Patent Publication Number: US-2023134662-A1

Title: Liquid crystal lens, head mounted display and polarized sunglasses

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2021-175563 filed on Oct. 27, 2021 and Japanese Patent Application No. 2022-110534 filed on Jul. 8, 2022, the contents of which are incorporated herein by reference in their entirety. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The following disclosure relates to liquid crystal lenses, head mounted displays, and polarized sunglasses. 
     Description of Related Art 
     Liquid crystal Fresnel lenses are varifocal lenses including a Fresnel lens on a flat or curved transparent substrate and a liquid crystal material filled along the shape of the Fresnel lens. The focal length of a liquid crystal Fresnel lens is varied by applying voltage to both sides of the portion filled with a liquid crystal material and thus varying the refractive index of the liquid crystal material. A liquid crystal Fresnel lens is also simply referred to as a liquid crystal lens hereinbelow. 
     JP 2009-98641 A, for example, discloses as a liquid crystal lens a liquid crystal Fresnel lens including: a first transparent substrate having a Fresnel lens on one of its surfaces and a first transparent electrode disposed on the Fresnel lens surface, wherein each circle of the Fresnel lens is provided with at least one notch in its ridge line; a second transparent substrate having a second transparent electrode on one of its surfaces; and liquid crystals between the first transparent substrate and the second transparent substrate, with the second transparent electrode on the second transparent substrate facing the Fresnel lens on the first transparent substrate. 
     JP 2009-98644 A discloses a liquid crystal Fresnel lens including a first transparent substrate having a Fresnel lens on one of its surfaces; a first transparent electrode formed only on the lens surfaces of the Fresnel lens; a second transparent substrate having a second transparent electrode on one of its surfaces, with the surface having the second transparent electrode formed thereon facing the first transparent electrode; and liquid crystals between the first transparent substrate and the second transparent substrate. 
     JP 5698328 B discloses a liquid crystal lens including a first substrate having a lens structure, a second substrate paired with the first substrate, and a liquid crystal layer between the lens structure and the second substrate, wherein the pre-tilt angle provided by an alignment treatment layer on the liquid crystal layer side of the second substrate is greater than the pre-tilt angle provided by an alignment treatment layer on the liquid crystal layer side of the lens structure. 
     BRIEF SUMMARY OF THE INVENTION 
       FIG.  26    is a schematic cross-sectional view of a conventional liquid crystal lens.  FIG.  27    is a schematic cross-sectional view of the conventional liquid crystal lens with no voltage applied.  FIG.  28    is a schematic cross-sectional view of the conventional liquid crystal lens with voltage applied. As shown in  FIG.  26    to  FIG.  28   , a conventional liquid crystal lens  10 R includes a first substrate  100 , a second substrate  200  facing the first substrate  100 , and a liquid crystal layer  300  sealed between the first substrate  100  and the second substrate  200  with a sealant  400  and containing liquid crystal molecules  310 . The first substrate  100  includes, sequentially toward the liquid crystal layer  300 , a first support substrate  110 , a Fresnel lens  120 , and a first electrode  130 . The second substrate  200  includes, sequentially toward the liquid crystal layer  300 , a second support substrate  210  and a second electrode  220 . Commonly known liquid crystal lenses have this structure of the liquid crystal lens  10 R in which the Fresnel lens  120  is disposed on one of the two substrates (first substrate  100  and second substrate  200 ) and is sandwiched between the support substrates. 
     The liquid crystal molecules  310  have an anisotropic refractive index. In the liquid crystal lens  10 R, the voltage applied between the first electrode  130  and the second electrode  220  is varied to control the alignment of the liquid crystal molecules  310 , so that the refractive index of the liquid crystal layer  300  for incident light can be varied between the extraordinary refractive index (ne) and the ordinary refractive index (no). The refractive indices satisfy the relationship ne &gt; no. The conventional liquid crystal lens  10 R which is based on these principles basically can turn on or off the lens functions for only one of s-polarized light and p-polarized light. 
     There may be various designs for the refractive index and the anisotropy of dielectric constant of the liquid crystal molecules  310 . For example, the ordinary refractive index no of positive liquid crystal molecules having a positive anisotropy of dielectric constant may be made substantially the same as the refractive index of the resin constituting the Fresnel lens  120 . In this case, with no voltage applied between the first electrode  130  and the second electrode  220 , the liquid crystal layer  300  experiences the extraordinary refractive index ne. This, as shown in  FIG.  27   , makes a difference in refractive index for polarized light  11 L between the Fresnel lens  120  and the liquid crystal layer  300 , thus allowing the liquid crystal lens  10 R to function as a lens. 
     Meanwhile, with voltage applied between the first electrode  130  and the second electrode  220 , the liquid crystal layer  300  experiences the ordinary refractive index no. This, as shown in  FIG.  28   , makes no difference in refractive index for the polarized light  11 L between the Fresnel lens  120  and the liquid crystal layer  300 , thus failing to allow the liquid crystal lens  10 R to function as a lens. 
     As shown in  FIG.  26    to  FIG.  28   , the surface of the Fresnel lens  120  is not flat but is uneven with steps whose vertex angle is sharp. The first electrode  130  may be open-circuited on such steps. 
     None of JP 2009-98641 A, JP 2009-98644 A, and JP 5698328 B mentions sufficient studies on liquid crystal lenses capable of reducing or preventing occurrence of an open circuit, and thus there is room for improvement. 
     In response to the above issues, an object of the present invention is to provide a liquid crystal lens capable of reducing or preventing occurrence of an open circuit, a head mounted display including the liquid crystal lens, and polarized sunglasses including the liquid crystal lens. 
     (1) One embodiment of the present invention is directed to a liquid crystal lens including: a first substrate; a second substrate facing the first substrate; and a liquid crystal layer held between the first substrate and the second substrate and containing liquid crystal molecules, the first substrate including a Fresnel lens and a first electrode sequentially toward the liquid crystal layer, the second substrate including a second electrode, the Fresnel lens including a Fresnel-shaped part and a flat part, the Fresnel-shaped part including a plurality of annular lens surfaces disposed in a concentric circle pattern, the flat part including a flat surface that extends in a radial direction of the concentric circle and intersects at least one of the annular lens surfaces, the annular lens surfaces disposed on a liquid crystal layer-facing surface of the Fresnel-shaped part and defining an uneven surface, the flat surface disposed on a liquid crystal layer-facing surface of the flat part. 
     (2) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), and the first electrode overlaps the flat surface. 
     (3) In an embodiment of the present invention, the liquid crystal lens includes the structure (1) or (2), and the flat surface in a plan view extends linearly from an outermost periphery of the Fresnel lens toward a center of the Fresnel lens. 
     (4) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), or (3), and the flat surface is disposed at the same height as a vertex of the uneven surface or higher than the vertex of the uneven surface. 
     (5) In an embodiment of the present invention, the liquid crystal lens further includes a spacer as well as the structure (1), (2), (3), or (4), and the spacer overlaps the flat surface. 
     (6) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), or (5), and the second substrate further includes, in a liquid crystal layer-facing surface of the second substrate, a tapered portion that is thick in its center and becomes thinner toward its periphery. 
     (7) In an embodiment of the present invention, the liquid crystal lens includes the structure (6), and the tapered portion in a plan view is rotationally symmetric. 
     (8) In an embodiment of the present invention, the liquid crystal lens includes the structure (6), and the tapered portion in a plan view is symmetric about a line at an initial alignment azimuth of the liquid crystal molecules. 
     (9) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), or (8), and further includes, on a liquid crystal layer side of the Fresnel lens, an alignment maintenance layer configured to control alignment of the liquid crystal molecules. 
     (10) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), or (9), and the Fresnel lens is provided, in a liquid crystal layer-facing surface of the Fresnel lens, with a plurality of grooves parallel to one another. 
     (11) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), or (10), and further includes an alignment film between the second substrate and the liquid crystal layer, wherein the alignment film contains a polymer having a cyclic aliphatic group. 
     (12) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), or (11), and the liquid crystal layer has a birefringence Δn of 0.2 or higher. 
     (13) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), or (12), and the liquid crystal layer has a nematic-isotropic phase transition temperature of 110° C. or higher. 
     (14) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), or (13), and the liquid crystal molecules have a tolane structure. 
     (15) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), or (14), the liquid crystal molecules have a positive anisotropy of dielectric constant, and the liquid crystal molecules have an ordinary refractive index equal to a refractive index of the Fresnel lens. 
     (16) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), or (15), and light incident on the liquid crystal lens is linearly polarized light vibrating at an azimuth parallel to an initial alignment azimuth of the liquid crystal molecules. 
     (17) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), or (16), and at least one of the first electrode or the second electrode is a stack of a plurality of films having different refractive indices. 
     (18) In an embodiment of the present invention, the liquid crystal lens includes the structure (17), and the stack includes a transparent conductive film and at least one type of an inorganic film. 
     (19) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), or (18), the liquid crystal layer is a first liquid crystal layer, the liquid crystal molecules are first liquid crystal molecules, the Fresnel lens is a first Fresnel lens, the annular lens surfaces are first annular lens surfaces, the Fresnel-shaped part is a first Fresnel-shaped part, the concentric circle pattern is a first concentric circle pattern, the flat surface is a first flat surface, and the flat part is a first flat part, the liquid crystal lens further includes a third substrate facing the first liquid crystal layer across the second substrate or facing the first liquid crystal layer across the first substrate; a fourth substrate facing the third substrate; and a second liquid crystal layer held between the third substrate and the fourth substrate and containing second liquid crystal molecules, the third substrate including a second Fresnel lens and a third electrode sequentially toward the second liquid crystal layer, the fourth substrate including a fourth electrode, the second Fresnel lens including a second Fresnel-shaped part and a second flat part, the second Fresnel-shaped part including a plurality of second annular lens surfaces disposed in a second concentric circle pattern, the second flat part including a second flat surface that extends in a radial direction of the second concentric circle and intersects at least one of the second annular lens surfaces, the second annular lens surfaces disposed on a second liquid crystal layer-facing surface of the second Fresnel-shaped part and defining an uneven surface, the second flat surface disposed on a second liquid crystal layer-facing surface of the second flat part. 
     (20) In an embodiment of the present invention, the liquid crystal lens includes the structure (19), and an alignment direction of the first liquid crystal molecules and an alignment direction of the second liquid crystal molecules are the same as each other or inverted from each other. 
     (21) In an embodiment of the present invention, the liquid crystal lens includes the structure (19), and an alignment direction of the first liquid crystal molecules and an alignment direction of the second liquid crystal molecules are perpendicular to each other. 
     (22) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), or (21), and further includes a first alignment film between the first substrate and the liquid crystal layer, and a second alignment film between the second substrate and the liquid crystal layer, wherein the first alignment film is a photoalignment film and the second alignment film is s rubbed alignment film. 
     (23) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), or (21), and further includes a first alignment film between the first substrate and the liquid crystal layer, a second alignment film between the second substrate and the liquid crystal layer, and a spacer disposed on a liquid crystal layer side of the second substrate, wherein the second alignment film is a photoalignment film. 
     (24) In an embodiment of the present invention, the liquid crystal lens includes the structure (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), or (21), and further includes a first alignment film between the first substrate and the liquid crystal layer, a second alignment film between the second substrate and the liquid crystal layer, and a spacer disposed on a liquid crystal layer side of the first substrate, wherein the first alignment film is a photoalignment film. 
     (25) Another embodiment of the present invention is directed to a head mounted display including the liquid crystal lens having any one of the structures (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), and (24). 
     (26) Yet another embodiment of the present invention is directed to polarized sunglasses including the liquid crystal lens having any one of the structures (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), and (24) . 
     The present invention can provide a liquid crystal lens capable of reducing or preventing occurrence of an open circuit, a head mounted display including the liquid crystal lens, and polarized sunglasses including the liquid crystal lens. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic plan view of a liquid crystal lens of Embodiment 1. 
         FIG.  2 A  is a schematic cross-sectional view of the liquid crystal lens of Embodiment 1 taken along line A1-A2 in  FIG.  1   . 
         FIG.  2 B  is a schematic cross-sectional view of an example in which the liquid crystal lens of Embodiment 1 has a curved shape. 
         FIG.  2 C  is a schematic cross-sectional view of another example in which the liquid crystal lens of Embodiment 1 has a curved shape. 
         FIG.  3 A  is a schematic perspective view of an example of a Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  3 B  is a schematic perspective view of another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  3 C  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  3 D  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  3 E  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  3 F  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  4 A  is a schematic cross-sectional view of an example of the Fresnel lens in the liquid crystal lens of Embodiment 1, taken along line B1-B2 in  FIG.  1   . 
         FIG.  4 B  is a schematic cross-sectional view of another example of the Fresnel lens in the liquid crystal lens of Embodiment 1, taken along line B1-B2 in  FIG.  1   . 
         FIG.  5    is a schematic cross-sectional view of an example of the structure of a spacer in the liquid crystal lens of Embodiment 1. 
         FIG.  6    is a schematic cross-sectional view of an example of the liquid crystal lens of Embodiment 1. 
         FIG.  7    is a schematic perspective view of an example of a tapered portion in the liquid crystal lens of Embodiment 1. 
         FIG.  8    is a schematic perspective view of another example of the tapered portion in the liquid crystal lens of Embodiment 1. 
         FIG.  9    is a schematic perspective view of yet another example of the tapered portion in the liquid crystal lens of Embodiment 1. 
         FIG.  10    is a schematic perspective view of yet another example of the tapered portion in the liquid crystal lens of Embodiment 1. 
         FIG.  11    is a schematic plan view of an example of the Fresnel lens in the liquid crystal lens of Embodiment 1. 
         FIG.  12    is a schematic plan view of an example of the alignment of liquid crystal molecules in the liquid crystal lens of Embodiment 1. 
         FIG.  13    is a schematic plan view of another example of the alignment of liquid crystal molecules in the liquid crystal lens of Embodiment 1. 
         FIG.  14    is an exemplary schematic cross-sectional view of a first substrate-side portion in a liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  15    is an exemplary schematic cross-sectional view of a second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  16    is another exemplary schematic cross-sectional view of the first substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  17    is another exemplary schematic cross-sectional view of the second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  18    is yet another exemplary schematic cross-sectional view of the first substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  19    is yet another exemplary schematic cross-sectional view of the second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. 
         FIG.  20    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 3 of Embodiment 1. 
         FIG.  21    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 4 of Embodiment 1. 
         FIG.  22    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 5 of Embodiment 1. 
         FIG.  23    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 6 of Embodiment 1. 
         FIG.  24    is a schematic perspective view of an example of a head mounted display of Embodiment 2. 
         FIG.  25    is a schematic perspective view of an example of polarized sunglasses of Embodiment 3. 
         FIG.  26    is a schematic cross-sectional view of a conventional liquid crystal lens. 
         FIG.  27    is a schematic cross-sectional view of the conventional liquid crystal lens with no voltage applied. 
         FIG.  28    is a schematic cross-sectional view of the conventional liquid crystal lens with voltage applied. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is described in more detail based on the following embodiments with reference to the drawings. The present invention is not limited to the embodiments. 
     Embodiment 1 
       FIG.  1    is a schematic plan view of a liquid crystal lens of Embodiment 1.  FIG.  2 A  is a schematic cross-sectional view of the liquid crystal lens of Embodiment 1 taken along line A1-A2 in  FIG.  1   . As shown in  FIG.  1    and  FIG.  2 A , a liquid crystal lens  10  of the present embodiment includes a first substrate  100 ; a second substrate  200  facing the first substrate  100 ; a liquid crystal layer  300  held between the first substrate  100  and the second substrate  200  and containing liquid crystal molecules  310 . The first substrate  100  includes a Fresnel lens  120  and a first electrode  130  sequentially toward the liquid crystal layer  300 . The second substrate  200  includes a second electrode  220 . This configuration can vary the focal length of the liquid crystal lens  10  by varying the voltage applied between the first electrode  130  and the second electrode  220  and thus varying the refractive index of the liquid crystal layer  300 . The liquid crystal lens  10  of the present embodiment is a varifocal lens. 
     The Fresnel lens  120  includes a Fresnel-shaped part  121  and a flat part  122 . The Fresnel-shaped part  121  includes a plurality of annular lens surfaces  121 A disposed in a concentric circle pattern. The flat part  122  includes a flat surface  122 A that extends in a radial direction of the concentric circle and intersects at least one of the annular lens surfaces  121 A. The annular lens surfaces  121 A are disposed on the liquid crystal layer  300 -facing surface of the Fresnel-shaped part  121  and define an uneven surface  121 B. The flat surface  122 A is disposed on the liquid crystal layer  300 -facing surface of the flat part  122 . When conductive lines are disposed on a conventional Fresnel lens, the conductive lines are on the uneven surface of the Fresnel lens, meaning that they may be rather easily open-circuited. In contrast, the present embodiment can reduce or prevent occurrence of such an open circuit since the Fresnel lens  120  has the flat surface  122 A and conductive lines can be disposed to overlap the flat surface  122 A. 
     Hereinafter, the liquid crystal lens  10  of the present embodiment is described in detail. 
     The liquid crystal lens  10  of the present embodiment includes, as shown in  FIG.  1    and  FIG.  2 A , the first substrate  100 , the second substrate  200  facing the first substrate  100 , and the liquid crystal layer  300  sealed between the first substrate  100  and the second substrate  200  with a sealant  400  and containing the liquid crystal molecules  310 . The first substrate  100  includes a first support substrate  110 , the Fresnel lens  120 , and the first electrode  130  sequentially toward the liquid crystal layer  300 . The second substrate  200  includes a second support substrate  210  and the second electrode  220  sequentially toward the liquid crystal layer  300 . 
     Preferably, the liquid crystal lens  10  includes an alignment film at least one of between the first substrate  100  and the liquid crystal layer  300  or between the second substrate  200  and the liquid crystal layer  300 . With this configuration, the alignment of the liquid crystal molecules  310  with no voltage applied can be controlled. In the present embodiment, the mode is described where the liquid crystal lens  10  includes a first alignment film  31  between the first substrate  100  and the liquid crystal layer  300  and a second alignment film  32  between the second substrate  200  and the liquid crystal layer  300 . Yet, an alignment film may be disposed only between the first substrate  100  and the liquid crystal layer  300  or only between the second substrate  200  and the liquid crystal layer  300 . Such a configuration also can achieve the effect of controlling the alignment of liquid crystal molecules  310  with no voltage applied. 
     Preferably, the height (thickness) of the liquid crystal lens  10  is 50 µm or lower. This configuration can control the cell thickness, and thus reduce or prevent a decline in response speed of the liquid crystal molecules  310 . The height of the liquid crystal lens  10  is, for example, 3 µm or higher. With a height of the liquid crystal lens  10  of lower than 3 µm, the lens may be divided into too many sections. With a height of the liquid crystal lens  10  of lower than 1 µm, the height of the liquid crystal lens  10  may be difficult to control. 
     The first support substrate  110  and the second support substrate  210  may be, for example, substrates such as glass substrates or plastic substrates. The glass substrates may be made of, for example, glass such as float glass or soda-lime glass. The plastic substrates may be made of, for example, a plastic such as polyethylene terephthalate, polybutylene terephthalate, polyethersulfone, polycarbonate, or alicyclic polyolefin. Preferably, the first support substrate  110  and the second support substrate  210  are transparent substrates. 
     The liquid crystal lens  10  of the present embodiment includes the first support substrate  110  on the surface of the Fresnel lens  120  remote from the liquid crystal layer  300 . The liquid crystal lens  10 , however, may not include the first support substrate  110 . 
     The first electrode  130  and the second electrode  220  are, for example, transparent conductive films. The first electrode  130  and the second electrode  220  can be formed by, for example, forming a single- or multi-layered film of a transparent conductive material such as indium tin oxide (ITO), indium zinc oxide (IZO), zinc oxide (ZnO), or tin oxide (SnO) or an alloy of any of these materials by sputtering or any other method, and patterning the film by photolithography or any other method. 
     Herein, the state with no voltage applied, where the voltage applied between the first electrode  130  and the second electrode  220  is lower than the threshold voltage (including no voltage application), is also referred to simply as “with no voltage applied”. The state with voltage applied, where the voltage applied between the first electrode  130  and the second electrode  220  is the threshold voltage or higher, is also referred to simply as “with voltage applied”. 
     The Fresnel lens  120  includes the Fresnel-shaped part  121  and the flat part  122 . 
     The Fresnel-shaped part  121  includes the annular lens surfaces  121 A, each having a refractive surface  121 AX and a non-refractive surface  121 AY, arranged in a concentric circle pattern in regions excluding the region where the flat part  122  is arranged. The Fresnel lens  120  utilizes the refractive surfaces  121 AX to refract light to change the direction that the light travels. The refractive surfaces  121 AX may be arranged at the same pitch or different pitches. The annular lens surfaces  121 A are arranged on the liquid crystal layer  300 -facing surface of the Fresnel-shaped part  121  and define the uneven surface  121 B. 
     The uneven surface  121 B, for example, has regular steps whose height is 0.01 µm or higher and 200 µm or lower. Examples of the regular steps include steps formed at a constant pitch, steps formed at a constant height, and steps formed at a constant pitch and a constant height. The uneven surface  121 B may include a non-step portion as well as the regular steps. The non-step portion is flat (smooth), for example. Specifically, the non-step portion has a ten-point mean roughness (Rzjis) as measured in conformity with JIS B 0601 of 0.2 µm or less. 
     The flat part  122  includes the flat surface  122 A that extends in the radial direction of the concentric circle and intersects at least one of the annular lens surfaces  121 A. The flat surface  122 A is disposed on the liquid crystal layer  300 -facing surface of the flat part  122 . 
     Conventional Fresnel lenses have only the Fresnel-shaped part without any flat part. This means that the conventional Fresnel lenses include conductive lines on an uneven surface and thus are prone to causing open circuits. 
     In order to prevent occurrence of breakage of the conductive lines due to the steps on the Fresnel lens, JP 2009-98641 A mentions provision of at least one notch in the ridge line of each circle of the Fresnel lens. With the notches, however, the conductive lines are still bent sharply in some areas, and thus this measure is considered insufficient. 
     In contrast, the present embodiment can reduce occurrence of an open circuit (breakage due to the steps) owing to the configuration in which the conductive lines overlap the flat surface  122 A. For example, in the present embodiment, preferably, the first electrode  130  overlaps the flat surface  122 A. This configuration can reduce occurrence of an open circuit in the first electrode  130 . 
     The flat surface  122 A is smooth and has, for example, a ten-point mean roughness (Rzjis) as measured in conformity with JIS B0601 of 0.2 µm or less. The lower limit of the ten-point mean roughness (Rzjis) of the flat surface  122 A is not limited and may be, for example, 0 µm or more. In the case of the liquid crystal lens  10  having a curved shape, the flat surface  122 A, if smooth, may be curved following the curved shape of the liquid crystal lens  10  as shown in  FIG.  2 B  and  FIG.  2 C .  FIG.  2 B  and  FIG.  2 C  each are a schematic cross-sectional view showing an example where the liquid crystal lens of Embodiment 1 has a curved shape. 
     Preferably, the flat surface  122 A in a plan view extends linearly. Here, use of an imprint mold in production of the liquid crystal Fresnel lens of JP 2009-98641 A would require addition of the shapes corresponding to the notches to the mold for the Fresnel lens, which may complicate the production of the mold. In contrast, the present embodiment allows easy production of a mold for the Fresnel lens  120  owing to the flat surface  122 A extending linearly in a plan view. Preferably, the flat part  122  is formed using a mold simultaneously with the Fresnel-shaped part  121  from the same material. 
     Preferably, the flat surface  122 A in a plan view extends linearly from an outermost periphery  120 A of the Fresnel lens  120  toward a center  120 B of the Fresnel lens  120 . In Fresnel lenses, the vertex angle of the steps of the uneven surface decreases from the center toward the outermost periphery to cause the inclination angle of the steps to be sharp, so that the electrodes on the Fresnel lens are prone to being open-circuited. However, with the flat surface  122 A which in a plan view extends linearly from the outermost periphery  120 A of the Fresnel lens  120  toward the center  120 B of the Fresnel lens  120 , the present embodiment can effectively reduce or prevent occurrence of an open circuit. The present embodiment also can prevent occurrence of an open circuit in the diametral direction of the liquid crystal lens  10 . 
       FIG.  3 A  is a schematic perspective view of an example of a Fresnel lens in the liquid crystal lens of Embodiment 1. Preferably, as shown in  FIG.  3 A , the flat surface  122 A covers a region  123 X 1  corresponding to a refractive surface  121 AX 1  at the outermost periphery  120 A of the Fresnel lens  120  (i.e., covers the edge including the outermost periphery  120 A of the Fresnel lens  120 ). Herein, the region corresponding to a refractive surface of the Fresnel lens is a region overlapping a flat part in a case where the refractive surface of the Fresnel lens is extended hypothetically in a concentric circle pattern to the flat part in the structure in which the flat part constitutes part of the Fresnel lens as shown in  FIG.  3 A  to  FIG.  3 F . 
     Since the vertex angle of the steps of the uneven surface in the Fresnel lens decreases toward the outermost periphery to cause the inclination angle of the steps to be sharp, the electrodes on the Fresnel lens are prone to being open-circuited. Yet, occurrence of an open circuit can be effectively reduced or prevented when the flat surface  122 A covers the region corresponding to the refractive surface  121 AX 1  at the outermost periphery  120 A of the Fresnel lens  120  (i.e., covers the edge including the outermost periphery  120 A of the Fresnel lens  120 ). In this manner, occurrence of an open circuit can be effectively reduced or prevented when the flat part  122  fills the gaps in the edge including at least the outermost periphery  120 A. 
       FIG.  3 B  is a schematic perspective view of another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. As shown in  FIG.  3 B , the flat surface  122 A may cover the region  123 X 1  corresponding to the refractive surface  121 AX 1  at the outermost periphery  120 A of the Fresnel lens  120  and a region  123 X 2  corresponding to a refractive surface  121 AX 2  at an inner position relative to the outermost periphery  120 A. The flat part  122  may fill the gaps from the outermost periphery  120 A up to somewhere in the path from the outermost periphery  120 A to the center  120 B. 
       FIG.  3 C  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. As shown in  FIG.  3 C , the flat surface  122 A in a plan view may extend linearly from the outermost periphery  120 A of the Fresnel lens  120  to the center  120 B of the Fresnel lens  120 . This configuration can prevent occurrence of an open circuit in the diametral direction of the liquid crystal lens  10 . 
       FIG.  3 D  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. As shown in  FIG.  3 D , the flat surface  122 A in a plan view may extend linearly from an outermost periphery  120 A 1  of the Fresnel lens  120  to an outermost periphery  120 A 2  facing the outermost periphery  120 A 1 . 
       FIG.  3 E  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. As shown in  FIG.  3 E , preferably, the flat surface  122 A is disposed at the same height as vertices  121 BX of the uneven surface  121 B or higher than the vertices  121 BX of the uneven surface  121 B. In other words, preferably, the flat surface  122 A is disposed at the same height as the vertices  121 BX of the uneven surface  121 B or closer to the liquid crystal layer  300  than the vertices  121 BX are. This configuration enables the flat part  122  to fill the gaps due to the Fresnel shape, thus facilitating production of a mold for the Fresnel lens  120 . 
     The heights of the vertices  121 BX of the uneven surface  121 B may be the same as or different from one another. When the heights of the vertices  121 BX are different, the flat surface  122 A is preferably disposed at the same height as the highest vertex  121 BX among the vertices  121 BX of the uneven surface  121 B or higher than the highest vertex  121 BX. This configuration can facilitate production of a mold for the Fresnel lens  120 . 
       FIG.  3 F  is a schematic perspective view of yet another example of the Fresnel lens in the liquid crystal lens of Embodiment 1. The flat part may have a shape that completely fills the gaps due to the Fresnel shape as shown in  FIG.  3 E , or a shape that partially fills the gaps due to the Fresnel shape as shown in  FIG.  3 F . Specifically, the flat surface  122 A may be disposed lower than the vertices  121 BX of the uneven surface  121 B. In this manner, the flat part  122  may be at a height where the flat part  122  partially fills the gaps due to the Fresnel shape (height where the steps of the Fresnel shape are partially flattened). 
     Although  FIG.  3 A  to  FIG.  3 F  show only one flat surface  122 A, any number of flat surfaces  122 A may be formed. The Fresnel lens  120  may include two or more flat surfaces  122 A. 
       FIG.  4 A  and  FIG.  4 B  each are a schematic cross-sectional view of an example of the Fresnel lens in the liquid crystal lens of Embodiment 1, taken along line B1-B2 in  FIG.  1   . Preferably, as shown in  FIG.  4 A  and  FIG.  4 B , the flat part  122  has a tapered shape with a width that decreases toward the liquid crystal layer  300 . This configuration allows the conductive lines (e.g., first electrode  130 ), when disposed on the Fresnel lens  120 , to curve gently, thus effectively reducing or preventing occurrence of an open circuit in the circumferential direction of the liquid crystal lens  10 . Specifically, preferably, the portions of the flat part  122  connected to the Fresnel-shaped part  121  have a tapered shape with a width decreasing toward the liquid crystal layer  300 . 
     As shown in  FIG.  2 A , the refractive surfaces  121 AX are oblique to a bottom surface  120 U of the Fresnel lens  120 . The non-refractive surfaces  121 AY are perpendicular to the bottom surface  120 U. The angle formed by each refractive surface  121 AX and the corresponding non-refractive surface  121 AY, i.e., the angle of the vertices  121 BX, preferably increases from the center  120 B of the Fresnel lens  120  toward the outermost periphery  120 A of the Fresnel lens  120 . This configuration can increase the refractive index for light as the light travels away from the center  120 B of the Fresnel lens  120 , so that the light-gathering power of the Fresnel lens  120  can be increased. 
     The Fresnel lens  120  preferably includes a resin, more preferably a transparent resin having a refractive index of 1.4 to 1.8. Examples of the transparent resin having a refractive index of 1.4 to 1.8 include acrylic resin, polycarbonate resin, and polyethylene resin. Herein, the transparent resin means one having a transmittance, excluding interfacial reflection, for light in the visible range (wavelength of 380 to 780 nm) of 90% or higher when formed into a 1-mm-thick plate. 
     The liquid crystal layer  300  contains a liquid crystal material and controls the amount of light passing therethrough by changing the alignment of the liquid crystal molecules  310  in the liquid crystal material according to the voltage applied to the liquid crystal layer. 
     The liquid crystal molecules  310  have an anisotropic refractive index. In the liquid crystal lens  10 , the voltage applied between the first electrode  130  and the second electrode  220  is varied to control the alignment of the liquid crystal molecules  310 , so that the refractive index of the liquid crystal layer  300  for incident light can be varied between the extraordinary refractive index (ne) and the ordinary refractive index (no). The refractive indices satisfy the relationship ne &gt; no. The liquid crystal lens  10  which is based on these principles basically can turn on or off the lens functions for only one of s-polarized light and p-polarized light. 
     The liquid crystal molecules  310  may have a positive or negative anisotropy of dielectric constant (Δε) according to the following (formula L). The liquid crystal molecules  310  having a positive anisotropy of dielectric constant are also referred to as positive liquid crystals. The liquid crystal molecules  310  having a negative anisotropy of dielectric constant are also referred to as negative liquid crystals. The long axis direction of the liquid crystal molecules  310  corresponds to the direction of the slow axis. The liquid crystal molecules  310  with no voltage applied are homogeneously aligned. The azimuth of the long axes of the liquid crystal molecules with no voltage applied is also referred to as the initial alignment azimuth of the liquid crystal molecules. 
     Δε= (dielectric constant in long axis direction of liquid crystal molecules) - (dielectric constant in short axis direction of liquid crystal molecules) (formula L) 
     Preferably, the liquid crystal layer  300  has a nematic-isotropic phase transition temperature (Tni) of 110° C. or higher. This configuration can stabilize the interfacial refractive index with no voltage applied. For example, when the liquid crystal layer has a Tni of lower than 110° C., the liquid crystal layer contains liquid crystal molecules having a positive anisotropy of dielectric constant, and the liquid crystal molecules with no voltage applied are aligned horizontally to the alignment films, the lens effect may not be completely removed with no voltage applied, which may lead to an unintentional lens effect. With the liquid crystal layer  300  having a Tni of 110° C. or higher, the lens effect can be effectively exerted with no voltage applied. 
     Liquid crystal layers having a low Tni typically tend to cause a high degree of misalignment. With a liquid crystal layer having a high Tni (e.g., Tni of 110° or higher), the elastic constant of the liquid crystal layer may be high and thus reduce the chances of misalignment. This can further stabilize the alignment of liquid crystal molecules with no voltage applied, also stabilize the interfacial refractive index, and thus achieve the desired lens effect. 
     Preferably, the liquid crystal layer  300  has a birefringence Δn of 0.20 or higher at a wavelength of 589 nm. This configuration can increase the refractive power of the liquid crystal lens  10 . In other words, the modulation width of the liquid crystal lens  10  can be widened. Preferably, the liquid crystal layer  300  has a Δn of 0.30 or higher at a wavelength of 589 nm. 
     Preferably, the liquid crystal molecules  310  each have at least one bond selected from the group consisting of —CΞC— (acetylene bond), —CH═CH—, —CF═CF—, —CF═CH—, —CH═CF—, —(CO)O—, —O(CO)—, and —O—. This configuration can increase the Tni and Δn of the liquid crystal layer  300 . The liquid crystal molecules  310  each more preferably have a —CΞC— bond, still more preferably a tolane structure (diphenylacetylene structure). This configuration can further increase the Δn of the liquid crystal layer  300 . 
     Preferably, the liquid crystal molecules  310  each have at its end at least one functional group selected from the group consisting of halogen (F, Cl, Br groups), SCN, NCS, CN, OCN, NCO, CF 3 , OCF 3 , and SF 5  groups. This configuration also can increase the Tni and Δn of the liquid crystal layer  300 . 
     Preferably, the liquid crystal molecules  310  have a positive anisotropy of dielectric constant, and the ordinary refractive index no of the liquid crystal molecules  310  is equal to the refractive index of the Fresnel lens  120 . This configuration can effectively turn on/off the lens functions. Here, the expression that the ordinary refractive index no of the liquid crystal molecules is equal to the refractive index of the Fresnel lens means that the difference in refractive index between them is 0.05 or less. 
     The liquid crystal material described above exerts its effects especially in the liquid crystal lens  10  of the present embodiment including the Fresnel lens  120  in the liquid crystal cell. Since the present embodiment includes the Fresnel lens  120  in the liquid crystal cell, there are regions where the liquid crystal layer is thick due to the uneven structure of the Fresnel lens  120 . Liquid crystal molecules are typically aligned in one direction by the alignment regulating force provided by alignment films on the surfaces of a pair of substrates. Such alignment is easily disturbed when the liquid crystal layer is thick. Even under such conditions, use of the liquid crystal material above can stabilize the alignment of liquid crystal molecules. 
     The liquid crystal material described above exerts its effect especially in a configuration including an alignment film only on the later-described substrate (second substrate  200 ) with no Fresnel lens (i.e., in a mode where no first alignment film  31  is used and only the second alignment film  32  is used). With alignment films on substrates on both sides, liquid crystal molecules are easily aligned by the alignment regulating forces from both sides. Meanwhile, with an alignment film only on a substrate on one side, liquid crystal molecules need to be aligned by the alignment regulating force from the one side. Even in such a case, use of the liquid crystal material described above can stabilize the alignment of liquid crystal molecules. 
     Also preferably, for stabilization of the alignment of the liquid crystal molecules  310  near the substrate (first substrate  100 ) with the Fresnel lens  120 , polymer sustained alignment (PSA) treatment is performed as described later. In this case, preferably, a photopolymerizable monomer is added to the liquid crystal material. The addition concentration is preferably 0.01 wt% to 10 wt%, more preferably 0.1 wt% to 2 wt%. 
     The first alignment film  31  and the second alignment film  32  have a function of controlling the alignment of the liquid crystal molecules  310  in the liquid crystal layer  300 . With no voltage applied, the alignment of the liquid crystal molecules  310  in the liquid crystal layer  300  is controlled mainly by the actions of the first alignment film  31  and the second alignment film  32 . The first alignment film  31  and the second alignment film  32  can be made of a material commonly used in the field of liquid crystal panels, such as a polymer having a polyimide structure in its main chain, a polymer having a polyamic acid structure in its main chain, or a polymer having a polysiloxane structure in its main chain. The first alignment film  31  and the second alignment film  32  can be formed by applying an alignment film material to a substrate. The application method may be any method such as flexo printing or inkjet coating. 
      The first alignment film  31  and the second alignment film  32  may each be a horizontal alignment film that aligns the liquid crystal molecules  310  substantially horizontally to its surface, or a vertical alignment film that aligns the liquid crystal molecules  310  substantially vertically to its surface. The horizontal alignment film has a function of aligning liquid crystal molecules in a liquid crystal layer horizontally to its surface with no voltage applied. The expression that the horizontal alignment film aligns the liquid crystal molecules horizontally to its surface means that the pre-tilt angle of the liquid crystal molecules from the surface of the horizontal alignment film is 0° to 5°, preferably 0° to 2°, more preferably 0° to 1°. The vertical alignment film has a function of aligning liquid crystal molecules in a liquid crystal layer vertically to its surface with no voltage applied. The expression that the vertical alignment film aligns the liquid crystal molecules vertically to its surface means that the pre-tilt angle of the liquid crystal molecules from the surface of the vertical alignment film is 86° to 90°, preferably 87° to 89°, more preferably 87.5° to 89°. The pre-tilt angle of liquid crystal molecules means an angle at which the long axes of the liquid crystal molecules are inclined from the main surface of each substrate with no voltage applied. 
     The first alignment film  31  and the second alignment film  32  may each be a photoalignment film, a rubbed alignment film, or an alignment film having undergone no alignment treatment. The photoalignment film contains a polymer having a photo-functional group and has undergone as the alignment treatment a photoalignment treatment where the film is irradiated with light (e.g., linearly polarized ultraviolet light) from a predetermined direction. The rubbed alignment film has undergone the rubbing treatment as the alignment treatment. The polymer having a photo-functional group is preferably a polymer having as a photo-functional group a cyclobutane ring which is an aliphatic polycyclic structure (photolysis polymer). 
     Preferably, the second alignment film  32  contains a polymer having a cyclic aliphatic group (alicyclic group). For an increase in refractive power of a liquid crystal lens, a liquid crystal layer having a high refractive index difference (birefringence Δn) is sometimes used. However, liquid crystal molecules in such a liquid crystal layer having a high refractive index difference are easily excited by light, and are thus likely to be unreliable. In contrast, an alignment film containing a polymer hacing an alicyclic group does not easily transmit light (especially ultraviolet light) to the liquid crystal layer. Thus, when the second alignment film  32  contains a polymer having a cyclic aliphatic group, the chances that the liquid crystal molecules  310  are excited by light are reduced even when the liquid crystal layer  300  having a high refractive index difference is used for an increase in refractive power of the liquid crystal lens  10 . This can reduce a decline in reliability. Also, when the second alignment film  32  contains a polymer having a cyclic aliphatic group, the chances of coloring of the second alignment film  32  can be reduced, so that the transmittance can be enhanced. This can lead to a high degree of transparency of the liquid crystal lens  10 . 
     Similarly, the first alignment film  31  also preferably contains a polymer having a cyclic aliphatic group. In this configuration, the chances that the liquid crystal molecules  310  are excited by light are reduced even when the liquid crystal layer  300  having a high refractive index difference is used for an increase in refractive power of the liquid crystal lens  10 . This can reduce a decline in reliability. Also, the chances of coloring of the first alignment film  31  can be reduced, so that the transmittance can be enhanced. This can lead to a high degree of transparency of the liquid crystal lens  10 . 
     Preferably, the first alignment film  31  and the second alignment film  32  each contain a polymer having a structure represented by the following general formula (P-1). Structures represented by the following general formula (P-1) have a polyamic acid skeleton.  
     
       
         
         
             
             
         
       
     
     In the formula, X 1  represents a tetravalent aliphatic group, Y 1  represents a divalent organic group, R 1 , R 2 , R 3  and R 4  each independently represent a hydrogen atom or a monovalent hydrocarbon group, and n is an integer of 1 or greater. 
     In general formula (P-1), X 1  preferably has a group represented by any of the following general formulas (X-1) to (X-14). This configuration can enhance the reliability of the liquid crystal molecules  310  and achieve a liquid crystal lens  10  with a high degree of transparency. 
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     In the formulas, * represents a bonding site. 
     In general formula (P-1), X 1  more preferably has a group represented by any of general formulas (X-1), (X-2), and (X-4) to (X-14) above. Polymers having a structure represented by general formula (P-1) are those having a cyclic aliphatic group. This configuration can further enhance the reliability of the liquid crystal molecules  310   and achieve a liquid crystal lens  10  with a higher degree of transparency. 
     More specifically, * in general formulas (X-1) to (X-14) represents a bonding site with the corresponding —C(═O)— group in general formula (P-1). 
     In general formula (P-1), Y 1  is not limited, and is preferably, for example, a group represented by any of the following general formulas (Y-1) to (Y-9). This configuration can enhance the alignment property of the liquid crystal molecules  310 .  
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     In the formulas, a represents an integer of 1 or greater and 10 or smaller, and * represents a bonding site. 
     More specifically, * in general formulas (Y-1) to (Y-9) represents a bonding site with the —N(R 3 )— group or the N(R 4 ) - group in general formula (P-1) . 
     R 1 , R 2 , R 3 , and R 4  in general formula (P-1) each independently represent a hydrogen atom or a monovalent hydrocarbon group. The monovalent hydrocarbon group is preferably a C1-C20 alkyl group, more preferably a C1-C3 alkyl group, still more preferably a methyl group or an ethyl group. The alkyl group may have a linear or branched structure. R 1 , R 2 , R 3 , and R 4  particularly preferably each independently represent a hydrogen atom, a methyl group, or an ethyl group. 
     In general formula (P-1), n is an integer of 1 or greater. The upper limit is not limited, and is 1000 or smaller, for example. 
     The polymer having a cyclic aliphatic group may be, for example, a homopolymer consisting of a repeating unit having a structure represented by general formula (P-1) (where X 1  has a group represented by any of general formulas (X-1), (X-2), and (X-4) to (X-14)), or a copolymer including a repeating unit having a structure represented by general formula (P-1) (where X 1  has a group represented by any of general formulas (X-1), (X-2), and (X-4) to (X-14)) and a repeating unit having a different structure. Examples of the different structure include a structure in which the group corresponding to X 1  in general formula (P-1) is an aromatic group. In the polymer having a cyclic aliphatic group, preferably, 50 mol% or more of all the repeating units have a cyclic aliphatic group. 
     The alignment film containing a polymer having a cyclic aliphatic group may contain one or more polymers having different structures as well as the polymer having a cyclic aliphatic group. Examples of the different structures include a structure in which the group corresponding to X 1  in general formula (P-1) is an aromatic group. Preferably, in the alignment film containing a polymer having a cyclic aliphatic group, 50 mol% or more of all the repeating units, which is the sum of the repeating units of all the polymers in the alignment film, have a cyclic aliphatic group. 
     The liquid crystal lens  10 , as in the present embodiment, may include the first alignment film  31  between the first substrate  100  and the liquid crystal layer  300  as well as the second alignment film  32 . Yet, the liquid crystal lens  10  may include the second alignment film  32  and include no alignment film between the first substrate  100  and the liquid crystal layer  300 . Since the substrate including the Fresnel lens is uneven with large recesses and projections, application of an alignment film material for formation of an alignment film on the substrate may cause the liquid (alignment film material) to be accumulated in the recesses, which may change the shape of the Fresnel lens from the designed shape and thereby change the characteristics of the liquid crystal lens. In contrast, with an alignment film (second alignment film  32 ) only on the substrate (second substrate  200 ) including no Fresnel lens  120 , the shape of the Fresnel lens  120  can be maintained, so that a change in characteristics of the liquid crystal lens  10  can be reduced or prevented. 
     On the substrate (first substrate  100 ) including the Fresnel lens  120 , instead of disposing an alignment film, chemical treatment may be performed using a silane coupling agent described in JP H11-125823 A or JP 2001-021897 A, for example. Also, as described later, PSA treatment or alignment stabilization treatment using fine grooves may be performed. 
     Described above are alignment films containing a polymer having a polyamic acid (polyimide) skeleton as shown in general formula (P-1). Also, alignment films containing a polymer having a polysiloxane skeleton or a poly(meth)acrylic acid skeleton are preferred in terms of high degree of reliability and high transmittances. 
     As shown in  FIG.  2 A , the sealant  400  surrounds the liquid crystal layer  300  between the first substrate  100  and the second substrate  200  and has a function of sealing the liquid crystal layer  300 . The sealant  400  also has a function of bonding the first substrate  100  and the second substrate  200  to each other. The sealant  400  has a frame shape surrounding the liquid crystal layer  300  in a plan view of the liquid crystal lens  10 . 
     Preferably, the sealant  400  contains a cured product of a curable resin, for example. Examples of the curable resin include resins having at least one of a functional group reactive to ultraviolet light or a functional group reactive to heat. The curable resin preferably has a (meth)acryloyl group and/or an epoxy group for rapid progress of curing reaction and favorable adhesiveness. Examples of such a curable resin include (meth)acrylate resin and epoxy resin. Each of these resins may be used alone or two or more of these resins may be used in combination. The term “(meth)acrylic” herein means acrylic or methacrylic. 
     As shown in  FIG.  2 A , the liquid crystal lens  10  includes spacers  500 . The spacers  500  have a function of maintaining the gap in which the liquid crystal layer  300  is formed. With the spacers  500 , the cell thickness can be controlled. The spacers  500  are in contact with at least of the first substrate  100  or the second substrate  200 , and may be in contact with both substrates or only one of the substrates. In the present embodiment, the spacers  500  are on the first substrate  100 . Yet, the spacers  500  may be disposed at any positions and may be disposed on the second substrate  200 . The expression “in contact with” as used herein includes not only the case of direct contact but also the case of contact through other component(s). 
     The spacers  500  each have a columnar shape, for example. The planar shape of each spacer  500  may be, for example, a polygonal shape, a circular shape, or an elliptical shape. 
     Preferably, the spacers  500  contain a cured product of a photosensitive resin, for example. Examples of the photosensitive resin include resins having a functional group reactive to ultraviolet light. Preferably, the photosensitive resin has a (meth)acryloyl group. Examples of such a photosensitive resin include (meth)acrylate resin. 
     Preferably, the height of each spacer  500  is 1 µm or higher and 5 µm or lower, and the diameter of each spacer  500  in a plan view is 5 µm or greater and 20 µm or smaller. The spacers  500  having such a shape are easy to produce. 
     Preferably, the spacers  500  overlap the flat surface  122 A. Conventional Fresnel lenses have only the Fresnel-shaped part without any flat part. This means that spacers overlap the uneven surface, which makes it difficult to stabilize the cell thickness. In contrast, the structure in which the spacers  500  overlap the flat surface  122 A can stabilize the cell thickness. 
     Preferably, in a plan view, the width of the flat surface  122 A is greater than the width of each spacer  500  by 5 µm or more and 20 µm or less. This configuration facilitates arrangement of the spacers  500  in a region(s) overlapping the flat surface  122 A when the spacers  500  are on the second substrate  200  and the first substrate  100  is attached to the second substrate  200 . For example, in a plan view, when the width of each spacer  500  is 5 µm or greater and 20 µm or smaller, the width of the flat surface  122 A is preferably 10 µm or greater and 40 µm or smaller. 
     Preferably, the spacers  500  are disposed on the liquid crystal layer  300  side of the flat surface  122 A. This configuration can stabilize the cell thickness and reduce or prevent electrical connection between the first substrate  100  and the second substrate  200 . Also, the spacers  500  can be made of the same material as the Fresnel lens  120  and integrally formed using a mold as with the flat part  122 . The expression of being (disposed) “on the liquid crystal layer side” of a certain element as used herein includes not only the case of being disposed on a liquid crystal layer-facing surface of the certain element but also the case of being disposed on the liquid crystal layer-facing surface of the certain element through other component(s) except for the liquid crystal layer. 
       FIG.  5    is a schematic cross-sectional view of an example of the structure of a spacer in the liquid crystal lens of Embodiment 1. The spacers  500  may be disposed on the second substrate  200 , not on the first substrate  100 . In this case, as shown in  FIG.  5   , preferably, the spacers  500  are disposed in a region that is disposed on the liquid crystal layer  300  side of the second substrate  200  and overlaps the flat surface  122 A, and no conductive component is disposed in a region on the liquid crystal layer  300 -facing surface of the second substrate  200  overlapping a spacer  500 . This configuration also can stabilize the cell thickness and reduce or prevent electrical connection between the first substrate  100  and the second substrate  200 . Examples of the conductive component include transparent conductive films, specifically the second electrode  220 . 
     Electrical connection between the first substrate and the second substrate may lead to improper application of voltage to the liquid crystal lens. Also, unevenness in cell thickness affects the light-gathering efficiency of the liquid crystal lens, the stability of in-plane response of the liquid crystal molecules, and inclusion of air bubbles, for example. Thus, preferably, arrangement of the spacers is designed as described above, so that the cell thickness is stabilized and the electrical connection between the first substrate  100  and the second substrate  200  is reduced. 
       FIG.  6    is a schematic cross-sectional view of an example of the liquid crystal lens of Embodiment 1. As shown in  FIG.  6   , the second substrate  200  preferably includes, in the liquid crystal layer  300 -facing surface thereof, a tapered portion  210 T that is thick in its center and becomes thinner toward its periphery. Conventional Fresnel lenses, having only the Fresnel-shaped part without any flat part, are under the influence of the uneven surface of the Fresnel lens and therefore have difficulty in stabilizing the alignment of the liquid crystal molecules  310 . However, when the second substrate  200  includes the tapered portion  210 T in the liquid crystal layer  300 -facing surface of the second substrate  200 , the in-plane alignment of the liquid crystal molecules  310  can be stabilized. 
     In the liquid crystal Fresnel lens disclosed in JP 2009-98644 A, the liquid crystal molecules near the Fresnel lens surface of the first transparent substrate including the Fresnel lens are often tilted in different directions from the liquid crystal molecules near the flat surface of the second transparent substrate. This may easily cause disclination or a decline in response property of the liquid crystal molecules. 
     In a liquid crystal lens including a Fresnel lens in its substrate on one side, the steps and steep slopes of the Fresnel lens are likely to destabilize the alignment of liquid crystal molecules. In such a region where the alignment of the liquid crystal molecules is unstable, unintentional stray light such as scattered light may be produced. Also, the structure may affect the response speed in switching of the lens functions. 
     In the present embodiment, as shown in  FIG.  6   , preferably, the second substrate  200  includes the tapered portion  210 T in the liquid crystal layer  300 -facing surface of the second substrate  200 , and the refractive surfaces  121 AX of the Fresnel lens  120  are inclined along the tapered portion  210 T. This configuration can, as shown in  FIG.  6   , allows the liquid crystal molecules  310  to rotate easily in the direction along the refractive surfaces  121 AX of the Fresnel lens  120 , thus stabilizing the alignment of the liquid crystal molecules  310 . This can reduce or prevent disclination. In this manner, the alignment of the liquid crystal molecules  310  can be stabilized by changing the direction of rotation of the liquid crystal molecules  310  using the inclination directions of the refractive surfaces  121 AX in the Fresnel lens  120  (the slope inclined upward to the left or the slop inclined upward to the right as shown in  FIG.  6   ). 
     Preferably, the inclination of the tapered portion  210 T, i.e., the angle formed by a liquid crystal layer  300 -facing surface  210 TA of the tapered portion  210 T and the bottom surface  120 U of the Fresnel lens  120 , is 2° or smaller. This configuration can reduce the thickness of the liquid crystal lens  10 . 
     The tapered portion  210 T may overlap the entire Fresnel lens  120 , or may be disposed only in the region overlapping the central part of the Fresnel lens  120 , excluding the region overlapping the edge of the Fresnel lens  120 . This configuration can effectively reduce the thickness of the liquid crystal lens  10  even when the diameter of the Fresnel lens  120  is large. The center of the Fresnel lens means the center of the Fresnel lens in a plan view. The central part of the Fresnel lens means a region at and near the center of the Fresnel lens in a plan view. The outermost periphery of the Fresnel lens means the outer periphery of the Fresnel lens in a plan view. The edge of the Fresnel lens means the edge region of the Fresnel lens including the outer periphery of the Fresnel lens in a plan view. 
     Preferably, the tapered portion  210 T contains a transparent resin. Examples of the transparent resin include acrylic resin, polycarbonate resin, and polyethylene resin. 
       FIG.  7    is a schematic perspective view of an example of the tapered portion in the liquid crystal lens of Embodiment 1. The tapered portion  210 T, for example, may have a conical shape as shown in  FIG.  7    or a conical shape overlapping the entire Fresnel lens  120 . 
       FIG.  8    is a schematic perspective view of another example of the tapered portion in the liquid crystal lens of Embodiment 1. The tapered portion  210 T, for example, has a conical shape as shown in  FIG.  8   , and may be disposed in the region overlapping the central part  120 C of the Fresnel lens  120  but not in the region overlapping an edge  120 D of the Fresnel lens. 
     As shown in  FIG.  7    and  FIG.  8   , the tapered portion  210 T in a plan view may be rotationally symmetric. 
       FIG.  9    is a schematic perspective view of yet another example of the tapered portion in the liquid crystal lens of Embodiment 1. The tapered portion  210 T, for example, may have a shape with a bilaterally symmetric slope (shape obtained by rounding an isosceles triangular prism from the long sides thereof) as shown in  FIG.  9   . 
       FIG.  10    is a schematic perspective view of yet another example of the tapered portion in the liquid crystal lens of Embodiment 1. The tapered portion  210 T, for example, has a shape with a bilaterally symmetric slope (shape obtained by rounding an isosceles triangular prism from the long sides thereof) as shown in  FIG.  10    and may be disposed in the region overlapping the central part  120 C of the Fresnel lens  120  but not in the region overlapping the edge  120 D of the Fresnel lens. 
     As shown in  FIG.  9    and  FIG.  10   , the tapered portion  210 T in a plan view may be symmetric about a line at an initial alignment azimuth of the liquid crystal molecules  310 . 
     As described above, with the tapered portion  210 T in the second substrate  200 , the alignment of the liquid crystal molecules  310  can be stabilized. 
     Also, PSA treatment may be performed on the liquid crystal layer  300  side of the Fresnel lens  120 , and an alignment maintenance layer that controls the alignment of the liquid crystal molecules  310  may be disposed on the liquid crystal layer  300  side of the Fresnel lens  120 . This configuration also can stabilize the alignment of the liquid crystal molecules  310 . 
     The alignment maintenance layer is a polymer layer formed by adding a polymerizable monomer to the liquid crystal layer and irradiating the liquid crystal layer with ultraviolet light to polymerize the polymerizable monomer after attachment of the substrates. Preferably, the polymerizable functional group of the polymerizable monomer constituting the alignment maintenance layer is a (meth)acrylate, vinyl, vinyloxy, or epoxy group. In other words, preferably, the polymer layer has a monomer unit derived from a monomer having at least one group selected from the group consisting of acrylate, methacrylate, vinyl, vinyloxy, and epoxy groups. In particular, acrylate and methacrylate groups are suitable. 
     Also, the polymerizable monomer desirably has a mesogen skeleton such as a biphenyl, naphthalene, anthracene, phenanthrene, or terphenyl structure. The polymerizable monomer is particularly preferably a monomer represented by any of the following chemical formulas (M1) to (M5). 
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
     
     In the formulas, P 2  represents a polymerizable functional group. 
     Specifically, the alignment maintenance layer is preferably a polymer of a monomer represented by the following chemical formula (M11).  
     
       
         
         
             
             
         
       
     
       FIG.  11    is a schematic plan view of an example of the Fresnel lens in the liquid crystal lens of Embodiment 1. In  FIG.  11   , the flat part  122  of the Fresnel lens  120  is omitted. As shown in  FIG.  11   , the Fresnel lens  120  may have a plurality of parallel grooves  120 X in its liquid crystal layer  300 -facing surface. This configuration also can stabilize the alignment of the liquid crystal molecules  310 . Preferably, the width of each of the grooves  120 X is 10 nm or greater and 1000 nm or smaller, and the depth thereof is 10 nm or greater and 1000 nm or smaller. 
       FIG.  12    and  FIG.  13    each are a schematic plan view of an example of the alignment of liquid crystal molecules in the liquid crystal lens of Embodiment 1. Preferably, as shown in  FIG.  12    and  FIG.  13   , the initial alignment azimuth of the liquid crystal molecules  310  is parallel or perpendicular to the linear flat surface  122 A. For effective actions by the liquid crystal lens, the refractive index difference needs to be as large as possible during turning on and off the voltage. Thus, preferably, light to be incident on the liquid crystal lens  10  is linearly polarized light vibrating at an azimuth parallel to the initial alignment azimuth of the liquid crystal molecules  310 . This is because while a structure parallel or perpendicular to linearly polarized light is not likely to disturb the polarization, a structure oblique to linearly polarized light is likely to disturb polarization and thus influences, though slightly, the lens functions. 
     Modified Example 1 of Embodiment 1 
       FIG.  14    is an exemplary schematic cross-sectional view of a first substrate-side portion in a liquid crystal lens of Modified Example 1 of Embodiment 1.  FIG.  15    is an exemplary schematic cross-sectional view of a second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1.  FIG.  16    is another exemplary schematic cross-sectional view of the first substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1.  FIG.  17    is another exemplary schematic cross-sectional view of the second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1.  FIG.  18    is yet another exemplary schematic cross-sectional view of the first substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1.  FIG.  19    is yet another exemplary schematic cross-sectional view of the second substrate-side portion in the liquid crystal lens of Modified Example 1 of Embodiment 1. As shown in  FIG.  14    to  FIG.  19   , in Embodiment 1, at least one of the first electrode  130  or the second electrode  220  may be a stack ( 130 A or  220 A) of films having different refractive indices. This configuration can reduce reflection and increase the transmittance. 
     The liquid crystal lens  10  of Embodiment 1 includes the first electrode  130  and the second electrode  220 , which are transparent conductive films (also referred to as transparent electrode layers), for application of voltage to the liquid crystal layer  300 . Here, common transparent conductive films such as ITO films have a high refractive index which may cause reflection in an interface, e.g., the Fresnel resin/ITO interface, the ITO/liquid crystal layer interface, or the ITO/glass interface, to decrease the transmittance of the device. The present modified example can reduce reflection and increase the transmittance since at least one of the first electrode  130  and the second electrode  220  is a stack ( 130 A or  220 A) of films having different refractive indices. The Fresnel resin is the resin constituting the Fresnel lens. 
     As shown in  FIG.  14    to  FIG.  19   , preferably, the stack  130 A includes a transparent conductive film  131  and at least one type of inorganic film  132 , and the stack  220 A includes a transparent conductive film  221  and at least one type of inorganic film  222 . This configuration can more effectively reduce reflection and increase the transmittance. 
     The inorganic films  132  and  222  are suitably SiO 2 , SiNO, SiNx, or Nb 2 O 5  films, for example. 
     The transparent conductive film  131  and the at least one type of inorganic film  132  constituting the stack  130 A, and the transparent conductive film  221  and the at least one type of inorganic film  222  constituting the stack  220 A are arranged such that, for example, as shown in  FIG.  14    and  FIG.  15   , the magnitude of refractive index gradually varies. 
     When the first electrode  130  is the stack  130 A, for example, as shown in  FIG.  14   , sequentially from the Fresnel lens  120  toward the liquid crystal layer  300 , the Fresnel lens  120  (Fresnel resin, refractive index n = 1.5), an inorganic film  132  (SiNO, refractive index n = 1.7), another inorganic film  132  (SiN x , refractive index n = 1.8), the transparent conductive film  131  (ITO, refractive index n = 1.9), yet another inorganic film  132  (SiNO, refractive index n = 1.7), and the liquid crystal layer  300  (refractive index n = 1.55) are arranged. 
     Similarly, when the second electrode  220  is the stack  220 A, for example, as shown in  FIG.  15   , sequentially from the second support substrate  210  toward the liquid crystal layer  300 , the second support substrate  210  (glass, refractive index n = 1.5), an inorganic film  222  (SiNO, refractive index n = 1.7), another inorganic film  222  (SiNx, refractive index n = 1.8), the transparent conductive film  221  (ITO, refractive index n = 1.9), yet another inorganic film  222  (SiNO, refractive index n = 1.7), and the liquid crystal layer  300  (refractive index n = 1.55) are arranged. 
     The inorganic films  132  shown in  FIG.  14    and  FIG.  15    are common inorganic films used in liquid crystal panels and thus highly production friendly. The multi-layered film structure including the ITO film and the inorganic films  132  shown in  FIG.  14    and  FIG.  15    are also referred to as index-matched ITO (IM-ITO). 
     Also, as shown in  FIG.  16    and  FIG.  17   , the transparent conductive films  131  and the at least one type of inorganic film  132  constituting the stack  130 A and the transparent conductive film  221  and the at least one type of inorganic film  222  constituting the stack  220 A may be arranged such that films having a higher magnitude of refractive index than an adjacent film and films having a lower magnitude of refractive index than an adjacent film are alternated. This configuration can cause multilayer interference to effectively reduce reflection and further increase the transmittance. 
     When the first electrode  130  is the stack  130 A, for example, as shown in  FIG.  16   , sequentially from the Fresnel lens  120  toward the liquid crystal layer  300 , the Fresnel lens  120  (Fresnel resin, refractive index n = 1.5), an inorganic film  132  (Nb 2 O 5 , refractive index n = 2.3), another inorganic film  132  (SiO 2 , refractive index n = 1.45), the transparent conductive film  131  (ITO, refractive index n = 1.9), yet another inorganic film  132  (Nb 2 O 5 , refractive index n = 2.3), and the liquid crystal layer  300  (refractive index n = 1.55) are arranged. 
     Similarly, when the second electrode  220  is the stack  220 A, for example, as shown in  FIG.  17   , sequentially from the second support substrate  210  toward the liquid crystal layer  300 , the second support substrate  210  (glass, refractive index n = 1.5), an inorganic film  222  (Nb 2 O 5 , refractive index n = 2.3), another inorganic film  222  (SiO 2 , refractive index n = 1.45), the transparent conductive film  221  (ITO, refractive index n = 1.9), yet another inorganic film  222  (Nb 2 O 5 , refractive index n = 2.3), and the liquid crystal layer  300  (refractive index n = 1.55) are arranged. 
     As shown in  FIG.  14    to  FIG.  17   , the transparent conductive films  131  and  221  are typically ITO films. Yet, the transparent conductive films  131  and  221  may be films other than ITO films. For example, as shown in  FIG.  18    and  FIG.  19   , AZO (ZnO doped with Al, refractive index n = 1.9) films can also be used. Although having lower conductivity than ITO, AZO is highly transparent and is particularly suitable for liquid crystal lens uses. 
     Modified Example 2 of Embodiment 1 
     A liquid crystal lens  10  of the present modified example includes the first alignment film  31  between the first substrate  100  and the liquid crystal layer  300  and the second alignment film  32  between the second substrate  200  and the liquid crystal layer  300 . The first alignment film  31  may be a photoalignment film, while the second alignment film  32  may be a rubbed alignment film. When the liquid crystal molecules  310  are positive liquid crystals, the liquid crystal molecules  310  are horizontally aligned with no voltage applied, and vertically aligned with voltage applied (with vertical electric fields generated). Thus, a pre-tilt angle is preferably set for the liquid crystal molecules  310 . For setting of the pre-tilt angle, the first alignment film  31  and the second alignment film  32  are preferably those having undergone rubbing treatment. However, the liquid crystal layer  300 -facing surface of the first substrate  100  including the Fresnel lens  120  is uneven with projections and recesses, and an alignment film lying along the recesses cannot be rubbed with a rubbing cloth. This produces regions where the alignment film is not sufficiently imparted with the alignment regulating force. In the present modified example, the first alignment film  31  disposed near the first substrate  100   including the Fresnel lens  120  is a photoalignment film, so that alignment treatment can be appropriately performed even with such projections and recesses. 
     Modified Example 3 of Embodiment 1 
       FIG.  20    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 3 of Embodiment 1. As shown in  FIG.  20   , a liquid crystal lens  10  of the present modified example includes the first alignment film  31  between the first substrate  100  and the liquid crystal layer  300 , the second alignment film  32  between the second substrate  200  and the liquid crystal layer  300 , and the spacers  500  disposed on the liquid crystal layer  300  side of the second substrate  200 . The second alignment film  32  may be a photoalignment film. When the second alignment film  32  near the second substrate  200  on which the spacers  500  are disposed is subjected to rubbing treatment, the spacers  500  disrupt the rubbing treatment. This may produce regions where the alignment treatment is not performed on the second alignment film  32 . In the present modified example, since the second alignment film  32  is a photoalignment film, occurrence of a region can be reduced or prevented where the alignment treatment is not performed on the second alignment film  32  near the second substate  200  on which the spacers  500  are disposed. The first alignment film  31  is, for example, a rubbed alignment film. 
     Modified Example 4 of Embodiment 1 
       FIG.  21    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 4 of Embodiment 1. As shown in  FIG.  21   , a liquid crystal lens  10  of the present modified example includes the first alignment film  31  between the first substrate  100  and the liquid crystal layer  300 , the second alignment film  32  between the second substrate  200  and the liquid crystal layer  300 , and the spacers  500  disposed on the liquid crystal layer  300  side of the first substrate  100 . The first alignment film  31  may be a photoalignment film. When the first alignment film  31  near the first substrate  100  on which the spacers  500  are disposed is subjected to rubbing treatment, the spacers  500  disrupt the rubbing treatment. This may produce regions where the alignment treatment is not performed on the first alignment film  31 . In the present modified example, since the first alignment film  31  is a photoalignment film, occurrence of a region can be reduced or prevented where the alignment treatment is not performed on the first alignment film  31  near the first substate  100  on which the spacers  500  are disposed. The second alignment film  32  is, for example, a rubbed alignment film. 
     Modified Example 5 of Embodiment 1 
     While the liquid crystal lens  10  of Embodiment 1 includes one liquid crystal cell, the liquid crystal lens of the present modified example includes a plurality of liquid crystal cells. A stack including a pair of substrates, one of which includes a Fresnel lens, and a liquid crystal layer held between the substrates is also referred to as a liquid crystal cell. 
       FIG.  22    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 5 of Embodiment 1. The liquid crystal layer  300  is a first liquid crystal layer  300 . The liquid crystal molecules  310  are first liquid crystal molecules  310 . The Fresnel lens  120  is a first Fresnel lens  120 . The annular lens surfaces  121 A are first annular lens surfaces  121 A. The Fresnel-shaped part  121  is a first Fresnel-shaped part  121 . The concentric circle pattern is a first concentric circle pattern. The flat surface  122 A is a first flat surface  122 A. The flat part  122  is a first flat part  122 . The liquid crystal lens further includes a third substrate  700  facing the first liquid crystal layer  300  across the second substrate  200  or facing the first liquid crystal layer  300  across the first substrate  100 ; a fourth substrate  800  facing the third substrate  700 ; and a second liquid crystal layer  900  held between the third substrate  700  and the fourth substrate  800  and containing second liquid crystal molecules  910 . The third substrate  700  includes, sequentially toward the second liquid crystal layer  900 , a second Fresnel lens  720  and a third electrode  730 . The fourth substrate  800  includes a fourth electrode  820 . The second Fresnel lens  720  includes a second Fresnel-shaped part  721  and a second flat part  722 . The second Fresnel-shaped part  721  includes a plurality of second annular lens surfaces  721 A disposed in a second concentric circle pattern. The second flat part  722  includes a second flat surface  722 A that extends in a radial direction of the second concentric circle and intersects at least one of the second annular lens surfaces  722 A. The second annular lens surfaces  721 A are disposed on a second liquid crystal layer 900-facing surface of the second Fresnel-shaped part  721  and define an uneven surface. The second flat surface  722 A is disposed on a second liquid crystal layer 900-facing surface of the second flat part  722 . 
     The stack including the first substrate  100 , the first liquid crystal layer  300 , and the second substrate  200  is a first liquid crystal cell (first liquid crystal lens)  10 A. The stack including the third substrate  700 , the second liquid crystal layer  900 , and the fourth substrate  800  is a second liquid crystal cell (second liquid crystal lens)  10 B. 
     Although the liquid crystal lenses  10  of Embodiment 1 and the modified examples thereof each include one liquid crystal cell, the liquid crystal lens  10  of the present modified example includes a plurality of liquid crystal cells. Specifically, the liquid crystal lens  10  of the present modified example includes the first liquid crystal cell  10 A and the second liquid crystal cell  10 B. A liquid crystal lens including a plurality of liquid crystal cells is also referred to as a liquid crystal lens module. 
     While Embodiment 1 achieves, for example, the liquid crystal lens  10  having a focal length corresponding to power 8D with one liquid crystal cell, the liquid crystal lens  10  having the above focal length may be achieved with two liquid crystal cells  10 A and  10 B as in the present modified example. When the two liquid crystal cells  10 A and  10 B are used as in the present modified example, the power of one of the liquid crystal cells is, for example, 4D, so that the differences in height of the uneven surface of the Fresnel lens can be reduced. In other words, production of the Fresnel lens is facilitated. Also, substantially, the liquid crystal layer of one of the liquid crystal cells can be reduced in thickness, so that the response speed can be enhanced. 
     The liquid crystal lens  10  includes an adhesive layer  600  between the first liquid crystal cell  10 A and the second liquid crystal cell  10 B (specifically, between the second substrate  200  and the third substrate  700 ). The adhesive layer  600  is, for example, an optical clear adhesive (OCA) sheet. 
     The third substrate  700  is the same as the first substrate  100 . The third support substrate  710  is the same as the first support substrate  110 . The second Fresnel lens  720  is the same as the first Fresnel lens  120 . The second Fresnel-shaped part  721  is the same as the first Fresnel-shaped part  121 . The second annular lens surfaces  721 A are the same as the annular lens surfaces  121 A. The second flat part  722  is the same as the first flat part  122 . The second flat surface  722 A is the same as the first flat surface  122 A. The third electrode  730  is the same as the first electrode  130 . The fourth substrate  800  is the same as the second substrate  200 . The fourth support substrate  810  is the same as the second support substrate  210 . The fourth electrode  820  is the same as the second electrode  220 . The second liquid crystal layer  900  is the same as the first liquid crystal layer  300 . The second liquid crystal molecules  910  are the same as the first liquid crystal molecules  310 . 
     The liquid crystal lens  10  may include a third alignment film  33  between the third substrate  700  and the second liquid crystal layer  900  and a fourth alignment film  34  between the fourth substrate  800  and the second liquid crystal layer  900 , or may include only one of the third alignment film  33  and the fourth alignment film  34 . 
     The alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  are the same as each other or inverted from each other. Preferably, the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  are inverted from each other. When the alignment treatment is the rubbing treatment, liquid crystal molecules are pre-tilted in or near the substrate interface, i.e., liquid crystal molecules are aligned with a tilt in the direction vertical to the substrate, which means that there is viewing angle dependence. With the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  inverted from each other (specifically, inverted by 180 degrees), the viewing angle dependence is optically compensated, so that the viewing angle characteristics of the liquid crystal lens  10  can be enhanced. 
     Although the present modified example describes a case where the third substrate  700  faces the first liquid crystal layer  300  across the second substrate  200 , the same effect can be achieved when the third substrate  700  faces the first liquid crystal layer  300  across the first substrate  100 . 
     Although the present modified example describes a case of including, sequentially from the first liquid crystal cell  10 A, the third substrate  700 , the second liquid crystal layer  900 , and the fourth substrate  800 , the same effect can be achieved in a case of including, sequentially from the first liquid crystal cell  10 A, the fourth substrate  800 , the second liquid crystal layer  900 , and the third substrate  700 . 
     Modified Example 6 of Embodiment  1   
       FIG.  23    is a schematic cross-sectional view of a liquid crystal lens of Modified Example 6 of Embodiment 1. In Modified Example 5 of Embodiment 1, the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  are the same as each other or inverted from each other. In the present modified example, as shown in  FIG.  23   , the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  are perpendicular to each other. 
     The liquid crystal lens  10  utilizes the difference in refractive index between the liquid crystal layer and the Fresnel lens (Fresnel resin) to refract light. Thus, when including only one liquid crystal cell, the liquid crystal lens  10  has difficulty in exerting its lens effect on linearly polarized light vibrating in the direction parallel to the alignment direction of the liquid crystal molecules. Meanwhile, as in the present modified example, when the liquid crystal lens  10  includes two liquid crystal cells  10 A and  10 B and the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  are perpendicular to each other, the liquid crystal lens  10  can exert its lens effect on both linearly polarized light vibrating in the direction parallel to the liquid crystal molecules and linearly polarized light vibrating in the direction perpendicular to the liquid crystal molecules. Since common unpolarized light is optically the sum of two linearly polarized lights, exerting a lens effect on two linearly polarized lights means being capable of exerting a lens effect on polarized light and unpolarized light. The liquid crystal lens  10  of the present modified example can achieve a liquid crystal lens independent of the polarization state of incident light. Herein, the expression that two linear lines (including axes, directions, and azimuths) are perpendicular to each other means that the angle (absolute value) formed by the lines is within the range of 90 ± 3°, preferably 90 ± 1°, more preferably 90 ± 0.5°, particularly preferably 90° (perfectly perpendicular). 
     Embodiment 2 
     The features unique to the present embodiment are mainly described here, and description of the matters already described in Embodiment 1 is omitted. The present embodiment relates to a head mounted display including the liquid crystal lenses of Embodiment 1 as its eyepieces. 
       FIG.  24    is a schematic perspective view of an example of a head mounted display of Embodiment 2. A head mounted display (HMD)  1  of the present embodiment shown in  FIG.  24    includes, when worn by a user U, includes a display panel  1 P and the liquid crystal lenses  10  as eyepieces between the display panel  1 P and the user U. The liquid crystal lenses  10  of Embodiment 1 can be used as eyepieces of an HMD as shown in  FIG.  24   . In this configuration, the focal length can be adjusted with the liquid crystal lenses  10 . This enables adjustment of the user’s vision and adjustment of the position (depth) at which an image (virtual image) is formed. 
     Preferably, the focal length of the liquid crystal lenses  10  is 50 mm or longer, the diameter is 40 mm or greater and 65 mm or smaller, and the height is 10 µm or higher and 30 µm or lower. The upper limit of the focal length of the liquid crystal lenses  10  is, for example, 1000 mm or shorter, though there is no upper limit for the focal length since the focal length is ∞ when the liquid crystal lenses  10  are turned off. 
     The display panel  1 P can be one commonly used in the field of HMDs. 
     Embodiment 3 
     The features unique to the present embodiment are mainly described here, and description of the matters already described in Embodiment 1 is omitted. The present embodiment relates to polarized sunglasses including the liquid crystal lenses of Embodiment 1 as their lenses. 
       FIG.  25    is a schematic perspective view of an example of polarized sunglasses of Embodiment 3. Polarized sunglasses  2  of the present embodiment shown in  FIG.  25    include stacks each including the liquid crystal lens  10  of Embodiment 1 and a common lens  20 . This configuration can utilize the liquid crystal lenses  10  to control light entering the eyes of a user wearing the polarized sunglasses  2 . 
     EXAMPLES 
     The present invention is described in more detail based on the following examples. The present invention is not limited to these examples. 
     Example 1 
     The head mounted display of Embodiment 2 was produced which included the liquid crystal lenses  10  of Embodiment 1 as its eyepieces. The focal length of the liquid crystal lenses  10  corresponded to 8D (= 125 mm), the diameter was 60 mm, and the height was 25 µm. 
     The liquid crystal layer  300  (liquid crystal material) had a Δn of 0.24 (no = 1.5, ne = 1.74) and contained the liquid crystal molecules  310  having a tolane structure. 
     The flat surface  122 A was disposed at the same height as the vertices  121 BX of the Fresnel lens  120  and extended linearly across the entire diameter of the Fresnel lens  120 . The width of the flat surface  122 A in a plan view was 15 µm. 
     The first alignment film  31  and the second alignment film  32  were horizontal alignment films each containing a polymer having a cyclic aliphatic group. 
     The spacers  500  were disposed on the second substrate  200 . The height of the spacers  500  was 3 µm and the diameter of each spacer  500  in a plan view was 10 µm. 
     Example 2 
     The liquid crystal lens  10  of Modified Example 5 of Embodiment 1 was produced. The focal length of each of the first liquid crystal cell  10 A and the second liquid crystal cell  10 B of the liquid crystal lens  10  corresponded to 4D, the diameter was 60 mm, and the height was 12 µm. The first liquid crystal cell  10 A and the second liquid crystal cell  10 B were attached to each other with an OCA as the adhesive layer  600  such that the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  would be the same as each other. 
     Example 3 
     The liquid crystal lens  10  of Modified Example 6 of Embodiment 1 was produced. The focal length of each of the first liquid crystal cell  10 A and the second liquid crystal cell  10 B of the liquid crystal lens  10  corresponded to 4D, the diameter was 60 mm, and the height was 12 µm. The first liquid crystal cell  10 A and the second liquid crystal cell  10 B were attached to each other with an OCA as the adhesive layer  600  such that the alignment direction of the first liquid crystal molecules  310  and the alignment direction of the second liquid crystal molecules  910  would differ from each other by 90 degrees. 
     Reference Signs List 
     
         
           1 : head mounted display 
           1 P: display panel 
           2 : polarized sunglasses 
           10 ,  10 R: liquid crystal lens 
           10 A: first liquid crystal cell (first liquid crystal lens) 
           10 B: second liquid crystal cell (second liquid crystal lens) 
           11 L: polarized light 
           20 : common lens 
           31 : first alignment film 
           32 : second alignment film 
           33 : third alignment film 
           34 : fourth alignment film 
           100 : first substrate 
           110 : first support substrate 
           120 : Fresnel lens (first Fresnel lens) 
           120 A,  120 A 1 ,  120 A 2 : outermost periphery 
           120 B: center 
           120 C: central part 
           120 D: edge 
           120 U: bottom surface 
           120 X: groove 
           121 : Fresnel-shaped part (first Fresnel-shaped part) 
           121 A: annular lens surfaces (first annular lens surfaces) 
           121 AX,  121 AX 1 ,  121 AX 2 : refractive surface 
           121 AY: non-refractive surface 
           121 B: uneven surface 
           121 BX: vertex 
           122 : flat part (first flat part) 
           122 A: flat surface (first flat surface) 
           123 X 1 ,  123 X 2 : region 
           130 : first electrode 
           130 A,  220 A: stack 
           131 ,  221 : transparent conductive film 
           132 ,  222 : inorganic film 
           200 : second substrate 
           210 TA: liquid crystal layer-facing surface 
           210 : second support substrate 
           210 T: tapered portion 
           220 : second electrode 
           300 : liquid crystal layer (first liquid crystal layer) 
           310 : liquid crystal molecule (first liquid crystal molecule) 
           400 : sealant 
           500 : spacer 
           600 : adhesive layer 
           700 : third substrate 
           710 : third support substrate 
           720 : second Fresnel lens 
           721 : second Fresnel-shaped part 
           721 A: second annular lens surfaces 
           722 : second flat part 
           722 A: second flat surface 
           730 : third electrode 
           800 : fourth substrate 
           810 : fourth support substrate 
           820 : fourth electrode 
           900 : second liquid crystal layer 
           910 : second liquid crystal molecule 
         U: user