Stereoscopic image display apparatus
A stereoscopic image display apparatus includes: a plane display device; a lens array provided in front of the display surface to distribute light rays from pixels of the display device to predetermined angles, and having a plurality of lenses arranged in a first direction; a variable polarizer provided between the plane display device and the lens array to polarize light rays from the pixels; and a double refraction prism array provided on an opposite side of the lens array from the display device, and including a plurality of double refraction prisms. Each of the double refraction prisms has a ridge in a second direction perpendicular to the first direction and arranged in the first direction with a pitch which is substantially twice a lens pitch in the lens array, and has double refraction in which a refractive index in a ridge direction is different from a refractive index in a direction perpendicular to the ridge direction.
1. A stereoscopic image display apparatus comprising:
a plane display device including a plurality of pixels arranged in a display surface;
a lens array provided in front of the display surface to distribute light rays from the pixels to predetermined angles, the lens array having a plurality of lenses arranged in a first direction;
a variable polarizer provided between the plane display device and the lens array to polarize light rays from the pixels; and
a double refraction prism array provided on an opposite side of the lens array from the plane display device, the double refraction prism array including a plurality of double refraction prisms each having a ridge in a second direction perpendicular to the first direction and arranged in the first direction with a pitch which is substantially twice a lens pitch in the lens array, each of the double refraction prisms having double refraction in which a refractive index in the second direction is different from a refractive index in the first direction,
wherein the double refraction prism array comprises:
a prism having a flat surface on an opposite side from the lens array and a surface on the lens array side provided with a groove which extends in the second direction and takes a triangular prism; and
a double refraction substance inserted into the groove of the prism,
and wherein when r is a curvature radius of a bottom part of a groove of the double refraction prism, t_top_prism is a distance between a surface of the prism of the lens array side and a vertex of the groove taking a shape of a triangular prism, t_lens is a thickness of a lens in the lens array, n is a refractive index of the prism, and θ is a half of a viewing angle, following expression is satisfied:
r= 5×( t _top_prism+ t _lens)×tan(arcsin(sin(θ)/ n )).
2. The apparatus according to claim 1 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied;
| n−no|< 0.1×( ne−no )
0.4≦2 ×N ×tan θ shift ( ne )/tan θ≦0.6
θ shift ( ne )= A sin(sin( A sin(sin( A sin(sin θ k /ne )+θ prism )× ne/n )−θ prism )× n ).
3. The apparatus according to claim 1 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, θ shift (no) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a minor axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied:
| n−ne|< 0.1×( ne−no )
−0.6<2 ×N ×tan θ shift ( no )/tan θ≦−0.4
θ shift ( no )= A sin(sin( A sin(sin( A sin(sin θ k /no )+θ prism )× no/n )−θ prism )× n ).
4. The apparatus according to claim 1 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, θ shift (no) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a minor axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied:
0.4×( ne+no )≦ n≦ 0.6×( ne+no )
0.4≦tan θ/(4 N )/(tan θ shift ( ne )−tan θ shift ( no ))≦0.6
θ shift (ne)= A sin(sin( A sin(sin( A sin(sin θ k /ne )+θ prism )× ne/n )−θ prism )× n )
θ shift ( no )= A sin(sin( A sin(sin( A sin(sin θ k /no )+θ prism )× no/n )−θ prism )× n ).
5. The apparatus according to claim 1 , wherein when lprism_p is a pitch of the double refraction prisms, t_top_prism is a distance between a surface of the prism of the lens array side and a vertex of the groove taking a shape of a triangular prism, t_lens is a thickness of a lens in the lens array, n is a refractive index of the prism, lp is a lens pitch in the lens array, and L is a distance between a vertex of the lens array and a viewer, the following expressions is satisfied:
l prism — p =( L−t _top_prism)× lp× 2/( L+t _lens).
6. The apparatus according to claim 1 , wherein the double refraction prism comprises:
a lower prism having a flat lower surface and an upper surface provided with a plurality of first grooves each taking a shape of a triangular prism;
an upper prism having a flat upper surface and a lower surface provided with a plurality of second grooves each taking a shape of a triangular prism with the same pitch as that of the first grooves so as to be opposed to the first grooves; and
a double refraction substance provided between the opposed first grooves and second grooves.
7. The apparatus according to claim 6 , wherein when lprism_p is a pitch of the double refraction prisms, L is a distance between a vertex of the lens array and a viewer, t_prism is a distance between the lower surface of the lower prism and the upper surface of the lower prism, lp is a lens pitch in the lens array, and t_lens is a thickness of a lens in the lens array, the following expression is satisfied:
l prism — p =( L−t _prism)× lp× 2/( L+t _lens).
8. The apparatus according to claim 6 , wherein when n down is a refractive index of the lower prism, n up is a refractive index of the upper prism, ne is a refractive index in a major axis direction of the double refraction substance, and no is a refractive index in a minor axis direction of the double refraction substance, the following expression is satisfied:
0.4×( ne+no )≦ n up =n down ≦0.6×( ne+no ).
9. A stereoscopic image display apparatus comprising:
a plane display device including a plurality of pixels arranged in a display surface;
a lens array provided in front of the display surface to distribute light rays from the pixels to predetermined angles, the lens array having a plurality of lenses arranged in a first direction;
a double refraction prism array provided on an opposite side of the lens array from the plane display device, the double refraction prism array including a plurality of double refraction prisms each having a ridge in a second direction perpendicular to the first direction and arranged in the first direction with a pitch which is substantially twice a lens pitch in the lens array, each of the double refraction prisms having double refraction in which a refractive index in the second direction is different from a refractive index in the first direction; and
a first variable polarizer provided on an opposite side of the double refraction prism array from the lens array to polarize light rays from the double refraction prism array,
wherein the double refraction prism comprises:
a prism having a flat surface on an opposite side from the lens array and a surface on the lens array side provided with a groove which extends in the second direction and takes a triangular prism; and
a double refraction substance inserted into the groove of the prism,
and wherein when r is a curvature radius of a bottom part of a groove of the double refraction prism, t_top_prism is a distance between a surface of the prism of the lens array side and a vertex of the groove taking a shape of a triangular prism, t_lens is a thickness of a lens in the lens array, n is a refractive index of the prism, and θ is a half of a viewing angle, following expression is satisfied:
r= 5×( t _top_prism+t_lens)×tan(arcsin(sin(θ)/ n )).
10. The apparatus according to claim 9 , wherein
the plane display device is a liquid crystal display device having a backlight, and
the stereoscopic image display apparatus further comprises a second variable polarizer to polarize light rays from the backlight.
11. The apparatus according to claim 9 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied:
| n−no|< 0.1×( ne−no )
0.4≦2 ×N ×tan θ shift ( ne )/tan θ≦0.6
θ shift ( ne )= A sin(sin( A sin(sin( A sin(sin θ k /ne )+θ prism )× ne/n )−θ prism )× n ).
12. The apparatus according to claim 9 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, θ shift (no) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a minor axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied:
| n−ne|< 0.1×( ne−no )
−0.6<2× N ×tan θ shift ( no )/tan θ≦−0.4
θ shift ( no )= A sin(sin( A sin(sin( A sin(sin θ k /no )+θ prism )× no/n )−θ prism )× n ).
13. The apparatus according to claim 9 , wherein when n is a refractive index of the prism, θ prism is a base angle of the prism, θ k is an incidence angle of a light ray incident on the double refraction prism, θ shift (ne) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a major axis direction of the double refraction substance, θ shift (no) is a projection angle of a light ray projected from the double refraction prism when the light ray incident on the double refraction prism is polarized in a minor axis direction of the double refraction substance, ne is a refractive index of the double refraction substance in the major axis direction, no is a refractive index of the double refraction substance in the minor axis direction, N is the number of parallaxes, and θ is half of a viewing angle, the following expressions are satisfied:
0.4×( ne+no )≦ n≦ 0.6×( ne+no )
0.4≦tan θ/(4 N )/(tan θ shift ( ne )−tan θ shift ( no ))≦0.6
θ shift ( ne )= A sin(sin( A sin(sin( A sin(sin θ k /ne )+θ prism )× ne/n )−θ prism )× n )
θ shift ( no )= A sin(sin( A sin(sin( A sin(sin θ k /no )+θ prism )× no/n )−θ prism )× n ).
14. The apparatus according to claim 9 , wherein when lprism_p is a pitch of the double refraction prisms, t_top_prism is a distance between a surface of the prism of the lens array side and a vertex of the groove taking a shape of a triangular prism, t_lens is a thickness of a lens in the lens array, n is a refractive index of the prism, lp is a lens pitch in the lens array, and L is a distance between a vertex of the lens array and a viewer, the following expressions is satisfied:
l prism — p =( L−t _top_prism)× lp× 2/( L+t _lens).
15. The apparatus according to claim 9 , wherein the double refraction prism comprises:
a lower prism having a flat lower surface and an upper surface provided with a plurality of first grooves each taking a shape of a triangular prism;
an upper prism having a flat upper surface and a lower surface provided with a plurality of second grooves each taking a shape of a triangular prism with the same pitch as that of the first grooves so as to be opposed to the first grooves; and
a double refraction substance provided between the opposed first grooves and second grooves.
16. The apparatus according to claim 15 , wherein when lprism_p is a pitch of the double refraction prisms, L is a distance between a vertex of the lens array and a viewer, t_prism is a distance between the lower surface of the lower prism and the upper surface of the lower prism, lp is a lens pitch in the lens array, and t_lens is a thickness of a lens in the lens array, the following expression is satisfied:
l prism — p =( L−t _prism)× lp× 2/( L+t _lens).
17. The apparatus according to claim 15 , wherein when n down is a refractive index of the lower prism, n up is a refractive index of the upper prism, ne is a refractive index in a major axis direction of the double refraction substance, and no is a refractive index in a minor axis direction of the double refraction substance, the following expression is satisfied:
0.4×( ne+no )≦ n up =n down ≦0.6×( ne+no ).