Anti-reflection glass substrate

1. A glass substrate comprising a roughened surface, wherein:

the roughened surface comprises multiple concave portions and multiple convex portions;

the roughened surface has a structure such that, in at least three locations within an area of the roughened surface having a width of 1,000 nm, a line normal to the roughened surface would pass through a void between two glass regions;

a surface roughness (Ra) of the roughened surface as defined in JIS B 0601 (1994) is 2 nm to 100 nm;

a maximum height difference (P−V) of the roughened surface is 35 nm to 400 nm;

an area ratio (S-ratio) of an area of concave portions to an area of convex portions in an inspection area is 1.1 to 3.0; and

when the roughened surface is subjected to approximation through two-dimensional Fourier transformation in which each convex portion is approximated to a regular quadrangular pyramid, a length of one side of a base of the regular quadrangular pyramid is considered a size (R) of the convex portion, and a base angle of the convex portion in cross section is considered a tilt angle (θ) of the convex portion, in a frequency distribution:

a maximum frequency of the size (Rp) of the convex portions is 37 nm to 200 nm;

a maximum frequency of the tilt angle (θp) of the convex portions is 20° to 75°; and

an absolute value of a difference between the maximum frequency of the tilt angle (θp) and 50% of a cumulative frequency distribution of the tilt angle (θ 50 ), (θp−θ 50 ), is 30° or less.

2. The glass substrate according to claim 1 , wherein an atomic number concentration ratio of F/Si in the roughened surface is 0.05 or more to a depth of 5 nm.

3. The glass substrate according to claim 2 , wherein the F/Si ratio continuously decreases from the roughened surface in a depth direction.

4. The glass substrate according to claim 1 , wherein:

the roughened surface has a relative specific surface area of 1.1 to 5.0;

the relative specific surface area is a ratio of a specific surface area of the roughened surface to a specific surface area of a glass substrate that has not been roughened; and

specific surface area is measured by a BET adsorption method using krypton gas.

5. The glass substrate according to claim 1 , wherein at least 50% of the roughened surface is coated with a film comprising SiO 2 as a main component.

6. The glass substrate according to claim 1 , further comprising a film comprising SiO 2 formed on at least one concave portion of the roughened surface.

7. The glass substrate according to claim 1 , wherein the maximum frequency of the size (Rp) of the convex portions is 40 nm to 150 nm.

8. The glass substrate according to claim 1 , wherein the maximum frequency of the size (Rp) of the convex portions is 60 nm to 130 nm.

9. The glass substrate according to claim 1 , wherein the maximum frequency of the tilt angle (θp) of the convex portions is 20° to 70°.

10. The glass substrate according to claim 1 , wherein the maximum frequency of the tilt angle (θp) of the convex portions is 25° to 70°.

11. The glass substrate according to claim 1 , wherein the absolute value of the difference between the maximum frequency of the tilt angle (θp) and 50% of the cumulative frequency distribution of the tilt angle (θ 50 ), (θp−θ 50 ), is 20° or less.

12. The glass substrate according to claim 1 , wherein the absolute value of the difference between the maximum frequency of the tilt angle (θp) and 50% of the cumulative frequency distribution of the tilt angle (θ 50 ), (θp−θ 50 ), is 13° or less.

13. The glass substrate according to claim 1 , wherein the surface roughness (Ra) of the roughened surface is 2 nm to 70 nm.

14. The glass substrate according to claim 1 , wherein the surface roughness (Ra) of the roughened surface is 2 nm to 50 nm.

15. The glass substrate according to claim 1 , wherein the maximum height difference (P−V) of the roughened surface is 35 nm to 350 nm.

16. The glass substrate according to claim 1 , wherein the maximum height difference (P−V) of the roughened surface is 35 nm to 200 nm.

17. The glass substrate according to claim 1 , wherein the area ratio (S-ratio) of the area of concave portions to the area of convex portions in the inspection area is 1.1 to 2.7.

18. The glass substrate according to claim 1 , wherein the area ratio (S-ratio) of the area of concave portions to the area of convex portions in the inspection area is 1.1 to 2.5.

19. The glass substrate according to claim 1 , wherein:

the maximum frequency of the size (Rp) of the convex portions is 40 nm to 150 nm;

the maximum frequency of the tilt angle (Op) of the convex portions is 20° to 70°;

the absolute value of the difference between the maximum frequency of the tilt angle (θp) and 50% of the cumulative frequency distribution of the tilt angle (θ 50 ), (θp−θ 50 ), is 20° or less;

the surface roughness (Ra) of the roughened surface is 2 nm to 70 nm;

the maximum height difference (P−V) of the roughened surface is 35 nm to 350 nm; and

the area ratio (S-ratio) of the area of concave portions to the area of convex portions in the inspection area is 1.1 to 2.7.

20. The glass substrate according to claim 1 , wherein:

the maximum frequency of the size (Rp) of the convex portions is 60 nm to 130 nm;

the maximum frequency of the tilt angle (θp) of the convex portions is 25° to 70°;

the absolute value of the difference between the maximum frequency of the tilt angle (θp) and 50% of the cumulative frequency distribution of the tilt angle (θ 50 ), (θp−θ 50 ), is 13° or less;

the surface roughness (Ra) of the roughened surface is 2 nm to 50 nm;

the maximum height difference (P−V) of the roughened surface is 35 nm to 200 nm; and

the area ratio (S-ratio) of the area of concave portions to the area of convex portions in the inspection area is 1.1 to 2.5.