Optical element and display device

Abstract

An optical element includes a substrate and a resin and satisfies the following formula, RTmax/RTmin9/5, wherein RTmin represents the resin thickness at the thinnest regions of a major patterned component that is made of the resin, and RTmax represents the resin thickness at the thickest regions of the major patterned component which is made of the resin.

Claims

1. An optical element comprising a substrate and a resin and satisfies the following formula:
RTmax/RTmin9/5Formula (1) wherein RTmin represents the resin thickness at the thinnest regions of a major patterned component that is made of the resin, and RTmax represents the resin thickness at the thickest regions of the major patterned component which is made of the resin, and wherein the optical element satisfies the following formula:
/EsRTmax/T<13.0 ppmFormula (3a) wherein represents the internal stress of the resin, Es represents the Young's modulus of the substrate, and T represents the thickness of the substrate.

2. The optical element according to claim 1, wherein the optical element satisfies the following formula:
/EsRTmax/T3.0 ppmFormula (3b)

3. The optical element according to claim 1, wherein the substrate is a glass substrate that has a thickness of 200 m or more.

4. The optical element according to claim 1, wherein the optical element is a lenticular lens sheet, a fly-eye lens sheet, or a Fresnel lens sheet.

5. A display device that comprises the optical element according to claim 1.

6. An optical element comprising a substrate and a resin and satisfies the following formula:
RTmax/RTmin9/5Formula (1) wherein RTmin represents the resin thickness at the thinnest regions of a major patterned component that is made of the resin, and RTmax represents the resin thickness at the thickest regions of the major patterned component which is made of the resin, and wherein the resin has pencil hardness of 6B or softer.

7. An optical element that comprises a substrate and two or more resin laminate layers, wherein the resin laminate layers comprise a stress-release resin layer and a patterned resin layer, wherein the stress-release resin layer is disposed between the patterned resin layer and the substrate, wherein the patterned resin layer forms a major patterned component, and wherein the optical element satisfies the following formula:
RTmax1/RTrx9/5Formula (7) wherein RTrx represents the resin thickness of the stress-release resin layer, and RTmax1 represents the resin thickness at the thickest regions of the resin laminate layers, and wherein the optical element satisfies the following formula:
1/EsRTmax1/T<13.0 ppmFormula (9) wherein 1 represents the internal stress of the resin laminate layers, Es represents the Young's modulus of the substrate, and T represents the thickness of the substrate.

8. The optical element according to claim 7, wherein the optical element satisfies the following formula:
RTmax1/RTrx5/3Formula (8).

9. The optical element according to claim 7, wherein the optical element satisfies the following formula:
1/EsRTmax1/T3.0 ppmFormula (10).

10. The optical element according to claim 7, wherein the substrate is a glass substrate that has a thickness of 200 m or more.

11. The optical element according to claim 7, wherein the stress-release resin layer has pencil hardness of 6B or softer.

12. The optical element according to claim 7, wherein the optical element is a lenticular lens sheet, a fly-eye lens sheet, or a Fresnel lens sheet.

13. A display device that comprises the optical element according to claim 7.

14. An optical element comprising a substrate and a resin and satisfies the following formula:
RTmax/RTmin9/5Formula (1) wherein RTmin represents the resin thickness at the thinnest regions of a major patterned component that is made of the resin, and RTmax represents the resin thickness at the thickest regions of the major patterned component which is made of the resin, wherein the resin includes a lens portion having a predetermined curvature radius and a base portion of the lens portion, and wherein a change rate r of the curvature radius after a light fastness test is 10% or less.

15. The optical element according to claim 14, wherein the optical element satisfies the following formula:
RTmax/RTmin5/3Formula (2), and wherein the change rate r of the curvature radius after the light fastness test is 5.5% or less.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a cross-sectional view illustrating part of a process for producing a lenticular lens sheet described in Patent Document 1.

(2) FIG. 2 is a cross-sectional view of a lenticular lens sheet described in Patent Document 1.

(3) FIG. 3 is a cross-sectional view illustrating the definitions of a lens array according to the present invention.

(4) FIG. 4 is a cross-sectional view illustrating the definitions of a base according to the present invention.

(5) FIG. 5 is a cross-sectional view illustrating a phenomenon exhibited by a lenticular lens sheet in a light fastness test.

(6) FIG. 6 is a cross-sectional view illustrating a phenomenon exhibited by a lenticular lens sheet according to the present invention in a light fastness test.

(7) FIG. 7 is a cross-sectional view of a lenticular lens sheet according to the first embodiment of the present invention.

(8) FIG. 8 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and the rate of change of the radius of curvature (r) of a lenticular lens sheet that includes a resin A after a light fastness test. (RTmaxRTmin is maintained at a constant value of about 21 m.)

(9) FIG. 9 is a graph illustrating a relationship between RTmax/RTmin and the rate of change of the radius of curvature (r) of a lenticular lens sheet that includes a resin A after a light fastness test. (RTmaxRTmin is maintained at a constant value of about 21 m.)

(10) FIG. 10 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and the rate of change of the radius of curvature (r) of a lenticular lens sheet that includes a resin B after a light fastness test. (RTmaxRTmin is maintained at a constant value of about 21 m.)

(11) FIG. 11 is a cross-sectional view illustrating the definitions of the shape and the size of a warped lenticular lens.

(12) FIG. 12 is a cross-sectional view of a stereoscopic display device that includes a lenticular lens sheet according to the third embodiment of the present invention, the sheet being attached to a display panel.

(13) FIG. 13A is a perspective view of the first example of an electronic apparatus to which a stereoscopic display device according to the third embodiment is applicable.

(14) FIG. 13B is a perspective view of the second example of an electronic apparatus to which a stereoscopic display device according to the third embodiment is applicable.

(15) FIG. 13C is a perspective view of the third example of an electronic apparatus to which a stereoscopic display device according to the third embodiment is applicable.

(16) FIG. 14 is a cross-sectional view of a stereoscopic display device that includes a lenticular lens sheet according to the third embodiment of the present invention, the sheet being attached to a liquid crystal display panel.

(17) FIG. 15 is a cross-sectional view of a lenticular lens sheet according to the second embodiment of the present invention.

(18) FIG. 16 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and /EsRTmax/T of a lenticular lens sheet that includes a resin A in the initial state and after reliability assessment (a constant temperature test and a constant temperature and humidity test). (RTmaxRTmin is maintained at a constant value of about 21 m.)

(19) FIG. 17 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and /EsRTmax/T of a lenticular lens sheet that includes a resin B in the initial state and after reliability assessment (a constant temperature test and a constant temperature and humidity test). (RTmaxRTmin is maintained at a constant value of about 21 m.)

(20) FIG. 18 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax1) and 1/EsRTmax1/T of a lenticular lens sheet that includes resin laminate layers that include a stress-release resin layer made of a resin B and a patterned resin layer made of a resin A after reliability assessment (a constant temperature test and a constant temperature and humidity test). (RTmax1RTrx is maintained at a constant value of about 30 m.)

(21) FIG. 19 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax1) and 1/EsRTmax1/T of a lenticular lens sheet that includes resin laminate layers that include a stress-release resin layer made of a resin B and a patterned resin layer made of a resin A after reliability assessment (a constant temperature test and a constant temperature and humidity test). (RTmax1RTrx is maintained at a constant value of about 30 m.)

(22) FIG. 20 is a cross-sectional view of a lenticular lens sheet of a comparative example.

(23) FIG. 21 is a cross-sectional view illustrating cutting of a lenticular lens sheet.

DESCRIPTION OF THE EMBODIMENTS

First Embodiment

(24) Now, embodiments of the present invention will be described in detail with reference to the drawings.

(25) FIG. 7 is a cross-sectional view of a lenticular lens sheet according to the first embodiment. FIG. 8 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and the rate of change of the radius of curvature (r) of the lenticular lens sheet that includes a resin A after a light fastness test. FIG. 9 is a graph illustrating a relationship between RTmax/RTmin and the rate of change of the radius of curvature (r) of the lenticular lens sheet that includes a resin A after a light fastness test. FIG. 10 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and the rate of change of the radius of curvature (r) of the lenticular lens sheet that includes a resin B after a light fastness test. In the graphs of FIGS. 9 and 10, RTmaxRTmin is maintained at about 21 m.

(26) As illustrated in FIG. 7, a lenticular lens sheet 10 according to the first embodiment includes a lens 12 that is made of a UV curable resin 13 and that is formed on a generally planar surface of a glass substrate 11. The lenticular lens according to the present invention can be produced by the following method. The UV curable resin 13 is applied in an appropriate amount onto the glass substrate 11. A lens mold is used to transfer its pattern to the applied UV curable resin 13. The UV curable resin 13 is cured by irradiation with UV light. Then, the lens mold is removed. The major pattern of the lenticular lens is the lens 12. The lens pitch is designated as lp.

(27) The inventors used the lenticular lens sheet 10 to find a method for improving the reliability of the UV curable resin, especially, for preventing a change in the radius of curvature in a light fastness test, which is one of the conventional problems. To assess the reliability, a light fastness test was performed by using a resin A, which was a UV curable resin, fixing the curved shape of the lens 12, and varying RTmax (thus also varying RTmin). The distance from the lens valleys to the lens peaks (RTmaxRTmin) was about 21 m. The glass substrate 11 had a thickness of from 100 m to 300 m. The lens pitch of the lens 12 was in the range of from 100 m to 500 m. Before a light fastness test, the radius of curvature rI and the resin thickness at the thickest regions (RTmax) were measured. After the light fastness test, the radius of curvature rA was measured.

(28) The results of the assessment is illustrated in FIG. 8 as a graph illustrating a relationship between the resin thickness at the thickest regions (RTmax) and the rate of change of the radius of curvature (r). r is (rArI)/rI. FIG. 8 shows a very high correlation between RTmax and r with regard to the resin A. Maintenance of RTmax at 58 m or more allows maintenance of r within the range of from +5.5% to 5.5%.

(29) To generalize the result illustrated in FIG. 8, a graph illustrating a relationship between RTmax/RTmin and the rate of change of the radius of curvature (r) is illustrated in FIG. 9. FIG. 9 shows that when RTmax/RTmin is equal to or less than 9/5, the lens sheet that includes a resin A can maintain r within the range of from +10% to 10% after assessing the light fastness. Additionally, when RTmax/RTmin is equal to or less than 5/3, the lens sheet that includes a resin A can maintain r within the range of from +5.5% to 5.5%. The assessment was performed under the condition of RTmax<T.

(30) In the first embodiment, only r is described, although no problems are detected with regard to other properties such as the transmittance and the appearance in the light fastness test.

(31) A light fastness test was also performed by using a resin B, which was a UV curable resin different from the resin A, in a similar manner to the test performed for the resin A. The results are illustrated in FIG. 10, as in FIG. 8. FIG. 10 illustrates that the resin B did not substantially exhibit a change in r after the light fastness test, regardless of RTmax. No problems were also detected with regard to other properties such as the transmittance and the appearance after the light fastness test. With regard to light fastness, the resin B had acceptable properties. Although other UV curable resins mostly became yellow in the light fastness test, the resin A and the resin B did not substantially exhibit a change in visible light transmittance and did not substantially become colored.

(32) As used herein, the term A type refers to a resin that has a rate of change of the radius of curvature (r) after a light fastness test, the rate r increasing as the resin thickness at the thickest regions (RTmax) decreases after a light fastness test, as illustrated by the graph of FIG. 8. The term B type refers to a resin that has a rate of change of the radius of curvature (r) after a light fastness test, the rate r remaining substantially constant even as the resin thickness at the thickest regions (RTmax) changes after a light fastness test, as illustrated by the graph of FIG. 10. The radius of curvature of an A type changes in a light fastness test, and thus the resin is curing during the test. The radius of curvature of a B type does not change regardless of the resin thickness at the thickest regions in a light fastness test, and thus the resin is not being curing during the test.

(33) However, a lenticular lens sheet 10 that includes a resin B suffers from the problem of large warpage in production and use of a display device. The amount of the warpage depends on the thickness of the glass substrate 11 (T) and the thickness of the UV curable resin. Thus, in order to compare the potential of UV curable resins to exhibit warpage, /EsRTmax/T is calculated from the amount of warpage of the lens array. refers to the internal stress of the UV curable resin 13, and Es refers to the Young's modulus of the glass substrate 11.

(34) /Es is calculated from Formula (5), which is a modification of the Stoney's Formula (4). The Stoney's Formula is an equation for calculation of the stress of a thin film on a substrate from the amount of the warpage. Although the UV curable resin for the lenticular lens sheet 10 was not a thin film, the Stoney's Formula can be applied without significant problems. Although the lenticular lens sheet 10 is not round, the Stoney's Formula can be applied without significant problems, because the lenticular lens sheet 10 that is assessed for the amount of warpage has a dimension of 100 mm100 mm or less and thus is considered as having a round shape.
=EsT.sup.2/(6(1v)RRTmax)Formula (4)
/Es=T.sup.2/(6(1v)RRTmax)Formula (5)

(35) T is the thickness of the glass substrate as defined above, v is the Poisson's ratio of the glass substrate, R is the radius of curvature of the lenticular lens sheet 10 (R differs from the radius of curvature of the lens array (r)), and RTmax is a resin thickness at the thickest regions as defined above. The Poisson's ratio can be defined as physical property of a glass substrate. The radius of curvature (R) is the difference of the radius of curvature before and after molding the resin. The radius of curvature (R) can be determined by directly measuring a lens sheet by laser scanning and fitting the measure to a circular arc. The radius of curvature (R) can also be calculated from the amount of warpage of the substrate. FIG. 11 illustrates a lenticular lens sheet 10 that exhibits a warpage () after molding the UV curable resin. The warpage () can be determined by directing a laser beam at the side of the glass substrate using, for example, a laser displacement meter. The measuring length (L) is a length for measuring the warpage. If the area for measuring the warpage has a square shape, L is the length of a side of the square. Next, Formula (6) is used to calculate the radius of curvature (R) from and L.
R=(.sup.2+(L/2).sup.2)/2Formula (6)

(36) Generally, as the warpage of the lenticular lens sheet 10 increases, the radius of curvature (R) tends to become easily fitted (in the case, R decreases). It has been confirmed that even when the warpage of the sheet is small, the radius of curvature (R) can be fitted to some extent (in the case, R increases).

(37) As seen from Formula (6), as warpage () increases, the radius of curvature (R) decreases, and /Es in Formula (5) increases. Thus, when T, v, and RTmax remain constant, a smaller value of warpage indicates a smaller value of internal stress.

(38) Table 1 illustrates pencil hardness and /EsRTmax/T immediately after producing the lenticular lens sheet 10 with regard to a resin A and a resin B. In Table 1, the same lens mold is used to produce the respective lens sheets. And the maximum warpage (max) exhibited in assessment of the reliability of these lenticular lens sheets (a constant temperature test and a constant temperature and humidity test) is used to compare /EsRTmax/T after the reliability assessment. With regard to both of the resin A and the resin B, the lens sheets for measuring /EsRTmax/T have an RTmax of about 60 m and include a glass substrate that is made of a same material and that has a same thickness. In the reliability assessment, the maximum amount of warpage (max) of the lenticular lens sheets 10 is a saturated value. In Table 1, the initial warpage is assessed as good (no problems) when the lenticular lens sheets 10 have no problems with the initial warpage and can be attached to a display device or as poor (problematic) when the lenticular lens sheets 10 have a problem. The warpage after the reliability assessment, which indicates the result of a thermal cycle test of a display device to which the respective lens sheets are attached, is assessed as good or poor in the similar manner. In Table 1, r represents the rate of change of the radius of curvature. With regard to both of the resin A and the resin B, r after the constant temperature test and the constant temperature and humidity test is in a range of from 2% to 3% regardless of the resin thickness at the thickest regions (RTmax). Thus, the resin B is curing during the constant temperature test and the constant temperature and humidity test, while the resin A is curing during the light fastness test, as well as during the constant temperature test and the constant temperature and humidity test, as described above.

(39) TABLE-US-00001 TABLE 1 Constant Temperature Test and Constant Temperature and Humidity Test /Es RTmax/T (ppm) Warpage Light After After Fastness Test Pencil Reliability Reliability Rtmax-r Resin Hardness Initial Assessment Initial Assessment r Curve A 6B 2.6 2.6 Good Good 2-3% A type B H 13.0 43.4 Poor Poor 2-3% B type

(40) In Table 1, the resin A has very soft pencil hardness of 6B, while the resin B has pencil hardness of H. Table 1 shows that the resin B has an initial /EsRTmax/T of 13.0 ppm and a /EsRTmax/T after the reliability assessment of 43.4 ppm, which is significantly increased. The lenticular lens sheet that includes the resin B has a large initial warpage and is difficult to attach to a display device. A lens sheet that includes the resin B and that is then attached to a display device has a low yield and peeled off of the display device in the thermal cycle test. On the other hand, the /EsRTmax/T of the resin A after the reliability assessment does not change from the initial /EsRTmax/T, which are 2.6 ppm. A lenticular lens sheet 10 that includes the resin A in the initial state can be attached to a display device without problems and has no problems in the thermal cycle test.

(41) With regard to a relationship between /EsRTmax/T and failure due to the warpage, Table 1 shows that a problem does not arise when /EsRTmax/T is equal to or less than 3.0 ppm, while a problem arises when /EsRTmax/T is equal to or more than 13.0 ppm. 3.0 ppm is a value obtained by introducing an error of 15% into 2.6 ppm. Thus, the UV curable resin 13 preferably has a /EsRTmax/T of less than 13.0 ppm. More preferably, the UV curable resin 13 has a /EsRTmax/T of 3.0 ppm or less.

(42) While the resin B does not substantially cure in the light fastness test, the resin B cures and exhibits a slight change in its radius of curvature in the constant temperature test and the constant temperature and humidity test. The resin A cures and exhibits a slight change in its radius of curvature in the constant temperature test and the constant temperature and humidity test, and also cures in the light fastness test. In the constant temperature test and the constant temperature and humidity test, the UV curable resins have a substantially uniform temperature and thus uniformly cures, which results in a change in the radius of curvature of from 2% to 3%, regardless of the resin thickness at the thickest regions. In the light fastness test, cure of the UV curable resins is advanced from the side that is irradiated with light, as illustrate in FIGS. 5 and 6, and thus a resin that does not have a resin thickness ratio according to the present invention exhibits a large change in its radius of curvature.

(43) As illustrated in Table 1, both of the resin A and the resin B exhibit a rate of change of the radius of curvature (r) of from 2% to 3% in the constant temperature test and the constant temperature and humidity test. However, the /EsRTmax/T after the reliability assessment of the resin A does not substantially change from the initial /EsRTmax/T in the constant temperature test and the constant temperature and humidity test, while the /EsRTmax/T after the reliability assessment of the resin B is three times or more than the initial /EsRTmax/T in the constant temperature test and the constant temperature and humidity test. With regard to both of the resin A and the resin B, the lens sheets for measuring /EsRTmax/T illustrated in Table 1 have an RTmax of about 60 m and include a glass substrate that is made of a same material and that has a same thickness, as described above. Thus, the difference in modulus between the resin A and the resin B greatly affects the difference in /EsRTmax/T. Unlike metal, high hardness resins generally have a high elastic modulus. Thus, the resin A that has pencil hardness of 6B has a lower elastic modulus, compared with the resin B that has pencil hardness of H. As the resin A and the resin B is curing in the constant temperature test and the constant temperature and humidity test, the lens array shrinks, and the radius of curvature slightly increases. As the resin A has a low elastic modulus, curing shrinkage of the resin A is compensated by deformation of the resin A itself, and thus the lens sheet that is made of the resin A does not exhibit a change in warpage. On the other hand, as the resin B has a high elastic modulus, curing shrinkage of the resin B is not substantially compensated by deformation of the resin B itself, and thus the lens sheet exhibits a large warpage. The low elastic modulus of the resin A may readily cause a change in the density of the photocurable resin to maintain the volume of the resin, as illustrated in FIG. 6. Use of a resin that exhibits a small /EsRTmax/T can reduce warpage of the lens sheet after the constant temperature test and the constant temperature and humidity test and can reduce a change in the radius of curvature in the light fastness test.

(44) In a case in which the lenticular lens sheet 10 includes the glass substrate 11, and in which there is the problem of warpage of the lenticular lens sheet after molding the UV curable resin 13, it is generally attempted to reduce the thickness of the UV curable resin 13 and not the thickness of the glass substrate 11. The glass substrate 11 has a small coefficient of linear expansion and does not substantially change its size when the substrate is exposed to heat while molding the UV curable resin 13. On the other hand, the UV curable resin 13 exhibits curing shrinkage when the resin 13 is molded, and the resin 13 increases ten-fold in size, compared with the glass substrate, when the resin 13 is exposed to heat. Thus, it is generally attempted to reduce the thickness of the UV curable resin, which exhibits larger curing shrinkage and larger thermal expansion, to prevent the warpage.

(45) When the thickness of the UV curable resin 13 is reduced, a change in the shape of the lens array affects the optical properties. Thus, it is generally attempted to reduce the thickness of the base (RTmin) to 0, the base not affecting the optical properties. In the present invention, instead of simply reducing RTmin to 0, thickness of the major patterned component (RTmaxRTmin) is set as described above to ensure the light fastness, and RTmin necessary to achieve the effect of the present invention is determined using Formula (1) or Formula (2).

(46) Although the first embodiment has been described with regard to a lenticular lens sheet, it should be appreciated that the embodiment is not limited to a lenticular lens sheet, and that the embodiment is also applicable to other optical elements that can be produced by patterning a photocurable resin on a substrate according to the embodiment. Examples of the other optical elements include fly-eye lens sheets and Fresnel lens sheets. The major patterned component of fly-eye lens sheets is a lens array. The major patterned component of Fresnel lens sheets is a pattern that constitutes the Fresnel lenses.

(47) Although the first embodiment has been described with regard to the UV curable resin 13, it should be appreciated that a visible-light curable resin is applicable to the optical element according to the embodiment. Although the embodiment is not limited to a photocurable resin, it should be appreciated that any resin is applicable to the optical element according to the embodiment as long as the resin exhibits curing shrinkage due to the action and the effect of the present invention, when the resin is patterned and exposed to light.

(48) Although the first embodiment has been described with regard to the glass substrate 11, it should be appreciated that a resin substrate is applicable to the optical element that can be produced by patterning a resin on a substrate according to the embodiment. In a case in which a resin substrate is used, the effects of preventing curvature change in a light fastness test and of preventing warpage can be provided. However, a resin substrate that has a certain thermal expansion coefficient may cause a problem of misalignment due to the difference in thermal expansion coefficient between a lens sheet made of the resin and a display device, as described in TECHNICAL FIELD. In a case in which a resin substrate has a thermal expansion coefficient similar to that of a glass substrate, the resultant lens sheet does not cause a problem of thermal misalignment.

(49) In a case in which the resin thickness at the thickest regions (RTmax) of a lens sheet significantly varies with the position of the optical element, it is preferred to divide the area and to apply the embodiment to each of the divided parts.

Second Embodiment

(50) While the optical element according to the first embodiment addresses a problem of deformation of a resin that constitutes the element in a light fastness test, the optical element according to the second embodiment addresses a problems of warpage of a resin that constitutes the element.

(51) The second embodiment will be described with reference to FIGS. 15-20. As illustrated in FIG. 15, an optical element according to the second embodiment is produced by forming a stress-release resin layer 62 on a substrate 51 and then forming a patterned resin layer 63 on the stress-release resin layer 62 to produce curved pieces (lenses).

(52) In an optical element that includes a substrate 51 and a resin 64 as illustrated in FIG. 20, use of a resin that exhibits large warpage such as a resin B as the resin 64 causes the problem that the resultant element exhibits large warpage in the initial state and after reliability assessment. On the other hand, use of a resin such as a resin A as the resin 64 causes the problem that the resultant element exhibits large deformation if the element does not have a configuration according to the first embodiment, although the element exhibits small warpage.

(53) FIG. 17 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and /EsRTmax/T of an optical element that includes a resin B in the initial state and after reliability assessment (a constant temperature test and a constant temperature and humidity test). RTmaxRTmin is maintained at about 21 m. The substrate 51 is a glass substrate. FIG. 17 shows that the optical element that includes the resin B increases /EsRTmax/T, as a resin thickness at the thickest regions (RTmax) increases, both in the initial state and after reliability assessment. Due to curing shrinkage, /EsRTmax/T after reliability assessment is larger than /EsRTmax/T in the initial state. When RTmax is 30 m, /EsRTmax/T in the initial state and after reliability assessment are respectively 4.2 ppm and 17.6 ppm.

(54) FIG. 16 is a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax) and /EsRTmax/T of an optical element that includes a resin A in the initial state and after reliability assessment (a constant temperature test and a constant temperature and humidity test). RTmaxRTmin is maintained at about 21 m. The substrate 51 is a glass substrate. FIG. 16 shows that the optical element that includes the resin A has a /EsRTmax/T of 2.9 ppm or less, regardless of a resin thickness at the thickest regions (RTmax), both in the initial state and after reliability assessment.

(55) In the second embodiment, a resin B that does not exhibit deformation in a light fastness test but exhibits large warpage is used for the patterned resin layer 63 illustrated in FIG. 15, and a soft resin A that exhibits small warpage is used for the stress-release resin layer 62. The thickness of the substrate 51 is designated as T. The thickness of the stress-release resin layer 62 is designated as RTrx. The total thickness of the stress-release resin layer 62 and the patterned resin layer 63 is designated as RTmax1.

(56) Next, the lenticular lens sheet 18 is used to consider the conditions for preventing warpage, which is a problem of the resin B. The assessment is performed by fixing a thickness of the resin B, i.e., RTmax1RTrx, which is the thickness of the patterned resin layer, at about 30 m, varying RTmax1 (thus also varying RTrx), and determining 1/EsRTmax1/T after a constant temperature test and after a constant temperature and humidity test. 1 is the internal stress of a resin laminate layers that is constituted by the patterned resin layer 63 and the stress-release resin layer 62. 1/Es is determined by the method described in the first embodiment. The distance from a lens valley to a lens peak is about 21 m. The substrate 51 is a glass substrate that has a thickness of from 100 m to 300 m. The lens 12 has a pitch of from 100 m to 500 m.

(57) The result of the assessment is illustrated in FIG. 18 as a graph illustrating a relationship between a resin thickness at the thickest regions (RTmax1) and 1/EsRTmax1/T. FIG. 18 shows a very high correlation between RTmax1 and 1/EsRTmax1/T, as in FIG. 8 according to the first embodiment. Maintenance of RTmax at 73 m or more allows maintenance of 1/EsRTmax1/T at 3.0 ppm or less.

(58) To generalize the result illustrated in FIG. 18, a graph illustrating a relationship between RTmax1/RTrx and 1/EsRTmax1/T is illustrated in FIG. 19. FIG. 19 shows that when RTmax1/RTrx is equal to or less than 9/5, 1/EsRTmax1/T can be maintained at 13.0 ppm or less after the constant temperature test and after the humidity constant temperature test, as in FIG. 9 according to the first embodiment. Additionally, when RTmax1/RTrx is equal to or less than 5/3, 1/EsRTmax1/T can be maintained at 3.0 ppm or less. The assessment is performed under the condition of RTmax1<T.

(59) The warpage problem do not arise when 1/EsRTmax1/T is equal to or less than 3.0 ppm, while the warpage problem arises when 1/EsRTmax1/T is equal to or more than 13.0 ppm, as in the first embodiment.

(60) In the second embodiment, only the warpage is described, although no problems are detected with regard to other properties such as the transmittance and the appearance.

(61) In the second embodiment, use of a soft resin that has pencil hardness of 6B or softer can reduce warpage of the lens sheet after a constant temperature test and a constant temperature and humidity test and can reduce a change in the radius of curvature in a light fastness test, as in the first embodiment.

(62) Although both of the patterned resin layer 63 and the stress-release resin layer 62 are a resin monolayer in the second embodiment, either or both of the layers may be a resin multilayer, which complicates the process.

Third Embodiment

(63) An optical element according to the third embodiment differs from the optical elements according to the first and the second embodiments, in that the element is combined with a display panel such as a liquid crystal display, an organic EL (electroluminescent) display panel, and a PDP (plasma display panel) to form a stereoscopic display device.

(64) As illustrated in FIG. 12, a lens sheet such as a lenticular lens sheet 10 is attached via an adhesive 16 to a display panel 15. The adhesive 16 is a liquid adhesive or a film adhesive. A lens 12 is disposed such that each of the lenses is placed above at least a pair of right and light side pixels (two rows). In this way, a stereoscopic display device 21 that can display 3D images is completed. The stereoscopic display device 21 according to the third embodiment includes a lens sheet according to the first embodiment. The stereoscopic display device 21 according to the third embodiment may also include a lens sheet according to the second embodiment.

(65) In the stereoscopic display device illustrated in FIG. 12, the distance between the lens sheet such as the lenticular lens sheet 10 and the pixels of the display panel 15 (referred to as lens-pixel distance) is important for displaying 3D images. The lens-pixel distance depends on the lens pitch (lp), the pixel pitch, the distance from which 3D images are most readily viewed (optimum 3D viewing distance), and the number of viewpoints. The number of viewpoints refers to the number of different viewpoint images projected into a space for displaying 3D images. For example, in a case in which each of the lenses is placed above a pair of right side pixel and a left side pixel, an image are projected individually for the right side viewpoint and the left side viewpoint, i.e., two viewpoints. For example, in a case in which each of the lenses is placed above two pairs of pixels, the number of viewpoints is 4. The number of viewpoints can be varied depending on the relationship between pixels and lenses. When the optimum 3D viewing distance and the number of viewpoints remain constant, the pixel pitch is proportional to the lens-pixel distance. Thus, as the pixel pitch decreases, it is necessary to reduce the lens-pixel distance. In recent years, display panels tend to provide images of increasingly higher resolution and to have a smaller lens-pixel distance. To describe the lens-pixel distance in detail, FIG. 14 illustrates an exemplary cross-section of a stereoscopic display device that uses a liquid crystal. In the case of a liquid crystal display device, the lens-pixel distance 36 is defined as the distance from a lens peak 17 to the liquid crystal layer 34. It is necessary to reduce the thickness of the photocurable resin 60, the thickness of the glass substrate 11, the thickness of the adhesive 16, the thickness of the polarizing plate 31, and the thickness of the color filter substrate 32 to reduce the lens-pixel distance 36. Reduction of the thickness of the adhesive 16, the thickness of the polarizing plate 31, and the thickness of the color filter substrate 32 without increasing cost is limited, and thus it is also necessary to reduce the thickness of the lenticular lens sheet 10.

(66) Use of the glass substrate 11 as a substrate of the lenticular lens sheet 10 provides technical and cost problems for achieving a thin display. In particular, a glass substrate that has a thickness of 200 m can be cut with a relatively cheap glass scriber with a roll cutter, while a glass substrate that has a thickness of 100 m is difficult to cut with a scriber and has a significantly reduced yield.

(67) A method of molding plural lens using a single lens mold (single-mold method) is used to reduce costs. In this case, it is necessary to be able to section the resultant sheet to obtain a cross-section that includes the resin 64, such as the cross-section taken along the line A-A in FIG. 21. Thus, it is also necessary to cut the resin 64, together with the glass substrate 11. In a case in which a lens sheet includes a glass substrate that has a thickness of 200 m and has an RTmax of about 100 m, the glass substrate and the resin 64 can be cut together with a scriber without any additional operation.

(68) In a case in which a lens sheet includes a glass substrate that has a thickness of 100 m, it is difficult to cut the glass substrate and the resin 64 together. Even if the glass substrate and the resin 64 are tried to be cut together, the resin 64 cannot be cut together with the substrate, which induces fracture of the glass in an area away from the scribe lines. Thus, the glass substrate preferably has a thickness of 200 m or more.

(69) In a case in which the substrate is a commonly-used resin substrate, both of a resin substrate that has a thickness of 200 m and a resin substrate that has a thickness of 100 m can be punched out with a Thomson blade. Unlike a commonly-used resin substrate, a glass substrate that has a smaller thickness has a more severe handleability problem such as ease of fracture due to impact. At present, there are no resin substrates that are as cost effective as glass substrates and that have a thermal expansion coefficient similar to that of glass substrates. Glass substrates are very useful for maintaining the good positional relationship between lenses and pixels with respect to temperature.

(70) However, thinning of the glass substrate 11 is limited, and thus it is very important to reduce the thickness of the photocurable resin 60 as far as possible, as described above. In the present invention, to ensure light fastness, the thickness of a major patterned component (RTmaxRTmin) is set as described above, and a resin thickness at the thickest regions (RTmax or RTmax1) that is necessary to achieve the effect of the present invention and that is the thinnest is determined using Formula (1) or Formula (2).

(71) Display panels provide images of increasingly higher resolution in recent years, and thus a resin thickness at the thickest regions (RTmax or RTmax1) is preferably 100 m or less.

(72) FIGS. 13A-C are respectively a perspective view of the first, the second, and the third examples of an electronic apparatus to which a stereoscopic display device according to the third embodiment is applicable.

(73) FIGS. 13A-C illustrates an electronic apparatus to which a stereoscopic display device 21 according to the third embodiment is applicable. As examples of the electronic apparatuses, a personal computer 22 (FIG. 13A), a television set 23 (FIG. 13B), and a pachinko machine 24 (FIG. 13C) are illustrated, although the stereoscopic display device 21 according to the third embodiment is applicable to various electronic apparatuses such as cellular phones, smartphones, PDA, game consoles, digital cameras, digital video cameras, display screens of car navigation systems, and in-car display screens. Use of the lenticular lens sheet 10 according to the first embodiment can prevent a change in the radius of curvature of the lens 12 after a light fastness test. The warpage can be also prevented in production and use of a display device, which facilitates the production and eliminates peeling of the sheet. Thus, the reliability is improved, and the costs are reduced.

(74) According to the embodiments described above, an electronic apparatus that has excellent visual properties and superior viewing quality and that can provide different images on different viewpoints can be provided at low cost.

DESCRIPTION OF THE REFERENCE NUMERAL

(75) 10, 18 lenticular lens sheet 11 glass substrate 12 lens 13 UV curable resin 15 display panel 16 adhesive 17 lens peak 21 stereoscopic display device 22 personal computer 23 television set 24 pachinko machine 31 polarizing plate 32 color filter substrate 33 TFT substrate 34 liquid crystal layer 35 polarizing plate 36 lens-pixel distance 50 lenticular lens sheet 51 substrate 52 UV curable resin 53 lens mold 54 lens 55 protrusion 56 lens array 57 base 58 lens peak 59 lens valley 60 photocurable resin 61 light 62 stress-release resin layer 63 patterned resin layer 64 resin