unit, the liquid crystal layer having a refractive index distribution of light that is variably controlled by an electric field according to the potential difference; and 
     a non-conductive layer formed between the common electrode unit and the electrode pattern unit, the non-conductive layer being formed of a light-transmissive medium, 
     wherein a ratio a/d is greater than 3.0 and is less than 8.5 where a is a distance between two adjacent conductive portions on the first electrode, and d is a distance between the common electrode unit and the electrode pattern unit. 
     [Note 15] 
     The liquid crystal lens according to Note 14, wherein the electrode pattern unit further includes a second electrode, the second electrode including a conductive portion and a non-conductive portion which are repeated at predetermined intervals, and 
     the controller is configured to control the potentials of the electrode pattern unit and the common electrode unit so that the potential difference between the first electrode and the common electrode differs from the potential difference between the second electrode and the common electrode. 
     [Note 16] 
     The liquid crystal lens according to Note 14 or 15, wherein liquid crystal molecules in the liquid crystal layer are oriented substantially parallel to one direction of the display region when no potential difference is generated between the electrode pattern unit and the common electrode portion. 
     [Note 17] 
     The liquid crystal lens according to Note 14 or 15, wherein when no potential difference is generated between the electrode pattern unit and the common electrode unit, an orientation direction of the liquid crystal molecules included in the liquid crystal layer on a side of the common electrode unit is substantially perpendicular to that on a side of the electrode pattern unit. 
     [Note 18] 
     The liquid crystal lens according to Note 17, wherein the orientation direction and a direction substantially perpendicular to an arrangement direction of the first electrode form an angle of approximately 45 degrees. 
     [Note 19] 
     The liquid crystal lens according to Note 17 or 18, further comprising: 
     a polarizing plate on a light emitting side of the light controller, 
     wherein a polarization axis of the polarizing plate is substantially parallel to the orientation direction of the liquid crystal molecules on the side of the electrode pattern unit or the common electrode portion. 
     [Note 20] 
     The liquid crystal lens according to Note 14 or 15, wherein when no potential difference is generated between the electrode pattern unit and the common electrode portion, the liquid crystal molecules included in the liquid crystal layer are oriented substantially parallel to a thickness direction of the liquid crystal layer. 
     [Note 21] 
     A stereoscopic display apparatus comprising: 
     the liquid crystal lens according to any one of Notes 14 to 20; and 
     a display panel configured to display an image. 
     Other Embodiment 
     Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications or combinations can be made within the scope of the invention. 
     INDUSTRIAL APPLICABILITY 
     The present invention is industrially applicable as a liquid crystal lens or a stereoscopic display apparatus.