Method of generating a control program for a device for photorefractive corneal surgery of the eye

1. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea;

wherein adjusting the laser-beam profile further comprises increasing a time interval that at least one elementary beam is incident on the corneal surface at an incident point of the corneal surface as a function of the distance of the incident point of the elementary beam center on the cornea from an axis running parallel to the elementary beam direction, which axis meets the corneal surface at a substantially right angle.

2. The method of claim 1 further comprising adjusting the laser-beam profile based on a fraction of the one or more elementary beams incident on the corneal surface that is reflected away.

3. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea; and

adjusting the laser-beam profile based on the fact that the energy density F of an emitted elementary beam of radius r s is reduced to F/k1(r), in the case of a cornea assumed to be substantially hemispherical with radius R, when incident on its curved surface, where

kl

⁡

(

r

)

=

A

eff

⁡

(

r

)

A

0

=

A

eff

⁡

(

r

)

π

·

r

2

⁢

2

and

A

eff

⁡

(

r

)

=

∫

-

rs

rs

⁢

∫

rs

2

-

x

2

+

r

rs

2

-

x

2

+

r

⁢

1

+

(

ⅆ

ⅆ

x

⁢

f

⁡

(

x

,

y

)

)

2

+

(

ⅆ

ⅆ

x

⁢

f

⁡

(

x

,

y

)

)

2

⁢

ⅆ

x

⁢

⁢

ⅆ

y

with

z

=

f

⁡

(

x

,

y

)

=

f

⁡

(

r

)

=

R

2

-

x

2

-

y

2

=

R

2

-

r

2

,

r

=

(

x

2

+

y

2

)

L

2

,

where x, y, z are the coordinates of the incidence point of the elementary beam center in a Cartesian coordinate system in which the origin lies at the sphere centre of the cornea.

4. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea; and

adjusting the laser-beam profile based on a distance r of an incidence point of the center of the one or more elementary beams on the cornea from an axis running parallel to the one or more elementary beam directions which meets the corneal surface at a substantially right angle.

5. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea;

wherein adjusting the laser-beam profile includes adjusting the ablation depth of the one or more elementary beams based on the determination that the ablation depth due to a particular elementary beam pulse is reduced to d·kor(r) in relation to the ablation depth d in the case of normal incidence of the elementary beam when the elementary beam is incident on the curved surface, where

kor

⁡

(

r

)

=

ln

⁡

(

(

1

-

k2

⁡

(

r

)

)

·

F

k

⁢

⁢

l

⁡

(

r

)

·

F

th

)

ln

⁡

(

F

F

th

)

and F th is the energy-density threshold above which ablation takes place.

6. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea; and

adjusting the laser-beam profile based on the fact that in the case of a cornea assumed to be substantially spherical, the unreflected fraction of the energy density F/k1(r) of the one or more elementary beams incident on the curved surface is given as (1−k2(r))·F/k1(r), where

k2

⁡

(

r

)

=

q

2

_

⁡

(

r

)

+

q

2

_

⁡

(

r

)

′

2

,

with

q

'

⁢

(

α

1

)

=

n

2

-

sin

2

⁡

(

α

1

)

-

cos

⁡

(

α

1

)

1

-

n

2

q

⁢

''

⁢

⁢

(

α

1

)

=

n

2

⁢

cos

⁡

(

α

1

)

-

n

2

-

sin

2

⁡

(

α

1

)

n

2

⁢

cos

⁡

(

α

1

)

+

n

2

-

sin

2

⁡

(

α

1

)

where π/2−α 1 is the angle between the one or more elementary beams and the corneal surface, where

α

1

⁡

(

r

)

=

a

⁢

⁢

tan

(

r

R

2

-

r

2

)

⁢

⁢

with

⁢

⁢

0

≤

r

2

<

R

2

.

and n is the empirically determined refractive index of the cornea at the wavelength of the one or more elementary beams which are used.

7. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea;

determining the local radius of curvature of the cornea; and

determining the angle between the one or more elementary beams and the surface of the cornea based on the local radius of curvature.

8. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea;

wherein adjusting the laser-beam profile includes adjusting the laser-beam profile based on the fact that the angle between the elementary beams and the corneal surface changes during the ablation due to the ablation of at least a portion of the corneal surface.

9. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a cornea and thereby ablating a predetermined ablation profile from the cornea;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams of the laser-beam profile and a surface of the cornea on an energy density of the laser-beam profile on the surface of the cornea;

sensing movements of the eye during ablation; and

adjusting the laser-beam profile based on the effect of the eye movements on the energy density of the laser-beam profile on the cornea.

10. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a corneal surface and thereby ablating a predetermined ablation profile from the corneal surface;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

adjusting the laser-beam profile based on a distance r of an incidence point of the center of the one or more elementary beams on the cornea from an axis running parallel to the one or more elementary beam directions which meets the corneal surface at a substantially right angle.

11. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a corneal surface and thereby ablating a predetermined ablation profile from the corneal surface; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

wherein adjusting the laser-beam profile further comprises:

adjusting the laser-beam profile based on the determination that, in the case of a cornea assumed to be substantially hemispherical with radius R, the unreflected fraction of the energy density F of the one or more elementary beams incident on the curved surface is given as (1−k2(r))·F, where

k2

⁡

(

r

)

=

q

'

2

⁢

(

r

)

+

q

⁢

''

2

⁢

(

r

)

2

,

with

q

'

⁢

(

α

1

)

=

n

2

-

sin

2

⁡

(

α

1

)

-

cos

⁡

(

α

1

)

1

-

n

2

q

⁢

''

⁢

⁢

(

α

1

)

=

n

2

⁢

cos

⁡

(

α

1

)

-

n

2

-

sin

2

⁡

(

α

1

)

n

2

⁢

cos

⁡

(

α

1

)

+

n

2

-

sin

2

⁡

(

α

1

)

where π/2−α 1 is the angle between the one or more elementary beams and the corneal surface, where

α

1

⁡

(

r

)

=

a

⁢

⁢

tan

(

r

R

2

-

r

2

)

⁢

⁢

with

⁢

⁢

0

≤

r

2

<

R

2

.

and n is the empirically determined refractive index of the cornea at the wavelength of the one or more elementary beams.

12. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a comeal surface and thereby ablating a predetermined ablation profile from the corneal surface; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

wherein adjusting the laser-beam profile includes adjusting the ablation depth of the one or more elementary beams based on the determination that the ablation depth due to a particular elementary beam pulse is reduced to d·kor(r) in relation to the ablation depth d in the case of normal incidence of the elementary beam when the elementary beam is incident on the curved surface, where

kor

⁡

(

r

)

=

ln

⁡

(

(

1

-

k2

⁡

(

r

)

)

·

F

k

⁢

⁢

l

⁡

(

r

)

·

F

th

)

ln

⁡

(

F

F

th

)

and F th is the energy-density threshold above which ablation takes place.

13. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a corneal surface and thereby ablating a predetermined ablation profile from the corneal surface;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

determining the local radius of curvature of the cornea; and

determining the angle between the one or more elementary beams and the surface of the cornea based on the local radius of curvature.

14. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a corneal surface and thereby ablating a predetermined ablation profile from the corneal surface; and

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

wherein adjusting the laser-beam profile includes adjusting the laser-beam profile based on the fact that the angle between the elementary beams and the corneal surface changes during the ablation due to the ablation of at least a portion of the corneal surface.

15. A method of laser corneal ablation comprising:

generating a laser-beam profile having one or more elementary laser beams;

projecting the laser-beam profile onto a corneal surface and thereby ablating a predetermined ablation profile from the corneal surface;

adjusting the laser-beam profile according to an effect of an angle between the one or more elementary beams and the corneal surface on the fraction of laser-beam energy incident on the corneal surface which is reflected away;

sensing movements of the eye during ablation; and

adjusting the laser-beam profile based on the effect of the eye movements on the energy density of the laser-beam profile on the cornea.