JPH095505A - Lens sheet, surface light source and display device - Google Patents

Abstract

PURPOSE: To eliminate oblique unnecessary light without decreasing normal luminance by making the angle that two surfaces on the side in contact with the translucent base material of a unit pentagonal prism contain acuter than the angle that two surfaces on the noncontact side of the translucent base material contain. CONSTITUTION: The lens sheet 1 has unit pentagonal prisms 10 formed projecting on a light projection side and the sectional shapes in one or two orthogonal direction are pentagonal. Of each unit pentagonal prism 10, the angle θa that the two surfaces (steeply slanting surface) 12 and 13 on the base side (side in contact with the translucent base material) is acuter than the angle θa ' that the two surfaces (gently slanting surfaces) 14 and 15 on the vertex side (side not in contact with the light-transmissive base material) (θa '>θa ). Here, θ2 <θ1 holds, where θ1 and θ2 are the angles of the steeply slanting surfaces 12 and 13, and gently slanting surfaces 14 and 15 to a base 11. The steeply slanting surfaces 12 and 13 function to increase the luminance and the gently slanting surfaces 14 and 15 function to suppress a side lobe.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a lens sheet in which unit lens portions are arranged so as to be convex on the light exit side, a surface light source using the lens sheet, and a transmissive type using the surface light source as a backlight. Display device.

[0002]

2. Description of the Related Art As a liquid crystal display device, one using a direct surface type or edge light type diffusion surface light source is known (Japanese Patent Application Laid-Open Nos. 5-173134 and 2-257188,
(Japanese Utility Model Laid-Open No. 4-107201, JP-A-6-18707, JP-A-6-67178, etc.).

FIG. 23 is a diagram showing a conventional example of an edge light type surface light source. The surface light source 100A is disclosed in JP-A-5-17.
No. 3134, Japanese Utility Model Laid-Open No. 4-107201, etc., a light isotropic diffusive layer 102 is formed on one surface of a transparent substrate 101, and the apex angle α is 90.
Degree Isosceles Triangular Prism Linear Array Lens Sheet 105
Are laminated. The reflective layer 10 is formed on the other surface.
3 is formed, and the point-like or linear light source 104 is formed on the side surface.
Are arranged. The surface light source 100B has specifications disclosed in JP-A-6-18707, JP-A-6-67178, etc., and has an apex angle α of 110 degrees instead of the lens sheet 105 of the surface light source 100A. An isosceles triangular prism prism is formed by stacking linear array lens sheets 106.

[0004]

[Problems to be Solved by the Invention] The former surface light source 100A
Since the light isotropically diffused by the isotropic light diffusing layer 102 is deflected by the prism action of the lens sheet 105, the light energy is concentrated near the normal line direction of the light emitting surface,
High energy utilization efficiency, low power consumption and high brightness are possible. However, as shown by the curve (A) in FIG. 15, a phenomenon (side lobe in the angular distribution of transmitted light intensity) in which a part of light deviates from a predetermined angular range near the normal direction occurs (A-1 The light emitted in the oblique direction is unnecessary light for nearby workers (stray light, noise light)
There was a problem that

In the latter surface light source 100B, as shown by the curve (B) in FIG. 15, the side lobes disappear or become smaller, but the normal brightness (meaning the brightness in the normal direction of the light emitting surface, the same applies hereinafter). Has a problem of being reduced by about 25%.

An object of the present invention is to provide a lens sheet, a surface light source and a display device which can eliminate unnecessary light in an oblique direction without lowering the normal luminance.

[0007]

In order to solve the above-mentioned problems, the invention of claim 1 provides a unit pentagonal prism formed on the surface of the light-transmissive substrate on the light-exiting side in a convex shape on the light-exiting side. A lens sheet having a two-dimensional or two-dimensionally arranged lens array layer, wherein the main cut surface shape of a unit pentagonal prism is two steep surfaces in contact with a light-transmissive substrate having an apex angle of θ _a , It has two gentle slopes that are not in contact with the translucent base material whose angle is θ _a ', and the vertical angle when the refractive index of the unit pentagonal prism is n1 and the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0. θ _a and θ _a 'are θ _a <90 ° + (10/9) sin ^-1 ((1 / √2) (n0 / n1))-(6/9) sin ^-1 (n0 / n1) and , Θ _a '≧ θ _a .

According to a second aspect of the invention, in the lens sheet according to the first aspect, the range of the apex angle θ _a 'is θ _a ' ≧ 60 ° + (4/3) sin ^-1 (n0 / n1) It is characterized by being.

According to a third aspect of the present invention, a lens array layer in which a large number of unit pentagonal prisms formed in a convex shape on the light output side are arrayed one-dimensionally or two-dimensionally is formed on the surface of the light-transmissive substrate on the light output side. In the lens sheet, the pentagonal prism unit has a main cut surface shape of two steep slopes in contact with a translucent base material having an apex angle of θ _a and a translucent base material having an apex angle of θ _a ′. It has two gentle slopes that do not touch, and the refractive index of the unit pentagonal prism is
n1, the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0, and the maximum emission angle of the side lobe light emitted from the two steep slopes measured from the normal line of the prism bottom surface is Θ _{so, max} and the minimum emission angle Θ _{so, min} , And the vertical angle θ _a and θ _a 'when the base angle of the prism steep surface is θ _b , θ _a <90 ° + (10/9) sin ^-1 ((1 / √2) (n0 / n1)) -(6/9) sin ^-1 (n0 / n1) and θ _a + 2sin ^-1 (n0 / n1)-EQ1 ≥ θ _a '≥ θ _a + 2sin ^-1 (n0 / n1)-EQ2 However, EQ1 = 2sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b )) EQ2 = 2sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b )) .

The invention of claim 4 is claim 1 or claim 2.
In the lens sheet described in (1), the maximum emission angle of the side lobe light emitted from the two steep slopes of the unit pentagonal prism including the steep slope measured from the normal line of the prism bottom surface is Θ.
_{where so, max} , minimum exit angle Θ _{so, min} , and the base angle of the steep slope of the prism is θ _b , the length x1 'of the gentle slope and the length x2 of the steep slope are e / (c0-1) ≤ x1 '/ x2 ≤ e / (d0-1) where c0 = c1 / c2 d0 = d1 / d2 c1 = sin (90 ° -sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b ))) c2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b ))-θ _a ) d1 = sin (90 ° -sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b ))) d2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b ))-θ _a ) e = sin (θ _a / 2) / sin (θ _a '/ 2).

According to a fifth aspect of the present invention, there is provided a light guide body comprising a light-transmissive flat plate or a rectangular parallelepiped cavity, a light reflecting layer provided at least partially on a back surface of the light guide body, and a side end surface of the light guide body. A point-shaped or linear light source provided adjacent to at least one of the surfaces, and the lens sheet according to any one of claims 1 to 4, which is disposed on the front surface side of the light guide. Including a light isotropic diffusive layer laminated on the outside or inside of the sheet,
The surface of the lens sheet is a diffused light emitting surface.

According to a sixth aspect of the present invention, one or more point-shaped or linear light sources are surrounded, and the light source is enclosed by the light sources, one surface of which is an opening, and the inner surface of the opening is a light reflecting surface. And a lens sheet according to any one of claims 1 to 4 disposed on the opening side of the light source storage portion, and a light isotropic diffusing layer laminated on the outside or inside of the lens sheet. The lens sheet surface is a diffused light emitting surface.

According to a seventh aspect of the present invention, there is provided a transmissive display element,
The surface light source according to claim 5 or 6 provided on the back surface of the display element.

[0014]

1 is a schematic view for explaining the operation of the unit pentagonal prism of the lens sheet according to the present invention. In the lens sheet 1 of the present invention, the unit pentagonal prism 10 is formed in a convex shape on the light output side, and has a pentagonal cross section (main cut surface) in one direction or two directions orthogonal to each other. The unit pentagonal prism 10 may be one in which a number of pentagonal prisms are arranged one-dimensionally so that they are parallel to each other in the ridge direction, or a pentagonal prism having a cross section in which a tetragonal pyramid is stacked on a tetragonal pyramid. It may be arranged two-dimensionally in an array.

The unit pentagonal prism 10 has two surfaces (a steep surface) 12, 13 on the base side (the side in contact with the translucent base material).
Angle (this is the angle that the pentagonal prism is seen among the angles formed by the virtual extension lines of the two surfaces 12 and 13 as shown in the figure) θ _a is on the top side (transparent substrate It is _a steeper angle (θ _a '> θ _a ) than the angle (that is, the apex angle) θ _a ′ formed by the two surfaces (the gentle slopes) 14 and 15 on the non-contact side. Therefore, if the angles formed by the steep slopes 12 and 13 and the gentle slopes 14 and 15 with the bottom face 11 are θ ₁ and θ ₂ , respectively, θ ₂ <θ ₁
Holds. Here, the steep slopes 12 and 13 are portions that perform a function of increasing brightness, and the gentle slopes 14 and 15 are portions that perform a function of suppressing side lobes.

Hereinafter, in order to show the function of the lens sheet according to the present invention, first, the apex angles are 90 ° and 140 °, respectively.
The behavior of incident light rays in the unit triangular prism will be described. Next, in the unit pentagonal prism according to the present invention, the behavior of incident light rays will be described, and it will be described that the unit pentagonal prism having an appropriate shape realizes improvement of brightness and prevention of generation of sidelobe light. Furthermore, in order to exert such a function, the conditions that the unit pentagonal prism must satisfy (the conditions that the angles θ _a 'and θ _a in FIG. 1 must satisfy and the ratio of the lengths of the steep slope and the gentle slope) are derived. The procedure will be described.

FIG. 2 shows the structure of a unit prism of an isosceles triangular prism linear array lens sheet having an apex angle of 90 ° and, when this lens sheet is arranged on a light guide plate of an edge light type surface light source, it is arranged in the unit prism. It is the figure which showed the locus | trajectory of the incident light ray.

For the sake of simplicity, the trajectory of the light ray is calculated and obtained under the following assumptions. 1) The refractive index of air was n0 = 1.0, and the refractive index of the prism was n1 = 1.5. 2) The incident angle of the light ray R1 on the bottom of the prism is 4 counterclockwise.
It was set to 5.7 °. 3) The incident angles of the light rays R2 and R3 on the bottom surface of the prism were both 22.8 ° clockwise or counterclockwise. 4) From the linear array lens sheet, one unit prism was taken out and simulated. 5) Considering the main cut surface of the prismatic prism, it is assumed that the incident ray is inside the main cut surface. 6) The behavior of light rays was examined with the bottom of the prism as the diffused light incident direction (downward in the figure).

Further, on each outer peripheral surface of the unit prism,
The loci of rays that are reflected or refracted are as follows: (a) law of reflection (where incident angle θ and reflection angle θ ′, θ = θ ′), (b)
The law of refraction (refractive index n1 in medium 1, the angle between the ray and the normal of the interface between media 1 and 2 is θ ₁ , refractive index n2 in medium 2 and the angle between the outgoing ray and its normal are θ ₂ Then, it was calculated based on n1sinθ ₁ = n2sinθ ₂ ).

In FIG. 2, the rays to be traced are
Among the reflected lights having the angular distribution which are reflected by the light diffusive reflection layer on the back surface of the light guide plate and are incident on the prism, three representative lights R1, R2, and R3 are selected. Of these, ray R2
Represents a diffused light ray entering the prism, which is incident from the left side, is deflected in the normal direction of the light emitting surface, and is emitted. The light ray R3 represents, among diffused light rays that enter the prism, one that is incident from the right side, is deflected in the normal direction of the light emitting surface, and is emitted.

The ray R1 is a ray causing the sidelobe light. Especially, the remarkable vertical angle of 90 ° for the sidelobe light
In the case of the lens sheet of No. 3, the main factor of the side lobe is that the light enters the slope of the unit prism at a large angle equal to or greater than the critical angle, is totally reflected, is deflected in the horizontal direction, and is further inclined in the horizontal direction by the opposing slope. Is a light beam that is deflected to. Ray R1 is representative of such a ray. Although one ray R1 should be selected for each of the left and right sides, the unit prism is symmetrical, and in order to avoid complication of the drawing, only one ray from the right side is represented.

As can be seen in FIG. 2, the ray R2 travels along the optical path G ₂ → H ₂ → I ₂ . As a result, the ray R2 becomes
When the light is emitted from the unit prism, it is deflected in a direction close to the normal line n of the light emitting surface (the angle with the normal line n is 3.8 ° counterclockwise), and the normal line luminance of the lens sheet is increased. You can see that it is contributing to doing. Similarly, the light ray R3 is also deflected in the direction close to the normal line of the light emitting surface in the process of passing through the unit prism (the angle with the normal line n is 3.8 ° clockwise), and the normal line of the lens sheet. It contributes to the increase in brightness.

On the other hand, the ray R1 passes through A ₂ → B ₂ and enters the prism, and the incident angle 73.5 ° is the critical angle 41.8 ° or more at the point C ₂ on the right slope f2. Because of this, total reflection occurs. As a result, it is deflected to the left near horizontal,
The point D ₂ on the left slope f1 is reached. Then, when it goes out into the air, it is further deflected in the horizontal direction to reach E ₂ . The ray R1 (emitted light) at this time and the normal line n of the light emitting surface of the surface light source
The angle formed by and is 70.7 °, and the light ray R1 deviates from the viewing angle (up to approximately ± 45 ° with respect to the normal line of the light emitting surface) used in a normal display device, and becomes a side lobe light. You can see. Here, the emission direction of the ray R1 will be compared with the actually measured emission direction of the sidelobe light.

FIG. 15 is a diagram showing the results of measurement of the brightness of transmitted light in various prism linear array sheets as a function of angle. The measurement was performed by placing a light diffusion / transmission sheet on the surface of the edge light type surface light source, and installing the above-mentioned triangular prism linear array sheet so that the prism surface faces outward (opposite the light guide plate side). ing. In the figure, a curve (A) drawn by a solid line is a measurement result for a triangular prism linear array sheet having an apex angle of 90 °, and particularly (A-1) shows the luminance of the side lobe light. As can be seen from FIG. 15, the exit angle of the ray R1 is 70.7 °.
Is approximately equal to the angle 68 ° formed by the actually measured peak direction of the side lobe light and the normal line of the light emitting surface.

FIG. 3 shows the structure of a unit prism of a triangular prism linear array lens sheet having an apex angle of 140 °, and when this lens sheet is arranged on a light guide plate of an edge light type surface light source, the light enters the unit prism. It is the figure which showed the locus | trajectory of a light ray. The ray R1 that has become side lobe light in FIG. 2 is totally reflected at a point C ₁ on the right slope f2 of the unit prism, and further, a point D _{1 on the} bottom face f3 and a point E ₁ on the left slope f1.
However, it was totally reflected, and went from F _{1 to} G ₁ back to the bottom side. Therefore, this unit prism does not generate sidelobe light. This agrees with the result of measuring the brightness of the transmitted light of the lens sheet by an experiment (see FIG. 15, broken line (B)).
However, in an actual surface light source, various light rays other than R1 also exist, so that some sidelobe light is generated.

On the other hand, the light rays R2 and R3 are both deflected in the direction close to the normal line n of the light emitting surface, as in the case of FIG. Since the figure is bilaterally symmetric, only the ray R3 is shown in the figure. The angle formed by the ray R3 and the normal line n is 12.5 °, and the apex angle is 90 °.
It is slightly increased as compared with 8 °. This means that in a unit prism with an apex angle of 140 °, the normal direction luminance is
It means that the angle of view is slightly decreased and that the viewing angle is increased. This also matches the tendency of the experimental result (see FIG. 15).

FIG. 4 shows a structure of a unit prism of a pentagonal prism linear array lens sheet according to the present invention and a light beam incident on the unit prism when the lens sheet is arranged on a light guide plate of an edge light type surface light source. It is the figure which showed the locus.

In the illustrated unit pentagonal prism, the steep slopes (f1, f2) below the prism have the same shape as the unit triangular prism having an apex angle of 90 °. Therefore, the light ray R1 enters the prism through A ₀ → B ₀ , is totally reflected at the point C ₀ on the slope f2, and is deflected to the vicinity of the horizontal line to the left. Then, the ray R1 reaches a point D ₀ on the slope f4 above the prism. Here, the slope f4 above the prism
Since f and f5 have the same shape as a triangular prism having an apex angle of 140 °, the incident angle of the light ray R1 on the slope f4 is 50 ° which is larger than the critical angle. Therefore, the ray R1 is totally reflected at the point D ₀ , and is fed back to the light guide plate through the points E ₀ and F ₀ on the bottom surface f3.
Therefore, the ray R1 does not become sidelobe light.

The above calculation results also agree well with the actual measurement data (see FIG. 15, data when the apex angle of the gentle slope shown in the curve (C) is 108 °). In the experiment, various light rays not simulated in FIG. 3 are emitted from the surface light source to the prism, so that the side lobe light is not completely lost. However, the vertical angle 90
Its brightness is greatly reduced compared to the sidelobe light measured in the prism of °. (Fig. 15
The side lobe luminance of (C) is 58% of the side lobe luminance of FIG. 15 (A). )

In FIG. 4, the light ray R1 is totally reflected twice in the prism and then fed back to the light guide plate side through the bottom surface f3. The number of total reflections is shown in Fig. 3.
In the case of the unit triangular prism with an apex angle of 140 ° shown in (3
Less than the number of times). Further, the optical path length of the light ray R1 traveling in the prism is shorter in the case of FIG. 4 than in the case of FIG. Therefore, in the unit pentagonal prism,
The proportion of rays that are attenuated by the time of being fed back to the light guide plate is small, and the proportion of rays that are diffused and reflected on the back surface of the light guide plate after being fed back to the light guide plate and are incident on the prism as output light again is large.

Further, in FIG. 4, the light ray R3 is refracted in the prism and, as a result, is deflected and converged by a method of 3.8 ° from the normal line n of the light emitting surface, and then emitted. This is smaller than 12.5 ° shown in FIG. 3 and indicates that the pentagonal prism according to the present invention converges the output light with higher density in the normal direction.

The simulations shown in FIGS. 2 to 4 are all performed for the case where the prism surface faces the light emitting surface side (the side opposite to the light guide plate). On the other hand, FIG. 5 is a simulation when the prism surface faces the incident surface side (light guide plate side).

In the figure, the light path of the ray R1 is A ₃ → B ₃ →
Since C ₃ → D ₃ → E _3, which is finally fed back to the light guide plate, it does not cause the sidelobe light. However, when this light ray is slightly shifted to the left and enters the prism, that is, in the case of the light ray R1 ′, the optical path is F ₃ →
G ₃ → H ₃ → I ₃ , and the light is emitted from the bottom surface f ₃ of the prism at an angle of 64.0 ° with respect to the normal line n of the light emitting surface. Therefore, the light ray R1 ′ is a cause of generation of side lobe light. Further, the light ray R2 and the light ray R2 ′ which is slightly shifted to the right and enters the prism are the normals n and 3 of the light emitting surface.
The light is emitted from the bottom surface f3 at angles of 5.5 ° and 49.4 °. Although not shown in the figure, the one corresponding to the ray R3 exhibits the same behavior as the ray R2.

As described above, in the pentagonal prism according to the present invention, when the prism surface is used in the light guide plate direction, the normal brightness is lower than that in the case where the prism surface is in the light emitting direction, and , Side lobe light is generated. A similar tendency is obtained in the measured data (Fig. 1).
6).

From the above simulations, in the case of the edge light type surface light source using the light guide plate, the pentagonal prism linear array lens sheet according to the present invention has the prism surface facing the light emitting surface side (the side opposite to the light guide plate). It is understood that the above is preferable for increasing the normal luminance. Further, even in the case of the direct type surface light source, in the case of the mode in which the diffused light is incident on the prism through the light transmitting / diffusing sheet, as shown in FIG.
By directing the prism surface to the light emitting surface side (the side opposite to the light guide plate) by the same mechanism as in FIG. 5, it is possible to increase the normal luminance and reduce the side lobes to obtain a necessary and sufficient viewing angle. It turns out to be preferable.

Next, the generation of side lobe light will be discussed in more detail with reference to FIG. In Figure 6, the apex angle is θ
The main cut surface of the isosceles triangular prism (a) (a unit prism represented by an isosceles triangle PQJ) is shown. Unless otherwise specified below, the apex angle θ _a and the critical angle θ _c of the prism / air interface have a relationship of θ _a > 2θ _c (1). However, θ _c = sin ⁻¹ (n0 / n1) (2).

Rays R11, R12, and R13 are rays that are incident on the prism from the bottom surface f3 and are totally reflected at a point C on the right slope f2. It should be noted that a ray whose incident angle with respect to the slope f2 is smaller than the critical angle θ _c is a ray which is transmitted through the slope f2 while refracting in the direction of the normal line n of the light emitting surface and does not participate in the sidelobe light, and therefore description thereof is omitted. To do.

The ray R11 has an incident angle θ _{c11 at the} point C.
Is slightly larger than the critical angle θ _c , and after total reflection at the point C, reaches the point D on the slope f1 at the incident angle θ _d11 . Here, from the condition of Expression (1), θ _d11 = θ _a −θ _c11 > θ _c (3). Therefore, the ray R11 is totally reflected also at the point D. After that, the light ray R11 is fed back from the bottom surface f3 to the light guide plate side, and thus does not become side lobe light.

On the other hand, the ray R12 is a ray whose incident angle θ _{c12 at} the point C is θ _c12 = θ _a -θ _c (4). The ray R12 is totally reflected at the point C, and then is incident on the slope f1 at the point I. The incident angle θ _{d12 at} this time is θ _d12 = θ _a −θ _c12 = θ _c (5). Therefore, since the ray R12 travels to the point J along the slope f1 after reaching the point I, and is fed back from the point J to the bottom surface side (light guide plate), like the ray R11.
It does not become a sidelobe light.

The ray R13 has an incident angle θ _{c13 at the} point C.
Is θ _c13 > θ _a -θ _c (6), and therefore the incident angle θ at the point M on the slope f1 is
_d13 is θ _d13 <θ _c (7). As a result, the light ray R13 is emitted from the slope f1 at a large angle with respect to the normal line n (angle close to the left horizontal direction in the drawing), and becomes side lobe light. From this, it can be seen that the ray totally reflected at the point C and passing through the corner ICQ to reach the slope f1 becomes the side lobe light. Here, since the angle ICQ = 90 °-(θ _a -θ _c ) (8), θ _c13 = (θ _a -θ _c ) + k (90 °-(θ _a -θ _c )) where 0 <K <1, (9) is derived.

FIG. 7 shows a main cutting surface of a triangular prism having the same apex angle of θ _{a as} in FIG. Ray R in the figure
_{1, max} , R _{1, peak} and R _{1, min} respectively enter the prism from the bottom surface f3, and the incident angles θ _{R, max} , θ _{R, peak} and θ _{R, min} are _calculated on the inclined surface f2 by the formula (9). ) Is a light beam that is totally reflected so as to satisfy. Specifically, θ _{R, min} = (θ _a -θ _c ) + (8/10) (90 °-(θ _a -θ _c )) (10) θ _{R, peak} = (θ _a -θ _c ) + (6/10) (90 °-(θ _a -θ _c )) (11) θ _{R, max} = (θ _a -θ _c ) + (4/10) (90 °-(θ _a -θ _c )) ) (12). That is, the angle of reflection of these rays on the slope f2 is an angle range in which the side lobe light can be reflected (Equation (9)).
Is the angle that divides into 8/10, 6/10, and 4/10, respectively.

When θ _{R, max} , θ _{R, peak} , and θ _{R, min} are thus determined, the angles at which these rays are emitted from the left slope f1 are the normals to the bottom face f3, that is, the light emitted from the surface light source. Value measured from the surface normal n (sidelobe exit angle) Θ _{so, min} ,
When specific values of Θ _{so, peak} and Θ _{so, max} are calculated for the case of apex angle θ _a = 90 °, they are 57.7 ° and 70.
It becomes 7 ° and 84.7 °.

On the other hand, as can be seen from the curve (A) in FIG. 15, the minimum angle direction of the side lobe light of the isosceles triangular prism having the measured apex angle θ _a = 90 ° is Θ _{so, min}
= 52 °, the direction in which the light energy is maximum (peak direction) is Θ _{so, peak} = 68 °, and the maximum angle method is
Θ _{so, max} = 82 °. These values are almost the same as the calculated values Θ _{so, min} , Θ _{so, peak} , and Θ _{so, max} . From this, in the following, the light rays R _{1, max} , R _{1, peak} , R
_{1 and min} respectively approximate the sidelobe light in the minimum angular direction, the peak direction, and the maximum angular direction measured from the normal line n of the light emitting surface.

Next, the rays R _{1, max to} R _{1, min} from the slope f1.
It is described how to identify the area where the light penetrates and replace the area with a prism that does not generate sidelobe light. By doing so, in the isosceles triangular prism having the apex angle θ _a , it is possible to eliminate the sidelobe light while making the most of the high output luminance characteristic.

First, a method for identifying the region on the slope f1 that emits the side lobe light will be described with reference to FIG. FIG. 8 shows a main cutting surface of a triangular prism having an apex angle θ _a = 90 °. The light ray R11 represents the light ray R _{1, peak} which is the side lobe light with the maximum luminance in FIG. 7, and the side lobe emission angle θ _so is 70.7 °.

The ray R11 enters the prism through the optical path E ₁ → D ₁ , is totally reflected at the point C ₁ on the right slope f2, and then is emitted in the direction A ₁ from the point P ₁ on the left slope f1. To do.
Now, the reflection point on the slope F2 C _1, C _2, when progressively moving in the direction of the bottom surface f3 and ..., rays, R11, R1
As shown in 2, ..., It gradually moves in the direction of the base f3 on the slope f1. The reflection point of the ray R _1c is the base f3 and the slope f2.
In the limit, it almost coincides with the point B _c where E intersects, and E _c → B _c
It is a light ray that _{travels as} → P _c → A _c . Thus, the ray R
The rays 11 to R _1c enter the prism from the bottom surface f3 and exit as side lobe light from the inclined surface f1.

Next, the emission point on the hypotenuse f1 is the ray R
Assume ray R13, R14 was present as side lobe light is point P _3, P ₄ of the base f3 side from the emission point P _c of _1c. When these rays are traced back, the angles of incidence on the bottom surface f3 of these rays exceed the critical angle θ _c , so that they no longer enter the prism from below the bottom surface f3,
For example, the optical path E ₃ → G ₃ → F ₃ → P ₃ → A ₃
Must be incident on the bottom surface f3 and totally reflected on the bottom surface f3. However, when a normal surface light source is used and the bottom surface f3 of the prism is installed so as to face the surface light source side,
There are almost no rays similar to the rays R13 and R14.
Therefore, it can be seen that, on the slope f1 of the prism, practically most sidelobe light is emitted from between the point P _c and the apex angle of the prism.

Then, the position of the point P _c is next obtained. Up to the above, the side lobe emission angle is θ _{so, peak} R
_{Although 1, peak} is taken as an example, in the following, the problem is generalized and a ray R _1c having a side lobe emission angle of θ _so is considered. FIG. 9 is a diagram showing a main cutting surface abc of a triangular prism having the same apex angle as θ _a as in FIG. 8 and _a light ray R _1c that crosses the cross section and passes through the vertex c.

Angle θ at which the ray R _1c is incident on the left slope f1
Using θ _so from the law of refraction, _si becomes θ _si = sin ⁻¹ ((n0 / n1) sin θ _so ) (13). However, from FIG. 7, Θ _{so, min} to Θ _{so, max} are exceptionally the normal line n of the light emitting surface (the same as the normal line of the prism bottom surface f3).
Although it measured from the angle theta _so used the law of refraction, both to measure the normal N of the light emitting surface f1 _{is, θ so, min = Θ so} , min - θ b θ so, peak = Θ so, peak _{- θ b θ so, max =} Θ so, max - θ b ······ (13a) are connected by a relation such as (but, theta _b is the base angle of the triangle prism main cutting plane). On the other hand, in the triangle aP _c c, the angle aP _c c = 90 ° −θ _si (14a) and the angle P _c ca = 90 ° + θ _si −θa (14b).

Generally, if the diagonals of the sides of a triangle whose three sides are A, B, and C are α, β, and γ, then (A + B) / (A-B) = (sinα + sinβ) / (sinα-sinβ) (15) holds. Therefore, the lengths of the surfaces ca, aP _c , and P _c b are set to x, x1, and x2, respectively, and equation (15) is transformed into equation (13),
Substituting (14a) and (14b), x1 = (sin (90 ° + θ _si -θ _a ) / sin (90 ° -θ _si )) x (17) x2 = x-x1 = (1- (sin (90 ° + θ _si -θ _a ) / sin (90 ° -θ _si ))) x (18) Therefore, x1 / x2 = 1 / ((sin (90 ° -θ _si) ) / Sin (90 ° + θ _si − θ _a )) ー 1) (19a) is obtained. From this, aP _c1 / bP _c1 = x1 / x2 (20) or aP _c2 / cP _c2 = x1 / x2 (at the surfaces ca and ab of the main cutting surface abc of the isosceles triangular prism whose apex angle is θ _a. 21), the points P _c1 and P _c2 are determined, and the triangle P _c1 aP _c2 may be replaced with a prism that does not generate side lobe light or has a shape that reduces the amount of side lobe light.
By doing so, it becomes possible to suppress the generation of side lobe light having an emission angle θ _so or an angle larger than that.

Since θ _si in the equation (19a) depends on θ _so as shown in the equation (13), the position of the point P _c defined as described above is the exit angle θ of the side lobe light. _so to θ
_It changes depending on whether _{so, min} ≤θ _so ≤θ _{so, max} is set. That is, if the expression (19a) is described more strictly, 1 / (c0-1) ≤ x1 / x2 ≤ 1 / (d0-1) (21a) where c0 = c1 / c2 d0 = d1 / d2 c1 = sin (90 ° -sin ^-1 ((n0 / n1) sinθ _{so, min} )) c2 = sin (90 ° + sin ^-1 ((n0 / n1) sinθ _{so, min} )-θ _a ) d1 = sin (90 ° -sin ^-1 ((n0 / n1) sinθ _{so, max} )) d2 = sin (90 ° + sin ^-1 ((n0 / n1) sinθ _{so, max} ) -θ _a ). When θ _so is close to θ _{so, max} and the position of the point P _c is determined, the sidelobe light is completely erased. On the other hand, as understood from FIG. 7 or the equation (19a), the distance x1 between the point P _c and the apex angle a becomes longer, and the surface length x2 contributing to the normal luminance becomes shorter. Therefore, the normal brightness decreases and the diffusion angle (half-width of the main lobe) also increases. Generally, these performance requirements are
A good balance is obtained by setting θ _so = θ _{so, peak} .

Next, a prism shape in which side lobe light is not emitted or is further reduced is obtained. As is clear from the curve A in FIG. 7 or FIG. 15, the intensity of the side lobe light is large especially in the triangular prism having the apex angle θa of 90 °. The intensity of the sidelobe light sharply decreases at a constant angle when the apex angle is gradually increased. Hereinafter, this point will be described.

FIG. 26 shows that when the refractive index of air is n0 = 1 and the refractive index of the prism is n1 = 1.5, the sidelobe light R _1, which has a peak intensity in a prism with an apex angle θ _a = 90 ° _. FIG. 11 is a diagram showing how _peak , that is, a light ray incident on the bottom surface f3 at an incident angle of 45.7 ° changes its path as the apex angle θ _a increases. From FIG. 26, it can be seen that when the apex angle θ _a gradually increases from 90 °, the emission direction of the side lobe light gradually tilts in the horizontal direction.
This corresponds to that the outgoing rays of R _{1, min to} R _{1, max} gradually rotate counterclockwise in FIG. 7.
As shown in FIG. 26 (B), as a result of the increase in the apex angle θ _a , the emitted light hits the slope of the adjacent prism (the prism next to the left in the drawing), a part of which is reflected, and the normal line of the light emitting surface The output ray R _{1R, peak} near n is obtained. The remaining emitted light is
A light ray R _{1t, peak} that is transmitted and refracted and is fed back to the light guide plate or the light source side is reused. in this way,
The side lobe light gradually decreases as θ _a increases.
When θ _a is further increased, the sidelobe light becomes
As shown in FIG. 3, the light is totally reflected on the inclined surface of the prism, and all of the light is fed back to the light guide plate side, so that it completely disappears.

Next, the above process will be described while tracing a ray. As can be easily seen in FIG. 7, when the apex angle θ _a is increased from 90 °, the side lobe light R _{1, min} ˜
_R1, among the _max, the largest R _{1, max} output angle becomes in contact with the inclined surface of the prism adjacent to the first. Therefore,
The description will be given below based on the sidelobe light R _{1, max} . FIG. 24 is a diagram showing paths of side lobe light in a triangular prism having an apex angle θ _a = 90 ° + α.
Here, α satisfies the relationship of 0 ° <α <90 °,
When θ _a = 90 ° + α, side lobe light R emitted from the left slope f1 in the triangular prism shown in the figure.
_{1, max} (ray from point D to point E in the figure) is the bottom surface f3
The angle is parallel to (side JI in the figure). If such an angular relationship is satisfied, the side lobe light R _{1, max} will be irrespective of the distance between the adjacent unit prisms or the position of the emission point of R _{1, max} , as can be seen from FIG. ,
Be sure to hit the adjacent (on the left) prism slope.

Further, as the apex angle θ _a becomes 90 ° + α, the angle θ _b formed by the bottom surface f3 and the slope f1 or f2.
Is 45 ° − (α / 2). This is because the sum of the interior angles of the triangle is 180 °, the base angles of the isosceles triangle are equal, and the slope f2 and its normal are counterclockwise with the base reduced by (α / 2). If attention is paid to the rotation by (α / 2), it can be easily obtained in elementary geometry. As a result, the side lobe light R at the point D on the left slope f1
The incident angle θ _{si, max} of _{1, max} is θ _{Si, max} = (90 ° + α)-(θ _{R, max} -α / 2 because the sum of the internal angles of the triangle KDC in FIG. 24 is 180 °. ) = 90 ° -θ _{R, max} + (3/2) α (21b) Further, the total reflection angle θ _{R, max} at the right slope f2 is _calculated by the formula (12).
Therefore, θ _{R, max} = ((90 ° + α) −θ _c ) + (4/10) (90 ° − ((90 ° + α) −θ _c )) = 90 ° + (6/10) α -(6/10) θ _c (21c).

The exit angles θ _{so, max} and θ _{R, max} of the side lobe light R _{1, max at} the slope f1 are related as follows by the law of refraction at the point D. n0sinθ _{so, max} = n1sin (90 ° ー θ _{R, max} + (3/2) α) (21d) Therefore, θ _{so, max} = sin ^{ー 1} ((n1 / n0) sin (90 ° ー θ _{R, max} + (3/2) α)) (21e) The direction (D → E) of the emitted light rays is parallel to the bottom surface f3, which means that the side lobe light R _{1, max} is the bottom surface f3.
Since it means that it is orthogonal to the normal line n (normal line of the surface light emitting surface) n, from FIG. 24, (45 ° −α / 2) + θ _{so, max} = 90 ° (21f). Therefore, from equations (21e) and (21f), (45 ° -α / 2) + sin ^-1 ((n1 / n0) sin (90 ° -θ _{R, max} + (3/2) α)) = 90 ° ∴ sin ^-1 ((n1 / n0) sin (90 ° ー θ _{R, max} + (3/2) α)) = 45 ° + α / 2 ・ ・ ・ (21g)

Taking the sine of both sides in the equation (21g), (n1 / n0) sin (90 ° -θ _{R, max} + (3/2) α) = sin (45 ° + α / 2) ∴ sin ( 90 ° -θ _{R, max} + (3/2) α) = (n0 / n1) sin (45 ° + α / 2) (21h) is obtained.

Here, θ _a = 90 ° + α is the apex angle of the triangle and 0 ° <θ _a <180 °, so 0 ° <α <90 ° ∴ 45 ° <(α / 2) + 45 ° <90 ° ∴ 1 / √2 <sin ((α / 2) + 45 °) <1 (21i), and the right side of (21h) is (1 / √2) (n0 / n1) <( n0 / n1) sin (45 ° + α / 2) <n0 / n1 (21j)

Therefore, from equations (21h) and (21j), (n0 / n1)> sin (90 ° −θ _{R, max} + (3/2) α)> (1 / √2) (n0 / n1) (21k) (note that the inequality sign in equation (21k) is
In the inequality sign and its direction is the opposite). to this,
Substituting θ _{R, max} in equation (21c), (n0 / n1)> sin ((6/10) θ _c + (9/10) α)> (1 / √2) (n0 / n1)・ It becomes (21m).

On the other hand, the angle in the sine of equation (21m) is
Originally, the incident angle θ _{Si, max} at the point D on the slope f2 in FIG. 24, that is, (6/10) θ _c + (9/10) α = 90 ° −θ _{R, max} + (3/2 ) α = θ _{Si, max} (21n), 0 ° <(6/10) θ _c + (9/10) α <90 ° (21p). In this section, since the main value of the inverse sine function is a monotonically increasing function with a single valence, the same inequality sign holds even if the inverse sine of equation (21m) is used, and θ _c > (6/10) θ _c + (9 / 10) α> sin ⁻¹ ((1 / √2) (n0 / n1)) (21q). However, from the definition of the critical angle, sin ^-1 (n0 / n1) =
θ _c . When equation (21q) is solved for α, α> (10/9) sin ^-1 ((1 / √2) (n0 / n1))-(6/9) θ _c (21r), as shown in Fig. 24. Angle θ
_{a, max} is θ _{a, max} = 90 ° + α> 90 ° + (10/9) sin ^-1 ((1 / √2) (n0 / n1)) ー (6/9) θ _c・ ・ ・It can be seen that the condition (21s) must be satisfied.

When the apex angle θ _a is further increased, the side lobe lights R _{1, peak} and R _{1, min} become parallel to the base f3,
It disappears with sidelobe light. When the same calculation as above is performed using θ _{R, peak} and θ _{R, min} in the equations (11) and (10), θ _{a, peak} > 90 ° for each of θ _{a, peak} and θ _{a, min} + (10/11) sin ^-1 ((1 / √2) (n0 / n1)) ー (4/11) θ _c・ ・ ・ (21t) θ _{a, min} ＞ 90 ° + (10/13) sin ^-1 obtain ((1 / √2) (n0 / n1)) over _{(2/13) θ c ··· (21u} ). Note that here, in the equations (10) and (11), 90 ° is calculated as 90 ° + α.

Summarizing the above results, the apex angle θ _a = 90
When the angle is °, the exit angle θ _{so, min} from the left slope f1 of the prism
Sidelobe light R _{1, min to} R in the range of ≦ θ ≦ θ _{so, max
All of 1, peak to} R _{1, max} are directly emitted (FIG. 7).
When the apex angle θ _a is increased, the output side lobe light gradually tilts counterclockwise, and the light beam emitted from the lower left slope first begins to be deflected by the adjacent prism as shown in FIG. 26 (B). However, most of the light is emitted as it is. When the apex angle is changed to θ _{a, max} , first, the maximum emission angle R _{1, max of the} side lobe light emerges from the slope f1 and then becomes parallel to the prism bottom face f3, as shown in FIG. As shown in FIG. 26 (c), the outgoing light ray is reflected and transmitted by the adjacent prism oblique surface regardless of the outgoing position on the left oblique surface f1, changes its direction, and becomes a side lobe light.

Further, when θ _a increases and reaches θ _{a, peak} , side lobe light R _{1, peak} giving peak intensity is also emitted from the left slope f1 and then becomes parallel to the bottom face f3 and disappears as side lobe light. . Finally, when θ _a reaches θ _{a, min} , the side lobe light R _{1, min at the} minimum emission angle is no longer a side lobe light, and all side lobe lights R _{1, min.}
˜R _{1, max} are converted into reflected light R _1R emitted in the vicinity of the normal direction and a light ray R _1t fed back to the light guide plate (light source) side.

If θ _a is further increased from θ _{a, min, the} side lobe light having a large emission angle is sequentially arranged on the left slope f2.
Will cause total internal reflection. When θ _a > 60 ° + (4/3) θ _c = 60 ° + (4/3) sin ^-1 (n0 / n1) (21v), the total sidelobe light is totally reflected on the left slope f2. Then, the light returns from the bottom surface f3 to the light guide plate side. FIG. 3 shows n0
= 1.0 and n1 = 1.5, this is an example of a triangular prism that satisfies Expression (21v), and the apex angle θ _a = 140 °.

Next, a method of deriving the equation (21v) will be described. FIG. 10 is a view showing a main cutting surface of a triangular prism having an apex angle of θ _a . In the figure, the light ray R5 has an optical path C.
It is a light ray that _travels in the prism along → D (total reflection) → E and is emitted from the slope f1 in the F direction at an emission angle θ _so .

[0066] If the rays R5 is also angle theta _si and theta _R1, when respectively incident on the inclined surface f1 and slope f2, light traveling from point C to point D and the angle theta _R2 formed between the bottom surface f3, theta _si <Θ _c (22) θ _R1 = θ _a -θ _si (23) θ _R2 = (3/2) θ _a -θ _si -90 ° (24) Here, if θ _R2 = (3/2) θ _a -θ _si -90 °> (3/2) θ _a -θ _c -90 °> θ _c (25) is satisfied, the light can be emitted from the slope f1. Ray R5 is
It is not a light ray incident from the bottom surface f3, but a light ray entering the prism from the inclined surface f2 and totally reflecting at the point C.

On the other hand, if θ _R2 <θ _c (26), the light ray R5 is a light ray that has entered the prism from the bottom surface f3. As described above, the number of light rays entering the prism from the slope f2 is extremely small. Therefore,
The apex angle θ is set so that the expressions (22) and (25) are simultaneously satisfied.
By defining _a , it becomes possible to prevent the presence of a ray that enters the prism from the bottom surface f3 and then becomes sidelobe light. Θ _a that satisfies these conditions is
From Expressions (22) to (25), the following expression is given. θ _a ＞ 60 ° + (4/3) θ _c ＝ θ _{a, perfect} (27)

That is, the apex angle θ _a is θ in the equation (21u).
_When it further increases from _{a, min} and also satisfies the expression (27), the emission of the sidelobe light is still suppressed, but the suppressed sidelobe light is
All are totally reflected on the slopes f1 and f2, fed back to the light guide plate or the light source side, and are not used as output light. Therefore, the brightness of the output light (in particular, the brightness in the normal direction n of the light emitting surface) is reduced. Instead, the viewing angle (half-value angle) of the output light widens as the apex angle becomes wider,
Further, the light fed back to the light guide plate propagates inside the light guide plate, and part of the light is re-output. As a result, the surface distribution of luminance becomes more uniform.

Therefore, in order to obtain a particularly high normal luminance and a small side lobe, 90 ° + (10/9) sin ^-1 ((1 / √2) (n0 / n1))-(6/9) θ _c <θ _a <60 ° + (4/3) θ _c (27a) In addition, the viewing angle of output light and sidelobe light removal and brightness in the light emitting surface are higher than the normal brightness. To obtain a uniform distribution, 60 ° + (4/3) θ _c <θ _a <180 ° (27b) is preferable.

FIG. 17 shows the maximum emission angle θ of a typical material when the refractive index, the critical angle, and the 90 ° apex angle are set.
_max , direction of peak intensity θ _peak , and minimum exit angle θ
A gentle slope apex angle θ _{a, max} , θ for each ray that causes side lobes of _min to be suppressed by adjacent slope reflection
It is a figure which enumerates the gentle slope apex angle (theta) _Ref which suppresses emission | emission by _{a, peak} , (theta) _{a, max} and side lobe cause light being totally reflected in both slopes f1 and f2. However, the calculation is performed assuming that the refractive index of air is 1.00.

FIG. 11 is a view showing the main cross section of the pentagonal prism obtained based on the above description. The apex angles of the gentle slopes f4 and f5 above the prism are θ _a '(θ _a '> θ
_{a, max} ) is a part of the hypotenuse of the isosceles triangle a'b'c '. The steep slopes f1 and f2 below the prism have an apex angle of θ.
It is a part of the hypotenuse of the isosceles triangle abc that is _a (θ _a ≦ θ _{a, max} ). The reason for θ _a <θ _{a, max} is that when θ _a ≧ θ _{a, max} , the side lobe light is reduced, but the light rays (R2, R3, etc. in FIG. 2) that pass through the prism are not refracted or converged. This is because it is sufficient, and unfavorable results such as a decrease in the normal luminance of the emitted light and an increase in the diffusion angle are brought about. Further, the ratio of the length of the steep slope to the length of the gentle slope satisfies Expression (36) described later. The two slopes are connected so that stepwise steps are not formed at the points P _c1 and P _c2 .

In the prism shown in FIG. 11, the bottom surface f3
Of the rays incident on the prism, the steep slopes f1 and f2
Those that pass through are efficiently converged in the direction normal to the light emitting surface, so that the normal luminance is improved. In addition, for example, a light ray that is totally reflected on the gentle slope f5 and travels to the gentle slope f4 exits the gentle slope f4 and then the prism slope (f
At 5), a part of the light is reflected, travels in the direction normal to the light exit surface, and the rest is refracted and fed back to the bottom surface f3, which does not cause side lobe light. As described above, the pentagonal prism shown in FIG. 11 is a prism having both low side lobe characteristics and high normal luminance characteristics.

However, in the prism shown in FIG. 11, after entering the prism from the bottom surface f3 like the ray R6 in the figure, the light is totally reflected at the point C on the steep slope f2 and transmitted through the gentle slope f4 to the side. There may be light rays that are lobe light. That is, when the light ray R6 is totally reflected at a large angle at the point C, it reaches the point D on the gentle slope with a small incident angle. Here, if the apex angle θ _a 'is not sufficiently large and the slope f4 is steep, the incident angle θ _si of the ray R6 at the point D becomes less than the critical angle θ _c , and the ray R
6 passes through the slope f4. When actually calculated, for example, the incident angle θ _in of the light ray R6 at the point B = 48.9 °,
Assuming that the apex angle θ _a '= 120 ° of the gentle slope, the incident angle θ _si is 31 °, and the ray R6 has an incident angle θ _so = 50 °.
Emit at. The exit optical path R6 travels to the upper left, and as already discussed, most of it becomes sidelobe light without being reflected by the prism on the left.

Such side lobe light can be prevented by the conditions obtained as follows. That is, all the light rays incident on the prism through the path shown in FIG. 11 may be totally reflected by the steep slopes f4 and f5 and fed back to the bottom surface f3.
FIG. 12 is a diagram showing a main cutting surface ABC of an isosceles triangular prism having an apex angle of θ _a (<θ _{a, max} ). In the figure, a light ray R7 is a light ray that reaches the point E on the left slope f1 at an incident angle θ _si (<θ _c ) after being totally reflected on the right slope f2, and is emitted from the prism as side lobe light.

Here, it is considered that the slope f1 is rotated clockwise about the point E by an angle Δθ. This is slope f1
Corresponding to the decrease of the slope of Δθ. Conversely, θ _si
Increases by Δθ. If Δθ is θ _si + Δθ ≧ θ _c , that is, Δθ ≧ θ _c −θ _si (28), then θ _si is larger than the critical angle θ _c . As a result, the light ray R7 can be prevented from being totally reflected on the slope f1 and becoming sidelobe light.

FIG. 13 is a diagram showing a main cross section of a pentagonal prism whose shape is determined based on the above consideration. The pentagon A′P _c1 BCP _c2 has a side P _c2 A which is a part of the right hypotenuse CA (left hypotenuse AB) in the triangle ABC having the apex angle θ _a.
Turn (side P _c1 A) half an hour clockwise (clockwise) using equation (28).
It is rotated by an angle Δθ that satisfies the above condition, and a point where the two sides P _c1 A and P _c2 A intersect is newly set as a point A ′. Therefore, in the pentagon A'P _c1 BCP _c2 , the planes P _c2 A '(f5) and P _c1 A' (f4) are gentle slopes and the plane CP _c2 (f
2) and P _c1 B (f1) are steep slopes.

[0077] Here, when the angle of the corner ABC (base angle) and theta _b, the relationship of the apex angle theta _a 'and theta _b, considering that both the base of the isosceles triangle are equal, theta _b over [Delta] [theta] = (180 ° -θ _a ') / 2 (29) Therefore, θ _a ′ = 180 ° −2 (θ _b −Δθ) = θ _a + 2Δθ (30). Further, from equations (13) and (28), θ _a ′ ≧ θ _a + 2θ _c −2sin ⁻¹ ((n0 / n1) sinθ _so ) (31) is derived. θ _so is expressed as Θ _{so, min to} Θ _{so, max} (13
From the relationship a), considering that the emission angle of the emitted side lobe light has a range of θ _{so, min} to θ _{so, max} , θ _{so, min} −θ _b ≦ θ _so ≦ Θ _{so, Since max} −θ _b , the pentagonal prism shown in FIG. 13 has θ _a ′ ≧ θ _a + 2sin ⁻¹ (n0 / n1) − 2sin ⁻¹ ((n0 / n1) sin (Θ _{so, max} − θ _b )) ... (32) More preferably, θ _a '≧ θ _a + 2sin ^-1 (n0 / n1)-2sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b )) = By satisfying the condition of θ _{a, perfect} (32 a), it is possible to prevent the light rays incident from the bottom surface f 3 and traveling on the path of FIG. 13 from becoming sidelobe light. However, if θ _a 'is too large, the viewing angle unnecessarily widens, and the normal brightness decreases, which is not preferable. Therefore, θ _a + 2sin ^-1 (n0 / n1)-2sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b )) ≤ θ _a '≤ θ _{a, perfect} (32 _aa ) preferable. FIG. 17 shows an example of θ _{a, perfect} . However, the apex angle of the steep slope is θ _a = 90 °, and the refractive indices are n0 = 1 and n1 = 1.5.

Next, in the pentagonal prism as described above,
Calculate the ratio of the gentle slope length x1 'to the steep slope length x2. Figure
FIG. 14 is a view showing a main cut surface of the pentagonal prism.
Main cutting surface ABP_c1 C'P_c2Is the apex angle θ_aIsosceles triangle
ABC critical point P_c1, P_c2The upper part than the vertical angle θ_a’
(Θ_a’> Θ_a) Isosceles triangle P_c1C'P_c2Replaced with
It has a different shape. P in the figure_c1C (P_c2C) is the formula
This corresponds to x1 in (19a). Also, P_c1C '(P
_c2C ') = x1'.

As is clear from the figure, P _c1 C ″ = P _c2 C ″ = x1sin (θ _a / 2) (33), and at the same time, P _c1 C ″ = P _c2 C ″ = x1'sin (θ _a '/ 2) (34). Therefore, the equation (33) and (34) from _{x1 '= (sin (θ a} / 2) / sin (θ a' / 2)) · x1 (35).

Here, by comparing equation (19a) with equation (35), the following equation can be obtained. x1 '/ x2 = e / (k0-1) (36) where k0 = k1 / k2 k1 = sin (90 ° -sin ^-1 ((n0 / n1) sinθ _so )) k2 = sin (90 ° + sin ^-1 ((n0 / n1) sin θ _so ) − θ _a ) e = sin (θ _a / 2) / sin (θ _a '/ 2) As in the case of equation (31), θ _so is (θ _{so , min} −
Considering that it has a range of θ _b )-(θ _{so, max} −θ _b ), e / (c0-1) ≤ x1 '/ x2 ≤ e / (d0-1) (37) where c0 = c1 / c2 d0 = d1 / d2 c1 = sin (90 ° -sin ^-1 ((n0 / n1) sin (Θ _{so, min}ー θ _b ))) c2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, min}ー θ _b ))-θ _a ) d1 = sin (90 ° -sin ^-1 ((n0 / n1) sin (Θ _{so, max}ー θ _b ))) d2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, max}ー θ _b ))-θ _a ) e = sin (θ _a / 2) / sin (θ _a '/ 2) is obtained.

In FIG. 18, the apex angle θ _a = 90 ° of the steep slope and the critical angle θ _c = 41.8 ° (refractive index of the prism n0 = 1.5,
When the refractive index of air is n1 = 1.0), the apex angle θ _a 'of the gentle slope and the ratio of the length of the gentle slope to the steep slope x1' / x2
It shows the result of calculating. The emission angles of the sidelobe lights to be removed are respectively Θ _{so, max} = 84.7 °, Θ _{so, peak} = 70.7 °, Θ _{so, min} = 5 measured from the light output surface normal n.
It is set at 7.7 °.

Finally, the relationship between the apex angle θ _a and the critical angle θ _c is θ
_The conditions that the shape of the unit pentagonal prism according to the present invention should satisfy in the case of _a ≦ 2θ _c will be described with reference to FIG. In this case, the incident angle θ _si of the light ray at the point D becomes less than the critical angle when the incident angle θ _R of the light ray at the point C slightly exceeds θ _c . Thus, by using a light beam R12 comprised of a θ _R = θ _c perform calculations described in FIGS. 8 and 9 to obtain the critical point P _c. Other calculations, etc.
The procedure is similar to that described above.

[0083]

【Example】

(Examples of Lens Sheet) Hereinafter, examples will be described in more detail with reference to the drawings. FIG.
FIG. 4 is a diagram showing an example of a lens sheet according to the present invention together with a comparative example. In addition, FIG. 19 (A), (B),
The arrangements of (C) and (D) correspond to FIGS. 2, 3, 4, and 5. Each of these lens sheets was formed on the surface of a transparent biaxially stretched PET (polyethylene terephthalate) sheet having a thickness of 50 μm by using a urethane acrylate resin having a refractive index of 1.50 which was cross-linked and cured by ultraviolet rays. It is a thing.

Comparative Example 1 As shown in FIG. 19 (A), a triangular prism linear array lens sheet 105 having an apex angle of 90 ° is laminated on a backlight described later. The repetition cycle of the prism is 50μ
m, and the lengths of the two sides sandwiching the apex angle in the main cross section are 36 μm.

Comparative Example 2 As shown in FIG. 19B, the vertical angle 108 ° (θ _{a, min} <
A triangular prism linear array lens sheet 106 of θ _a <θ _{a, Ref} ) is laminated on a backlight described later. The repeating period of the prism is 50 μm, and the lengths of the two sides sandwiching the apex angle in the main cross section are each 27 μm.

Example As shown in FIG. 19C, the side on the base side has an apex angle of 90 °,
A lens sheet 1 of a pentagonal prism linear array having an apex angle of 108 ° on the apex side is laminated on a backlight described later so that a unit pentagonal prism faces the observation side. The repeating period of the prism is 50 μm, the side length of the steep slope (L _{1 in} FIG. ₁ ) in the main cross section is 18 μm, and the side length of the gentle slope (L _{2 in} FIG. 1) is 16 μm.

Comparative Example 3 As shown in FIG. 19D, the side on the base side has an apex angle of 90 °,
A pentagonal prism linear array lens sheet 1B having the apex angle of 108 ° on the apex side is laminated on a backlight described later so that the unit pentagonal prism faces the light source side.

The backlight is a 9.4 inch screen,
A light guide plate 101 having a thickness of 4 mm, which has a light isotropic diffusion layer 102 made of a sandblasted PET sheet on the front surface and a light diffusion reflection layer 103 in the form of a dot pattern formed by printing white ink on the back surface, is used. Approximately φ3 cm with two lights
The light source 104 consisting of a cold cathode fluorescent lamp (power consumption 4 watts) was used. This brightness measurement is performed on the lens sheets 105 and 10
A backlight is placed on the back side of 6, 1, 1B, and a luminance meter [Topcon BM is placed 30 cm from the front of each lens sheet.
-8 (2 °)]. The normal brightness when nothing is placed on the light guide plate of the backlight and when only the light isotropic diffusion layer is placed on the light guide plate are 770 [c], respectively.
d / cm ² ], 968 [cd / cm ² ].

FIGS. 15 and 16 are diagrams showing the results of measuring the luminance of the lens sheets of the above-mentioned Examples and Comparative Examples 1 to 3. In Comparative Example 1, as shown in FIG. 15A, the normal luminance was high, but the side lobes were large. The value of normal luminance was 1244 [cd / cm ² ], the half-value angle was 66 °, and the luminance ratio of side lobe / main lobe (normal luminance) was 0.23. Comparative example 2 is shown in FIG.
(B), the side lobes were almost eliminated, but the normal luminance was 1045 [cd / cm ² ] which was about 16% lower than that of Comparative Example 1. The half-value angle was 74 °, and the viewing angle was wider than that of Comparative Example 1, but the side lobe had a luminance ratio of side lobe / main lobe = 0.00 (see FIG. 1).
(Reading value from the graph of 5). In the example, as shown in (C) of FIG.
5 [cd / cm ² ], half-value angle 70 °, side lobe /
The luminance ratio of the main lobe was 0.14, the decrease in normal luminance was small, the viewing angle was wide, and the side lobe was small. Comparative Example 3 has a normal luminance of 4 as shown in FIG.
It is as low as 35 [cd / cm ² ] and has side lobes /
The luminance ratio of the main lobe = 1.34, and a side lobe larger than the main lobe was generated. Further, the half-value angle is as large as 125 ° (however, it is evaluated as an angle range having half or more of the side lobe peak luminance), and light is emitted to an angle range which is not necessary for practical use.

(Example of Edge Light Type Surface Light Source) FIG.
FIG. 0 is a perspective view showing a first embodiment (edge light type) of the surface light source according to the present invention. The surface light source of the first embodiment is provided on the upper surface of the light guide plate 41 of the edge light type backlight 40.
The light isotropic diffusive layer 20 and the lens sheet 1 of the present invention are arranged. In this backlight 40, a light diffusion reflection layer 42 having a scattered pattern is formed on a lower surface of a light guide plate 41, and the linear light sources 4 are provided on both sides of a side end surface of the light guide plate 41.
3, a reflection film 44, and a lighting cover 45 are provided. The edge light type surface light source has an advantage that the light emitting surface is less likely to generate heat.

(Embodiment of direct type surface light source) FIG. 21 is a sectional view showing a second example (direct type) of the surface light source according to the present invention. In the surface light source of the second embodiment, the light isotropic diffusing layer 20 and the lens sheet 1 of the present invention are provided on the opening side of a direct type backlight 30 in which a linear light source 32 such as a fluorescent lamp is provided in a case 31. Is arranged. Also, case 31
The inner surface on the light source side of is processed into a light diffusive reflection surface.

(Example of Display Device) The surface light source shown in FIGS. 20 and 21 can be used as a liquid crystal display device by disposing it on the back surface of a known transmissive liquid crystal display element. Further, in addition to the transmissive liquid crystal display element, it can be applied to an element such as an electrochromic display element which requires a back light source.

(Other Embodiment of Lens Sheet) FIG.
It is the figure which showed the other Example of the lens sheet by this invention. In the example of FIG. 19C, the unit pentagonal prism 10 of the pentagonal prism is described as one-dimensionally arranged. However, as shown in FIG. 22, a steep slope of a steep slope is formed on a four-sided frustum of a gentle slope. Even if the unit pentagonal prism 10 'in which four-sided pyramids are continuously arranged is two-dimensionally arranged, the same effect can be obtained.

Further, in each of the above-mentioned embodiments, the left and right lengths of the slopes are the same, but in the case of being used for a display device of a laptop personal computer, the unit pentagonal prism is directed in a specific direction. You may lean. That is, the shape may be left-right asymmetric in which both base angles are not equal. Further, if necessary, minute unevenness composed of minute protrusions having a height not less than the wavelength of light as disclosed in JP-A-6-324205 is formed to prevent optical contact with the light guide plate. You can also

[0095]

As described in detail above, according to the present invention, the unit pentagonal prism is formed in a convex shape on the light output side, and the cross-sectional shape in one direction or two directions orthogonal to each other is a pentagon. The steep slope of the lens on the base side increases the brightness in the normal direction of the light emitting surface to regulate the viewing angle, and the gentle slope of the lens on the top side suppresses the generation of side lobes and realizes high normal brightness. As a result, bright surface emission is possible, which is condensed at a predetermined angle near the normal.

[Brief description of drawings]

FIG. 1 is a schematic diagram illustrating the operation of a unit pentagonal prism of a lens sheet according to the present invention.

FIG. 2 Triangular prism linear array lens sheet (apex angle 9
The figure which showed the light ray which injected into the unit lens part of (0 degree).

FIG. 3 is a triangular prism linear array lens sheet (vertical angle 1
The figure which showed the light ray which injected into the unit lens part of (40 degrees).

FIG. 4 is a diagram showing light rays incident on a unit lens portion of a pentagonal prism linear array lens sheet according to the present invention.

FIG. 5 is a diagram showing rays of light when the lens portion of the pentagonal prism linear array lens sheet is arranged facing the light incident side.

FIG. 6 is a diagram illustrating a cause of generation of side lobe light in _a triangular prism having an apex angle θ _a .

FIG. 7 is a diagram showing a locus of sidelobe light in a minimum angle direction, a peak direction, and a maximum angle direction in _a triangular prism having an apex angle θ _a .

FIG. 8 is a diagram showing a relationship between a region where a light ray is incident and a region where a side lobe light is emitted in _a triangular prism having an apex angle θ _a .

FIG. 9 is a diagram showing a relationship between a length x1 of a region emitting side lobe light and a length x2 of a region not emitting side lobe light in _a triangular prism having an apex angle θ _a .

FIG. 10 is a bottom surface f of _a triangular prism having an apex angle θ _a .
The figure which showed the locus | trajectory of the side lobe light which injects from 3 and radiate | emit from the slope f1 with an emission angle (theta) so.

FIG. 11 is a diagram showing trajectories of light rays that become sidelobe light in a pentagonal prism that satisfies Expressions (19a) and (27).

FIG. 12 shows a slope f of _a triangular prism having an apex angle θ _a .
Slope f of the light ray that has undergone total reflection at 2 and reaches slope f1
The figure which showed the incident angle (theta) _si with respect to 1 and the relationship of the inclination of the slope f1.

FIG. 13 is a diagram illustrating the shape of a main cut surface of a pentagonal prism that satisfies Expression (31).

FIG. 14 is a main cut surface of an isosceles triangle ABC with an apex angle θ _a .
_Above the critical points P _c1 and P _c2 of the apex angle θ _a '(θ _a '> θ
shows a main cross of being pentagonal prism prism has a shape obtained by replacing an isosceles triangle P _c1 C'P _c2 of _a).

FIG. 15 is a diagram showing the results of measuring the luminance of the lens sheets of Comparative Example 1 (A), Comparative Example 2 (B) and Example (C).

16 is a diagram showing the results of measuring the luminance of the lens sheet of Comparative Example 3. FIG.

FIG. 17: Refractive index, critical angle, 9 for typical materials
The maximum slope angle θ _{max at} 0 ° apex angle, the direction of peak intensity θ _peak , and the gentle slope apex that suppresses each ray that causes a side lobe with a minimum exit angle θ _min by adjacent slope reflection. FIG. 6 is a diagram listing angles θ _{a, max} , θ _{a, peak} , θ _{a, max} and gentle slope apex angle θ _Ref that suppresses emission by total reflection of sidelobe-causing light on both slopes f1 and f2.

FIG. 18 is a vertical angle θ _a = 90 ° of _a steep slope and a critical angle θ _c = 4.
1.8 ° (refractive index of prism n0 = 1.5, refractive index of air
FIG. 6 is a diagram showing the results of calculating the apex angle θ _a ′ of the gentle slope and the ratio x1 ′ / x2 of the lengths of the gentle slope and the steep slope in the case where n1 = 1.0).

FIG. 19 is a view showing an example of an edge light type surface light source provided with a lens sheet according to the present invention together with a comparative example.

FIG. 20 is a perspective view showing a first embodiment (edge light type) of the surface light source according to the present invention.

FIG. 21 is a second embodiment (direct type) of a surface light source according to the present invention.
It is sectional drawing which showed.

FIG. 22 is a view showing another embodiment of the lens sheet according to the present invention.

FIG. 23 is a diagram showing a conventional example of an edge light type surface light source.

FIG. 24 is a diagram showing paths of side lobe light in a triangular prism having an apex angle θ _a = 90 ° + α.

FIG. 25 is a view different from FIG. 24 showing a path of sidelobe light in a triangular prism having an apex angle θ _a = 90 ° + α.

FIG. 26: Refractive index n0 = 1 of air, refractive index n of prism
It is a figure showing the relation between the apex angle of the triangular prism and the path of the side lobe light R _{1, peak} at which the intensity peaks when 1 = 1.5.

[Explanation of symbols]

 1, 1 ', 1B Lens sheet 10, 10' Unit pentagonal prism 31 Case 32, 43 Line light source 40 Backlight 41, 101 Light guide plate 42, 103 Light diffusion reflection layer 44 Reflection film 45 Lighting cover 102 Light isotropic diffusion layer 105 , 106 lens sheet

 ─────────────────────────────────────────────────── ─── Continued front page (72) Inventor Hiroshi Kojima 1-1-1, Ichigayaka, Shinjuku-ku, Tokyo Within Dai Nippon Printing Co., Ltd. No. 1 Dai Nippon Printing Co., Ltd.

Claims (7)

[Claims] 1. A lens sheet having a lens array layer in which a plurality of unit pentagonal prisms formed in a convex shape on the light output side are arrayed one-dimensionally or two-dimensionally on the surface of the light-transmissive substrate on the light output side. , the main cross-shape of the unit pentagonal prism is not in contact with two steep in contact with the translucent base apex angle of theta _a, in the translucent base apex angle of theta _a '2 And two gentle slopes, the apex angle θ when the refractive index of the unit pentagonal prism is n1 and the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0.
_a , θ _a 'is θ _a <90 ° + (10/9) sin ^-1 ((1 / √2) (n0 / n1))-(6/9) sin ^-1 (n0 / n1) and A lens sheet characterized in that θ _a '≧ θ _a . 2. The lens sheet according to claim 1, wherein the range of the apex angle θ _a 'is θ _a ' ≧ 60 ° + (4/3) sin ^-1 (n0 / n1). And lens sheet. 3. A lens sheet having a lens array layer in which a plurality of unit pentagonal prisms formed in a convex shape on the light exit side are arrayed one-dimensionally or two-dimensionally on the light exit side surface of a light-transmissive substrate. Te, main cross-sectional shape of the unit pentagonal prism, and two steep in contact with the translucent base apex angle of theta _a, not in contact with the translucent base apex angle of theta _a ' The unit pentagonal prism has a refractive index of n1, the ambient atmosphere of the unit pentagonal prism has a refractive index of n0, and from the normal line of the prism bottom surface of the side lobe light emitted from the two steep slopes. Letting the measured maximum exit angle be Θ _{so, max} , the minimum exit angle Θ _{so, min} , and the base angle of the steep surface of the prism be θ _b , the apex angles θ _a and θ _a 'are θ _a <90 ° + (10 / 9) sin ^-1 ((1 / √2) (n0 / n1))-(6/9) sin ^-1 (n0 / n1) and θ _a + 2sin ^-1 (n0 / n1)-EQ1 ≥ θ _a '≧ θ _a + 2sin ^-1 (n0 / n1)- EQ2 However, EQ1 = 2sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b )) EQ2 = 2sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b )) Lens sheet characterized by. 4. The lens sheet according to claim 1, wherein the maximum emission angle of the side lobe light emitted from the two steep slopes of the unit pentagonal prism including the steep slope is measured from the normal line of the prism bottom surface. Where Θ _{so, max is} the minimum output angle Θ _{so, min} , and the base angle of the steep slope of the prism is θ _b , the length x1 ′ of the gentle slope and the length x2 of the steep slope are e / ( c0-1) ≤ x1 '/ x2 ≤ e / (d0-1) where c0 = c1 / c2 d0 = d1 / d2 c1 = sin (90 ° -sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b ))) c2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, min} -θ _b ))-θ _a ) d1 = sin (90 ° -sin ^-1 (( n0 / n1) sin (Θ _{so, max} -θ _b ))) d2 = sin (90 ° + sin ^-1 ((n0 / n1) sin (Θ _{so, max} -θ _b ))-θ _a ) e = sin A lens sheet having a relationship of (θ _a / 2) / sin (θ _a '/ 2). 5. A light guide body formed of a light-transmissive flat plate or a rectangular parallelepiped cavity, a light reflection layer at least partially provided on a back surface of the light guide body, and at least one of side end surfaces of the light guide body. A point-like or linear light source provided adjacent to a surface or more, and the lens sheet according to any one of claims 1 to 4, which is arranged on a front surface side of the light guide, the lens A surface light source comprising: a light isotropic diffusing layer laminated on the outside or inside of the sheet, wherein the surface of the lens sheet serves as a diffused light emitting surface. 6. A light source accommodating one or more point-like or linear light sources, a light source housing portion surrounding the light source, having one surface as an opening, and having an inner surface on the opening side as a light reflecting surface, the light source. The said 1st aspect arrange | positioned at the opening part side of a storage part.
5. The lens sheet according to claim 4 and a light isotropic diffusing layer laminated on the outside or inside of the lens sheet, wherein the surface of the lens sheet serves as a diffused light emitting surface. Area light source. 7. A display device comprising a transmissive display element, and the surface light source according to claim 5 or 6 provided on the back surface of the display element.