Glass container comprising a glass bottom with improved properties

1. A glass container, comprising:

a glass tube having a first end, a second end, an outer diameter (d 1 ), an inner diameter (d 2 ), and a glass thickness (s 1 );

a circular glass bottom that closes the glass tube at the first end, wherein the circular glass bottom comprises an inner surface directed to an inside of the glass tube and an outer surface directed to an outside of the glass tube;

a longitudinal axis (L tube ) that passes through a center of the glass tube and the circular glass bottom;

a curved glass heel extending from an outer end the circular glass bottom to the first end of the glass tube;

a two-dimensional distance h(x,y) between a contact plane and the outer surface, wherein the contact plane is the plane on which the glass tube rests,

wherein the outer surface at a given position x,y, with x=0 and y=0 in the center of the circular glass bottom,

wherein the two-dimensional distance is measured in a direction that is parallel to the longitudinal axis (L tube ),

wherein

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}

is a slope magnitude of the outer surface at the given position x,y,

wherein a 75% quantile of values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

for all given positions x,y within a circular area having a radius of 0.4×d 2 /2 and a center that corresponds to the center of the glass circular bottom is less than 4100 μm/mm,

wherein adjacent positions x,y increase stepwise by 200 μm, and

wherein h(x,y) delta =h(x,y) max −h(x,y) min , h(x,y) max is a maximum value for h(x,y) and h(x,y) min is a minimum value for h(x,y) being determined in that circular area.

2. The glass container of claim 1 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3900 μm/mm.

3. The glass container of claim 1 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3500 μm/mm.

4. The glass container of claim 1 , wherein the radius is 0.6×d 2 /2.

5. The glass container of claim 4 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3900 μm/mm.

6. The glass container of claim 4 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3500 μm/mm.

7. The glass container of claim 1 , wherein the radius is 0.8×d 2 /2.

8. The glass container of claim 7 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3900 μm/mm.

9. The glass container of claim 7 , wherein the 75% quantile of the values that have been determined for the term

√{square root over ((dh/dx) 2 +(dh/dy) 2 )}×d1/h(xy) delta

is less than 3500 μm/mm.

10. The glass container of claim 1 , wherein for a wavefront distortion W( ,φ) of a laser light with a wave length of 520 nm, a beam width of at least 0.6×d 2 and less than 0.85×d 2 , that passes through the circular glass bottom in a direction from the outer surface to the inner surface, that is aligned collinear with the longitudinal axis (L tube ), and that has been corrected for piston, tilt and defocus, a peak to valley difference

(W( ,φ) corrected ) max −(W( ,φ) corrected ) min

is less than 100 waves.

11. The glass container of claim 10 , wherein the peak to valley difference is less than 40 waves.

12. The glass container of claim 1 , wherein for a wavefront distortion W( ,φ) of a laser light with a wave length of 520 nm, a beam width of at least 0.6×d 2 and less than 0.85×d 2 , that passes through the circular glass bottom in a direction from the outer surface to the inner surface, that is aligned collinear with the longitudinal axis (L tube ), and that has been corrected for piston and tilt, the corrected wavefront distortion is point symmetric and wherein for a fixed set of radii 0 =¼, 0 =½ and 0 =1, a azimuthal peak to valley difference

(W( ,φ) corrected ) max −(W( ,φ) corrected ) min

is less than 100 waves.

13. The glass container of claim 12 , wherein the azimuthal peak to valley difference is less than 40 waves.

14. The glass container of claim 1 , wherein the outer surface of the circular glass bottom has a topography is defined by a function ĥ(x),

wherein ĥ (x) is an azimuthal average of a distance between the contact plane and the outer surface at any given position that is located on a circle having a center that corresponds to the center of the circular glass bottom and the radius |x|,

wherein individual values ĥ for ĥ (x) are determined for a plurality of circles the radius of which increases stepwise by 500 μm, starting with a circle around the center having a radius of 500 μm,

wherein the individual values ĥ are determined in a range from x=−0.4×d 2 /2 to x=+0.4×d 2 /2, d 2 having a size such that at least 4 values ĥ are determined,

wherein the individual values ĥ can be fitted in a least square fit with a curvature function

h

^

⁡

(

x

)

⁢

=

-

c

×

x

2

1

+

1

-

c

2

×

x

2

+

h

0

wherein c and h 0 are free fitting parameters, and

wherein Δc is the standard deviation error for constant c when fitting the individual values ĥ(x) with the curvature function and wherein the relative standard deviation error Δc/c is less than 0.1.

15. The glass container of claim 14 , wherein the individual values h have been determined in a range from x=−0.6×d 2 /2 to x=+0.6×d 2 /2 and the relative standard deviation error Δc/c is less than 0.1.

16. The glass container of claim 14 , wherein the individual values ĥ have been determined in a range from x=−0.8×d 2 /2 to x=+0.8×d 2 /2 and the relative standard deviation error Δc/c is less than 0.1.

17. The glass container of claim 1 , wherein for any cut surface of the circular glass bottom that is obtainable by cutting the circular glass bottom in a plane that includes the longitudinal axis (L tube ) a condition is fulfilled that comprises:

s 2 max /s 1×( s 2 max /s 2 min −1)≤1.1

wherein s 2 max corresponds to a maximum glass thickness of the circular glass bottom,

wherein s 2 min corresponds to a minimum glass thickness of the circular glass bottom,

wherein s 2 max and s 2 min are determined within a given cut surface within the range from x=−0.4×d 2 /2 to x=+0.4×d 2 /2, and

wherein s 2 min and s 2 max are both measured in a direction that is parallel to the longitudinal axis (L tube ).

18. The glass container of claim 17 , wherein s 2 max and s 2 min are determined within a given cut surface at least within the range from x=−0.6×d 2 /2 to x=+0.6×d 2 /2.

19. The glass container of claim 17 , wherein s 2 max and s 2 min are determined within a given cut surface at least within the range from x=−0.8×d 2 /2 to x=+0.8 X d 2 /2.

20. The glass container of claim 1 , wherein the glass container comprises a pharmaceutical composition.