Renticular lens, surface light source, and liquid crystal display apparatus

• US 5,592,332 A
• Filed: 12/27/1993
• Issued: 01/07/1997
• Est. Priority Date: 12/25/1992
• Status: Expired due to Term

• Current Assignee: Dai Nippon Printing Company Limited
• Original Assignee: Dai Nippon Printing Company Limited
• Inventors: Yamashita, Yoshiyuki, Masubuchi, Nobu, Amemiya, Hiroyuki, Takeuchi, Michiko, Nishio, Toshikazu
• Primary Examiner(s): Epps, Georgia Y.
• Assistant Examiner(s): MACK, RICKY LEVERN
• Application Number:
  US08/173,118
• Time in Patent Office: 1,107 Days
• Field of Search: 359/455, 359/456, 359/615, 359/619, 359/591, 359/625, 359/639, 359/640, 359/707, 359/620, 359/621, 359/622, 359/626, 359/627, 359/628, 359/454, 359/459, 359/592, 359/597
• US Class Current: 359/619
• CPC Class Codes: G02B 3/0031 Replication or moulding, e.g. hot embossing, UV-casting, injection moulding
• CPC Class Codes: G02B 3/005 arranged along a single direction only, e.g. lenticular sheets G02B3/0043 takes precedence
• CPC Class Codes: G02B 3/0062 Stacked lens arrays, i.e. refractive surfaces arranged in at least two planes, without structurally separate optical elements in-between
• CPC Class Codes: G02B 5/045 Prism arrays
• CPC Class Codes: G02F 1/133607 the light controlling member including light directing or refracting elements, e.g. prisms or lenses
• CPC Class Codes: G03B 21/625 Lenticular translucent screens

Abstract

A lenticular lens has a light transmitting substrate and a plurality of lens elements formed on the light transmitting substrate. The lens elements are defined in such a way that ridges thereof are aligned in parallel with each other, wherein 30°≦θ_10% ≦100° and R≦20%, where θ_10% is a diffusing angle range with respect to normal of the one surface in the case that when light is entered from the opposite surface and transmitted from the one surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and R is the ratio of side lobes to main lobe. The intensity of side lobes which causes light loss and light stray can be remarkably reduced. Light can be equally and isotropically focused on in a predetermined diffusing angle range.

Claims

1. A lenticular lens, comprising:

a light transmitting substrate having one a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

30°

≦

θ

_10% ≦

100° and

R≦

20%, where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe.

2. The lenticular lens, according to claim 1,

wherein each of said lens element has a triangular prism shape, the vertical angle of each of said lens elements being in the range from 95°

to 110°

.

3. The lenticular lens, according to claim 2, further comprising:

a second light transmitting substrate having two flat surfaces,

wherein said lens elements are layered over one flat surface of said second light transmitting substrate, the vertical angle of said lens elements being in the range from 95°

to 110°

.

4. The lenticular lens, according to claim 3,

wherein at least one of said light transmitting substrate and said lens elements has a light isotopic diffusing characteristic.

5. The lenticular lens, according to claim 3,

wherein a light isotopic diffusing layer is formed on one side of said second light transmitting substrate or said lens elements.

6. The lenticular lens, according to claim 1,

wherein said lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function.

7. The lenticular lens, according to claim 6, further comprising:

a second light transmitting substrate having two flat surfaces,

wherein said lens elements are elongated on one surface of said second light transmitting substrate.

8. The lenticular lens, according to claim 7,

wherein at least one of said light transmitting substrate and said lens elements has a light isotopic diffusing characteristic.

9. The lenticular lens according to claim 7,

wherein a light isotopic diffusing layer is formed on one side of said second light transmitting substrate or said lens elements.

10. The lenticular lens, according to claim 1,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied:

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements.

11. The lenticular lens, according to claim 1,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied:

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 slope of asymptotic line≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements.

12. The lenticular lens, according to claim 1,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by:

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50.

13. A surface light source, comprising:

a light guiding plate made of a light transmitting plate;

a linear light source arranged adjacent to at least one side edge of said light guiding plate;

a light isotopic diffusing layer layered on the front surface of said light guiding plate; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel, wherein 30°

≦

θ

_10% ≦

100° and

R≦

20%, where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, and wherein each of said lens elements has a triangular prism shape, the vertical angle of each of said lens elements being in the range from 95°

to 110°

,

wherein the front surface of said lenticular lens is defined on a diffused light emitting surface.

14. A liquid crystal display apparatus having a rear surface, comprising:

a transmission type liquid crystal display device; and

a surface light source, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, and

wherein each of said lens elements has a triangular prism shape, the vertical angle of each of said lens elements being in the range from 95°

to 110°

, said surface light source being disposed on the rear surface of said liquid crystal display device.

15. A surface light source, comprising:

a light guiding member formed of a light transmitting plate;

a linear light source arranged adjacent to at least one side edge of said light guiding plate;

a light isotopic diffusing layer layered on the front surface of said light guiding plate; and

a lenticular lens, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, wherein aid lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function,

wherein the front surface of said lenticular lens is defined on a diffused light emitting surface.

16. A surface light source, comprising:

at least one point light source;

a lamp house adapted to cover said light source and having a surface with an opening; and

a lenticular lens, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, wherein aid lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function, said lenticular lens being adapted to cover said opening,

wherein the front surface of said lenticular lens is defined on a diffused light emitting surface.

17. A liquid crystal display apparatus having a rear surface, comprising:

a transmission type liquid crystal display device; and

a surface light source comprising;

a light guiding member formed of a light transmitting plate;

a linear light source arranged adjacent to at least one side edge of said light guiding plate;

a light isotopic diffusing layer layered on the front surface of said light guiding plate; and

a lenticular lens, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, wherein aid lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function,

wherein the front surface of said lenticular lens is defined on a diffused light emitting surface.

18. A lens sheet having a mat surface whose surface roughness is up to 100 μ

m, and the mat surface is formed on the non-lens surface of a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens element.

19. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

20. The surface light source according to claim 19, wherein the light source is formed of a light transmitting plate having a smooth surface whose surface roughness is equal to or less than the wavelength of the light of a light source, the above-mentioned lenticular lens sheet has a fine mat surface whose surface roughness is equal to or larger than the wavelength of the light of the light source, and the fine mat surface is layered on the smooth surface of the light guiding member, whereby, a cavity with a depth of equal to or larger than the wavelength of the light of the light source is disposed at least partly between the light guiding member and the lens sheet.

21. The surface light source according to claim 19, wherein the light source has a light guiding member which is formed of a light transmitting plate having a smooth surface whose surface roughness is equal to or less than the wavelength of the light of a light source, a light diffusing layer is disposed between the rear surface of the above-mentioned lenticular lens sheet and the front surface of the light guiding member, and the light diffusing layer has fine mat surfaces whose surface roughness is equal to or larger than the wavelength of the light of the light source, whereby, two cavities whose depth is equal to or larger than the wavelength of the light of the light source are formed at least partly between the front surface of the light guiding member and the light diffusing layer and between the light diffusing layer and the rear surface of the lens sheet.

22. A display apparatus, comprising:

a the surface light source comprising;

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member; and

a transmission type display device which is layered over the light emitting urface of the surface light source.

23. A surface light source, comprising:

at least one linear light source having a lower surface;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 a length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements covering the opening of said lamp house.

24. A display apparatus, comprising:

a surface light source comprising;

at least one linear light source having a lower surface;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements covering the opening of said lamp house; and

a transmission type display device that is layered over the light emitting surface of the surface light source.

25. A lens sheet, having a mat surface whose surface roughness is up to 100 μ

m, and the mat surface is formed on the non-lens surface of a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements.

26. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 a slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

27. A display apparatus, comprising:

a surface light source comprising;

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member; and

a transmission type display device that is layered over the light emitting surface of the surface light source.

28. A surface light source, comprising:

at least one linear or point light source;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements covering the opening of said lamp house.

29. A display apparatus, comprising:

a surface light source comprising;

at least one linear or point light source;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements covering the opening of said lamp house; and

a transmission type display device that is layered over the light emitting surface of the surface light source.

30. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

31. The surface light source, according to claim 30, wherein a light diffusing sheet between the opposite surface of the lens surface of the lenticular lens and the light guiding member.

32. The surface light source, according to claim 31, wherein the surface light source has a random fine mat pattern at least on one surface of the light diffusing sheet, the surface roughness of the mat pattern is in the range from the wavelength of the light of the light source to 100 μ

m, and the surface roughness of the front surface of the light guiding plate is equal to or less than the wavelength of the light of the light source.

33. A display apparatus, comprising:

a surface light source comprising;

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member; and

a transmission type display device that is layered over the light emitting surface of the surface light source.

34. A surface light source, comprising:

at least one linear light source having a lower surface;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 covering the opening of said lamp house.

35. A lenticular lens, comprising:

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having convex shaped cross sections, and defined in such a way that ridges thereof are aligned an parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe.

36. A surface light source comprising:

a light guiding plate made of a rectangular parallelpiped cavity;

a linear light source arranged adjacent to at least one side edge of said light guiding plate;

a light isotopic diffusing layer layered on the front surface of said light guiding plate; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity o the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe wherein each of said lens elements has a triangular prism shape, the vertical angle of each of said lens elements being in the range from 95°

to 110°

,

wherein the front surface of said lenticular lens is defined on a diffused light emitting surface.

37. A surface light source comprising:

a light guiding member formed of a rectangular parallelpiped cavity;

a linear light source arranged adjacent to at least one side edge of said light guiding plate;

a light isotopic diffusing layer layered on the first surface of said light guiding plate; and

a lenticular lens, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, wherein aid lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function,

wherein the first surface of said lenticular lens is defined on a diffused light emitting surface.

38. A surface light source, comprising:

at least one linear light source;

a lamp house adapted to cover said light source and having a surface with an opening; and

a lenticular lens, comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe, wherein aid lens elements have concave shapes and are continuously formed in such a way that the shape of the main cross section which is cut perpendicular to the longer axis accords with a quadratic curve, a Rankine egg shape, or a curve expressed by a linear function, said lenticular lens being adapted to cover said opening,

wherein the first surface of said lenticular lens is defined on a diffused light emitting surface.

39. A lens sheet, having a mat surface whose surface roughness is up to 100 μ

m, and the mat surface is formed on the non-lens surface of a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements.

40. A lens sheet, having a mat surface whose surface roughness is up to 100 μ

m, and the mat surface is formed on the non-lens surface of a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements.

41. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

42. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

43. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

44. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

45. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

46. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

47. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

48. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

49. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

50. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

51. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

52. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

53. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

54. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have a have a hyperbolic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

slope of asymptotic line

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements layered on a light emitting surface of the light guiding member.

55. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

56. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting .depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

57. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6, layered on a light emitting surface of the light guiding member.

58. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

59. A surface light source comprising:

a light guiding member made of a light transmitting plate;

at least one point light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a convex lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

60. A surface light source comprising:

a light guiding member made of a rectangular parallelpiped cavity;

at least one linear light source arranged on at least one side edge of the light guiding member;

at least one light reflecting layer disposed on the rear surface of the light guiding member; and

a concave lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 layered on a light emitting surface of the light guiding member.

61. A surface light source comprising:

at least one point light source having a lower surface;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate, having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% ≦

100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the following relation being satisfied;

space="preserve" listing-type="equation">1.1×

n/(n.sup.2 -1).sup.1/2 ≧

length of longer axis/length of shorter axis

space="preserve" listing-type="equation">≧

0.9×

n/(n.sup.2 -1).sup.1/2

where n is the refractive index of said lens elements covering the opening of said lamp house.

62. A surface light source, comprising:

at least one point light source having a lower surface;

a lamp house that covers the lower surface and side surface of the light source and has an opening on the upper surface of the light source and an inner reflecting surface; and

a lenticular lens comprising;

a light transmitting substrate having a first surface and a second surface opposite to said first surface; and

a plurality of lens elements elongated on the first surface of said light transmitting substrate having concave shaped cross sections, and defined in such a way that ridges thereof are aligned in parallel,

wherein

space="preserve" listing-type="equation">30°

≦

θ

.sub.10% 100° and

R≦

20%,

where θ

_10% is a diffusing angle range with respect to normal of the first surface in the case that when light is entered from the second surface or first surface and transmitted from the first surface or second surface, the intensity of the light transmitted is equal to or more than 10% of the intensity of the light transmitted in a peak direction of a main lobe; and

R is the ratio of side lobes to main lobe,

wherein said lens elements have an elliptic shape and are defined in such a way that ridges thereof are aligned in parallel with each other, the longer axis direction of said lens elements according with the normal direction of a light emitting surface thereof, the cutting depth and the refractive index of said lens elements being given by;

1.40≦

refractive index≦

1.6,

1.20≦

length of longer axis/length of shorter axis≦

2.00, and

0.1≦

cutting depth/length of longer axis≦

0.50 covering the opening of said lamp house.