Method for generating an ablation program, method for ablating a body and means for carrying out said method

Abstract

In a method for generating an ablation program for ablation of material from a surface of a body according to a predetermined desired ablation profile by emission of pulses of a pulsed laser beam onto the surface, the ablation program is generated from the desired ablation profile as a function of the shape of a beam profile of the laser beam and of an inclination of the surface to be ablated and/or considering a water content of the material to be ablated.

Claims

1. A method for generating an ablation program for ablation of material from a surface of a body according to a predetermined desired ablation profile by emission of pulses of a pulsed laser beam onto the surface, the method comprising: generating the ablation program starting from the predetermined desired ablation profile utilizing a function of the shape of a beam profile of the laser beam and utilizing a function of an inclination of the surface to be ablated; using the predetermined desired ablation profile to determine a pre-compensated desired ablation profile utilizing a function of a refractive index of the material at a respective target location of the surface; and generating the ablation program on a basis of the pre-compensated desired ablation program.

2. The method as claimed in claim 1, further comprising, in order to consider the inclination of the surface and the shape of the beam profile, using the predetermined desired ablation profile to determine the pre-compensated desired ablation profile utilizing a function of at least one of a shape of the beam profile and the inclination of the surface at the respective target location on the surface; and generating the ablation program on the basis of the pre-compensated desired ablation program.

3. The method as claimed in claim 2, further comprising, for at least two regions to be ablated from the surface, respectively determining one value of a modification function utilizing a function of at least one of the shape of the beam profile and the inclination of the surface in the respective region and determining the pre-compensated desired ablation profile using the predetermined desired ablation profile and the values of the modification function.

4. The method as claimed in claim 3, wherein the modification function additionally depends on intensity, energy, or fluence of the pulses to be used for ablation.

5. The method as claimed in claim 1, further comprising determining a preliminary ablation program from the predetermined desired ablation profile, for at least one of the pulses to be emitted and determining a desired value for energy or fluence of the at least one pulse depending on the shape of the beam profile, on the inclination of the surface at the region onto which the at least one pulse is to be emitted, and on a prediction of ablation depth using the preliminary ablation program, and wherein the generated ablation program comprises the target location of the pulse according to the preliminary ablation program and the determined value for the energy or fluence of the pulse.

6. The method as claimed in claim 1, further comprising determining the a preliminary ablation program from the predetermined desired ablation profile, using the preliminary ablation program to predict a predicted ablation profile utilizing a function of the beam profile shape and of the inclination of the surface, and generating the ablation program to be used using the predicted ablation profile.

7. The method as claimed in claim 6, further comprising determining the predicted ablation profile at at least two locations which are spaced apart from each other by less than a diameter of the laser beam on the surface of the body.

8. The method as claimed in claim 6, further comprising using the predicted ablation profile and the predetermined desired ablation profile to determine the pre-compensated desired ablation profile, and wherein the ablation program to be used is generated from the pre-compensated desired ablation profile.

9. The method as claimed in claim 6, further comprising generating the ablation program to be used in an iterative manner in that, in an actual iteration step, a preliminary ablation program is determined from a modified desired ablation profile determined in a preceding iteration step, an actual predicted ablation profile is predicted on the basis of the preliminary ablation program utilizing a function of the beam profile shape and of the inclination of the surface, an actual modified desired ablation profile is determined using the actual predicted ablation profile, and the ablation program to be used is generated utilizing a function of the predetermined desired ablation profile and at least one of the modified desired ablation profiles after a last iteration loop.

10. The method as claimed in claim 1, further comprising using a model to predict the course of the ablation depth for a pulse utilizing a function of the shape of the beam profile.

11. The method as claimed in claim 1, wherein the material contains water, the method further comprising guiding the laser beam over the surface during the ablation to be effected, and generating the ablation program starting from the predetermined desired ablation profile, and additionally considering a water content of the material to be ablated.

12. A device for generating an ablation program for ablation of material from a surface according to a predetermined desired ablation profile by emission of pulses of a pulsed laser beam onto the surface, said device comprising: a data processing device which is configured to carry out a generating method for generating an ablation program, the generating method comprising: generating the ablation program from the predetermined desired ablation profile utilizing a function of the shape of a beam profile of the laser beam and a function of an inclination of the surface to be ablated; and using the predetermined desired ablation profile to determine a pre-compensated desired ablation profile utilizing a function of a refractive index of the material at a respective target location of the surface, and generating the ablation program on a basis of the pre-compensated desired ablation program.

13. The device as claimed in claim 12, wherein the data processing device comprises an interface configured for input of data which characterize the shape of the beam profile of the laser beam.

14. The device as claimed in claim 12, further comprising a device for acquisition of topographical data of the surface to be ablated.

15. A method for generating an ablation program for ablation of water-containing material from a surface of a body according to a predetermined desired ablation profile by emission of pulses of a pulsed laser beam onto the surface, comprising: generating the ablation program starting from the predetermined desired ablation profile and; considering a water content of the material to be ablated by taking into account corresponding data including at least one of different absorption of radiation and a different evaporation heat than at least one further substance which the material comprises.

16. The method as claimed in claim 15, further comprising, in order to generate the ablation program, taking into consideration the water content utilizing a function of the location on the surface or in a region to be ablated.

17. The method as claimed in claim 15, further comprising using a model which indicates dependence of the ablation depth, which is achieved by at least one pulse emitted onto a target location on the surface, or of the ablation volume, which is achieved by at least one pulse emitted onto a target location on the surface, on the water content of the material to be ablated by said pulse.

18. The method as claimed in claim 15, further comprising using a further model, which indicates, for a predetermined region of the material, an influence that pulses of the pulsed laser beam impinging on this region or on adjacent regions have on the water content.

19. The method as claimed in claim 15, further comprising using a model for the water content or the change in the water content of the material utilizing a function of at least one of the number, the position of pulses previously emitted onto the same location, and adjacent locations in order to take the water content into consideration when generating the ablation program.

20. The method as claimed in claim 15, further comprising determining the water content from data measured on the body.

21. The method as claimed in claim 20, further comprising using data which indicate the temperature of the surface to determine the water content.

22. The method as claimed in claim 20, further comprising using data which indicate properties of optical radiation originating from the material in the region to be ablated from the body to determine the water content, wherein, in particular, data which are available by confocal Raman spectroscopy of optical radiation from the surface are used to determine the water content, wherein in particular data which indicate the properties of fluorescent radiation originating from the region to be ablated from the body are used to determine the water content.

23. The method as claimed in claim 20, further comprising using data indicating the refractive index in the material to determine the water content.

24. The method as claimed in claim 15, further comprising taking the water content into consideration by determining from the predetermined desired ablation profile a pre-compensated ablation profile utilizing a function of the water content and generating the ablation program from the pre-compensated ablation profile, in particular, using a modification function in order to determine the pre-compensated ablation profile, said function depending explicitly or implicitly on the water content of the material to be ablated.

25. The method as claimed in claim 24, wherein for at least two regions to be ablated from the surface, one value of at least one of the beam-dependent and of inclination-dependent modification function is determined utilizing a function of at least one of the shape of the beam profile and the inclination of the surface in the respective region, and a value of the water content-dependent modification function is determined, and the pre-compensated desired ablation profile is determined using the predetermined desired ablation profile and the values of the modification functions, in particular of the modification functions' product.

26. The method as claimed in claim 15, further comprising generating a preliminary ablation program from the predetermined desired ablation profile and, in order to establish the ablation program to be generated utilizing a function of the water content, from at least one fluence value implicitly or explicitly given by the preliminary ablation program, or modifying a pulse energy of a pulse to be emitted onto the target location given by the ablation program, which energy is implicitly or explicitly given by the preliminary ablation program, utilizing a function of the water content at the target location and is assigned to the target location as an indication.

27. The method as claimed in claim 15, further comprising generating the ablation program also utilizing a function of the shape of a beam profile of the laser beam and/or of an inclination of the surface.

28. The method as claimed in claim 27, further comprising, in order to consider at least one of the shape of the beam profile of the inclination of the surface, determining a predetermined desired ablation profile, which is pre-compensated with respect to the influences of at least one of the beam profile shape and of the inclination of the surface, from the predetermined desired ablation profile, using a modification function which depends on at least one of the shape of the beam profile and of the inclination of the surface, and generating the ablation program from the predetermined desired ablation profile which has been pre-compensated with respect to the influences of at least one of the beam profile shape and of the inclination of the surface.

29. The method as claimed in claim 28, wherein for at least two regions to be ablated from the surface, one value of at least one of the beam-dependent and of inclination-dependent modification function is determined utilizing a function of at least one of the shape of the beam profile and the inclination of the surface in the respective region, and a value of the water content-dependent modification function is determined, and the pre-compensated desired ablation profile is determined using the predetermined desired ablation profile and the values of the modification functions, in particular of the modification functions' product.

30. A method for forming control signals for controlling a laser of a laser ablation device to emit a pulsed laser beam and/or for controlling a deflecting device of the laser ablation device to deflect the laser beam in order to ablate water-containing material from a surface of a body according to a predetermined desired ablation profile by application of pulses of a pulsed laser beam, comprising: using a generating method for generating an ablation program to generate the ablation program for the predetermined desired ablation profile; and outputting control signals to at least one of the laser and of the deflecting device according to the ablation program; generating the ablation program starting from the predetermined desired ablation profile; and considering a water content of the material to be ablated by taking into account corresponding data including at least one of different absorption of radiation and a different evaporation heat than at least one further substance which the material comprises.

31. The method as claimed in claim 30, further comprising, after generating a first part of the ablation program and emission of corresponding control signals generating at least one further executable part of the ablation program and emitting corresponding control signals.

32. The method as claimed in claim 30, further comprising generating a preliminary ablation program on the basis of the predetermined desired ablation profile and determining the water content in order to generate the at least one further part of the ablation program for at least one target location on the surface given by the preliminary ablation program, and changing the preliminary ablation program by generating the ablation program utilizing a function of the determined water content.

33. A device that generates an ablation program for ablation of water-containing material from a surface of a body according to a predetermined desired ablation profile by emission of pulses from a pulsed laser beam onto the surface, said laser beam being passed over the surface, the device comprising a data processing device which is provided for execution of a method for generating an ablation program, wherein the ablation program is generated starting from the predetermined desired ablation profile and considering a water content of the material to be ablated by taking into account corresponding data including at least one of different absorption of radiation and a different evaporation heat than at least one further substance which the material comprises.

34. A non-transitory computer readable data storage medium that is not a carrier wave or signal comprising program code to carry out a method for generating an ablation program for ablation of material from a surface of a body according to a predetermined desired ablation profile by emission of pulses of a pulsed laser beam onto the surface, wherein the program is being executed on a computer, the non-transitory computer readable data storage medium comprising instructions to: generate the ablation program from the predetermined desired ablation profile utilizing a function of the shape of a beam profile of the laser beam and of an inclination of the surface to be ablated; use the predetermined desired ablation profile to determine a pre-compensated desired ablation profile utilizing a function of a refractive index of the material at a respective target location of the surface; and generate the ablation program on basis of the pre-compensated desired ablation program.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Subject matter hereof may be more completely understood in consideration of the following detailed description of various embodiments in connection with the accompanying figures, in which:

(2) The invention will be explained in more detail below, by way of example and with reference to the drawings, wherein:

(3) FIG. 1 shows a schematic perspective view of a patient during treatment with a laser surgical instrument comprising an ablation device of a preferred embodiment according to a first aspect of the invention;

(4) FIG. 2 shows a schematic block diagram of the ablation device of FIG. 1;

(5) FIG. 3 shows a schematic representation of a spherical body to be processed;

(6) FIG. 4 shows a flow scheme of a method for generating an ablation program for the instrument of FIG. 2 according to a first preferred embodiment of the first aspect of the invention;

(7) FIG. 5 shows a representation of a modification function depending on the location in the rotation-symmetrical beam profile of a laser beam for three different generating methods;

(8) FIG. 6 shows a block diagram of an ablation device according to a second preferred embodiment of the first aspect of the invention for a laser surgical instrument;

(9) FIG. 7 shows a schematic representation of a device for detecting a shape of a beam profile of a laser beam emitted by the laser of the ablation device of FIG. 6;

(10) FIG. 8 shows a flow scheme of a method for generating an ablation program according to a third preferred embodiment of the first aspect of the invention;

(11) FIG. 9 shows a block diagram of a laser surgical instrument comprising an ablation device which includes a device for generating an ablation program according to a further preferred embodiment of the first aspect of the invention;

(12) FIG. 10 shows a flow scheme of a method for generating an ablation program according to a further preferred embodiment of the first aspect of the invention;

(13) FIGS. 11a and b show diagrams for comparison of ablation depths achieved by ablation using the method according to FIG. 10 and using a known method, and

(14) FIG. 12 shows a diagram in which a ratio of a fluence and a threshold value for said fluence is shown as a function of the radius in the laser beam for a Gaussian beam profile and a truncated Gaussian beam profile;

(15) FIG. 13 shows a schematic block diagram of the laser ablation device comprising a signal-generating device according to a first preferred embodiment of a second aspect of the invention;

(16) FIG. 14 shows a schematic representation of a sectional view of a desired ablation profile taken along a diameter through the body in FIG. 3 and of single pulse ablation volumes;

(17) FIG. 15 shows a flow scheme of a method for forming control signals according to a first ablation program generated by said method for the instrument in FIG. 13 according to a first preferred embodiment of the second aspect of the invention;

(18) FIG. 16 shows a flow scheme of a method for forming and emitting control signals according to an ablation program generated by said method according to a further preferred embodiment of the second aspect of the invention;

(19) FIG. 17 shows a flow scheme comprising partial steps of step S128 according to the flow scheme of FIG. 16;

(20) FIG. 18 shows a block diagram of an ablation device comprising a signal-forming device according to a third preferred embodiment of the second aspect of the invention for a laser surgical instrument;

(21) FIG. 19 shows a block diagram of an ablation device and a signal-forming device according to a further preferred embodiment of the second aspect of the invention, and

(22) FIG. 20 shows a flow scheme of a method for forming and emitting control signals according to an ablation program generated by said method according to the further preferred embodiment of the second aspect of the invention in the second variant.

(23) While various embodiments are amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the claimed inventions to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the subject matter as defined by the claims.

DETAILED DESCRIPTION

(24) Various embodiments of systems, devices, and methods have been described herein. These embodiments are given only by way of example and are not intended to limit the scope of the claimed inventions. It should be appreciated, moreover, that the various features of the embodiments that have been described may be combined in various ways to produce numerous additional embodiments. Moreover, while various materials, dimensions, shapes, configurations and locations, etc. have been described for use with disclosed embodiments, others besides those disclosed may be utilized without exceeding the scope of the claimed inventions.

(25) Persons of ordinary skill in the relevant arts will recognize that the subject matter hereof may comprise fewer features than illustrated in any individual embodiment described above. The embodiments described herein are not meant to be an exhaustive presentation of the ways in which the various features of the subject matter hereof may be combined. Accordingly, the embodiments are not mutually exclusive combinations of features; rather, the various embodiments can comprise a combination of different individual features selected from different individual embodiments, as understood by persons of ordinary skill in the art. Moreover, elements described with respect to one embodiment can be implemented in other embodiments even when not described in such embodiments unless otherwise noted.

(26) Although a dependent claim may refer in the claims to a specific combination with one or more other claims, other embodiments can also include a combination of the dependent claim with the subject matter of each other dependent claim or a combination of one or more features with other dependent or independent claims. Such combinations are proposed herein unless it is stated that a specific combination is not intended.

(27) Any incorporation by reference of documents above is limited such that no subject matter is incorporated that is contrary to the explicit disclosure herein. Any incorporation by reference of documents above is further limited such that no claims included in the documents are incorporated by reference herein. Any incorporation by reference of documents above is yet further limited such that any definitions provided in the documents are not incorporated by reference herein unless expressly included herein.

(28) For purposes of interpreting the claims, it is expressly intended that the provisions of 35 U.S.C. 112(f) are not to be invoked unless the specific terms means for or step for are recited in a claim.

(29) FIG. 1 shows a laser surgical instrument 1 for treatment of a patient's eye 2, which instrument serves to carry out a refractive correction of the eye. For this purpose, the instrument 1 emits a pulsed laser beam 3 onto the eye 1 of the patient whose head is fixed by a head support 4 that is securely connected to the instrument 1.

(30) FIG. 2 shows more detail of the structure of the instrument which is an ablation device according to the first preferred embodiment of the invention's first aspect. The instrument comprises a data processing device 5 with an integrated control unit 6, a laser 7 controlled by the control unit 6 and a deflecting device 8, which is also controlled by the control unit and by means of which the pulsed laser beam 3 emitted by the laser 7 can be directed and focused on target locations on the cornea of the eye 2 according to a given ablation program.

(31) The instrument further comprises a device 9 for acquiring topographical data of the surface of a region to be treated in the eye 2 and a device 10 for determining a desired ablation profile. Both devices are coupled to the data processing device 5. The data processing device 5, the control unit 6, the device 9 for acquiring the surface topography and the device 10 for determining the desired ablation profile constitute a device for generating an ablation program according to a first preferred embodiment of the invention's first aspect.

(32) The data processing device 5 with integrated control unit 6 serves to generate an ablation program by the use of data representing the surface topography of the region to be treated, data relating to the properties of the laser beam 3 and data relating to the desired ablation profile to be ablated. For this purpose, the data processing device 5 comprises a processor and a memory for storing data, in which, in particular, also a computer program including program code is stored, by means of which the ablation program is generated, when executing the program on the processor, and the actual ablation is effected using the integrated control unit 6. The memory and the processor are partially illustrated in the block diagram by the block generate ablation program.

(33) To this end, the data processing device 5 possesses interfaces for data input, namely an interface 11 for manual input of the surface topography, an interface 11 reading in surface topography data from the device for acquiring surface topography data, and an input interface 11 for input of coordinates of a reference point of the coordinate system in which the surface topography data are indicated, which coordinates, in the present example, are the coordinates of the coordinate system's origin, an interface 12 for manual input of the desired ablation profile, an interface 12 for reading in data with respect to the desired ablation profile from the device 10 for determining the desired ablation profile, and an interface 12 for input of the coordinates of a reference point of the coordinate system in which the desired ablation profile is given, which coordinates, in the present example, are those of the coordinate system's origin. Moreover, an interface 13 for manual input of beam parameters and an interface 13 for reading in data relating to the beam parameter of the laser beam 3 from a data source are provided. At least one of the beam parameters can serve to describe the shape of the beam profile.

(34) The interfaces for manual input and in particular also the interfaces for input of the coordinates of reference points may be one single interface in physical terms, said interface having connected to it, in a manner not shown in the Figures, a keyboard and a screen on which an input prompt can be displayed when corresponding data are to be read in. The interfaces further comprise corresponding modules of the computer program for reading in data from the keyboard.

(35) The other interfaces 11, 12 and 13 are conventional interfaces for data flows which, in addition to corresponding electronic modules, also comprise software modules.

(36) The control unit 6 is integrated into the data processing device 5 and further comprises interfaces, not shown in the Figures, for control of the laser 7 and of the deflecting device 8. Such control units are known, in principle, and therefore need not be explained in more detail.

(37) The laser 7 is connected to the control unit 6 and emits a pulsed laser beam with predetermined pulse energies as a function of the ablation program. For example, an excimer laser having a wavelength in the wavelength range of 193 nm can be used. The laser beam 3 emitted by the laser 7 has a beam profile which is shown in broken lines in FIG. 12 and has a Gaussian shape.

(38) The deflecting device 8 is also connected to the control unit 6 via a data link and, in accordance with control signals from the control unit 6, directs the pulsed laser beam 3 emitted by the laser 7 onto predetermined target locations on the surface of the eye 2 according to the ablation program to be executed. For this purpose, the deflecting device 8 comprises a focusing device 14 for focusing the laser beam along its direction of propagation and for deflection transverse to the laser beam via two mirrors 15, which are rotatable or tiltable about two mutually orthogonal axes and are arranged in the beam path following the focusing device 14.

(39) Both the laser 7 and the deflecting device 8 may be conventional, known devices of a laser surgical instrument.

(40) The surface topography is represented using two mutually parallel Cartesian coordinate systems whose x-y planes coincide. If possible, the z axis is aligned parallel to the optical axis of the eye with good approximation. This is shown in FIG. 3 for a spherical body or a sphere with a surface 2 as a simplified model of the eye 2, in which, for the sake of clarity, the z axis representing the desired ablation profile is not shown. The z axes are defined during alignment of the eye 2 relative to the instrument 1.

(41) In the example, the device 9 for acquiring surface topography data comprises an optical coherence tomograph which is arranged in the instrument 1 so as to allow acquisition of the surface topography of the eye 2 in the region to be treated. The optical coherence tomograph acquires surface topography data in the form of heights in the direction of z at grid points in the x-y plane, which is fixed with respect to the instrument 1 and approximately orthogonal to the laser beam 3. The data are read into the data processing device 5 via the interface 11.

(42) In the present example, the device 10 for determining the desired ablation profile comprises a wavefront analyzer of the Hartmann-Shack type as well as, where appropriate, devices for determining the refractive power of the eye 2, by which analyzer or devices, respectively, a desired ablation profile D.sub.Soll for the region to be treated in the eye 2 can be determined according to known methods. In doing so, the desired ablation profile is determined such that correction of imaging errors in the eye 2 can be achieved as far as possible by the ablation to be carried out. An example of the desired ablation profile is evident from FIG. 3. It is given by the distances, in the direction of z, between the initial surface, the calotte 2, and a desired surface 2 indicated by a broken line, as a function of the location in the x-y plane.

(43) In order to determine the desired ablation profile, the device 10 may comprise a suitable processor which evaluates data relating to the refractive power of the eye 2 and the wavefront data in order to determine the desired ablation profile again, in the present example, in the form of the desired ablation depths for points of a point grid in the x-y plane of the corresponding coordinate system which coincides with the x-y plane of the coordinate system for indicating the ablation profile. As far as the coordinate origins are not identical, the position of one of the reference points or coordinate origins in the respective other coordinate system can be given so that the data can be transformed by simple shifting into an identical coordinate system during a later process stage. This may turn out to be favorable if the center of the desired ablation profile, i.e. a point relative to which the desired ablation profile is approximately symmetrical, deviates from the center of the surface of the eye 2, i.e. from a point relative to which the surface of the eye is approximately symmetrical. Such a method for generating a desired ablation profile is described, for example, in WO 01/08075 A1, the respective contents of which are hereby incorporated in the description by reference.

(44) The method for generating an ablation program according to the first exemplary embodiment is based on the following considerations.

(45) In order to ablate the desired ablation profile D.sub.Soll from the eye 2, laser pulses having a predetermined pulse energy are emitted onto predetermined target locations according to a generated ablation program, each of said laser pulses individually leading to a removal of material. The depth of removal can be described by various models. In the present example, the so-called blow-off model is used, as described, for example, in Refraktive Chirurgie der Hornhaut, Theo Seiler (Ed.), 1st edition, ENKE Georg Thieme Verlag, Stuttgart/New York, 2000 (ISBN 3-13-118071-4), Chapter 6.1, p. 150, or in R. Srinivasan: Ablation of Polymers and Biological Tissue by Ultraviolet Lasers, Science vol. 234, p. 559-565, 31 Oct. 1986. Following this, material is removed to a depth D.sub.Ist at a location having the coordinates (x,y), by laser radiation impinging at this location and having an effective fluence F(x,y), i. e. energy per surface area, according to the following formula:

(46) $D_{\mathrm{Ist}}\left(x,y\right)=\{\begin{array}{cc}.Math.\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}},& \mathrm{if}F\left(x,y\right)>F_{\mathrm{thr}}\\ 0,& \mathrm{otherwise}\end{array}.$

(47) In this formula, designates a material-dependent ablation coefficient and F.sub.thr relates to a likewise material-dependent ablation threshold fluence value, below which value laser radiation no longer results in material removal from the eye 2.

(48) In the simple generating method for an ablation program used below, it is assumed that the desired ablation profile can be split into single-pulse ablation volumes which each form upon impingement of one pulse. In this case, generating the ablation program includes determining the target locations (x,y) onto which the pulses of a predetermined pulse energy have to be directed.

(49) In generating an ablation program, it is assumed that a laser pulse removes a single-pulse ablation volume or spot ablation volume V.sub.pulse, which is obtained as an integral of the ablation depth D.sub.Ist over the entire pulse area:

(50) $V_{\mathrm{pulse}}=\underset{\mathrm{Spot}}{}{D}_{\mathrm{Ist}}\left(x,y\right)\mathrm{dxdy}=\underset{\mathrm{Spot}}{}\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}.$

(51) The integral extends over the area designated as Spot, in which D.sub.Ist>0 holds.

(52) Whereas conventional methods assume the effective fluence F(x,y) to be constant over the area of the pulse or of the spot, respectively, the invention takes two influences into consideration at the same time. On the one hand, it is considered that the inclination of the surface to be processed reduces the effective fluence according to said inclination relative to the fluence of the laser beam 3. If the surface to be processed is described by a height function (x,y), which indicates the level of the surface above the x-y plane, the angle of inclination of the surface can be determined relative to the z axis and, thus, in approximation to the laser beam 3 incident on the surface 2, according to the formula
(x,y)=arctan(|grad (x,y)|)

(53) Thus, the fluence F(x,y) effective during ablation on the surface is obtained as
F(x,y)=F.sub.P(x,y).Math.cos (x,y),

(54) wherein F.sub.P(x,y) designates the fluence for vertical incidence of the laser beam 3 on the surface, i. e. at an angle =0. Therefore, F.sub.P corresponds to the fluence or the beam profile of the laser beam 3.

(55) The second effect taken into consideration is that the effective fluence varies in accordance with the intensity or energy profile of the pulses in a plane orthogonal to the direction of the laser beam 3 and that it may thereby, in particular, also be below the threshold value F.sub.thr.

(56) Thus, the actual single-pulse ablation volume results from the following formula:

(57) $V_{\mathrm{pulse}}=\underset{\mathrm{Spot}}{}{D}_{\mathrm{Ist}}\left(x,y\right)\mathrm{dxdy}=\underset{\mathrm{Spot}}{}\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}=\underset{\mathrm{Spot}}{}\ln \frac{F_P\left(x,y\right)\cos \left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}.$

(58) Therefore, the single-pulse ablation volume non-linearly depends on the angle of inclination of the surface and on the fluence profile F.sub.P(x,y).

(59) In the case of known single-pulse ablation volumes, an ablation program can be generated by known simple generating methods, as described, for example, in DE 19727573 C1 or EP 1060710 A2, according to which ablation program the mean ablation depth D.sub.M results, in a uniformly or slowly varying manner, for a distance a of laser beam pulses directed onto the surface according to:

(60) $D_M=c\frac{V_{\mathrm{pulse}}}{a^2}$

(61) In this case, c is a proportionality factor resulting from the pattern of the points of incidence of the laser beam's pulses. For example, an approximately square pattern yields c=1, whereas an approximately hexagonal pattern yields c=2/{square root over (3)}.

(62) In the following, it will be assumed that the ablation profile slowly changes spatially with respect to the length of the distance a, or that the inclination slowly changes with respect to the diameter of the laser beam 3 on the surface. In order to describe the spatial dependence of these spatially slowly varying parameters, coordinates u and v will be used in the following, which are given in a u-v coordinate system that coincides with the x-y coordinate system. Thus, the single-pulse ablation volume and, likewise, the mean depth D.sub.M resulting from the pulses placed next to each other are to be understood as a function of u and v.

(63) This allows to calculate a modification function K, which depends on u and v and results as

(64) $K\left(u,v\right)=\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(u,v\right)\cos \left(u,v\right)}{V_{\mathrm{pulse},E}\left(u,v\right)},$

(65) wherein the index E designates quantities which are determined when using a simple generating method, i. e. one that does not take the inclination and the shape of the beam profile into consideration. The factor cos((u,v)) results from the fact that the distance a in the x-y plane increases by 1/cos((u,v)) in one direction due to the inclination of the surface. V.sub.pulse,Ist(u,v) itself may depend on cos((u,v)). K depends on the shape of the beam profile via V.sub.pulse,Ist.

(66) If an ablation program were determined by any of the aforementioned simple generating methods on the basis of the desired ablation profile D.sub.Soll, this would yield an actual ablation profile reduced with respect to the desired ablation profile according to the modification function K:
D.sub.Ist(u,v)=K(u,v).Math.D.sub.Soll

(67) Therefore, in order to compensate this error in advance, the desired ablation profile D.sub.Soll that is to be ablated is divided by the modification function K, thus yielding a modified and pre-compensated desired ablation profile D.sub.Mod:

(68) $D_{\mathrm{Mod}}\left(u,v\right)=\frac{D_{\mathrm{Soll}}\left(u,v\right)}{K\left(u,v\right)}.$

(69) Using the simple generating method, this leads to an ablation program which, when being executed, yields the desired ablation profile D.sub.Soll. If the pre-compensated or modified desired ablation profile is used to determine an ablation program by the conventional simple generating methods, the desired ablation profile is obtained with very good approximation during ablation even in the case of surfaces inclined with respect to the laser beam and a non-constant beam profile.

(70) In order to determine the locations onto which the laser pulses are to be emitted, various known methods can be used, e. g. the methods described in DE 19727573 C1 and EP 1060710 A2. In DE 19727573 C1, ablation is effected in layers, i. e. locations of impingement are determined in a layer-wise fashion for pulses, with the desired profile then resulting from superposition of these layers. According to the method in EP 1060710 A2, the spot distance is varied in a quasi-continuous manner in order to achieve the desired ablation depth.

(71) The calculation of the modification function is explained using as an example the ablation of a spherical surface by a laser beam having a Gauss-shaped beam profile (cf. FIG. 3).

(72) The beam profile or fluence is described by the formula

(73) $F_P\left(r\right)=F_0{e}^{-\frac{r^2}{w^2}},$
wherein F.sub.0 is the peak fluence value, r is the radial distance from the center of the beam profile, and w is the distance after the profile has dropped to 1/e relative to the value at the center.

(74) For the actual ablation profile of a laser pulse impinging orthogonally on a planar surface, this yields:

(75) $D_{\mathrm{Ist}}\left(r\right)=\ln \frac{F_0}{F_{\mathrm{thr}}}-\frac{r^2}{w^2},$

(76) so that the single-pulse ablation volume for this pulse is calculated as

(77) $V_{\mathrm{pulse},E}=\frac{}{2}{w^2\left[\ln \frac{F_0}{F_{\mathrm{thr}}}\right]}^2.$

(78) As the mean depth of the desired profile for a square pattern of the points of impingement of the pulses, or spot pattern, having an edge length a, a mean depth of ablation according to

(79) 0$D_E\left(r\right)=\frac{V_{s,E}}{a^2}=\frac{}{2}{\frac{w^2}{a^2}\left[\ln \frac{F_0}{F_{\mathrm{thr}}}\right]}^2$

(80) can be expected. If D.sub.E were assumed to be equal to D.sub.Soll, a could be determined as a function of the location. However, the spherical surface is actually inclined, except at the center, with respect to the laser beam 3 that is assumed to impinge parallel to the z-axis with sufficiently good approximation. As is evident from FIG. 3, the angle of inclination can be calculated in the following manner as a function of the distance of a location on the surface of the eye 2:

(81) $\left(\right)=\arcsin \left(\frac{-}{R}\right)=\arcsin \left(\frac{-}{\sqrt{R^2-{}^2}}\right).$

(82) The inclination of the surface at the location then has the effect that both the spot distance in the direction of inclination and the spot width w in the direction of inclination are increased by the factor 1/cos(()). Therefore, the ratio w/a in the equation for D does not change with the inclination. However, the fluence does change in this equation. Therefore, the following result is obtained for the depth profile to be expected on the spherical surface:

(83) $D_{\mathrm{Ist}}\left(\right)=\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(\right)\cos \left(\right)}{a^2}=\frac{}{2}{\frac{w^2}{a^2}\left[\ln \frac{F_0.Math.\cos \left(\right)}{F_{\mathrm{thr}}}\right]}^2$
The modification function K() is then calculated as

(84) $K\left(\right)=\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(\right)\cos \left(\right)}{V_{\mathrm{pulse},E}}={\left(1+\frac{\ln \cos \left(\right)}{\ln \frac{F_0}{F_{\mathrm{thr}}}}\right)}^2$

(85) This result may be systematically obtained also by assuming cos() to be constant over the spot area in the formula for the single-pulse ablation volume.

(86) The method steps schematically shown in the flow scheme of FIG. 4 are used to determine the ablation program.

(87) At first, the surface topography of the region to be treated is determined in step S10 by the device 9 for acquiring the surface topography data. For example, the corresponding data may comprise heights of the surface with respect to the x-y plane, said heights being detected above a grid of points in the x-y plane.

(88) In step S12, these data are then read into the data processing device 5 via the interface 11 for the surface topography data. Surface inclinations are then determined from the height data by numerical determinations of gradients, as well as determining the above-indicated formula for the angle of inclination. The corresponding data are then stored in the memory of the data processing device 5.

(89) In the example, the desired ablation profile D.sub.Soll is determined in step S14, after steps S10 and S12, using the device 10 for determining the desired ablation profile. In other exemplary embodiments, this can also be effected prior to said steps. For this purpose, imaging errors are determined from wavefront data. Known methods are used to calculate at which locations of the eye's surface material is to be ablated to what depth. In the present example, the desired ablation profile D.sub.Soll is given by specifying the desired ablation depth as a function of the location on a grid in the x-y plane.

(90) In step S16, these data are then read via the interface 12 into the data processing device 5 and stored there in its memory.

(91) In step S18, beam parameters of the laser beam 3 to be used are then read in via the interface 13. For this purpose, only the diameter or the half-width of a Gaussian beam profile of the laser beam is input in this exemplary embodiment. The Gaussian shape of the laser beam 3 is assumed as fixed and is taken into consideration in the form of corresponding formulae in the program being executed on the processor of the data processing device 5.

(92) In step S20 the pulse energy to be used per surface area or the fluence to be used is then input and stored. More precisely, the peak value F.sub.0 of the fluence for the Gaussian profile is input.

(93) In step S22 values of the modification function K are then determined for the entire desired ablation profile, optionally determining, by interpolation, values of the angle of inclination on the grid used to specify the desired ablation profile. The above-specified formula for the function K is used for this purpose. The corresponding values are then stored again.

(94) Following this, step S24 determines a modified or pre-compensated desired ablation profile D.sub.Mod by dividing the desired ablation depths, which are given for the respective grid points due to the desired ablation profile read in, by the value of the modification function K determined for each respective grid point. The modified desired ablation profile is then stored.

(95) In the next step S26, an ablation program is generated on the basis of the modified desired ablation profile D.sub.Mod, the fluence read in, and the beam parameter, for which purpose a method is used that does not simultaneously take the surface inclination and the shape of the beam profile into consideration. For example, the method described in DE 19727573 C1 can be used. The ablation program thus generated comprises a sequence of target locations in the x-y plane, i.e. corresponding coordinates onto which the laser pulses have to be directed with the pulse energy determined by the fluence read in, in order to achieve the desired ablation profile to be achieved. The ablation program is stored in the data processing device 5. This step completes the actual generation of the ablation program.

(96) In the next step S28, control commands are output to the laser 7 and to the deflecting device 8 by the data processing device 5 using the integrated control unit 6 so as to remove material from the eye 2 according to the generated ablation program.

(97) The ablation method is suitable for both photo-refractive keratectomy and LASIK. Since these methods involve the removal of material in different layers of the eye, the use of different desired ablation profiles may be accordingly required in some cases.

(98) According to a further variant of the method just described, the required memory space can be reduced by combining steps S22 and S24 and by calculating the modification function for each point of support of the desired ablation profile without being stored after the corresponding modified desired ablation profile value has been determined.

(99) FIG. 5 shows the modification factor as a function of the radius with reference to a convex-spherical ablation profile on a circular region having a diameter of 8 mm, said region having been formed by ablation on a surface with a radius of curvature of 7.86 mm. The solid line shows a correction factor which is obtained by the method disclosed in WO 01/85075 A1, i. e. particularly without taking the shape of the beam profile into consideration. The broken line represents the result achieved by the method just described. It is easy to see that as the radial distance from the center of the calotte increases and, thus, as the inclination increases, the corrections by the present methods gain importance and differ considerably from those of the prior art.

(100) FIG. 6 shows an instrument according to a further preferred embodiment of the first aspect of the invention, which instrument differs from that of the first exemplary embodiment in that a device 16 for determining the beam profile of the laser beam 3 is arranged in the beam path of the laser beam 3 between the laser 7 and the deflecting device 8 here, by means of which device 16 the beam profile of the laser beam 3 can be determined and supplied to the data processing device 5 through a suitable data link via the interface 13 for the beam parameters, the data processing device 5 being programmed to execute the variant of the generating method described below.

(101) The device 16 for determining the beam profile is represented in more detail in FIG. 7. Before reaching the work plane 17, i. e. the plane in which ablation takes place, the laser beam 3 is split into a processing beam 19 and a measurement beam 20 with the help of a beam splitter 18 in the form of a wedge plate. By reflection at its second surface, the wedge plate 18 generates a further beam 21, which is absorbed by a stop 22.

(102) The measurement beam 20 is deflected by a mirror 23, impinges on an optional attenuator 24 and is then incident on a ground glass screen or, when UV light is used, a fluorescent screen 25. The mirror 23 and the frosted glass screen 25 are arranged such that the measurement beam 20 travels approximately the same path length as the processing beam 19 on its way from the beam splitter 18 to the work plane 17.

(103) Using a video camera 26 as space-resolving detector, e. g. a CCD camera, the image of the scattered light from the ground glass screen or of the fluorescent light is recorded in a space-resolved manner and is evaluated electronically. The video camera 26 is selected such that its recording rate is greater than the repetition rate used for the laser, thus allowing the beam profile to be measured even during the ablation operation. In the case of slow changes of the beam profile, a slow analysis of the beam profile may also be effected prior to performing the ablation operation.

(104) A corresponding method for generating an ablation program differs from the corresponding method of the first exemplary embodiment in that step S18 does not involve reading in the width of the Gaussian beam but the beam profile determined by the device 16.

(105) Moreover, step S22 involves determining the values of the modification function by numeric integration according to the following formula

(106) $K\left(u,v\right)=\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(u,v\right)\cos \left(u,v\right)}{V_{\mathrm{pulse},E}\left(u,v\right)}=\frac{{}_{\mathrm{Spot}}r\ln \frac{F_P\left(r\right)\cos \left(u,v\right)}{F_{\mathrm{thr}}}\mathrm{dr}}{{}_{\mathrm{Spot}}r\ln \frac{F_0}{F_{\mathrm{thr}}}\mathrm{dr}}\cos \left(u,v\right),$

(107) wherein the beam profile is assumed to have rotation symmetry and r designates the radius transverse to the propagation direction of the laser beam.

(108) A third exemplary embodiment of a method for generating an ablation program is illustrated in FIG. 8. A corresponding instrument differs from the instrument of the first exemplary embodiment by programming the data processing device 5 such that it can carry out the ablation method described below.

(109) The ablation method which encompasses the method for generating an ablation program comprises several steps which correspond to those of the method described in FIG. 4. Therefore, these will be referred to below by the same reference numerals and will not be described in detail again.

(110) Thus, data relating to the surface inclination are determined and stored in steps S10 and S12, and data relating to the desired ablation profile are determined and stored in steps S14 and S16.

(111) In step S30, which follows then, the width of a given Gaussian beam profile and a pre-set initial fluence value, i.e. a pre-set initial peak value, are read in.

(112) In step S32, which follows, a preliminary ablation program is then generated on the basis of the input desired ablation profile, the pre-set fluence read in, and the beam parameters, wherein the simple generating method used for this purpose does not take the shape of the beam profile into consideration simultaneously with the inclination. In particular, the above-mentioned method of DE 197 27 573 C1 can be used. The preliminary ablation program which in turn comprises a series of coordinates for locations on the surface of the eye 2, onto which the pulses are to be directed, is then stored.

(113) Next, in order to generate the ablation program to be finally used, fluence values or pulse energies which are modified with respect to the pre-set fluence peak value are determined for each pulse in step S34. If the simplified method used to generate the preliminary ablation program is based on a single-pulse ablation volume V.sub.S,E, the following relationship between the actual single-pulse ablation volume V.sub.S,Ist for one pulse and the single-pulse ablation volume V.sub.S,E used to generate the preliminary ablation program results as already described above:

(114) $K\left(u,v\right)=\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(u,v\right)\cos \left(\left(u,v\right)\right)}{V_{\mathrm{pulse},E}\left(u,v\right)},$

(115) wherein V.sub.pulse,Ist and V.sub.pulse,E are functions of the dimension-less ratio F.sub.0/F.sub.THR. In addition, V.sub.pulse,Ist also depends directly on the inclination or the angle at the corresponding location.

(116) The inclination is known for each pulse and, thus, for a corresponding location on the surface, so that this relationship can be regarded as an equation for determining a fluence to be used for the pulse or a peak value F.sub.0 or a corresponding pulse energy, on which the single-pulse ablation volumes or the modification function K, respectively, depend. This equation is then numerically calculated for each pulse, e. g. using a Newton method which is known to the person skilled in the art, for the relationship F.sub.0/F.sub.THR and stored. This yields a usable ablation program, which includes a series of target locations, onto which the pulses of the laser beam 3 are to be directed, according to the preliminary ablation program, and includes a corresponding position- or coordinate-dependent fluence peak value F.sub.0 or a corresponding pulse energy for each of the target locations.

(117) By suitable control of a high-voltage supply of the excimer laser 7 and, thus, of the charging of capacitors in which the energy for one pulse is respectively stored, according to the ablation program and by simultaneously controlling the deflecting device 8, ablation can be effected in step S36, using laser pulses with a position- or coordinate-dependent pulse energy and, thus, fluence.

(118) According to a further exemplary embodiment, the determination of the peak value of fluence may optionally be effected also during the actual ablation.

(119) A variant of this exemplary embodiment is shown in FIG. 9. The instrument schematically shown here differs from the instrument of the previous exemplary embodiment in that the beam path of the laser beam 3 between the laser 7 and the deflecting device 8 includes a modulator 27, which is a liquid crystal element, in the present example, whose transmission can be controlled by the control unit 6. Moreover, the control unit 6, compared to the control unit 6, comprises an output for control of the modulator 27, and the computer program executed in the data processing device 5 is provided to control fluence, not by controlling the laser 7, but by changing the transmission of the modulator 27.

(120) The fluence of the laser 7 is then set such that the maximum fluence required for ablation according to the ablation program is achieved by maximum transmission of the modulator 27. During ablation in accordance with the ablation program, the modulator 27 is controlled such that the pulses impinging on the surface have the desired energy or fluence.

(121) FIG. 10 shows a further exemplary embodiment of a method for generating an ablation program which can be executed by an instrument that differs from the instrument 1 only by the way in which the data processing device 5 is programmed.

(122) The method is identical with the method of the first exemplary embodiment in steps S10 to S20, so that the same reference numerals are used for these steps and the explanations apply accordingly. In this case, however, the ablation program is generated in an iterative manner, taking into consideration the shape of the beam profile with a spatial resolution of greater than the beam cross-section.

(123) Starting out with a preliminary ablation program generated on the basis of the desired ablation profile, a predicted actual ablation profile D.sub.I is predicted with high spatial resolution. The N single-pulse coordinates are described by the coordinates (x.sub.Pi,y.sub.Pi), i=1 . . . N. On a fine point grid of MM points (x.sub.m,y.sub.m), m=1, . . . , M, for which x.sub.mx.sub.m-1<<w and also y.sub.my.sub.m-1<<w hold true, the contribution of each of said N single pulses to the ablation depth is calculated with a spatial resolution that is better than the beam profile diameter:

(124) $\begin{array}{c}{D}_I\left(x_m,y_m\right)=\underset{\underset{D_j>0}{i=1}}{\overset{N}{.Math.}}{D}_i\left(x_m,y_m\right)\\ =\underset{\underset{D_j>0}{i=1}}{\overset{N}{.Math.}}\left(\begin{array}{c}\ln \frac{F_0\cos \left(x_m,y_m\right)}{F_{\mathrm{thr}}}-\\ \frac{{\left(x_{\mathrm{Pi}}-x_m\right)}^2+{\left(y_{\mathrm{Pi}}-y_m\right)}^2}{w^2}\end{array}\right)\end{array}$

(125) Thus, the correct local angle of inclination is taken into consideration at each location of the ablation profile, and the fluence is reduced by cos . At the same time, the shape of the beam profile is taken into consideration. This predicted ablation profile is used after further steps for generating a further preliminary ablation program. More precisely, the following steps are carried out.

(126) In step S38 a loop counter j is first set to the value 1 for the first iteration step.

(127) In step S40, a preliminary ablation program is then generated in the first iteration loop j=1, from the desired ablation profile D.sub.Soll,1, and in the subsequent iteration loops j=2, 3, . . . from modified desired ablation profiles D.sub.Soll,j from the preceding iteration loop by means of a simple generating method in the current iteration loop j, wherein the shape of the beam profile and the inclination of the surface are not taken into consideration simultaneously when generating the ablation program. For this purpose, the above-mentioned method of DE 19727573 C1 can be used, for example.

(128) In step S42, an actual ablation profile D.sub.Ij is predicted, using the blow-off model, on the basis of the preliminary ablation program, as previously described. For this purpose, a grid of points of support in the x-y plane is used, which is considerably finer than the extent of the laser beam, thus allowing the shape of the beam to be resolved. For each pulse, an ablation depth is calculated at each corresponding point of support according to the blow-off model and according to the fluence actually effective there, i.e. the fluence of the laser beam corrected by the surface inclination, and if components of several pulses are incident on the same location, these ablation depths are summed up.

(129) In the next step S44, values of a partial modification function K.sub.j=D.sub.Ij/D.sub.Soll,1 are then determined at the points of support, which function indicates how much the predicted actual ablation profile D.sub.Ij deviates from the predetermined desired ablation profile D.sub.Soll,1. The values are then temporarily stored. The function given by the values is computationally smoothened again by the use of a low-pass filter after the first computation.

(130) In the next step S46 it is then verified whether the values of the modification function determined in step S44 and, thus, the ratio of the ablation profiles for all of the locations or points of support (x,y) under consideration, deviates from 1 by less than a predetermined error e, e. g. 0.05.

(131) If such a deviation occurs, a further iteration loop is passed through by first forming a new, modified desired ablation profile D.sub.Soll,j+1=D.sub.Soll,j/K.sub.j in a step S48. Said profile then provides the basis for generating a new preliminary ablation program in the next step S40.

(132) In step S50, the loop counter j is increased by 1. Following this, the next iteration loop is started in step S40.

(133) On the other hand, if the partial modification function K.sub.j equals 1 sufficiently, step S46 of the method is followed by step S52, in which the value of a modification function K(x,y)=K.sub.1(x,y) . . . K.sub.j(x,y) is determined for each location or for each point (x,y) from all values determined for the partial modification functions K.sub.j in the iteration loops.

(134) In step S54, a pre-compensated desired ablation profile D.sub.Soll,mod is determined from the predetermined desired ablation profile D.sub.Soll,1 in that the desired ablation depth defined by D.sub.Soll,1 for all points (x,y) is divided by the corresponding value of the modification function K for the location.

(135) As in step S26 of the first exemplary embodiment, the ablation program to be used is generated in step S26 on the basis of the pre-compensated desired ablation profile D.sub.Soll,mod. By said pre-compensation, i.e. modification using the modification function K, the predetermined desired ablation profile is modified such that any errors that would occur when using the simple generating method to generate an ablation program directly from the predetermined desired ablation profile by not considering the influences of the beam profile shape and of the surface inclination are compensated for already prior to said generation, i.e. the generated ablation program intended for use leads to the desired ablation profile to be achieved with very good approximation in the case of an ablation according to the program.

(136) In step S58, suitable control commands can then be output to the laser 7 and/or the deflecting device 8 according to the ablation program in order to ablate the desired ablation profile to be achieved from the surface.

(137) FIG. 11a shows a horizontal curve of intersection through the center of the spherical ablation profile over a region having a diameter of 8 mm to be ablated from a sphere having a radius of 7.86 mm. The solid line indicates the predicted actual profile D.sub.E that would result in case of a surface not inclined relative to the laser beam 3, whereas the broken line indicates the actual ablation profile D.sub.I,1 taking the inclination and the beam profile shape into consideration. FIG. 11b shows the difference between these two curves.

(138) FIG. 5 compares the result of the method according to the last exemplary embodiment with the results of the two previously described methods. In this case, the modification after a complete cycle of a first iteration is indicated by black squares. As can be seen, the deviations from the modification factor that does not take the shape of the beam profile into consideration are again considerably greater at a greater distance from the center of the calotte, i.e. at greater angles of inclination, so that this method is expected to yield improved ablation results.

(139) It has been shown that a sufficiently good pre-compensation of errors is already achieved if only one iteration is carried out, i. e. by setting j=1. Therefore, a modified embodiment omits steps S38 and S46 to S52, with step S44 directly determining the values of the modification function K which then corresponds to the first partial modification function. The ablation program is then generated particularly quickly. The data processing device 5 and, thus, the generating device is programmed accordingly to carry out the method.

(140) In the preceding exemplary embodiments, it was assumed that the data of inclination and the data for the desired ablation profile are given in the same coordinate system. However, this is not necessary. Rather, a modified method allows to input data at the start which indicate the relative position of the origins of the corresponding coordinate systems, so that after the corresponding data have been read in, the inclination data and the desired ablation profile can be easily transferred to a common coordinate system by simple shifting.

(141) In a further embodiment of the method according to the invention, use is made of a beam having a particularly favorable beam profile shape at the surface to be ablated. The beam profile is shaped such that all regions of the two-dimensional fluence distribution or energy distribution are located above the threshold value F.sub.thr for ablation. An example of such beam profile is shown in FIG. 12. The beam profile results from a Gaussian profile in which the edges have been cut off according to the aforementioned criterion.

(142) If such beam profile is used, the entire beam cross-section has an ablating effect at the surface so that a thermal load on adjacent regions can be minimized.

(143) The shape of such beam profile can be caused by a stop which cuts off the desired parts of an output beam profile. In such case, the part of the laser energy incident on the stop is not used, which is a disadvantage in energy-critical applications. However, the effect of the reduced thermal load on the surface to be processed is present here as well.

(144) For shaping the beam profile, use is preferably made of a micro-optical element which generates the desired intensity distribution directly in a diffractive or refractive manner. WO 99/20429 A1 and DE 19623749 A1 describe corresponding micro-optical elements for generating a Gaussian intensity distribution. For example, a static refractive microlens array can be used wherein a predetermined angle distribution of the radiation is defined by the size distribution of the microlenses. The microoptical element re-arranges the incident laser beam with great efficiency such that the resulting re-shaped beam profile corresponds to the desired intensity distribution, but without losing any energy or power components.

(145) This allows not only to reduce the thermal load on the surface to be processed, but also considerable energy savings, which is particularly advantageous in applications where the radiation energy of the laser is critical. In case of a cut-off (truncated) Gaussian profile whose peak fluence amounts to four times the threshold fluence and whose fluence components below the threshold fluence are discarded, approximately 25% of energy can be saved as compared to the complete Gaussian profile with the same ablation effect. This also means that thermal heating of the surface to be processed, or of tissue in the case of treatment of an eye, is not translated to heat, which may be a great advantage especially in the field of corneal surgery. Such beam profiles can be employed in any spot scanning ablation method and, in particular, also in the ablation methods according to the invention.

(146) A laser surgical instrument 101 for treatment of a patient's eye 2 according to a first preferred embodiment of the invention's second aspect is applied in a similar manner as the instrument 1 for carrying out a refractive correction in the eye and insofar replaces the instrument 1 of FIG. 1. Accordingly, as in FIG. 1, the instrument 101 emits a pulsed laser beam 3 onto the eye 1 of the patient whose head is fixed by a head support 4 that is securely connected to the instrument 101.

(147) FIG. 13 schematically shows in more detail the design of the instrument which is a laser ablation device. The instrument comprises a data processing device 105 with an integrated control unit 106, a laser 107 controlled by the control unit 106 and a deflecting device 108, which is also controlled by the control unit and by means of which the pulsed laser beam 103 emitted by the laser 107 can be directed and focused on target locations on the cornea of the eye 2 according to a given ablation program.

(148) The instrument further comprises a device 109 for acquiring water content measurement data, from which the water content of a region to be treated in the eye 2, more specifically the cornea, can be determined, and a device 110 for determining a desired ablation profile. Both devices are coupled to the data processing device 105. The data processing device 105, the control unit 106, the device 109 for acquiring water content measurement data and the device 110 for determining the desired ablation profile form a device for generating an ablation program according to a first preferred embodiment of the invention's second aspect.

(149) The data processing device 105 with integrated control unit 106 serves to generate an ablation program by the use of data from which the water content in the material of the region to be treated can be determined, data relating to the properties of the laser beam 3, and data relating to the desired ablation profile to be ablated. For this purpose, the data processing device 105 comprises a processor and a memory for storing data in which, in particular, a computer program including program code is also stored, which code, when the program is executed on the processor, allows to generate the ablation program and to generate control signals using the integrated control unit 106 to control the laser 107 and/or the deflecting device 108, which signals are output to the laser 107 or to the deflecting device 108 so as to carry out the actual ablation. The memory and the processor are partially illustrated in the block diagram by the block generate ablation program.

(150) For this purpose, the data processing device 105 comprises interfaces for data input, namely an interface 111 for input of water content measurement data from the device 109 for acquiring water content measurement data, an interface 112 for manual input of the desired ablation profile, and an interface 112 for reading in data relating to the desired ablation profile from the device 110 for determining the desired ablation profile. Moreover, an interface 113 for input of beam parameters for the laser beam 3 is provided. In this exemplary embodiment, the interface 113 is provided as an interface for manual input.

(151) In physical terms, the interfaces for manual input may be one single interface to which, although not shown in the Figures, a keyboard and a screen, on which an input prompt can be displayed when corresponding data are to be read in, are connected. The interfaces further comprise corresponding modules of the computer program for reading in data from the keyboard.

(152) The other interfaces 111 and 112 are conventional interfaces for data streams which, in addition to corresponding electronic modules, also comprise software modules.

(153) The control unit 106 is integrated into the data processing device 105 and further comprises interfaces, not shown in the Figures, for output of control signals to control the laser 107 and the deflecting device 108. Such control units are basically known and therefore need not be explained in more detail.

(154) The laser 107 is connected to the control unit 106 and emits a pulsed laser beam with predetermined pulse energies as a function of the ablation program. For example, an excimer laser having a wavelength in the wavelength range of 193 nm can be used.

(155) The deflecting device 108 is also connected to the control unit 106 via a data link and, in accordance with control signals from the control unit 106, directs the pulsed laser beam 3 emitted by the laser 107 onto predetermined target locations on the surface of the eye 2 according to the ablation program to be executed. For this purpose, the deflecting device 108 comprises a focusing device 114 for focusing the laser beam along its direction of propagation and for deflection transverse to the laser beam via two mirrors 115, which are rotatable or tiltable about two mutually orthogonal axes and are arranged in the beam path following the focusing device 114.

(156) Both the laser 107 and the deflecting device 108 may be conventional, known devices of a laser surgical instrument.

(157) In order to indicate the water content and the desired ablation profile, two parallel Cartesian coordinate systems are used whose x-y planes coincide. If possible, the z axis is aligned parallel to the optical axis of the eye with good approximation. In the example, it is assumed for the sake of easier illustration that the origins of the coordinate systems coincide so that the coordinate systems coincide and are not distinguished any more in the following. If the coordinate origins do not coincide, the relative position can be manually input after reading in the data relating to the water content or the desired ablation profile, following which the data can be transferred to a common coordinate system. A corresponding interface for input of the relative position may then be provided. FIG. 3 shows the position of the coordinate system for a spherical body or a sphere having a surface 2 as a simplified model of the eye 2. The z-axes are defined during alignment of the eye 2 relative to the instrument 101, for which purpose a fixating light not shown in the Figures may be used, for example.

(158) In the example, the device 109 for acquiring water content measurement data comprises a device for confocal Raman spectroscopy of the cornea of the eye as described, for example, in Assessment of Transient Changes in Corneal Hydration Using Confocal Raman Spectroscopy, Brian T. Fischer et al., Cornea 22 (4), pages 363-370, 2003. The region of the cornea of the eye 2 intended for processing is scanned with a suitable laser beam that is focused both in depth and also laterally of the laser beam. Raman radiation coming from the eye 2 is then confocally detected so that the intensity of the Raman radiation can be detected for different locations in the volume to be ablated. The data indicating intensity, i. e. the water content measurement data, are input for each measured location to the data processing device 105 via the interface 111. The computer program in the data processing device 105 comprises program code by means of which the data can be converted to data describing the water content at the respective location.

(159) In the present example, the device 110 for determining the desired ablation profile comprises a wavefront analyzer of the Hartmann-Shack type as well as, where appropriate, devices for determining the refractive power of the eye 2, by which analyzer or devices, respectively, a desired ablation profile D.sub.Soll for the region to be treated in the eye 2 can be determined according to known methods. In doing so, the desired ablation profile is determined such that correction of imaging errors in the eye 2 can be achieved as far as possible by the ablation to be carried out. An example of the desired ablation profile is evident from FIG. 3. It is given by the distances, in the direction of z, between the initial surface, the calotte 2, and a desired surface 2 indicated by a broken line, as a function of the location in the x-y plane. A region to be ablated is formed by the volume between the surface 2 before ablation and the desired surface 2, the latter being formed by the desired ablation profile.

(160) In order to determine the desired ablation profile, the device 110 may comprise a suitable processor which evaluates data relating to the refractive power of the eye 2 and the wavefront data in order to determine the desired ablation profile again, in the present example, in the form of the desired ablation depths for locations of support in the form of points of a point grid in the x-y plane of the corresponding coordinate system which coincides with the x-y plane of the coordinate system for indicating the ablation profile. As far as the coordinate origins are not identical, the position of one of the reference points or coordinate origins in the respective other coordinate system can be given so that the data can be transformed by simple shifting into an identical coordinate system during a later process stage. This may turn out to be favorable if the center of the desired ablation profile, i.e. a point relative to which the desired ablation profile is approximately symmetrical, deviates from the center of the surface of the eye 2, i.e. from a point relative to which the surface of the eye is approximately symmetrical. Such a method for generating a desired ablation profile is described, for example, in WO 01/08075 A1, the respective contents of which are hereby incorporated in the description by reference. The method for generating an ablation program according to the first exemplary embodiment of the invention's second aspect is based on the following considerations.

(161) In order to ablate the desired ablation profile D.sub.Soll from the eye 2, laser pulses having a predetermined pulse energy are emitted onto predetermined target locations according to a generated ablation program, each of said laser pulses individually leading to a removal of material. The depth of removal by a pulse can be described by various models. In the present example, the so-called blow-off model is used, as described, for example, in Refraktive Chirurgie der Hornhaut, Theo Seiler (Ed.), 1st edition, ENKE Georg Thieme Verlag, Stuttgart/New York, 2000 (ISBN 3-13-118071-4), Chapter 6.1, p. 150, or in R. Srinivasan: Ablation of Polymers and Biological Tissue by Ultraviolet Lasers, Science vol. 234, p. 559-565, 31 Oct. 1986.

(162) Following this, material is removed to a depth D.sub.p at a location having the coordinates (x,y), by laser radiation impinging at this location and having an effective fluence F(x,y), i. e. energy per surface area, according to the following formula:

(163) $\begin{array}{cc}{D}_P\left(x,y\right)=\{\begin{array}{cc}.Math.\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}},& \mathrm{if}F\left(x,y\right)>F_{\mathrm{thr}}\\ 0,& \mathrm{otherwise}\end{array}.& \left(1\right)\end{array}$

(164) In this formula, designates a material-dependent ablation coefficient and F.sub.thr designates a likewise material-dependent ablation threshold fluence value, below which value laser radiation no longer results in material removal from the eye 2.

(165) In the simple generating method for an ablation program used below, it is assumed that the desired ablation profile can be split into single-pulse ablation volumes which form upon impingement of a pulse. In this case, generating the ablation program includes determining the target locations (x,y) onto which the pulses of a predetermined pulse energy have to be directed.

(166) In generating an ablation program, it is assumed that a laser pulse removes a single-pulse or spot ablation volume V.sub.pulse which is obtained as an integral of the ablation depth D.sub.p over the entire pulse area:

(167) $\begin{array}{cc}{V}_{\mathrm{pulse}}=\underset{\mathrm{Spot}}{}\mathrm{Dp}\left(x,y\right)\mathrm{dxdy}=\underset{\mathrm{Spot}}{}\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}.& \left(2\right)\end{array}$

(168) The integral extends over the area designated as Spot, in which D.sub.p>0 holds.

(169) In the following, the surface area in which D.sub.P>0 applies is assumed to be constant and to have an area d.sup.2, in which case V.sub.pulse=d.sup.2D.sub.P.

(170) In simple generating methods in which the water content of the material to be ablated and, in particular, variations in the water content of the material to be ablated are not taken into consideration, the ablation depth D.sub.P,0 of a pulse without taking the water content into consideration results as follows:

(171) $\begin{array}{cc}{D}_{P,0}={}_0.Math.\ln \left(\frac{F_0}{F_{\mathrm{thr}}}\right).& \left(3\right)\end{array}$

(172) .sub.0 designates an empirically determined ablation rate which is assumed to be constant. In this case, the empirical determination can be effected by testing ablation on a larger number of different eyes, i.e. on their cornea.

(173) When using a simple method to generate an ablation program, it is assumed that each pulse emitted onto the same location ablates the same single-pulse volume or the same single-pulse ablation depth D.sub.P,0, said volumes adding up. This is illustrated in FIG. 14a. This Figure schematically shows, by way of example, a desired ablation profile along a diameter through the eye 2, approximately along the x-axis. The single-pulse ablation volumes V.sub.S are successively ablated and result in the desired ablation depth, with each single-pulse ablation volume V.sub.S corresponding to a single-pulse ablation depth D.sub.P,0. If the coordinates of the target locations considered are designated by (x.sub.i, y.sub.i), i=1, . . . , G, G being a natural number, the number N.sub.0 of pulses to be emitted to a target location (x.sub.i,y.sub.i) is obtained as:

(174) 0$\begin{array}{cc}{N}_{i,0}=\frac{D_{\mathrm{ideal}}\left(x_i,y_i\right)}{D_{P,0}}.& \left(4\right)\end{array}$

(175) However, the ablation rate actually depends on the water content H in the material to be ablated. In the example, a model based on the blow-off model yields the single-pulse ablation depth D.sub.P,W of a pulsetaking the water content of the material into considerationas

(176) $\begin{array}{cc}{D}_{P,W}=\left(H\right).Math.\ln \left(\frac{F_0}{F_{\mathrm{thr}}}\right),& \left(5\right)\end{array}$
wherein the ablation rate (H) depending on the water content H may be assumed, for example, to be proportional to the water content H with a proportionality constant k:
(H)=k.Math.H(6)

(177) The value of the proportionality constant k is selected such that, for a mean water content H.sub.m of the cornea determined in the above surveys, k.Math.H.sub.m=.sub.0 holds true.

(178) However, the water content of the material or tissue to be ablated from the cornea may, in fact, change as a function of ambient conditions, such as air humidity, air stream above the eye, air temperature, and of the ablation conditions, e. g. the ablation rate, the number of pulses being emitted onto a target location (x.sub.i,y.sub.i) or already emitted in its vicinity, and the fluence of the pulses. In this exemplary embodiment, the following model for the water content H of material to be ablated above a target location (x.sub.i,y.sub.i), onto which n(x.sub.i,y.sub.i) pulses have already been emitted, will be assumed:
H(x.sub.i,y.sub.i;n(x.sub.i,y.sub.i))=a(x.sub.i,y.sub.i)+b.Math.log(n(x.sub.i,y.sub.i)).(7)

(179) The parameter a describes the water content at the target location (x.sub.i,y.sub.i) prior to the start of ablation. This water content may depend, for instance, on the type of treatment, e. g. photo-refractive keratectomy, LASIK, LASIK with photo-disruptive generation of a foldable cornea cover, or LASEK, the properties of the individual eye and the ambient conditions of ablation. The parameter b, which is assumed to be constant in this exemplary embodiment, describes the change in water content effected by emitting pulses onto the location (x.sub.i,y.sub.i). In particular, the parameter b may be obtained empirically by survey experiments.

(180) When N.sub.W,i pulses are emitted onto the same target location (x.sub.i,y.sub.i), the single-pulse ablation depths, which are now no longer constant due to their dependence on the water content H, add up to a total depth. The number of N.sub.W,i can be determined such that particularly the desired ablation depth D.sub.Soll(x.sub.i,y.sub.i) is achieved at the location (x.sub.i,y.sub.i):

(181) $\begin{array}{cc}{D}_{\mathrm{ideal}}\left(x_i,y_i\right)=\underset{1}{\overset{N_{w,i}}{.Math.}}{D}_{P,W}{}_0^{N_{W,i}}{D}_{P,W}\left(u\right)\mathrm{du}.& \left(8\right)\end{array}$

(182) As shown in equation (8), when a large number of pulses are emitted onto the same location, the sum may be replaced with an integral by approximation so as to enable approximate, but quicker computation of the sum.

(183) Since the ablation rate increases as the number of pulses increases, the ablation depth actually achieved by emitting N.sub.W,i pulses onto the location (x.sub.i,y.sub.i) changes with each pulse and differs from N.sub.i,0-times the single-pulse ablation depth D.sub.P,0 in the simple model in which the water content is not considered.

(184) Therefore, in order to enable the use of a simple, e. g. known, method which does not take the water content into consideration, for generating the ablation program, a modification function M is defined which serves to compute a pre-compensated or modified desired ablation profile D.sub.Mod from the predetermined desired ablation profile D.sub.Soll:

(185) $\begin{array}{cc}{D}_{\mathrm{Mod}}\left(x_i,y_i\right)=M\left(D_{\mathrm{Soll}}\left(x_i,y_i\right)\right)D_{\mathrm{Soll}}\left(x_i,y_i\right)\mathrm{with}& \left(9\right)\\ M\left(D_{\mathrm{Soll}}\left(x_i,y_i\right)\right)=\frac{N_{W,i}}{N_{i,0}}=\frac{N_{W,i}{D}_{P,0}}{D_{\mathrm{Soll}}\left(x_i,y_i\right)}.& \left(10\right)\end{array}$

(186) As expressed in formulae (9) and (10), the modification function depends on the desired ablation depth D.sub.Soll(x.sub.i,y.sub.i), on the parameter a and, thus, on the water content of the material prior to ablation, as well as on the parameter b and, thus, on the change in water content by said ablation. Moreover, there is a dependence on the model for D.sub.P,0 used in the simple generating method.

(187) In particular, the ablation effect of a single pulse may increase as the number of pulses emitted onto the same location increases, so that for a great desired ablation depth which requires a larger number of single pulses at the same location, fewer single pulses are to be used than would be expected according to the formula (4).

(188) Now, if a simpler generating method is used to generate the ablation program from the pre-compensated desired ablation profile D.sub.Mod, the factor M contained in D.sub.Mod compensates precisely those errors which result from not taking the water content into consideration in formula (3), so that when effecting ablation by an ablation program generated from the pre-compensated desired ablation profile by means of the simple generating method, the predetermined desired ablation profile is achieved with good approximation.

(189) In order to determine the locations onto which the laser pulses are to be emitted, various known simple generating methods can be used, e. g. the methods described in DE 19727573 C1 and EP 1060710 A2. In DE 19727573 C1, ablation is effected in layers, i. e. locations of impingement are determined in a layer-wise fashion for pulses, with the desired profile then resulting from superposition of these layers. According to the method in EP 1060710 A2, the spot distance is varied in a quasi-continuous manner in order to achieve the desired ablation depth.

(190) In order to determine the ablation program, the method steps schematically shown in the flow scheme of FIG. 15 are carried out, for which purpose the computer program executed in the data processing device comprises suitable program code.

(191) First of all, the desired ablation profile D.sub.Soll is determined in step S110 using the means 110 for determining the desired ablation profile. This determination is activated here by a user. In another exemplary embodiment, the data processing device 105 outputs a corresponding control signal to the means 110 for determining the desired ablation profile, via a control interface not shown in the Figures, to automatically start said determination. For said determination, imaging errors are determined from wavefront data. Known methods are used to calculate at which locations on surface of the eye material is to be ablated to what depth. In the present example, the desired ablation profile D.sub.Soll is given by specifying the desired ablation depth as a function of the location on a grid in the x-y plane.

(192) In step S112, these data are then read, via the interface 112, into the data processing device 105 and stored there in its memory.

(193) In step S114, i. e. after steps S110 and S112 in the example, but also prior to these steps in other embodiments, intensities of Raman radiation are detected in a space-resolved manner by means of confocal Raman spectroscopy as water content measurement data, and data indicating these intensities are transmitted to the data processing device 105 together with corresponding position coordinates. This determination is activated here by a user. In another exemplary embodiment, the interface 110 is also provided as a control interface, and the data processing device 105 outputs a corresponding control signal to the device 109 via said control interface 110 so as to automatically start said determination.

(194) In step S116, the water content measurement data are read in via the interface 110 and temporarily stored in the memory of the data processing device 105. Water content values a are then determined from the intensities for all locations for which water content measurement data have been acquired and these values are stored in a form assigned to the locations.

(195) In step S118, beam parameters of the laser beam 3 to be used are then read in via the interface 113. In this exemplary embodiment, the diameter of the beam profile of the laser beam 3 is input for this purpose. The shape of the laser beam 3 is assumed to be constant over the beam cross-section and fixed and is taken into consideration in the form of corresponding formulae in the program being executed on the processor of the data processing device 105. Further, the pulse energy to be used per surface area, or the fluence F.sub.0 to be used, is input and stored.

(196) In step S120, a pre-compensated desired ablation profile D.sub.Mod is then determined from the predetermined desired ablation profile D.sub.Soll. For this purpose, the following two partial steps are carried out for all supporting locations at which the desired ablation profile is given: The values for the proportionality constant k and the threshold value for the fluence F.sub.thr are stored in the program code. If (x.sub.i,y.sub.i) designates the location, the equation given by formula (8) is resolved for the pulse number N.sub.W,i using the desired ablation depth D.sub.Soll(x.sub.i,y.sub.i) given by the desired ablation profile and using the values a(x.sub.i,y.sub.i), b, k and F.sub.0/F.sub.thr, for example by means of a Newton method for resolving non-linear equations. If a is not present at the location (x.sub.i,y.sub.i), a corresponding value can be obtained by interpolation. The value M(D.sub.Soll(x.sub.i,y.sub.i)) of the modification function M is then determined according to formula (10).

(197) In the subsequent partial step, in order to obtain a pre-compensated desired ablation depth D.sub.Mod at the location (x.sub.i,y.sub.i), the predetermined desired ablation depth D.sub.Soll(x.sub.i,y.sub.i) is multiplied by the value M(D.sub.Soll(x.sub.i,y.sub.i)) of the modification function and stored as D.sub.Mod(x.sub.i,y.sub.i), assigned to the location (x.sub.i,y.sub.i).

(198) The pre-compensated desired ablation profile D.sub.Mod is then given by the locations (x.sub.i,y.sub.i) and the pre-compensated desired ablation depths D.sub.Mod(x.sub.i,y.sub.i) assigned to them.

(199) In the next step S122 an ablation program is generated on the basis of the modified desired ablation profile D.sub.Mod, the input fluence and the other beam parameter as well as formula (3), for which purpose a method is used that, therefore, does not take the water content of the tissue or the change in the water content of the tissue into consideration during ablation. For example, the method described in DE 19727573 C1 can be used. The ablation program thus generated comprises a sequence of target locations in the x-y plane, i.e. corresponding coordinates onto which the laser pulses have to be directed with the pulse energy determined by the fluence read in, in order to achieve the desired ablation profile to be achieved. The ablation program is stored in the data processing device 105. This step completes the actual generation of the ablation program.

(200) In the next step S126, control commands are output to the laser 107 and to the deflecting device 108 by the data processing device 105 with the integrated control unit 106 in order to remove material from the eye 2 according to the generated ablation program.

(201) The ablation method is suitable for both photorefractive keratectomy and LASIK. Since these methods involve the removal of material in different layers of the eye, the use of different desired ablation profiles may be accordingly required in some cases.

(202) A second exemplary embodiment of a method for forming and emitting control signals for ablation according to an ablation program generated by said method is shown in FIGS. 16 and 17. A corresponding signal-forming device differs from the signal-forming device according to the first exemplary embodiment of the invention's second aspect only in the programming of the data processing device 105 and, in that respect, only in that the latter can perform the method described below for forming control signals or for generating an ablation program, respectively. The method differs from the first method substantially in that the fluence of pulses of the pulsed laser beam is now changed according to the water content. Moreover, this is done during emission of the control signals and, thus, during ablation.

(203) The method for forming and emitting control signals, which encompasses the method for generating an ablation program, comprises several steps which correspond to those of the signal-forming or generating method shown in FIG. 15. Therefore, these will be referred to below by the same reference numerals and will not be described in detail again.

(204) Thus, in steps S110 and S112 or S114 and S116, respectively, data relating to the desired ablation profile or to the water content of the corneal tissue, respectively, are determined and stored prior to ablation.

(205) In step S118, which follows then, a beam cross-section and a pre-set initial fluence value F.sub.0 are input.

(206) In the next step S126, a preliminary ablation program is then generated on the basis of the read-in desired ablation profile, the input pre-set fluence and the beam parameter, the simple generating method used for this purpose not taking the water content of the cornea or variations in said water content into consideration. In particular, the above-mentioned method of DE 19727573 C1 can be used. The preliminary ablation program which in turn comprises a series of coordinates for locations on the surface of the eye 2, onto which the pulses are to be directed, is then stored.

(207) Following this, modified fluence values are determined for the corresponding pulses in step S128 from the series of target locations according to the preliminary ablation program, which values are assigned to the target locations while generating the ablation program to be used. After forming a modified fluence value, a control signal is formed directly and output to the laser 107 or the deflecting device 108, respectively. By suitable control of a high-voltage supply of the excimer laser 107 and, thus, of the charging of capacitors in which the energy for one pulse is respectively stored, according to the ablation program and by simultaneously controlling the deflecting device 108, ablation can be effected using a laser pulse with a position- or coordinate-dependent pulse energy and, thus, fluence.

(208) This involves successive processing of the series of target locations. The corresponding partial steps for determining a modified fluence of a pulse to be emitted onto a target location (x.sub.j, y.sub.j) are shown in FIG. 17.

(209) In partial step S128a, the first target location is initially read out in the first pass; in subsequent passes, the next target location is read out according to the preliminary ablation program. The latter location has the coordinates (x.sub.j, y.sub.j) with j being the ordinal number of the target location in the series.

(210) In partial step S128b an acquisition of suitable data for the target location (x.sub.j, y.sub.j) is then effected by controlling the device 109 for acquisition of water content measurement data through the data processing device 105 via a control interface which is not shown.

(211) The data are input via the interface 111 and are converted in partial step S128c to a water content H(x.sub.j, y.sub.j) at the target location (x.sub.j, y.sub.j) by means of the data processing device.

(212) In partial step S128d, a modified fluence value is then determined for the pulse to be emitted onto the target location (x.sub.j, y.sub.j), which value is assigned to said target location. The modified fluence value together with the target location (x.sub.j, y.sub.j) forms an element of the ablation program to be eventually used.

(213) The fluence value is then modified such that ablation with the modified fluence achieves the single-pulse ablation depths that had been assumed as the ablation depth for a single pulse without taking the water content into consideration while generating the preliminary ablation program. Thus, based on above equations (1), (3) and (4), the equation D.sub.P,W(F)=D.sub.P,0 (F.sub.0) has to be resolved with respect to F, wherein D.sub.P,W depends on the water content H at the target location via (H). Using the models according to equations (1), (3) and (4), the following equation is obtained for the modified fluence:

(214) $\begin{array}{cc}\frac{F}{F_{\mathrm{thr}}}=\frac{F_0}{F_{\mathrm{thr}}}{e}^{-\frac{{}_0}{\left(H\right)}}.& \left(11\right)\end{array}$

(215) This calculation can be carried out very quickly, so that partial step S28d can be passed through very quickly.

(216) Suitable control signals for the laser 107 and the deflecting device 108 can be formed and output to the laser 107, i.e. the high-voltage supply of the laser 107, or to the deflecting device 108. The method is then resumed in partial step S128a for the next element of the preliminary ablation program. Like steps S110 to S122 above, steps S110 to S128d without the formation and emission of the control signals provide an exemplary embodiment of a generating method of the invention according to the invention's second aspect.

(217) Thus, apart from the model for the ablation depth, no assumptions need to be made with respect to the water content of the cornea. In particular, unforeseen changes in water content can be fully taken into consideration during formation and emission of the control signals and, thus, during ablation.

(218) A third embodiment which represents a variant of the above-described exemplary embodiment is shown in FIG. 18. The instrument schematically shown here differs from the instrument of the previous exemplary embodiment in that a modulator 116 which, in the present example, is a liquid crystal element whose transmission can be controlled by the control unit 106 is arranged in the beam path of the laser beam 3 between the laser 107 and the deflecting device 108. Moreover, the control unit 106, compared to the control unit 106, comprises an output for control of the modulator 116, and the computer program executed in the data processing device 105 is provided to control fluence, not by controlling the laser 107, but by changing the transmission of the modulator 116.

(219) The fluence of the laser 107 is then set such that the maximum fluence required for ablation according to the ablation program is achieved by maximum transmission of the modulator 116. During ablation in accordance with the ablation program, the modulator 116 is controlled such that the pulses impinging on the surface have the desired energy or fluence.

(220) In another variant, a beam-shaping device may be provided instead of the modulator 116, which device responds to signals from the control unit by modifying the beam cross-section and, thus, fluence.

(221) In other embodiments of the above-described method, the ablation threshold value F.sub.thr for fluence may also depend on the water content H.

(222) In a fifth preferred embodiment of a control signal-forming method of the invention according to the invention's second aspect, equation (9) is used directly in generating the ablation program, by giving a pattern of target locations and resolving equation (9) for each target location as a function of the number of pulses N.sub.W,i to be emitted.

(223) In a sixth preferred embodiment of a signal-forming method according to the second aspect of the invention, the inclination of the surface of the cornea with respect to the laser beam 3 or to the z-direction is also taken into consideration, in addition to the water content, as an approximation for the direction of the laser beam 3 in combination with the actual shape of the beam profile. Insofar, this exemplary embodiment and modifications thereof, in particular, also represents an exemplary embodiment of the invention's first aspect. In the example, the laser beam 3 emitted by the laser 107 has a beam profile with a Gaussian shape.

(224) Whereas conventional methods assume the effective fluence F(x,y) to be constant over the area of the pulse or of the spot, respectively, two further influences are now taken into consideration in addition to the influence of the water content. On the one hand, it is taken into consideration that the inclination of the surface to be processed reduces the effective fluence according to said inclination relative to the fluence of the laser beam 3. If the surface to be processed is described by a height function (x,y), which indicates the height of the surface above the x-y plane, the angle of inclination of the surface can be determined relative to the z axis and, thus, in approximation to the laser beam 3 incident on the surface 2, according to the formula
(x,y)=arctan(|grad (x,y)|).(12)
Thus, the fluence F(x,y) effective during ablation on the surface is obtained as
F(x,y)=F.sub.P(x,y).Math.cos (x,y)(13)

(225) wherein F.sub.P(x,y) designates the fluence for vertical incidence of the laser beam 3 on the surface, i. e. at an angle =0. Therefore, F.sub.P corresponds to the fluence or the beam profile of the laser beam 3.

(226) The second effect taken into consideration is that the effective fluence varies in accordance with the intensity or energy profile of the pulses in a plane orthogonal to the direction of the laser beam 3 and that it may thereby, in particular, also be below the threshold value F.sub.thr.

(227) Thus, the actual single-pulse ablation volume results from the following formula:

(228) $\begin{array}{cc}\begin{array}{c}{V}_{\mathrm{pulse}}=\underset{\mathrm{Spot}}{}{D}_P\left(x,y\right)\mathrm{dxdy}\\ =\underset{\mathrm{Spot}}{}\ln \frac{F\left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}\\ =\underset{\mathrm{Spot}}{}\ln \frac{F_P\left(x,y\right)\cos \left(x,y\right)}{F_{\mathrm{thr}}}\mathrm{dxdy}.\end{array}& \left(14\right)\end{array}$

(229) Therefore, the single-pulse ablation volume non-linearly depends on the angle of inclination of the surface and on the fluence profile F.sub.P(x,y).

(230) In the case of known single-pulse ablation volumes, an ablation program can be generated by known, simple generating methods, as described, for example, in DE 19727573 C1 or EP 1060710 A2, according to which ablation program the mean ablation depth D.sub.M results, in a uniformly or slowly varying manner, for a distance d of laser beam pulses directed onto the surface according to

(231) $\begin{array}{cc}{D}_M=c\frac{V_{\mathrm{pulse}}}{d^2}& \left(15\right)\end{array}$

(232) In this case, c is a proportionality factor resulting from the pattern of the points of incidence of the laser beam's pulses. For example, an approximately square pattern yields c=1, whereas an approximately hexagonal pattern yields c=2/{square root over (3)}.

(233) In the following, it will be assumed that the ablation profile as well as the water content slowly changes in space with respect to the site of the distance d, or that the inclination slowly changes with respect to the diameter of the laser beam 3 on the surface. In order to describe the spatial dependence of these spatially slowly changeable parameters, coordinates u and v will be used in the following, which are given in a u-v coordinate system that coincides with the x-y coordinate system. Thus, the single-pulse ablation volume and, likewise, the mean depth D.sub.M resulting from the pulses placed next to each other are to be understood as a function of u and v.

(234) The effective ablation depth then results from

(235) $\begin{array}{cc}{D}_{M,\mathrm{Ist}}\left(u,v\right)=c\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(u,v\right)\cos \left(u,v\right)}{d^2}& \left(16\right)\end{array}$

(236) Now, it is only required to substitute D.sub.M,Ist for D.sub.P,W in formula (9), wherein V.sub.pulse,Ist is determined using formula (14) in which D.sub.P is replaced by D.sub.P,W.

(237) Thus, for all of the different surface regions to be ablated one respective value of the beam-dependent and/or inclination-dependent modification function as a function of at least the beam profile shape and/or the surface inclination in the respective region, and a value of the water content-dependent modification function is determined, as well as determining the pre-compensated desired ablation profile by the use of the desired ablation profile and of the values of the modification functions, in particular the product of the modification functions.

(238) In order to determine the locations onto which the laser pulses are to be emitted, various known methods can be used, e. g. the methods already mentioned above and described in DE 19727573 C1 and EP 1060710 A2. In DE 19727573 C1, ablation is effected in layers, i. e. locations of impingement or target locations are determined in a layer-wise fashion for pulses, with the desired profile then resulting from superposition of these layers. According to the method in EP 1060710 A2, the spot distance is varied in a quasi-continuous manner in order to achieve the desired ablation depth.

(239) The calculation of the modification function is explained using as an example the ablation of a spherical surface by a laser beam having a Gauss-shaped beam profile (cf. FIG. 3).

(240) The beam profile or fluence is described by the formula

(241) $\begin{array}{cc}{F}_P\left(r\right)=F_0{e}^{-\frac{r^2}{w^2}}& \left(17\right)\end{array}$

(242) wherein F.sub.0 is the peak fluence value, r is the radial distance from the center of the beam profile, and w is the distance after the profile has dropped to 1/e relative to the value at the center.

(243) For the actual ablation profile of a laser pulse impinging orthogonally on a planar surface, this results in:

(244) $\begin{array}{cc}{D}_{\mathrm{Ist}}\left(r\right)=\ln \frac{F_0}{F_{\mathrm{thr}}}-\frac{r^2}{w^2},& \left(18\right)\end{array}$
so that the single-pulse ablation volume for this pulse is calculated as

(245) 0$\begin{array}{cc}{V}_{\mathrm{pulse},E}=\frac{}{2}\left(H\right){w^2\left[\ln \frac{F_0}{F_{\mathrm{thr}}}\right]}^2.& \left(19\right)\end{array}$

(246) As the mean depth of the desired profile for a square pattern of the points of impingement of the pulses, or spot pattern, having an edge length a, a mean depth of ablation according to

(247) $\begin{array}{cc}{D}_E\left(r\right)=\frac{V_{s,E}}{d^2}=\frac{}{2}{\frac{w^2}{d^2}\left[\ln \frac{F_0}{F_{\mathrm{thr}}}\right]}^2& \left(20\right)\end{array}$
can be expected. If D.sub.E were assumed to be equal to D.sub.Soll, d could be determined as a function of the location.

(248) However, the spherical surface is actually inclined, except at the center, with respect to the laser beam 3 that is assumed to impinge parallel to the z-axis with sufficiently good approximation. As is evident from FIG. 3, the angle of inclination can be calculated in the following manner as a function of the distance of a location on the surface of the eye 2:

(249) $\begin{array}{cc}\left(\right)=\arcsin \left(\frac{-}{R}\right)=\arctan \left(\frac{-}{\sqrt{R^2-{}^2}}\right).& \left(21\right)\end{array}$

(250) The inclination of the surface at the location then has the effect that both the spot distance in the direction of inclination and the spot width w in the direction of inclination are increased by the factor 1/cos(()). Therefore, the ratio w/d in the equation for D does not change with the inclination. However, the fluence does change in this equation. Further, now depends on the water content H, for example according to the equations (6) and (7). Therefore, the following result is obtained for the depth profile to be expected on the spherical surface:

(251) $\begin{array}{cc}\begin{array}{c}{D}_{M,\mathrm{Ist}}\left(\right)=c\frac{V_{\mathrm{pulse},\mathrm{Ist}}\left(\right)\cos \left(\right)}{d^2}\\ =c\frac{}{2}\left(H\right){\frac{w^2}{d^2}\left[\ln \frac{F_0.Math.\cos \left(\right)}{F_{\mathrm{thr}}}\right]}^2\end{array}& \left(22\right)\end{array}$

(252) This result may be systematically obtained also by assuming cos() and =(H) to be constant over the spot area in the formula for the single-pulse ablation volume.

(253) FIG. 19 shows a laser ablation device comprising a generating device or a control signal-forming device according to a further preferred embodiment of the invention, which differs from the laser ablation device of the first exemplary embodiment according to the invention's second aspect in that the data processing device 105 is replaced by a data processing device 105 and that a device 117 for acquiring the surface topography of the eye 2 is provided, which device is connected, via a data link, to an interface of the data processing device 105 for the input of surface topography data to the data processing device 105. Control commands for acquisition of surface topography data can also be output to the device 117 via this interface. The other components are unchanged so that the same reference numerals are used for them, and the statements made in the exemplary embodiment with respect to these components accordingly apply here as well.

(254) In the example, the device 117 for acquisition of the surface topography of the eye may comprise an optical coherence tomography.

(255) The data processing device 105 differs from the data processing device 105 only by the interface 118 and the computer program used to program the data processing device 105 or its processor. The computer program comprises program code so that, during execution of the computer program in the data processing device 105, the method described below is carried out.

(256) In order to determine the ablation program and to form and emit the control signal, the method steps schematically shown in the flow scheme of FIG. 20 are carried out, among which the steps designated by the same reference numerals as in FIG. 15 are carried out as in the first exemplary embodiment of the invention's second aspect, and the explanations pertaining to those steps also apply here accordingly.

(257) Thus, in steps S110 and S112 or S114 and S116, respectively, data relating to the desired ablation profile or to the water content of the corneal tissue, respectively, are determined and stored prior to ablation.

(258) In step S118, which follows then, a beam radius w and a pre-set fluence value F.sub.0 are input, the latter being the peak value of fluence over the Gaussian beam profile of the laser 107. The shape of the beam profile is taken into consideration through the formulae used.

(259) Then, in the next step S130, controlled by the data processing device 105, the surface topography of the region to be treated is determined by means of the device 117 for acquiring the surface topography data. For example, the corresponding data may comprise heights of the surface with respect to the x-y plane, said heights being detected above a grid of points in the x-y plane.

(260) In step S132, these data are then read into the data processing device 105 via the interface 118 for the surface topography data. Surface inclinations are then determined from the height data by numerical determinations of gradients, as well as determining the above-indicated formula for the angle of inclination. The corresponding data are then stored in the memory of the data processing device 105.

(261) The next steps then correspond to the steps of the method in the first exemplary embodiment, although N.sub.W,i is now determined using formula (22) for D.sub.P,W in equation (8).

(262) In this way, a pre-compensation takes place both with respect to the water content as well as the inclination of the surface and the shape of the beam profile such that their influences, which are neglected when generating the ablation program by a simple generating method, are taken into consideration in advance in a compensating or pre-compensating manner, and the actual ablation profile comes very close to the desired ablation profile.

(263) The ablation method is suitable for both photorefractive keratectomy and LASIK. Since these methods involve the removal of material in different layers of the eye, the use of different desired ablation profiles may be accordingly required in some cases.

(264) The coherence tomograph of the device 117 may further be used to determine the thickness of the cornea before and/or during ablation, i.e. to effect a pachymetric measurement. In particular, this allows prevention of the residual thickness of the cornea being below a predetermined minimum value.

(265) In another exemplary embodiment, a temperature measuring device, e.g. an infrared camera whose optical axis is inclined at a sharp angle to the direction of the laser beam 3, may be used instead of the device 109 for carrying out confocal Raman spectroscopy. Said camera acquires data from which the temperature of the cornea and, thereby, its water content can be determined in a spatially resolved manner.

(266) As an alternative, an optical coherence tomograph allowing the acquisition of data which allow the refractive index of the corneal tissue to be calculated can be used instead of the device 109 for carrying out confocal Raman spectroscopy. The water content can then be determined in turn from the refractive index data by means of the data processing device 105. The coherence tomograph may be present in addition to a coherence tomograph for determining the surface topography, if the latter tomograph is provided. However, it is also possible to use the same coherence tomograph for both functions. The coherence tomograph may further be used to determine the thickness of the cornea before and/or during ablation, i.e. to effect a pachymetric measurement. In particular, this allows prevention of the residual thickness of the cornea being below a predetermined minimum value.

(267) Further, a device for determining the air humidity in the region of the cornea may be provided, which device transmits humidity data via a data link to the data processing device 105, where it can be included in the model for the ablation depth.

(268) In further exemplary embodiments, the repetition frequency at which the pulses are emitted onto the material or the cornea, respectively, can also be modified as a function of the water content.