Optical element including a plurality of structures and hard coat layer formed thereon and method for making the same, master and method for making the same, and display apparatus

1. An optical element comprising:

a substrate including a plurality of structures on a surface thereof, the structures being protrusions; and

a hard coat layer formed on the substrate,

wherein an irregular shape is formed by the structures on the surface of the substrate,

an irregular shape resembling the irregular shape of the substrate is formed on a surface of the hard coat layer,

the irregular shape of the surface of the hard coat layer is smoother than the irregular shape of the surface of the substrate,

a size of bottoms of the structures changes at random within a range of a minimum distance R m or more and a maximum distance R M or less where the minimum distance R m is a minimum value of a shortest distance from a center of gravity of the bottom of the structure to a rim of the bottom and the maximum distance R M is a maximum value of a longest distance from a center of gravity of the bottom of the structure to the rim of the bottom,

of the plurality of structures, neighboring structures have bottoms in contact or substantially in contact with one another, and

the minimum distance R m and the maximum distance R M satisfy a relationship R m /R M ≦0.9.

2. The optical element according to claim 1 , wherein the maximum distance R M is within a range of R m <R M ≦75 μm.

3. The optical element according to claim 1 , wherein the maximum distance R M and the minimum distance R m satisfy a relationship 10 μm≦R m <R M ≦75 μm.

4. The optical element according to claim 1 , wherein the structures include first structures and second structures,

a size of bottoms of the first structures changes at random within a range of 10 μm ≦R 1m <R 1M ≦75 μm where a minimum distance R 1m is a minimum value of a shortest distance from a center of gravity of the bottom of the first structure to the rim of the bottom and the maximum distance R 1M is a maximum value of a longest distance from a center of gravity of the bottom of the first structure to the rim of the bottom, and

a size of bottoms of the second structures changes at random within a range of R 2m <R 2M ≦R 1m where a minimum distance R 2m is a minimum value of a shortest distance from a center of gravity of the bottom of the second structure to the rim of the bottom and the maximum distance R 2M is a maximum value of a longest distance from a center of gravity of the bottom of the second structure to the rim of the bottom.

5. The optical element according to claim 1 , wherein the structures include:

first structures; and

second structures disposed in gaps between the first structures,

a size of bottoms of the first structures changes at random within a range of R 1m <R 1M ≦75 μm where a minimum distance R 1m is a minimum value of a shortest distance from a center of gravity of the bottom of the first structure to the rim of the bottom and the maximum distance R 1M is a maximum value of a longest distance from a center of gravity of the bottom of the first structure to the rim of the bottom, and

a size of bottoms of the second structures changes at random within a range of R 2m <R 2M ≦R 1m where a minimum distance R 2m is a minimum value of a shortest distance from a center of gravity of the bottom of the second structure to the rim of the bottom and the maximum distance R 2M is a maximum value of a longest distance from a center of gravity of the bottom of the second structure to the rim of the bottom.

6. The optical element according to claim 1 , wherein the hard coat layer contains an inorganic or organic viscosity adjustor.

7. The optical element according to claim 1 , wherein an average irregularity height PV of the surface of the hard coat layer is within a range of 0.2 μm≦PV≦1.6 μm.

8. The optical element according to claim 1 , wherein a ten-point mean roughness Rz of the surface of the hard coat layer is in a range of 0.1 μm≦Rz ≦1.6 μm.

9. The optical element according to claim 1 , wherein the optical element has a cloudiness of 0.7% or less.

10. The optical element according to claim 1 , wherein a shape of the bottoms of the structures is at least one selected from a circular shape, an elliptical shape, and a polygonal shape.

11. The optical element according to claim 1 , wherein the structures each have a side surface that spreads toward the bottom from the top, and

of the plurality of structures, neighboring structures have bottoms in contact or substantially in contact with one another.

12. A display apparatus comprising:

an optical element including a substrate including a plurality of structures on a surface thereof, the structures being protrusions; and

a hard coat layer formed on the substrate,

wherein an irregular shape is formed by the structures on the surface of the substrate,

an irregular shape resembling the irregular shape of the substrate is formed on a surface of the hard coat layer,

the irregular shape of the surface of the hard coat layer is smoother than the irregular shape of the surface of the substrate,

a size of bottoms of the structures changes at random within a range of a minimum distance R m or more and a maximum distance R M or less where the minimum distance R m is a minimum value of a shortest distance from a center of gravity of the bottom of the structure to a rim of the bottom and the maximum distance R M is a maximum value of a longest distance from a center of gravity of the bottom of the structure to the rim of the bottom,

of the plurality of structures, neighboring structures have bottoms in contact or substantially in contact with one another, and

the minimum distance R m and the maximum distance R M satisfy a relationship R m /R M ≦0.9.

13. A method for making an optical element, comprising the steps of:

forming a master having an irregular shape on a surface thereof by forming in the surface a plurality of structures for transfer that are recesses;

forming a substrate having an irregular shape on a surface thereof by transferring the irregular shape of the master onto the surface of the substrate; and

forming a hard coat layer on the irregular shape of the substrate,

wherein a size of bottoms of the structures for transfer changes at random within a range of a minimum distance R m or more and a maximum distance R M or less where the minimum distance R m is a minimum value of a shortest distance from a center of gravity of the bottom of the structure for transfer to a rim of the bottom and the maximum distance R M is a maximum value of a longest distance from a center of gravity of the bottom of the structure for transfer to the rim of the bottom,

of the plurality of the structures for transfer, neighboring structures for transfer have bottoms in contact or substantially in contact with one another,

the minimum distance R m and the maximum distance R M satisfy a relationship R m /R M ≦0.9,

an irregular shape resembling the irregular shape of the substrate is formed on a surface of the hard coat layer, and

the irregular shape of the surface of the hard coat layer is smoother than the irregular shape of the surface of the substrate.

14. The method according to claim 13 , wherein in the step of forming the master, the structures for transfer are formed by laser processing or etching.

15. The method according to claim 13 , wherein the master on which the structures for transfer are formed has a roll shape.

16. A master comprising:

a plurality of structures for transfer that are recesses;

wherein an irregular shape is formed on a surface of the master by the structures for transfer,

a size of bottoms of the structures for transfer changes at random within a range of a minimum distance R m or more and a maximum distance R M or less where the minimum distance R m is a minimum value of a shortest distance from a center of gravity of the bottom of the structure for transfer to a rim of the bottom and the maximum distance R M is a maximum value of a longest distance from a center of gravity of the bottom of the structure for transfer to the rim of the bottom,

of the plurality of the structures for transfer, neighboring structures for transfer have bottoms in contact or substantially in contact with one another, and

the minimum distance R m and the maximum distance R M satisfy a relationship R m /R M ≦0.9.

17. A method for making a master, comprising the steps of:

forming a plurality of recesses in a surface of a master by laser processing or etching; and

etching an entire surface of the master in which the plurality of recesses are formed so as to form structures for transfer,

wherein a size of bottoms of the structures for transfer changes at random within a range of a minimum distance R m or more and a maximum distance R M or less where the minimum distance R m is a minimum value of a shortest distance from a center of gravity of the bottom of the structure for transfer to a rim of the bottom and the maximum distance R M is a maximum value of a longest distance from a center of gravity of the bottom of the structure for transfer to the rim of the bottom,

of the plurality of the structures for transfer, neighboring structures for transfer have bottoms in contact or substantially in contact with one another, and

the minimum distance R m and the maximum distance R M satisfy a relationship R m /R M ≦0.9.

18. The method according to claim 17 , wherein a continuous wavy surface is formed in the surface of the master by etching the entire surface of the master in which the plurality of recesses are formed.

19. The method according to claim 17 , wherein the structures for transfer formed on the surface of the master by etching the entire surface of the master having the plurality of recesses are dome-shaped.