TREATMENT APPARATUS FOR SURGICAL CORRECTION OF DEFECTIVE EYESIGHT, METHOD OF GENERATING CONTROL DATA THEREFORE, AND METHOD FOR SURGICAL CORRECTION OF DEFECTIVE EYESIGHT

Abstract

A treatment method and apparatus for surgical correction of defective-eyesight in an eye of a patient, wherein a laser device is controlled by a control device, said laser device separating corneal tissue by irradiation of laser radiation to isolate a volume located within a cornea, wherein the control device controls the laser device to focus the laser radiation, by providing target points located within the cornea, into the cornea, wherein the control device, when providing the target points, allows for focus position errors which lead to a deviation between the predetermined position and the actual position of the target points when focusing the laser radiation, by pre-offsets depending on the positions of the respective target points to compensate for said focus position errors.

Claims

1. (canceled)

2. A method for laser based surgical correction of an eyesight defect in a patient's eye, wherein the eye comprises a cornea having an anterior corneal surface and corneal tissue located below the anterior corneal surface, the method comprising: creating a three dimensional (3D) cut within the cornea, the 3D cut confining a volume located within the cornea, isolating the volume within the cornea, and making the volume removable from the interior of the cornea, wherein the volume is sized such that removal of the volume from the corneal tissue below the anterior corneal surface changes a shape of the anterior corneal surface such that the eyesight defect is corrected or reduced, wherein creating the 3D cut comprises emitting pulsed laser radiation from a laser device and focusing the pulsed laser radiation to a three-dimensional pattern of target points in the cornea, wherein the target points are located in a 3D surface defining the 3D cut, wherein creating the 3D cut further comprises forming the 3D surface with two surface parts including an anterior surface part and a posterior surface part, wherein one of these two surface parts is located at a constant distance to from an anterior surface of the cornea and the other surface part does not have a constant distance from the anterior corneal surface.

3. The method as claimed in claim 2, wherein creating the 3D cut further comprises forming the 3D surface with a lateral side cut part connecting the volume with the anterior corneal surface, and wherein the method further comprises removing the volume from the corneal tissue through the lateral side cut part.

4. The method as claimed in claim 2, further comprising determining measurement data on parameters of the eye and defective-eyesight data on the eyesight defect, defining the volume on basis of the measurement data and the defective-eyesight data, determining the 3D surface to confine the defined volume within the cornea, determining the three-dimensional pattern of target points located in the 3D surface, and generating a control data set which relates to the three-dimensional pattern for control of a laser device providing the pulsed laser radiation.

5. The method as claimed in claim 4, further comprising providing a planning device remote from the laser device and performing the steps of claim 3 in the planning device and transmitting the control data set to a treatment apparatus comprising the laser device, and blocking operation of the laser device until a valid control data set is present at the laser device.

6. The method as claimed in claim 4, wherein the defective-eyesight data comprise a refractive power B.sub.BR of spectacles suitable for correction of eyesight defect, as well as a distance, at which the spectacles having the refractive power B.sub.BR should be located anterior of a vertex of the anterior corneal surface to achieve the correction of eyesight defect by use of the spectacles.

7. The method as claimed in claim 4, wherein the volume is defined such that the anterior corneal surface assumes a radius of curvature R.sub.cv* after removal of the volume, said radius satisfying the following equation:
R.sub.cv*=1/((1/R.sub.cv)+B.sub.BR/((n.sub.c−1) (1−d.sub.HS.Math.B.sub.BR)))+F, wherein R.sub.cv is the radius of curvature of the anterior corneal surface prior to removal of the volume, n.sub.c is a refractive index of the corneal tissue and F is a correction factor, wherein optionally F=(1−1/n.sub.c).Math.(d.sub.c*−d.sub.c) holds true, wherein d.sub.c or d.sub.c* is a thickness of the cornea before or after removal of the volume, respectively, and radius R.sub.cv* is computed in an iterative manner by deriving a quantity (d.sub.c*−d.sub.c) from the difference (R.sub.cv*−R.sub.cv) during each iteration step, and applying a corresponding result for a change in thickness to calculate R.sub.cv* in a next iteration step.

8. The method as claimed in claim 2, wherein focusing the pulsed laser radiation to the three-dimensional pattern of target points with the laser device comprises shifting a focus of the pulsed laser radiation along a path over the pattern of target points, with pulses of the pulsed laser radiation being emitted into the cornea at points located on the path and also between the target points.

9. The method as claimed in claim 2, wherein focusing the pulsed laser radiation to the three-dimensional pattern of target points with the laser device comprises shifting a focus of the pulsed laser radiation along a path over the pattern of target points, wherein in the posterior surface part the path is an elliptical spiral.

10. The method as claimed in claim 2, further comprising pressing a spherical contact surface of a contact glass onto the anterior corneal surface prior to creating the 3D cut, wherein focusing the pulsed laser radiation to the three-dimensional pattern of target points laser device comprises shifting a focus of the pulsed laser radiation along a path over the pattern of target points, wherein in the anterior surface part the path is a spherical spiral.

11. A method for preparing control data for laser based surgical correction of an eyesight defect in a patient's eye, wherein the eye comprises a cornea having an anterior corneal surface and corneal tissue located below the anterior corneal surface, the method comprising: determining measurement data on parameters of the eye and defective-eyesight data on the eyesight defect, defining a volume on a basis of the measurement data and the defective-eyesight data, wherein the volume is sized such that removal of the volume from the corneal tissue below the anterior corneal surface changes a shape of the anterior corneal surface such that the eyesight defect is corrected or reduced, determining a three dimensional (3D) surface to confine the defined volume within the cornea, wherein the 3D surface comprises two surface parts including an anterior surface part and a posterior surface part and wherein one of these two surface parts is located at a constant distance from an anterior surface of the cornea and the other surface part does not have a constant distance from the anterior corneal surface, determining a three-dimensional pattern of target points located in the 3D surface, wherein the 3D surface defines a 3D cut within the cornea, the 3D cut confining the volume located within the cornea, isolating the volume within the cornea, and making the volume removable from the interior of the cornea, and generating a control data set which relates to the three-dimensional pattern for control of a laser device providing the pulsed laser radiation to create the 3D cut.

12. The method as claimed in claim 11, wherein determining the 3D surface comprises forming the 3D surface with a lateral side cut part connecting the volume with the anterior corneal surface that facilitates removing the volume from the corneal tissue through the lateral side cut part.

13. The method as claimed in claim 11, further comprising providing a planning station remote from the laser device and performing the steps of claim 10 in the planning station and transmitting the control data set to a treatment apparatus comprising the laser device, and blocking operation of the laser device until a valid control data set is present at the laser device.

14. The method as claimed in claim 11, wherein the defective-eyesight data comprise a refractive power B.sub.BR of spectacles suitable for correction of eyesight defect, as well as a distance, at which the spectacles having the refractive power B.sub.BR should be located anterior of a vertex of the anterior corneal surface to achieve the correction of eyesight defect by use of the spectacles.

15. The method as claimed in claim 14, wherein the volume is defined such that the anterior corneal surface assumes a radius of curvature R.sub.cv* after removal of the volume, said radius satisfying the following equation:
R.sub.cv*=1/((1/R.sub.cv)+B.sub.BR/((n.sub.c−1) (1−d.sub.HS.Math.B.sub.BR)))+F, wherein R.sub.cv is the radius of curvature of the anterior corneal surface prior to removal of the volume, n.sub.c is the refractive index of the corneal tissue and F is a correction factor, wherein optionally F=(1−1/n.sub.c).Math.(d.sub.c*−d.sub.c) holds true, wherein d.sub.c or d.sub.c* is a thickness of the cornea before or after removal of the volume, respectively, and radius R.sub.cv* is computed in an iterative manner by deriving a quantity (d.sub.c*−d.sub.c) from the difference (R.sub.cv*−R.sub.cv) during each iteration step, and applying a corresponding result for a change in thickness to calculate R.sub.cv* in a next iteration step.

16. The method as claimed in claim 11, wherein the control dataset prescribes a path connecting the three-dimensional pattern of target points, wherein at least one of the following applies: in the posterior surface part the path is an elliptical spiral and in the anterior surface part the path is a spherical spiral.

17. A planning device for generating control data for a treatment apparatus for surgical correction of an eyesight defect in an eye of a patient, the eye comprising a cornea, wherein: the planning device is configured to generate the control data for the treatment apparatus comprising a laser device, which separates corneal tissue by irradiation of pulsed laser radiation, said laser radiation being focused on target points arranged in a pattern within the cornea; the planning device comprises an interface for receiving measurement data on parameters of the eye, and defective-eyesight data on the eyesight defect; and the planning device is further configured: to define a volume on basis of the measurement data and the defective-eyesight data, wherein the volume is sized such that removal of the volume from the corneal tissue below the anterior corneal surface changes a shape of the anterior corneal surface such that the eyesight defect is corrected or reduced; to determine a 3D surface to confine the defined volume within the cornea, wherein the 3D surface comprises two surface parts including an anterior surface part and a posterior surface part and wherein one of these two surface parts is located at a constant distance from an anterior surface of the cornea and the other surface part does not have a constant distance from the anterior corneal surface; to determine a three-dimensional pattern of target points located in the 3D surface, wherein the 3D surface defines a 3D cut within the cornea, the 3D cut confining the volume located within the cornea, isolating the volume within the cornea, and making the volume removable from the interior of the cornea; and to generate a control data set which relates to the three-dimensional pattern for control of a laser device providing the pulsed laser radiation to create the 3D cut.

18. The planning device as claimed in claim 17, wherein the planning device is further configured to determine the 3D surface to comprises a lateral side cut part connecting the volume with the anterior corneal surface that facilitates removing the volume from the corneal tissue through the lateral side cut part.

19. The planning device as claimed in claim 17, wherein the planning station is remote from the laser device and is further configured to transmit the control data set to a treatment apparatus comprising the laser device, wherein operation of the laser device is blocked until a valid control data set is present at the laser device.

20. The planning device as claimed in claim 17, wherein the control dataset prescribes a path connecting the three-dimensional pattern of target points, wherein at least one of the following applies: in the posterior surface part the path is an elliptical spiral and in the anterior surface part the path is a spherical spiral.

21. A treatment apparatus for laser based surgical correction of an eyesight defect in a patient's eye, wherein the eye comprises a cornea having an anterior corneal surface and corneal tissue located below the anterior corneal surface, wherein the apparatus comprises: a laser device for emitting pulsed laser radiation; a focusing device for focusing the pulsed laser radiation to a focus within the cornea; a scanning device for directing the focus to target points within the cornea; and a control device configured to control the scanning device for creating a 3D cut within the cornea, the 3D cut confining a volume located within the cornea, isolating the volume within the cornea, and making the volume removable from the interior of the cornea, wherein the volume is sized such that removal of the volume from the corneal tissue below the anterior corneal surface changes a shape of the anterior corneal surface such that the eyesight defect is corrected or reduced; wherein the control device is further configured to control the scanning device for shifting the focus of the pulsed laser radiation over a three-dimensional pattern of the target points in the cornea, wherein the target points are located in a 3D surface defining the 3D cut and wherein the 3D surface comprises two surface parts including an anterior surface part and a posterior surface part, wherein one of these two surface parts is located at a constant distance from an anterior surface of the cornea and the other surface part does not have a constant distance from the anterior corneal surface.

22. The treatment apparatus as claimed in claim 21, wherein at least one of the following applies: the 3D surface comprises a lateral side cut part connecting the volume with the anterior corneal surface that facilitates removing the volume from the corneal tissue through the lateral side cut part; in the posterior surface part the path is an elliptical spiral; in the anterior surface part the path is a spherical spiral; and the laser device emits pulses of the pulsed laser radiation into the cornea also to points located on the path between the target points.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0112] 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:

[0113] FIG. 1 shows a schematic view of a treatment apparatus or instrument for correction of defective eyesight,

[0114] FIG. 1a shows a schematic view with respect to the construction of the treatment instrument of FIG. 1,

[0115] FIG. 2 shows a schematic diagram relating to the introduction of pulsed laser radiation into the eye for the correction of defective eyesight by the treatment apparatus of FIG. 1,

[0116] FIG. 3 shows a further schematic representation of the treatment apparatus of FIG. 1,

[0117] FIG. 4 shows in partial Figures (a), (b) and (c) schematic sectional views illustrating the need for correction at the human eye in case of defective eyesight,

[0118] FIG. 5 shows a schematic sectional view through the eye's cornea and also represents a volume to be removed for correction of defective eyesight,

[0119] FIG. 6 shows a section through the eye's cornea after removal of the volume of FIG. 5,

[0120] FIG. 7 shows a sectional view similar to that of FIG. 5;

[0121] FIG. 8 shows a schematic sectional view through the eye's cornea illustrating the removal of said volume,

[0122] FIG. 9 shows a top view of a spiral-shaped path curve used to isolate the volume of FIGS. 5, 7 and 8,

[0123] FIG. 10 shows an enlarged view of the path curve of FIG. 9,

[0124] FIG. 11 shows an alternative path curve for the correction even of cylindrical eyesight defects,

[0125] FIG. 12 shows a schematic representation explaining the function of the contact glass in the treatment apparatus of FIG. 1,

[0126] FIGS. 13 to 15 show schematic representations with respect to the effects of the contact glass by deformation of the eye's cornea,

[0127] FIGS. 16 and 17 show schematic views relating to the approximation of the volume of the surface posteriorly limiting the volume in the case of corrections even of cylindrical eyesight defects,

[0128] FIG. 18 shows a schematic view of a correction of the image field curvature as applied when determining control data for the treatment apparatus of FIG. 1, and

[0129] FIG. 19 shows a schematic representation of the sequence of preparing and carrying out a correction of defective eyesight.

[0130] 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 OF THE DRAWINGS

[0131] FIG. 1 shows a treatment apparatus 1 for an ophthalmic method similar to those described in EP 1159986 A1 and U.S. Pat. No. 5,549,632. The treatment apparatus 1 causes a correction of defective eyesight at an eye 3 of a patient 4 by means of treatment laser radiation 2. The eyesight defect may include hyperopia, myopia, presbyopia, astigmatism, mixed astigmatism (astigmatism in which hyperopia is present in one direction and myopia is present in a direction perpendicular to the former), aspherical aberrations and higher-order aberrations. In the described embodiments, the treatment laser radiation 2 is applied as a pulsed laser beam focused into the eye 3. The pulse duration is e.g. in the femtosecond range, and the laser radiation 2 acts by means of non-linear optical effects in the cornea. For example, the laser beam comprises short laser pulses of 50 to 800 fs (preferably 100-400 fs) with a pulse repetition rate of between 10 and 500 kHz. In the described exemplary embodiment, the components of the apparatus 1 are controlled by an integrated control unit, which alternatively may be provided separately, of course.

[0132] Prior to using the treatment apparatus, the eyesight defect of the eye 3 is measured by one or more measuring devices.

[0133] FIG. 1a schematically shows the treatment apparatus 1. In this variant, it comprises at least two devices or modules. A laser device L emits the laser beam 2 onto the eye 3. Operation of the laser device L is fully automatic, i.e., upon a corresponding start signal, the laser device L starts deflection of the laser beam 2 and, thus, generates cut surfaces, which are composed in a manner yet to be described and which isolate a volume in the eye's cornea. The laser device L receives, via control lines not designated in detail, the control data required for operation in advance from a planning device P in the form of a control dataset. Transmission is done prior to operation of the laser device L. Of course, communication may also be wireless. As an alternative to a direct communication, it is also possible to arrange the planning device P spatially separate from the laser device L and to provide a corresponding data transmission channel.

[0134] The control dataset is preferably transmitted to the treatment apparatus 1 and, further, operation of the laser device L is preferably blocked until a valid control dataset is present at the laser device L. A valid control dataset may be any control dataset which is basically suitable for use with the laser device L of the treatment apparatus 1. In addition, validity may also be made subject to the condition that further tests are passed, e.g., whether additional details stored in the control data set in respect of the treatment apparatus 1, e.g., an apparatus serial number, or in respect of the patient, e.g., a patient identification number, correspond to other details, e.g., read out at the treatment apparatus or input separately, as soon as the patient is in the correct position for operation of the laser device L.

[0135] The planning unit P generates the control dataset which is provided to the laser unit L to perform the surgical operation, said dataset consisting of measurement data and defective-eyesight data determined for the eye to be treated. They are supplied to the planning unit P via an interface S and, in the exemplary embodiment shown, originate from a measuring device M, which previously measured the eye of the patient 4. Of course, the measuring unit M may transmit the corresponding measurement data and defective-eyesight data to the planning device P in any suitable way.

[0136] Data transmissions may be effected by means of memory chips (e.g. by USB or memory stick), magnetic storage devices (e.g. diskettes), by radio connections (e.g. WLAN, UMTS, Bluetooth) or by wire connections (e.g. USB, Firewire, RS232, CAN Bus, ethernet, etc.). Of course, the same applies with respect to the data transmissions between the planning device P and the laser device L.

[0137] A direct connection of the measuring device M to the treatment apparatus 1, with respect to the data transmissions which may be used in one variant, has the advantage that the use of false measurement and defective-eyesight data is avoided with maximum certainty. This applies, in particular, if the transfer of the patient from the measuring device M or the measuring devices, respectively, to the laser device L is effected by means of a positioning device (not shown in the FIG.) cooperating with the measuring device M or with the laser device L, respectively, such that the respective devices recognize whether the patient 4 is in the respective position for measurement or for introduction of laser radiation 2, respectively. Transferring the patient 4 from the measuring device M to the laser device L may simultaneously allow also the transmission of measurement or defective-eyesight data to the treatment apparatus 1.

[0138] Preferably, suitable means ensure that the planning device P always generates the control dataset assigned to the patient 4 and any erroneous use of a wrong control dataset for a patient 4 is virtually impossible.

[0139] The efforts of the laser beam 2 are schematically indicated in FIG. 2. The treatment laser beam 2 is focused into the cornea 5 of the eye 6 by optics not designated in detail. This forms in the cornea 5 a focus which covers a spot 6 and in which the power density of the laser radiation is so high that, in combination with the pulse duration, a non-linear effect occurs in the eye. For example, each pulse of the pulsed laser radiation 2 may generate an optical breakthrough in the eye's cornea 5, which breakthrough in turn initiates a plasma bubble schematically indicated in FIG. 2. Thereby, tissue is separated in the cornea 5 by means of this laser pulse. When a plasma bubble forms, the separation of tissue layers covers an area greater than the spot 6 which the focus of the laser radiation 2 covers, although the conditions for generating the breakthrough are achieved only in the focus. For each laser pulse to generate an optical breakthrough, the energy density, i.e., the fluence of the laser radiation, has to be above a certain pulse duration-dependent threshold value. This interrelationship is known to the person skilled in the art, for example, from DE 69500997 T2.

[0140] Alternatively, a tissue-separating effect by the pulsed laser radiation can also be produced by emitting several laser radiation pulses within one region, with the spots 6 of several laser radiation pulses overlapping. In this case, several laser radiation pulses will then cooperate to achieve a tissue-separating effect.

[0141] However, the type of tissue separation which the treatment apparatus 1 employs is of no further relevance to the following description. It is only essential that pulsed treatment laser radiation 2 is used for this purpose. For example, use can be made of a treatment apparatus 1 as described in WO 2004/032810 A2. Further, it is essential that a multiplicity of laser pulse foci form a cut surface in the tissue, the shape of said cut surface depending on the pattern in which the laser pulse foci are/will be arranged in the tissue. The pattern determines target points for the focus position at which one or more laser pulse(s) is (are) emitted and defines the shape and location of the cut surface. The pattern of the target points is of relevance to the methods and apparatuses explained hereinafter and will be described in more detail.

[0142] Now, in order to carry out correction of defective eyesight, material is removed by means of the pulsed laser radiation from an area within the cornea 5 by separating tissue layers which isolate the material and, thus, enable material removal. The material removal causes a change in volume in the cornea, which leads to a change in the optical imaging effect of the cornea 5. This change is dimensioned precisely such that the eyesight defect previously determined is/will be corrected thereby, if possible. In order to isolate the volume to be removed, the focus of the laser radiation 2 is directed at target points in the cornea 5, usually in a region located below the epithelium and Bowman's membrane as well as above Decemet's membrane and the endothelium. For this purpose, the treatment apparatus 1 comprises a mechanism for adjusting the position of the focus of the laser radiation 2 within the cornea 5. This is schematically shown in FIG. 3.

[0143] In FIG. 3, elements of the treatment apparatus 1 are indicated only insofar as they are required for understanding the focus adjustment. As already mentioned, the laser radiation 2 is collimated in a focus 7 in the cornea 5, and the position of the focus 7 in the cornea is shifted such that energy from laser radiation pulses is focused into the tissue of the cornea 5 at several locations to produce the cut surface. The laser radiation 2 is provided as pulsed radiation by a laser 8. An xy-scanner 9, which is realized in one variant by two galvanometer mirrors with substantially orthogonal deflections, two-dimensionally deflects the laser beam coming from the laser 8, so that a deflected laser beam 10 is present posterior to the xy-scanner 9. Thus, the xy-scanner 9 causes shifting of the position of the focus 7 in a direction substantially perpendicular to the main direction of incidence of the laser radiation 2 into the cornea 5. For adjustment of the depth position, a z scanner 11 is provided in addition to the xy-scanner 9, which z scanner 11 is provided, for example, as an adjustable telescope. The z scanner 11 ensures that the z position of the location of the focus 7, i.e. its position on the optical axis of incidence, is changed. The z scanner 11 may be arranged preceding or following the xy-scanner 9. Thus, the coordinates referred to hereinafter as x, y, z relate to the shift of the location of the focus 7.

[0144] The assignment of the individual coordinates to the spatial directions is not essential for the operative principle of the treatment apparatus 1, but for the sake of simpler description z hereinafter always refers to the coordinate along the optical axis of incidence of the laser radiation 2, and x as well as y designate two mutually orthogonal coordinates in a plane perpendicular to the direction of incidence of the laser beam. The person skilled in the art is certainly aware that a three-dimensional description of the position of the focus 7 in the cornea 5 can also be effected by other coordinate systems; in particular the coordinate system is not required to be orthogonal. Thus, it is not mandatory that the xy-scanner 9 deflects at mutually orthogonal axes; rather, any scanner may be used which is able to shift the focus 7 in a plane in which the axis of incidence of the optical radiation is not located. Thus, non-orthogonal coordinate systems are also possible.

[0145] Further, non-straight coordinate systems can also be used to describe or control the location of the focus 7, as will also be explained hereinafter. Examples of such coordinate systems are spherical coordinates as well as cylindrical coordinates.

[0146] In order to control the location of the focus 7, the xy-scanner 9 as well as the z scanner 11, which jointly realize a specific example of a three-dimensional focus shifting device, are controlled by a control device 12 via lines not designated in detail. The same applies to the laser 8. The control device 3 provides a suitably synchronous operation of the laser 8 as well as of the three-dimensional focus shifting device, realized by way of example using the xy-scanner 9 as well as the z scanner 11, so that the location of the focus 7 in the cornea 5 is shifted such that, in the end, a material of a determined volume is isolated, with the subsequent removal of the volume causing a desired correction of defective eyesight.

[0147] The control device 12 operates on the basis of predetermined control data which prescribe the target points for the focus adjustment. The control data are usually grouped to form a control dataset. According to one embodiment, said control dataset prescribes the coordinates of the target points as a pattern, with the sequence of the target points in the control dataset determining the serial arrangement of the focus locations and, thus, ultimately determining a path curve (also briefly referred to herein as path). In one embodiment, the control dataset contains the target points as more specific control values for the focus location shifting mechanism, e.g., for the xy-scanner 9 and the z scanner 11. For preparation of the ophthalmic method, i.e. before the actual surgical method can be executed, the target points and preferably also their sequence in the pattern are determined. Prior planning of the surgical operation has to be effected by determining the control data for the treatment apparatus 1 whose application will then result in optimal correction of defective eyesight for the patient 4.

[0148] First, the volume to be isolated and to be subsequently removed from the cornea 5 has to be determined. As already described with reference to FIG. 1a, this requires determination of the need for correction. FIG. 4 shows, in partial FIGS. a), b) and c), the optical conditions at the eye 3 of the patient 4. Without a correction of defective eyesight, the situation shown in partial FIG. a) may be present. Together with the eyelens 13, the cornea 5 causes focusing of an object, located at infinity, in a focus F which is located on the z axis behind the retina 14. The imaging effect results, on the one hand, from the eyelens 13, which is relaxed in the non-accommodated eye, as well as, on the other hand, from the eye's cornea 5, which is defined substantially by an anterior corneal surface 15 as well as by a posterior corneal surface 16 and, due to its curvature, also has an imaging effect. The optical effect of the cornea 5 is due to the radius of curvature R.sub.CV of the anterior corneal surface. Partial FIG. a) shows the eyesight defect only by way of example; in reality, the above-mentioned, more complex eyesight defects may be present. However, the following description also applies to them, but some of the indicated equations may then include an additional angular dependence, even if it is not explicitly mentioned.

[0149] For correction of defective eyesight, an ancillary lens 17 in the form of spectacles is placed in front of the eye 3, in a known manner and as shown in partial FIG. b) of FIG. 4, at a distance this from the vertex of the cornea 5. The lens 17 of the spectacles is adapted such, in terms of its refractive power B.sub.BR, that it shifts the far point of the entire system, i.e., of the eye with the spectacles, from the focal point F to the focal point F*, which is located on the retina 14.

[0150] With respect to the nomenclature used in this description, it should be noted that quantities having an asterisk added are quantities obtained after a correction. Accordingly, the focus F* is that focus which is present after the optical correction achieved by the lens 17 of the spectacles in the partial FIG. b) of FIG. 4.

[0151] Based on the justified assumption that a change in the thickness of the cornea 5 mainly modifies the radius of curvature of the anterior corneal surface 5 facing the air, but not the radius of curvature of the posterior corneal surface 16 facing the interior of the eye, the radius of curvature R.sub.CV of the anterior corneal surface 15 is modified by removing the volume. The cornea 5 reduced by said volume has an imaging effect modified such that the then corrected focus F* is located on the retina 14. After correction, a modified anterior corneal surface 15* is present, and a correction of defective eyesight is achieved even without spectacles.

[0152] Therefore, to define the pattern of the target points, the curvature of the modified anterior corneal surface 15* to be achieved is determined. The starting point for this is the refractive power of the lens 17 of the spectacles, because the determination of the corresponding parameters is a standard method in ophthalmology. The following formula holds true for the refractive power B.sub.BR(φ) of the lens 17 of the spectacles:

B.sub.BR(φ)=Sph+Cyl.Math.sin.sup.2(φ−θ).   (1)

[0153] In this equation, Sph and Cyl designate the correction values to be realized for spherical or astigmatic errors of refraction and θ refers to the position of the cylindrical axis of the cylindrical (astigmatic) eyesight defect, as they are known to the person skilled in the art of optometry. Finally, the parameter φ relates to a cylindrical coordinate system of the eye and is counted counter-clockwise, looking towards the eye, as is common in ophthalmology. Now, using the value B.sub.BR, the curvature of the modified anterior corneal surface 15* is set as follows:

R.sub.CV*=1/((1/R.sub.CV)+B.sub.BR/((n.sub.c−1) (1−d.sub.HS.Math.B.sub.BR)))+F,   (2)

[0154] In equation (2), n.sub.c refers to the refractive power of the material of the cornea. The corresponding value is usually 1.376; d.sub.HS refers to the distance at which spectacles with a refractive power B.sub.BR have to be located relative to the corneal vertex, so as to produce the desired correction of defective eyesight by means of spectacles; B.sub.BR refers to the aforementioned refractive power of the spectacles according to equation (1). The indication of the refractive power B.sub.BR may also cover eyesight defects which go beyond a normal spherical or cylindrical correction. B.sub.BR (and, thus, automatically also R.sub.CV*) will then show additional coordinate dependencies.

[0155] The factor F expresses the optical effect of the change in the thickness of the cornea and can be regarded as a constant factor as a first approximation. For a high-precision correction, the factor can be calculated according to the following equation:

F=(1−1/n.sub.c).Math.(d.sub.C*−d.sub.C),   (3)

wherein d.sub.C and d.sub.C*, respectively, are the corneal thickness respectively before and after the optical correction. For a precise determination, R.sub.CV* is calculated in an iterative manner by deducting the quantity (d.sub.C*−d.sub.C) from the difference (R.sub.CV*−R.sub.CV) during the i.sup.th calculation and applying the result of the change in thickness obtained in the (i+1).sup.th calculation. This may be continued until an abortion criterion is fulfilled, for example when the difference of the result for the change in thickness is below a suitably defined limit in two consecutive iteration steps. This limit may be defined, for example, by a constant difference which corresponds to a precision of the refractive correction that is adequate for the treatment.

[0156] If the change in thickness of the eye's cornea is neglected, which is, in fact, allowable for a simplified method, F in equation (2) may also be set to zero, i.e., neglected and omitted, for a simplified calculation. Surprisingly, this yields the following simple equation for the refractive power of the modified cornea 5*:

B.sub.CV*=B.sub.CV+B.sub.BR(1−B.sub.BR.Math.d.sub.HS)

[0157] For the person skilled in the art, the equation B.sub.CV*=(n−1)/R.sub.CV* will easily yield the radius R.sub.CV* of the anterior corneal surface 15* which has to be present after the modification so as to obtain the desired correction of defective eyesight as follows: R.sub.CV*=1/((1/R.sub.CV)+B.sub.BR/((n.sub.c−1) (1−d.sub.HS.Math.B.sub.BR))).

[0158] For the volume, whose removal causes the above change in the curvature of the anterior corneal surface 15, the boundary surface limiting the volume is then determined. In doing so, it is preferably to be taken into consideration that the diameter of the region to be corrected and, thus, the diameter of the volume to be removed should extend, if possible, over the size of the pupil in the dark-adapted eye.

[0159] In a first variant, a free form surface is defined by numeric methods known to the person skilled in the art, which surface circumscribes a volume whose removal causes the change in curvature. For this purpose, the change in thickness along the z axis required for the desired modification of the curvature is determined. This will yield the volume as a function of r and φ (in cylindrical coordinates), which will in turn yield the boundary surface thereof.

[0160] A simple analytic calculation is provided by the following, second variant, wherein the boundary surface of the volume is built up by two partial surfaces, namely an anterior partial surface located towards the corneal surface 15 and a posterior partial surface located opposite. The corresponding relationships are shown in FIGS. 5, 6 and 7. The volume 18 is limited towards the anterior corneal surface 15 by an anterior cut surface 19 which is at a constant distance d.sub.F below the anterior corneal surface 15. With analogy to laser keratomes, this anterior cut surface 19 is also referred to as a flap surface 19, because there, in combination with a cut opening the eye's cornea 5 towards the edge, it serves to enable lifting of a lamella in the form of a “flap” from the underlying cornea 5. This type of removal of the previously isolated volume 18 is also possible here, of course.

[0161] The anterior cut surface 19 has a curvature which is located at d.sub.F below the anterior corneal surface 15. If said curvature is spherical, a radius of curvature can be given for the flap surface 19 which is the radius of anterior corneal surface curvature R.sub.CV less d.sub.F. As will be described later for preferred variants, when generating the cut surface 19, a contact glass can ensure that the anterior corneal surface 15 is spherical at the time the cut surface is generated, so that the pattern of the target points will cause a spherical cut surface. Although the relaxation of the eye 3 after removal of the contact glass may then lead to a non-spherical cut surface 19, the latter will still be at a constant distance from the anterior corneal surface 15 or 15*, respectively. This will be explained later.

[0162] The volume 18 to be removed from the cornea 5 is posteriorly limited by a posterior cut surface 20 which, in principle, cannot not be at a constant distance from the anterior corneal surface 15. Therefore, the posterior cut surface 20 will be provided such that the volume 18 is present in the form of a lenticle. For this reason, the posterior cut surface 20 is also referred to as lenticle surface 20. By way of example, said surface is also indicated in FIG. 5 as a spherical surface having a radius of curvature R.sub.L, the center of said curvature, of course, not coinciding with the center of curvature of the anterior corneal surface, which is also spherical in FIG. 5.

[0163] FIG. 6 shows the conditions after removal of the volume 18. Now, the radius of the modified anterior corneal surface 15* is R.sub.CV* and can be calculated, for example, according to the previously described equations. The thickness d.sub.L of the removed volume 18 is decisive for the change in radius, as made clear by FIG. 7. This figure shows as further quantities the height hr of the spherical cap defined by the anterior cut surface 19, the height h.sub.L of the spherical cap defined by the posterior cut surface 20 as well as the thickness d.sub.L of the volume 18 to be removed.

[0164] Due to the constant distance between the anterior corneal surface and the anterior cut surface 19, the posterior cut surface determines the curvature of the anterior corneal surface 15* after removal of the volume 18. Thus, for example, in the case of a correction of defective eyesight taking cylindrical parameters into consideration, the posterior cut surface 20 will have an angularly dependent radius of curvature. The following generally applies for the lenticle surface 20 shown in FIG. 7:

R.sub.L(φ)=R.sub.CV*(φ)−d.sub.F,

or in cylindrical coordinates (z, r, φ):

z.sub.L(r, φ)=R.sub.L(φ)−(R.sub.L.sup.2(φ)−r.sup.2).sup.1/2+d.sub.L+d.sub.F.

[0165] If astigmatism is not to be taken into consideration, the dependence on φ will not occur and the lenticle surface 20 becomes spherical. However, assuming a need for a cylindrical correction of defective eyesight, the lenticle surface 20 usually has different radiuses of curvature on different axes, although these will generally have the same vertex, of course.

[0166] This further implies automatically that the theoretical intersection line between the flap surface 19 and the lenticle surface 20 will not be located in a plane, i.e. at constant z coordinates, in the case of a cylindrical correction. The smallest radius of curvature of the lenticle surface 20 is at φ=θ+π/2 and the greatest on the axis θ of the cylindrical eyesight defect, of course, i.e. at φ=θ. In the case of a correction of hyperopia, unlike the representation in FIG. 7, the vertex of the flap surface 19 and the lenticle surface 20 coincide and the lenticle surface 20 has a stronger curvature than the flap surface 19. The thickness d.sub.L of the lenticle results as the rim thickness.

[0167] The volume 18, which is to be construed as a lenticle, has the smallest rim thickness at φ=θ=π/2, because the lenticle surface 20 and the flap surface 19 intersect there. For all other values of φ a finite rim thickness is given if a given z coordinate is assumed as the lower limit of the lenticle surface 20.

[0168] Alternatively, an additional rim surface can be provided in addition to the flap surface 20 and the lenticle surface 19, said additional rim surface circumscribing the volume 18 in the region of intersection of the flap surface 20 and the lenticle surface 19 or connecting these surfaces, respectively, at points which do not converge at given z coordinates. Cutting of this rim surface is also affected by the pulsed laser beam. For example, the rim surface may have a cylindrical shape, an elliptical shape (in a top view) or a conical shape (in a lateral view).

[0169] The design of the volume 18 as being limited by an anterior cut surface 19 at a constant distance from the anterior corneal surface 15 as well as by a posterior cut surface 20 is only one variant for limiting the volume 18. However, it has the advantage that the optical correction is substantially defined only by one surface (the lenticle surface 20) so that the analytical description of the other partial surface of the boundary surface is simple.

[0170] Further, optimum safety margins are provided with respect to the distance of the volume to the anterior corneal surface 15 and the posterior corneal surface 16. The residual thickness d.sub.F between the anterior cut surface 19 and the anterior corneal surface 15 may be set to a constant value of, for example, 50 to 200 μm. In particular, said thickness may be selected such that the epithelium, which is sensitive to pain, remains within the lamella formed by the flap surface 19 below the anterior corneal surface 15. Also, the design of the spherical flap surface 19 is in continuity with previous keratometer cuts, which is advantageous for the acceptance of the method.

[0171] After generating the cut surface 19 and 20, the volume 18 thus isolated is then removed from the cornea 5. This is schematically represented in FIG. 8, which further shows that the cut surfaces 19 and 20 are generated by the influence of the treatment laser beam incident in a focus cone 21, for example by sequential arrangement of plasma bubbles, so that the flap cut surface 19 and the lenticle cut surface 20, in a preferred embodiment, are generated by suitable three-dimensional shifting of the focus position of the pulsed laser radiation 2.

[0172] As an alternative, only the flap surface 19 may be formed, in a simplified embodiment, by target points defining the curved cut surface 19 at a constant distance from the anterior corneal surface 15, by means of pulsed laser radiation, and removal of the volume 18 is effected by laser ablation, for example by the use of an excimer laser beam. For this purpose, the lenticle surface 20 can be defined as the boundary surface of such removal, although this is not mandatory. In this respect, the treatment apparatus 1 works like a known laser keratome; however, the cut surface 19 is produced on curved cornea. The features described above and below, respectively, are also possible in such variants, especially with respect to the determination of the boundary surface, its geometric definition and the determination of control parameters.

[0173] If both the lenticle surface 20 and the flap surface 19 are generated by means of pulsed laser radiation, it is convenient to generate first the lenticle surface 20 and second the flap surface 19, because the optical result in the lenticle surface 20 will be better (or even achieved in the first place), if no change of the cornea 5 has occurred above the lenticle surface 20 yet.

[0174] The removal of the volume 18 by the pulsed laser radiation can be achieved, as indicated in FIG. 8, by a peripheral cut 22, allowing to extract the volume 18 in the direction of an arrow 23 shown in FIG. 8. However, as an alternative, the peripheral cut 22 may be provided such that it connects the anterior cut surface 19, i.e., the flap surface 19, with the anterior corneal surface 15, thereby forming a ring, although said peripheral cut does not extend fully around an angle of 360°. The lamella isolated in this way remains connected to the residual tissue of the cornea 5 in a narrow region. This connecting bridge will then serve as a hinge, so as to be able to fold the otherwise isolated lamella away from the cornea 5 and to remove from the rest of the eye's cornea 5 the already isolated volume 18 made accessible in this manner. The position of the connecting bridge can be predetermined when generating the control data or the target points, respectively. Thus, the described method or apparatus, respectively, realizes, according to this aspect, the isolation of the volume 19 within the cornea 5 and generates a flap, connected with the rest of the eye's cornea via a tissue bridge, as a lid over the volume. Said lid can be folded away and the volume 18 can be removed.

[0175] To generate the cut surfaces 19 and 20, the target points can easily be arranged in various ways. The prior art, for example WO 2005/011546, discloses special spirals to generate cut surfaces in the eye's cornea, which spirals extend, for example, in the manner of a helical line around a main axis being substantially perpendicular to the optical axis (z axis). Also, the use of a scanning pattern is known which arranges the target points in lines (cf. WO 2005/011545). Of course, these options can be used to generate the above-defined cut surfaces and can be employed with by the below-explained transformations.

[0176] The adjustment of the position of the focus in the eye's cornea is effected by means of the three-dimensional deflecting device schematically shown in FIG. 3, which device employs the shifting of lenses or other optically effective elements to adjust the focus in the z direction. However, the adjustment of lenses or the like is usually not feasible as fast as the swiveling of mirrors which are usually used in the xy scanner. Therefore, the speed of adjustment of the z scanner generally limits the rate at which the cut surfaces can be generated in the eye's cornea. In order to generate the cut surfaces 18 and 19 as quickly as possible, the focus is, therefore, in a preferred embodiment, guided along a spiral-shaped path, with one spiral each being located in the spatially curved cut surface. Thus, while writing the spiral, the z scanner is adjusted such that the arms of the spiral follow the spatially curved cut surface.

[0177] By way of example FIG. 9 shows a path curve 24 as a spiral, which is a circular spiral in the representation shown. The radius of the planar spiral shown increases in circular coordinates as the angle of rotation φ increases, so that:

r(φ)=φ.Math.d.sub.T/(2π)   (4)

holds. In this equation, d.sub.T is the distance of the spiral arms; it is shown in FIG. 10, which depicts an enlarged detail of FIG. 9. The distance of the individual spots 6 onto which the pulsed laser radiation is focused and at which a plasma bubble, for example, is generated by a laser pulse constantly equals d.sub.S in the spiral, so that the angular spacing Δφ of the individual spots 6 at which a laser pulse is introduced into the tissue is:

Δφ=d.sub.S/r

[0178] Since the lenticle surface 20, as already mentioned, is usually not non-spherical, the path curve 24 along which the laser focus is adjusted is an elliptical spiral for which obviously no constant distance of the spiral arms exists. However, along the main axes a and b, a respective path distance d.sub.Tb as well as d.sub.Ta may be defined, as shown in FIG. 11.

[0179] FIG. 10 shows the spots 6 so as to make clear the position of the focus of the individual laser pulses. Of course, the plasma bubbles actually expand after introduction of the respective laser pulse to such extent that the cut surface is generated, and the path curve 24 is then no longer visible in the cut surface.

[0180] For preparation of the surgical method, the definition of the path curves 24 by which the cut surfaces are generated has to be effected after definition of the cut surfaces 19 and 20.

[0181] Of course, when determining the path curves 24, it should be noted that finally the volume 18 is to be defined for the eye under normal conditions. The cut surfaces 19 and 20 as explained so far relate to the natural eye. However, it should be taken into account that the treatment apparatus 1 uses a contact glass 25 for fixation of the eye, which contact glass 25 is placed on the anterior corneal surface 15 of the eye's cornea 5, as shown in FIG. 12. The contact glass 25, which is already the subject of several patent publications (by way of example, reference is made e.g., to WO 2005/048895 A), is of interest for the present description of the treatment apparatus 1 or the related methods, respectively, for preparing and/or carrying out the surgical operation only insofar as it imparts to the anterior corneal surface 15 a defined curvature, on the one hand, and as it spatially keeps the eye's cornea 5 in a predefined position relative to the treatment apparatus 1, on the other hand. With respect to the spherical curvature of the contact glass 25, however, the approach described herein differs considerably from the approach as described, for example, in WO 2003/002008 A, which uses a planar contact glass pressing the eye's cornea flat.

[0182] When the eye is pressed against the contact glass 25 having a spherical contact surface, spatial deformation of the eye occurs. Since the cornea is usually compressible only tangentially, i.e. does not change its thickness when pressing is done in this manner, said pressing corresponds to a transformation of the eye's coordinate system, as shown in FIG. 13, into the coordinate system of the contact glass shown in FIG. 14. This context is known to the person skilled in the art from WO 2005/011547 A1, whose disclosure is incorporated herein by full reference in this respect. In FIGS. 13 and 14, any coordinates provided with an apostrophe designate the coordinates of quantities relating to the contact glass 25 or to the contact glass bottom surface 26 facing the eye.

[0183] Moreover, the contact glass has a still further advantage. Due to the pressing onto the spherical contact glass bottom surface 26, the anterior corneal surface 15 becomes automatically spherical. Thus, the anterior cut surface 19 located at a constant distance below the cornea's anterior surface 15 is also spherical due to the pressing of the contact glass, which sphericity leads to a considerably simplified control. Therefore, completely independently of other features, it is preferred for the invention to use a contact glass 25 having a spherical contact glass bottom surface 26 and to limit the volume by an anterior cut surface 19 as well as by a posterior cut surface, predetermining target points for the anterior cut surface which form said cut surface as a spherical surface at a constant distance d.sub.F below the anterior corneal surface 15. For the posterior cut surface, target points are/are being predetermined which define for the relaxed eye, i.e., after removal of the contact glass, a curvature corresponding to that which is desired for the correction of defective eyesight, except for the distance d.sub.F from the anterior corneal surface. Analogous considerations apply to the method for defining the target points or to the method of surgical operation.

[0184] The representations in FIGS. 13 and 14 shows the coordinate transformation which occurs at the eye when fitting or removing the contact glass, respectively. They contain both spherical coordinates (R, α, φ) referring to the origin of the curved surface (anterior corneal surface 15 or contact glass bottom surface 26) and cylindrical coordinates (r, z, φ) referring to the vertex of the anterior corneal surface 15 or of the contact glass bottom surface 26, respectively, said vertex being defined by the point where the optical axis OA intersects.

[0185] During the coordinate transformation from the coordinate system referring to the eye, as shown in FIG. 13, to the system referring to the contact glass, according to FIG. 14, the arc length, i.e. α.Math.R, the radial depth (R.sub.CV−R) as well as the angle φ remain unchanged. Thus, the transformation of the shapes of the cut surfaces 19 and 20 used as the basis for the natural eye, i.e. in the coordinate system of FIG. 13, is an important step in the calculation of the control factors for the three-dimensional focus adjustment device. The calculation is basically different than for a planar contact glass, wherein e.g., the flap surface 19 degenerates to a plane. Substantially only the shape of the cut surface 20 has to be transformed because the cut surface 19 merely has to be generated at a constant distance d.sub.F from the anterior corneal surface 15. Thus, in the transformed system, the cut surface 19 is a sphere having a radius of curvature R.sub.F which is reduced with respect to the curvature radius of the contact glass bottom surface.

[0186] The pressing of the cornea 5 of the eye 3 against the spherically curved contact glass bottom surface 26 is illustrated in FIG. 15. There, the representation on the right-hand side schematically shows the condition when the contact glass bottom surface 26 touches the anterior corneal surface at the vertex. For a clearer illustration of the geometric relationships, the anterior corneal surface 15 is schematically drawn as a circle in FIG. 15, although the curvature is spherical only within a smaller circle segment, of course. Pressing the contact glass 25 onto the cornea 5 causes the transition, symbolized by the arrow 27, to the condition on the left-hand side of FIG. 15. Removal of the contact glass 25 causes a relaxation of the eye 3 in the opposite direction of the arrow 27.

[0187] Due to the conditions mentioned above, the coordinates for each point in the eye's cornea 5 transform from the system shown in FIG. 13 to the system of FIG. 14. Now, this is used as a basis for selecting the control factors for the focus adjustment such that the cut surfaces 19 and 20 are to be described in the transformed contact glass system, because only then will they have the desired shapes after removal of the contact glass 26, i.e., after being transformed back to the natural coordinate system of the eye. Since contacting of the anterior corneal surface 15 is usually effected by suction, the aforementioned transformation will be referred to hereinafter also as suction transformation.

[0188] Now, in order to cut the flap surface 19, which is spherical as mentioned above, the following speed of adjustment of the z scanner, i.e., the following feed rate in the z direction, is set:

v.sub.Z(t)=d.sub.S.Math.f.sub.L.Math.d.sub.T/(2π.Math.(R.sub.F.sup.2−t.Math.d.sub.S.Math.f.sub.L.Math.d.sub.T/π)).sup.1/2,   (5)

wherein f.sub.L is the frequency of the laser pulses of the laser radiation 2. Equation (5) requires that the z speed v.sub.Z can be freely set and continuously changed.

[0189] If it is desired to write a sphere at a speed v.sub.Z, which is selected from a group of discrete speeds, which is usually the case if the z scanner is driven by a stepping motor, the time dependence of the radial function r(t) will be obtained as:

r(t)=[d.sub.S.Math.f.sub.L.Math.d.sub.T.Math.t/π−(d.sub.S.Math.f.sub.L.Math.d.sub.T.Math.t).sup.2/(2π.Math.R.sub.F).sup.2].sup.1/2   (6)

as well as, for the angular function,

φ(t)=[4π.Math.d.sub.S.Math.f.sub.L.Math.t/d.sub.T−(d.sub.S.Math.f.sub.L.Math.t).sup.2/R.sup.2].sup.1/2.   (7)

[0190] The t.sup.2 terms under the square root of the radial function as well as of the angular function show that no ideal Archimedian spiral is written anymore, i.e., the path and spot bubble distances vary in favor of the z speed being variable only in steps.

[0191] If a constant z feed is desired for the focus adjustment, this will not result in a sphere, as with the speed according to equation (4), but in a paraboloid, and the following holds true:

z(r)=[v.sub.Z/(d.sub.s.Math.d.sub.r)][r.sup.2.Math.π/f.sub.L]  (8)

As mentioned, in some treatment apparatuses 1, the speed at which the z scanner shifts the focus in the z direction can be adjusted only within a set of discrete speeds. If it is then desired to write a specific parabola by a given speed v.sub.Z, the product d.sub.S.Math.d.sub.T has to be selected accordingly, so that the expression in the first square brackets of the equation (8) has the desired value. The distance of the paths, defined by d.sub.T, as well as the spot distance along the path described by d.sub.S, are consequently suitable to vary so as to write a specific parabola at given v.sub.Z.

[0192] Any of the equations (5), (6)/(7) and (8) can be used to determine the target points and, thus, the control of the focus adjustment, in which case the corresponding spiral shape/surface shape then has to be used as a basis, of course. Where it is mentioned below that the equations are used for control, this means, in particular, that the target points are determined by means of the equations, which can be effected, for example, by evaluating the functional equations at equidistant points in time. In one variant of the invention, the speed equations are used to ensure that the determined target points do not require adjustment speeds which cannot even be realized by the focus adjustment device.

[0193] For the shapes of the surfaces 19 and 20 mentioned above and determined as described, a spiral is fitted to the respective surface. The spiral is written under control as described. The calculation of the z speed as well as of the r- and φ-speeds takes into consideration the surface shape of the surface 19 or 20, respectively.

[0194] The lenticle surface 20 is spherical if no cylindrical correction is to be performed. Therefore, one uses control according to equations (4)/(5) or (6)/(7) to generate such sphere. However, as is known, a sphere can also be approximated by a paraboloid. Therefore, it is envisaged, according to one inventive variant, to approximate one sphere by a paraboloid in a manner known to the person skilled in the art and to perform control according to equation (8).

[0195] Due to the suction transformation according to FIG. 15, the geometry of the lenticle surface 20 changes. The lenticle surface 20 has to have the curvature of the corrected anterior corneal surface 15* in the coordinate system of the contact glass 25. It cannot be related to a center of curvature which coincides with the center of curvature of the contact glass. The curvature defined according to the equation (2) is, thus, converted with respect to the suction transformation.

[0196] Of course, the radius of curvature defined in equation (2) is a function of φ. As already mentioned and as common in ophthalmology, two radiuses of curvature r.sub.a and r.sub.b can be given, respectively: one on the axis θ of the cylindrical eyesight defect and one for an axis perpendicular thereto. Computationally, it is particularly favorable to approximate a toroidal curvature, which thus results in the general case, by a parabola such that the lenticle surface 20 is approximated by a paraboloid. This is preferably affected prior to the contact pressure transformation, but may also be carried out thereafter.

[0197] Said approximation is effected by searching a respective parabola for the two radiuses of curvature which extends both through the vertex of the lenticle surface 20 and through a point located, if possible, at the rim. FIG. 16 shows the corresponding conditions in the coordinate system of the eye. This figure shows the spherical lenticle surface 20 prior to the contact pressure transformation. In the figure, the sections through the lenticle surface 20, which is toroidal in the generalized case, are superimposed on one another along the two half-axes a and b. The corresponding curves are referred to as A and B and are circular, with a radius of curvature r.sub.a and r.sub.b, respectively. On each curve, a rim point T is described in cylindrical coordinates by the corresponding radius r as well as the height, these parameters referring to the vertex S which is identical for both half-axis sections. Thus, the point T.sub.a is characterized by the radius r.sub.a as well as the height h.sub.a. This applies analogously to T.sub.b.

[0198] Now, a parabola is being searched for, which satisfies h=k.Math.r.sup.2. The parabola parameters ha obtained thereby for the parabola along the semimajor axis a as well as k.sub.b for the parabola along the semiminor axis b define the paraboloid, which is then written while shifting the focal point in the z direction, e.g. by means of a constant z feed (cf. equation (7)) or which is selected from a set of discrete speeds when selecting the z speed (modification of equation (7)). The sections shown in FIG. 16 of the toroidal lenticle surface 20 along the semiminor axis b as well as the semimajor axis a refer to the representation in the coordinate system of the eye.

[0199] If the approximation has been carried out by parabola equations after the contact pressure transformation, the transformed values will appear there, of course. The explicit calculation of transformed values can be avoided at this point, if the approximation is effected first and the parabola parameters thus found for the contact pressure transformation are subjected to the coordinate system of the contact glass, whereafter the conditions shown in FIG. 17 are then present.

[0200] The specification of the parabola parameters in the coordinate system of the eye according to FIG. 16 is as follows:

k.sub.a=(z(T.sub.a)−z(S))/r(T.sub.a).sup.2,   (9)

k.sub.b=(z(T.sub.b)−z(S))/r(T.sub.b).sup.2.   (10)

[0201] In equations (9) and (10), z(S) refers to the z coordinate of the point S. Placing the origin of the coordinate system in the vertex, as in the previous figures, the z coordinate will be zero. The coordinate z(T.sub.a) or z(T.sub.b), respectively, as well as r(T.sub.a) or r(T.sub.b), respectively, are the z or r-coordinates, respectively, of the corresponding point T.sub.a or T.sub.b, respectively, in the cylindrical coordinate system.

[0202] If the parabola parameters k.sub.a or k.sub.b, respectively, are not needed in the coordinate system of the eye according to FIG. 16, but in the coordinate system of the contact glass according to FIG. 17, the points S, T.sub.a and T.sub.a will then be replaced by the transformed points S′, T.sub.a′, T.sub.b′ indicated in FIG. 17.

[0203] Now, in order to represent the lenticle surface 20 in the pressure-contacted eye 3 by a (then usually elliptical) spiral with semi axes r.sub.a′ and r.sub.b′, said spiral is constructed from a circular spiral of radius r.sub.0′ by elongation in the direction φ=0 and compression in the direction φ=θ+π/2. Due to the simultaneous elongation and compression, the average path or spot distance, respectively, is maintained. If compression or elongation were affected only in one direction, the average distance would change.

[0204] The actual radiuses can be calculated as follows from the radius r.sub.0 of the circular spiral, which is shown in broken lines in FIG. 17, with the help of ellipticity:

e′=r.sub.a′/r.sub.b′=(k.sub.B′/k.sub.a′).sup.1/2.

[0205] The ellipticity e′ is the ellipticity of the transformed toroidal lenticle surface 20. The parameters k.sub.b′ as well as k.sub.a′ are given by the equations (11) and (12) for the transformed points S′, T.sub.a′ and T.sub.b′, respectively. The parabola parameters result from the fact that the circular spiral of radius r.sub.0, from which the lenticle surface 20 is constructed here, is intended to be an arithmetic or geometric average of the curvatures of the great and small half-axes of the paraboloid, respectively. r.sub.0′=(r.sub.a′.Math.r.sub.b′).sup.1/2 yields k=(k.sub.a.Math.k.sub.b).sup.1/2 for the parabola parameter, as well as the main axes of the ellipse: r.sub.a′=r.sub.0′.Math.(e′).sup.1/2 and r.sub.b′=r.sub.0′.Math.(e′).sup.−1/2.

[0206] At this point of the determination of the target points, two path curves 24 are obtained, which are described by functional equations. The pattern of the target points is determined by evaluation of these functional equations.

[0207] However, it remains to be considered that the focusing of the laser beam in the focus 7 is subject to a focus position error. This focus position error is a property of the optical system, i.e. results from the optical realization used. It is governed substantially by the optical design. Moreover, due to limited manufacturing accuracy within the allowed tolerances, the focus position error is apparatus-specific. Therefore, it is convenient to determine said error individually for each apparatus.

[0208] Accounting for the focus position error is effected by a usually non-linear transformation (referred to hereinafter also as NL transformation), which makes it impossible to carry out the NL transformation by modification of the path curve parameters. In a preferred embodiment of the invention, the focus position error is expressed by a correction table or a correction function. Said function is derived from gauging the optics of the treatment apparatus 1. Such gauging can be effected for a type of apparatus or individually for each apparatus. The correction function can be obtained by interpolation of the results of gauging, e.g., by means of polynomials or splines. The focus position error is generally rotationally symmetric with respect to the optical axis. It will then depend only on r and z in cylindrical coordinates.

[0209] The points previously calculated by means of the path curves are pre-distorted in the NL transformation such that they are located exactly at the desired location after introduction of the laser spot by the optical system having said focus position error. Thus, the application of the pre-distorted coordinates compensates for the focus position error appearing in the optical system.

[0210] The NL transformation is based on the idea that for each point having the coordinates (z, r) a contact glass sphere, displaced by z.sub.0, can be found, on which this point is located. The vertex of said sphere is then exactly at z.sub.0(z, r)=z−z.sub.KGL(r). The effect of the pre-distortion in compensating the focus position error is illustrated in FIG. 18. It shows the contact glass bottom surface 26, which is spherical in the present example, but may also have any other shape. Due to said pre-distortion, said sphere becomes a transformed contact glass sphere 26{circumflex over ( )}. The parameters taking the pre-distortion of the focus position error into consideration are symbolized in FIG. 18 by adding a roof-like symbol “{circumflex over ( )}” to them. In this case, z.sub.0{circumflex over ( )}=z.sub.0 holds true for a transformed axial point in the cornea. This allows for the fact that, although the focus position error is rotationally symmetric in most cases, it also results in a shift along the z direction.

[0211] For pre-distortion, the calculated path curves are converted to individual target point coordinates for the spots, which are then shifted in the correction transformation, i.e., the NL transformation, symbolized by K(r, z) in FIG. 18. If the focus position error is indicated as function K, the coordinate of each target point merely has to be evaluated by said function to obtain the shift or the transformed coordinate, respectively.

[0212] As a result, a respective set of target points is present for the surfaces 19 and 20, along which points the focus is guided. Due to the NL transformation and the contact pressure transformation, the coordinates with respect to the natural, i.e., free, eyes are located precisely in the desired anterior and posterior cut surfaces 19, 20.

[0213] The coordinates thus obtained for the target points further have to be converted to control signals for the three-dimensional deflecting unit, e.g., the xy-scanners as well as the z scanner. For this purpose, a corresponding functional relationship or a corresponding characteristic map is used, which is known for the scanners and has been previously determined, where applicable.

[0214] In particular, the response function was previously determined, in particular, for the xy-scanners, which are realized as galvanometer mirrors in the exemplary embodiment. By applying a frequency sweep to the galvanometer mirrors as well as measuring the actual galvanometer movement, an amplitude response function and a phase response function will be obtained. These will be factored in determining the control signals.

[0215] To simplify control, not every target point results in a respective aiming point for the scanners. Instead, the control device 12 uses sample points to characterize the path of the scanner. The number of points is reduced considerably thereby. This may be benefitted from already during the NL transformation, by subjecting to said transformation only those target points of the path curves which are intended to be sample points for control. Thus, according to one embodiment of the invention, evaluation of the functional equations is effected by means of a time interval which is larger than the time interval between the laser pulses.

[0216] Thus, prior to the NL transformation, the path curve points are filtered to provide the aforementioned nodes, i.e., points occurring at a frequency of the scanner control, for the transformation. An equivalent to such filtering is an evaluation of the functionally described path curves at nodes, which are spaced apart in accordance with the scanner control. This reveals a further advantage of the function-based approach described herein: The decision, which points are target points for controlling the focus adjustment device, has to be made no sooner than prior to the NL transformation. Before, only the path parameters have to be converted in a suitable manner. Also, datasets comprising a multiplicity of points will not occur until then.

[0217] Thus, the sample points define target points which are only a subset of the set of points to which a laser pulse is emitted. This is illustrated in FIG. 10, in which those spots 6, which exist in the control dataset as target points 28, are shown as solid black circles.

[0218] This approach further has the advantage that the maximum frequency f.sub.S, which occurs during control of the scanner, is considerably smaller than the laser pulse frequency f.sub.p. For example, a control frequency of 20 kHz as well as a laser pulse frequency of 200 kHz can be worked with. This has the result that one or more spots 6 onto which pulsed laser radiation is also emitted are located between the target points 28 provided to control the scanner.

[0219] Thus, there is not only an emission of pulsed laser radiation while the scanners are being subjected to an adjustment operation, e.g., while the galvanometer mirrors are moving, but laser pulses are deflected by the scanners while the latter are moving from one predetermined target point to the next. In order to achieve a maximum speed of deflection, this movement represents an oscillation which, in the case of perfect circular spirals (as they occur in the anterior cut surface 19), is even a purely sinusoidal oscillation. Since, in the case of the lenticle surface 20, too, the actual spiral shape deviates only slightly from ideal circular or elliptical spirals, the scanners can be operated at near their maximum frequency, so that the written paths along which the spots are arranged allow very quick production of cut surfaces.

[0220] Determining the control datasets which contain the target points from the above-described sets of points, which were obtained for the path curves, completes the preliminary procedure, which was carried out so as to generate the corresponding control values or control parameters. This preliminary procedure requires no human intervention and, in particular, no intervention from a physician or surgeon. The method is carried out by the control device 12 without any action by a physician. The physician's presence is not required until the subsequent surgical operation.

[0221] The procedure of the method for preparing the apparatus 1 for use in an ophthalmic operation of defective eyesight is schematically summarized in FIG. 19. In a step S1, the eye 3 is measured. In doing so, correction parameters such as those which are common for conventional spectacles, for example, are obtained for the eyesight defect of the patient 4. The parameters established in step S2 are then used, in a step S3, to determine the new curvature of the cornea 5 required for the corrected eye. Once this calculation in step S3 has been completed, the volume which is to be removed from the cornea is determined in S4. This is usually done by defining the lenticle surface 20 as well as the flap surface 19 in a step S5. Once the corresponding functional descriptions of these surfaces have been achieved, the suction transformation, which is effective in sucking the eye to the contact glass, is taken into consideration in step S6.

[0222] Next, the coordinates of the path curves, from which the cut surfaces are constructed, are determined. This is schematically indicated in step S7 by the parameters r, φ, z. At the end of step S7, a point pattern is present, comprising the coordinates of the spots on which a laser radiation pulse is to act. The density of the target points can already be reduced to simplify the calculation effort. For this purpose, when controlling the scanners, not every spot to which laser radiation is applied is a sample point.

[0223] In the following, the set of coordinates thus obtained is transformed again in step S8 to allow for the focus position error. Then, in a step S11, the actual control parameters are determined, including a response function, which was obtained in a step S10 from a previous measurement (step S9) of the amplitude behavior and frequency behavior of the scanners.

[0224] Using the thus-determined control parameters, the actual operation is then performed in step S12, during which operation additional spots, preferably located between the individual locations of support upon which the control of the scanners is based, are irradiated with laser radiation pulses.

[0225] 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.

[0226] 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.

[0227] 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.

[0228] 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.

[0229] 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.