DE102022208269A1 - Device for changing a shape of a surface of an object - Google Patents

Abstract

A device (10) for changing the shape of a surface (12) of an object (14) comprises a shape manipulation device (16), which is configured to move the surface along a processing path (36) by means of a processing means (18) configured to process the surface. to scan and thereby change the surface shape, a control device (30), which is configured to determine a control command (34) for the shape manipulation device from a predetermined target change (28) in the surface shape of the object by optimizing a target function (54), in which a deviation (56) of a prediction (48) of the surface change that can be generated by means of the control command from the target change is minimized. The prediction (48) is represented in the target function by a term (50), which is dependent on the processing path (36).

Description

Background of the invention

The invention relates to a device and a method for changing a shape of a surface of an object.

Out of DE10 2012 212 199A1 For example, such a device is known. This includes a shape manipulation device for surface structuring of micro- or nanostructured components made of glass or ceramic using electron irradiation. For this purpose, a particle beam, such as an electron beam, with a diameter in the range of the smallest structures to be created can be directed onto selected subareas of the surface in order to achieve local densification and thus local lowering of the surface in accordance with the desired surface structuring. Furthermore, processing of an optical element of a projection exposure system for microlithography with an electron beam is described. Imaging errors in the projection exposure system caused by the manufacturing process can be compensated for by a suitably designed compression and an associated change in the shape of the optical surface of an optical element. In addition to the material compaction described, particle beams can also be used for direct material removal from the surface of the irradiated optical element. Furthermore, it is possible to apply material to the surface of the object through suitable irradiation. As an alternative to particle beam processes, surface structuring can also be carried out using other mechanical processes, such as polishing processes.

Usually, the actual shape of the surface of the optical element is first measured and its deviation from a predetermined target shape is determined. In order to adapt the surface shape to the desired shape, a specification for a control variable of the shape manipulation device to be introduced into the optical element by the irradiation is conventionally first determined, such as in the form of an energy dose distribution of an electron beam, which is suitable for a desired correction of the surface shape of the optical element to effect.

Unfortunately, the adjustment of the surface shape to the desired shape that can be achieved with conventional devices of the type mentioned at the beginning is often not sufficiently precise.

Underlying task

It is an object of the invention to provide a device and a method with which the aforementioned problems are solved, and in particular the surface shape of an object can be adapted to a target shape with improved accuracy.

Solution according to the invention

The aforementioned object can be achieved according to the invention, for example, with a device for changing a shape of a surface of an object, which comprises a shape manipulation device which is configured to scan the surface along a processing path by means of a processing means configured to process the surface and thereby change the surface shape . Furthermore, the device according to the invention comprises a control device which is configured to determine a control command for the shape manipulation device from a predetermined target change in the surface shape of the object by optimizing a target function, in which a deviation of a prediction of the surface change that can be generated by means of the control command from the target change is minimized . In the objective function, the prediction is represented by a term that depends on the processing path.

The object changed by the device is in particular an optical element of a projection exposure system, in particular a projection exposure system for EUV microlithography.

The control command includes in particular a control variable for the shape manipulation device. This can define an energy dose distribution of a processing beam, in particular a particle beam, such as an electron beam, which is suitable for bringing about a desired correction of the surface shape of the optical element. The energy dose distribution can be determined by a dwell time specification for the processing beam, i.e. the control variable can include such a dwell time specification. The shape manipulation device can be configured for material removal or material application on the surface of the object. Alternatively, the shape manipulation device can also use other mechanical methods for changing the shape of the surface of the object, for example polishing methods.

In particular, by determining a control command according to the invention, a ver Because time field can be calculated, which due to its smoothness can be easily implemented by a manufacturing system in the form of the mold manipulation device.

The processing path comprises a plurality of path sections which are scanned one after the other by the processing means, wherein the path sections can be arranged adjacent to one another or separated from one another on the surface.

Due to the inventive representation of the prediction in the target function by a term which is dependent on the processing path, the characteristics of the processing path can already be adequately taken into account during the optimization that takes place by minimizing the target function. This means that in particular the surface processing characteristics resulting from the interaction of the course of the processing path with the properties of the processing means can be taken into account when determining the control command within the scope of the optimization algorithm. The optimization of the objective function of the prediction dependent on the machining path can be configured as a 1-dimensional optimization with respect to a path parameter that parameterizes the route position along the machining path.

In an alternative configuration of the control device, in which the prediction is not represented by a term dependent on the processing path, but is formed by a folding of a residence time with a so-called tool function on the two-dimensional area of the surface of the object, the optimization takes place as a 2-dimensional one Optimization regarding the surface coordinates. The result is then a 2-dimensional residence time field on an equidistant grid above the surface. In a step following the optimization, a processing path must then be selected with which the dwell time field can be approximately implemented.

The surface deviation data measured to determine the target shape or target change and the removal function of the processing agent are interpolated onto the generally coarser grid of the dwell time field. Optimization along the path and between the paths is usually not possible satisfactorily. In the modeling mentioned above by folding the residence time with the tool function, the processing means stays in the grid points according to the residence times; the continuous movement of the processing means between the grid points is not taken into account. This results in restrictions in the choice of machining path and disadvantages in the accuracy of the removal calculation and the overall machining time. Furthermore, there are disadvantages when taking into account the dynamics of the shape manipulation device along a processing path. In 2-dimensional optimization, a smooth residence time field is implemented depending on the direction.

These problems are avoided by the inventive configuration of the target function with the term dependent on the processing path, since the course of the processing path is already included in the optimization and the processing path does not have to be selected afterwards in a further step. Furthermore, by taking the processing path into account according to the invention, a more precise removal or application calculation can be carried out and, in addition, speed changes in the path direction can be better taken into account (direction-dependent gradient of dwell times of the processing agent).

• - Die Bearbeitungsbahn muss in der alternativen Konfiguration eine zusammenhängende Kurve (z.B. Mäander, Spirale, etc.) sein, die ein regelmäßiges Raster (auf dem die Verweilzeiten vorgegeben sind) abfährt. Die Abtastpunkte auf der Bearbeitungsbahn haben somit uniforme Abstände und liegen auf einem regelmäßigen Gitter.
• - Eine niedrige Anzahl an Abtastpunkten (was einem groben Verweilzeitgitter entspricht) führt bei der alternativen Konfiguration zu einer ungenauen Abtragsvorhersage, da das ursprüngliche feine Messraster auf ein gröberes interpoliert und die kontinuierliche Bahnbewegung, d.h. Werkzeugbewegung bzw. Bewegung des Bearbeitungsmittels, nicht abgebildet wird.
• - Eine hohe Anzahl an Abtastpunkten führt bei der alternativen Konfiguration ggf. aufgrund der Satzwechselzeiten der Steuerung zu einer hohen Bearbeitungszeit, die mit dem ebenfalls erhöhten Grundabtrag zusammenhängt.
• - Durch die Wahl der Berechnungsparameter muss also bei der alternativen Konfiguration ein Kompromiss zwischen Genauigkeit und erreichbarer Gesamtbearbeitungszeit gefunden werden.
• - Die simultane Optimierung der Verweilzeitfelder mehrerer Werkzeuge bzw. Bearbeitungsmittel bei der alternativen Konfiguration ist umständlich, da jedes Werkzeug auf einem anderen Gitter optimiert wird und eine Interpolation zwischen den Ergebnissen stattfinden muss.
• - Für die praktische Umsetzbarkeit erforderliche Anforderungen an die Glattheit des Verweilzeitfeldes werden bei der alternativen Gestaltung isotrop (entlang und senkrecht zur Bearbeitungsbahn) durchgeführt. Das schränkt den Lösungsraum unnötig ein.

Further disadvantages that can be avoided by configuring the objective function according to the invention compared to the alternative configuration based on a 2-dimensional optimization are as follows:

• - In the alternative configuration, the processing path must be a coherent curve (e.g. meander, spiral, etc.) that follows a regular grid (on which the dwell times are specified). The scanning points on the processing path are therefore uniformly spaced and lie on a regular grid.
• - A low number of sampling points (which corresponds to a coarse dwell time grid) leads to an inaccurate removal prediction in the alternative configuration, since the original fine measuring grid is interpolated to a coarser one and the continuous path movement, i.e. tool movement or movement of the processing equipment, is not mapped.
• - In the alternative configuration, a high number of sampling points may lead to a long processing time due to the block change times of the control, which is also related to the increased basic removal.
• - By choosing the calculation parameters in the alternative configuration, a compromise must be found between accuracy and achievable total processing time.
• - The simultaneous optimization of the dwell time fields of several tools or processing means in the alternative configuration is cumbersome because each tool is optimized on a different grid and an interpola tion must take place between the results.
• - Requirements for the smoothness of the residence time field required for practical feasibility are carried out isotropically (along and perpendicular to the processing path) in the alternative design. This restricts the solution space unnecessarily.

According to an embodiment according to the invention, the term representing the prediction comprises a function which represents a position-dependent dwell time of the processing means when scanning the surface and is configured as a one-dimensional function with an independent variable, the independent variable defining a route position on the processing path.

According to a further embodiment, the prediction along a predetermined configuration of the processing path is represented in the term of the target function. This means that the representation of the prediction is based on a given configuration of the processing path.

According to a further embodiment, the control device is configured to carry out the optimization for different configurations of the processing path and to determine a respective preliminary control command for the processing of the surface along the respective configuration of the processing path, as well as to select the control command for the shape manipulation device from the determined preliminary control commands . The selection of the control command from the determined preliminary control commands is preferably carried out on the basis of a suitable quality criterion, which is determined, for example, from a combination of the total processing time and the approximation to the target change that can be achieved using the control command. The approximation is understood to mean how well the change in surface shape caused by the control command corresponds to the target change. According to one embodiment, the quality criterion can further take into account the feasibility of the control commands by the shape manipulation device.

According to a further embodiment, at least two of the different configurations of the processing path differ in a distance between parallel arranged sections of the processing path. The processing path comprises a plurality of path sections, which can be arranged adjacent to one another or separated from one another on the surface. The above-mentioned distance then applies to copies of these web sections arranged in parallel, whereby a parallel arrangement also means a deviation of up to +/- 10° from the exactly parallel arrangement. The distance is then an average distance between the relevant path sections.

According to a further embodiment, at least two of the different configurations of the processing path differ by a change in direction of the processing path. That is, for example, a first configuration has no change in direction, while the second configuration already has a change in direction. Furthermore, both configurations can also have changes in direction, but these are different.

According to a further embodiment, at least one path parameter relating to a design of the processing path serves as a variable of the optimization and the control command includes a specification for the at least one path parameter determined by the optimization.

According to a further embodiment, the at least one path parameter serving as an optimization variable comprises a distance between parallel arranged sections of the processing path. As already mentioned above, the processing path comprises a plurality of path sections, which can be arranged adjacent to one another or separated from one another on the surface. The above-mentioned distance then applies to copies of these web sections arranged in parallel, whereby a parallel arrangement also means a deviation of up to +/- 10° from the exactly parallel arrangement. The distance is then an average distance between the relevant path sections.

According to a further embodiment, the at least one path parameter serving as an optimization variable comprises a change in direction of the processing path.

According to a further embodiment, the at least one path parameter serving as an optimization variable comprises a course characterization of the processing path in at least a section of the processing path. This course characterization can include several consecutive curves and straight sections.

According to a further embodiment, the control command includes a position-dependent dwell time of the processing agent along the processing path, the dwell time being uniform at the positions of respective sections of the processing path and the sections of the path being adapted to the respective dwell time are adapted so that the length of stay of the processing agent in each section of the route is the same. This length of stay corresponds in particular to a so-called record change time, which is required to upload a changed control data record to the mold manipulation device. A changed control data set means, in particular, the data set that is required to adapt the mold manipulation device to a changed position-dependent dwell time, ie a different processing speed.

According to a further embodiment, the control device is configured to determine an approximation of the control command during the optimization and then to carry out a further optimization in which, based on the approximation, a final result of the control command is obtained by minimizing a total time required to generate the surface change by means of the shape manipulation device is needed is determined.

According to a further embodiment, the control device is configured to carry out the further optimization under a secondary condition that limits the deviation of the surface change from the target change.

According to a further embodiment, the shape manipulation device comprises a particle irradiation device or a mechanical removal device, which is configured to bring about local changes in the surface of the object by means of a spatially resolved effect distribution depending on the control command.

The aforementioned object can further be achieved, for example, with a method for changing a shape of a surface of an object, in which a control command for a shape manipulation device is determined from a predetermined target change in the surface shape of the object by means of an optimization of a target function, which is configured to do so by means of a Processing means configured to process the surface scan the surface along a processing path and thereby change the surface shape. During optimization, a deviation of a prediction of the surface change that can be generated using the control command from the target change is minimized and in the target function the prediction is represented by a term which is dependent on the processing path.

The features specified with regard to the above-listed embodiments, exemplary embodiments or embodiment variants, etc. of the device according to the invention can be transferred accordingly to the method according to the invention and vice versa. These and other features of the embodiments according to the invention are explained in the description of the figures and the claims. The individual features can be implemented either separately or in combination as embodiments of the invention. Furthermore, they can describe advantageous embodiments that are independently protectable and whose protection may only be claimed during or after the application is pending.

Brief description of the drawings

• 1 ein Ausführungsbeispiel einer Vorrichtung zum Verändern einer Form einer Oberfläche eines Objekts mit einer Formmanipulationseinrichtung sowie einer Steuerungseinrichtung zur Ermittlung eines Steuerungsbefehls der Formmanipulationseinrichtung,
• 2 eine Darstellung der Oberfläche des Objekts in Draufsicht,
• 3 die Darstellung der Oberfläche des Objekts gemäß 2 in Draufsicht mit einem zusätzlich eingezeichneten ersten Ausführungsbeispiel einer Bearbeitungsbahn der Formmanipulationseinrichtung,
• 4 die Darstellung der Oberfläche des Objekts gemäß 2 in Draufsicht mit einem zusätzlich eingezeichneten weiteren Ausführungsbeispiel einer Bearbeitungsbahn der Formmanipulationseinrichtung,
• 5 die Darstellung der Oberfläche des Objekts gemäß 2 in Draufsicht mit einem zusätzlich eingezeichneten weiteren Ausführungsbeispiel einer Bearbeitungsbahn der Formmanipulationseinrichtung,
• 6 die Darstellung der Oberfläche des Objekts gemäß 2 in Draufsicht mit einem zusätzlich eingezeichneten weiteren Ausführungsbeispiel einer Bearbeitungsbahn der Formmanipulationseinrichtung,
• 7 ein Ausführungsbeispiel eines Verarbeitungsmoduls in der Formmanipulationseinrichtung gemäß 1 zur Verarbeitung des von der Steuerungseinrichtung ermittelten Steuerungsbefehls, sowie
• 8 eine beispielhafte Einteilung einer Bearbeitungsbahn der Formmanipulationseinrichtung.

The above and further advantageous features of the invention are illustrated in the following detailed description of exemplary embodiments or embodiments according to the invention with reference to the attached schematic drawings. It shows:

• 1 an embodiment of a device for changing a shape of a surface of an object with a shape manipulation device and a control device for determining a control command of the shape manipulation device,
• 2 a representation of the surface of the object in top view,
• 3 the representation of the surface of the object 2 in plan view with an additionally drawn first exemplary embodiment of a processing path of the shape manipulation device,
• 4 the representation of the surface of the object 2 in plan view with an additional exemplary embodiment of a processing path of the shape manipulation device,
• 5 the representation of the surface of the object 2 in plan view with an additional exemplary embodiment of a processing path of the shape manipulation device,
• 6 the representation of the surface of the object 2 in plan view with an additional exemplary embodiment of a processing path of the shape manipulation device,
• 7 an embodiment of a processing module in the mold manipulation device according to 1 for processing the control command determined by the control device, as well as
• 8th an exemplary division of a processing path of the shape manipulation device.

Detailed description of exemplary embodiments of the invention

In the exemplary embodiments or embodiments or embodiment variants described below, functionally or structurally similar elements are provided with the same or similar reference numerals as far as possible. Therefore, to understand the features of the individual elements of a particular embodiment, reference should be made to the description of other embodiments or the general description of the invention.

For ease of description, in 1 a coordinate system is specified, from which the respective positional relationship of the components shown in the figures results. The x ₁ direction runs to the right, the x ₂ direction runs into the drawing plane and the z direction runs upwards. In the in 1 and the formulas given below, x denotes a two-dimensional position vector with the coordinates (x ₁ , x ₂ ).

In 1 An exemplary embodiment of a device 10 for changing a shape of a surface 12 of an object 14 in the form of an optical element by means of electron irradiation is shown schematically. As an example, a mirror for the EUV wavelength range, ie for electromagnetic radiation with a wavelength of less than 100 nm, in particular a wavelength of approximately 13.5 nm or approximately 6.8 nm, is shown as an optical element. This can be an optical element for an illumination system or projection optics of a projection exposure system for EUV microlithography or DUV microlithography with a wavelength of approximately 365 nm, approximately 248 nm or approximately 193 nm. The optical element that can be changed using the device 10 can be a deflection mirror, facets of a facet mirror of an illumination optics or a mirror of a projection optics of a projection exposure system.

However, the device 10 is also suitable for highly precise surface shape production or surface shape change in other optical elements, such as mirrors for other wavelength ranges, lenses or optical elements with diffractive structures, or even in objects that do not form an optical element.

The device 10 contains a shape manipulation device 16 in the form of a particle irradiation device for generating a particle beam 18 directed and focused at selectable locations on the surface 12. Alternatively, the shape manipulation device 16 can also be configured as a polishing system, which uses a polishing tool for the mechanical removal of material on the surface 12 direct contact of the polishing tool with the surface 12 includes. The shape manipulation device 16 is in the in 1 illustrated embodiment configured for material removal on the surface 12. Alternatively, the shape manipulation device 16 can also be designed to apply material to the surface 12.

In the in 1 In the illustrated embodiment of a particle irradiation device, the particle beam 18 is formed by electrons, so the particle irradiation device is an electron irradiation device. In other design variants, ions can also be used, for example in systems for IBF surface processing, or uncharged particles. When using ions, they are typically neutralized after acceleration in the electric field before hitting the surface. The particle beam 18 is, in particular, energetically designed in such a way that, depending on the energy dose, a more or less pronounced local removal or a more or less pronounced local compaction of the material of the object 14 on the surface 12 is brought about. The energy dose is the energy per area that is introduced into the object 14 by the particle beam 18. The absorbed dose is therefore particularly dependent on the duration of the electron beam at the selected location and on its intensity.

Both material removal and local compaction cause a local lowering of the surface 12 on the object 14, such as an optical element. Compaction occurs particularly in amorphous materials through a redistribution of electron bonds. The local compaction takes place in all spatial directions, i.e. there is not only a local surface depression in the area of a surface element in the negative z-direction but also a compaction parallel to the surface 12. This creates forces acting parallel to the surface 12, whereby stresses are induced in the object 14. These stresses can cause a deformation of a surface section that is significantly larger than the surface element affected by the local compaction. The surface section can include a part of the surface 12 or the entire surface 12.

To generate the particle beam 18 in the form of an electron beam, the form is designed as a particle irradiation device nipulation device 16 according to 1 an electron source 20 and an acceleration unit 22. An incandescent cathode, a crystal cathode or a field emission cathode can be used as the electron source 20, for example. The acceleration unit 22 accelerates and concentrates the electrons emitted by the electron source 20. For this purpose, the acceleration unit 22 can have an anode with a high positive electrostatic potential compared to the electron source 20 and a small outlet opening for the accelerated electrons. To focus and adjust the intensity of the particle beam 18, the acceleration unit 22 also contains a control electrode, for example a Wehnelt cylinder. The intensity or the beam current indicates the number of electrons that pass through an imaginary surface perpendicular to the electron beam per unit of time.

To focus the particle beam 18 coming from the acceleration unit 22, the particle irradiation device further comprises a focusing unit 24 with suitably designed electrical or magnetic components.

With a deflection unit 26 of the particle irradiation device 16, the particle beam 18 can be deflected in both the x ₁ and x ₂ directions. For this purpose, the deflection unit 26 also contains suitably designed electrical or magnetic components. Depending on the setting of the deflection unit 26, the particle beam 18 hits the surface 12 of the optical element 14 at a specific location x _i = (x ₁ ⁱ , x ₂ ⁱ ). Such a location x _i = (x ₁ ⁱ , x ₂ ⁱ ) is in 1 designated by the reference number 33.

In this way, a large number of different locations 33 on the surface 12 can be irradiated one after the other and thus a spatially resolved effect distribution in the form of an energy dose distribution over the surface 12 can be achieved. The spatially resolved energy dose distribution here is to be understood as a distribution of the energy introduced per area as a function of the spatial coordinate x = (x ₁ , x ₂ ) of the surface 12 of the optical element 14. The irradiation can, for example, take place in a grid pattern or continuously over the entire surface. An irregular or regular arrangement of different locations to be irradiated, for example in rows, circles, ellipses or the like, is also possible.

To avoid absorption of the electrons of the particle beam 18 by air, the shape manipulation device 16 also has a vacuum chamber in which the electron source 20, the acceleration unit 22, the focusing unit 24, the deflection unit 26 and the object 14 or at least the surface 12 of the object 14 are arranged.

The device 10 further contains a control device 30 for controlling the particle irradiation device 16. The control device 30 is designed to generate a control command 34 for the shape manipulation device from a predetermined target change h (x) for the shape of the surface 12 of the optical element 14, designated by the reference number 28 16 to determine. The control command 34 causes the effect distribution described above to be generated in the form of the energy dose distribution in a suitable form. The target change 28 is usually determined by measuring the actual surface shape and comparing the measured shape with a target shape, i.e. the target change 28 is the change in the surface shape that is required to give the surface 12 the target shape.

If surfaces 12 are processed by means of the shape manipulation device 16 in the present embodiment, the surface change, which can be represented by a function of the spatial coordinates, depends on a dwell time of the processing agent, in the present case the particle beam 18, over a respective position of its processing path 36 on the surface 12 off. Examples of such processing paths 36 are in the 3 until 6 shown and described in more detail below. The dependence of the surface change on the residence time of the processing agent can be a linear dependence, for example in the case of material removal caused by a particle beam, or a non-linear dependence, for example in electron beam compaction.

The control command 34 includes in the in 1 In the embodiment shown, a final result of a dwell time τ _E (s) of the processing agent in the form of the particle beam 18, denoted by reference number 32E, over the respective route position s of the processing path 36, also denoted by reference number 37. In other words, the dwell time is 32E about a position-dependent dwell time of the processing agent when scanning the surface along the processing path 36.

In the embodiment shown, the processing path 36 is predetermined. In this case, the position s of the dwell time 32E of the control command 34 relates to the predetermined processing path 36. According to a further embodiment, different configurations of the processing path 36 can be specified, with the control device 30 in the determination Development of the final result 32E of the dwell time τ _E (s) selects one of the predetermined processing paths 36 according to a suitable quality criterion, so that the position s dwell time 32E then relates to the selected processing path.

According to a further embodiment, the control command 34 can also include a final result 38E of at least one path parameter BP, which defines the design of the processing path 36. The end result 38E of the at least one trajectory parameter BP is shown in Figure 1 to illustrate this alternative embodiment 1 shown with a dashed circle shape. It should be understood that the in 1 Functionality illustrated using the formulas shown relates to the embodiment of the control device 30, in which the control command 34 only includes the dwell time 32E. In the further embodiment, in which the control command 34 additionally includes the final result 38E of the at least one path parameter, the functionality of the control device 30 is adapted accordingly. The final result 38E can, for example, provide information about the following with reference to the 3 until 6 explained trajectory parameters include BP1, BP2 and BP3.

2 shows an example of a top view of the surface 12 of the object 14. A circular area designated Q 'represents a processing area 40 on the surface 12 of the object 14, ie a processing area accessible to the particle beam 18 or generally to the processing means or processing tool Execution of the processing area as a circular area is to be understood as an example. Other shapes of the processing surface, such as oval, square, rectangular or other shapes are conceivable. The inner region of the processing surface Ω 'contains a useful surface 42, which is designated Ω. For the case in which the object 14 is an optical element for a lithography projection exposure system, the useful area Ω is a surface section on the optical element, which is arranged in a useful beam path when installed in the projection exposure system. In other words, the useful area Ω is or contains the area section actually used in the later operation of the optical element. The usable area Ω is also in the in 2 shown top view circular.

In 3 a first exemplary embodiment of the processing path 36 is shown. The processing path 36 includes a large number of processing trajectories 44 in the form of parallel lines or parallel sections of the processing path 36, only some of these processing trajectories being designated by the reference number 44. The processing trajectories 44 indicate the path of the particle beam 18 or generally of a processing agent on the surface 12 during operation of the device 10, with adjacent processing trajectories 44 being traveled in the opposite direction by the particle beam 18. The distance between adjacent processing trajectories 44 is in the embodiment according to 3 uniform and referred to as trajectory parameter BP1.

4 shows a further exemplary embodiment of the processing path 36. This differs from the exemplary embodiment according to 3 only in the path parameter BP1, the distance between adjacent machining trajectories 44 is according to 4 larger than according 3 .

5 shows a further exemplary embodiment of the processing path 36. This differs from the exemplary embodiment according to 4 only in that one of the machining trajectories 44, which is designated by the reference number 44M, has a modified course. The modified course is characterized in that the processing path 36 has a change in direction at three positions, which creates a V-shaped course. The changes in direction are defined by another path parameter BP2.

6 shows a further exemplary embodiment of the processing path 36. This differs from the exemplary embodiments according to FIG 3 and 4 that the course of the processing path 36 is not characterized by parallel processing trajectories, but is designed in a spiral shape. The exact course characterization of the processing path 36 is defined by a further path parameter BP3.

Below is with reference to 1 the functionality of the control device 30 is explained. As already mentioned above, the desired change 28 in the surface shape is denoted h(x). The dwell time 32 of the particle beam 18 or generally of a processing means or tool is described as τ(s) depending on the route position s of the processing path 36 on the surface 12 to be processed. The effect of the tool in the form of the particle beam 18 is characterized by a so-called tool function k, designated by reference number 46.

For example, referring to 3 the particle beam 18 moves along the processing path 36, which is characterized by a curve c: ℝ ⊃ S → Ω', S = [0,L], parameterized according to arc length, with length L and associated dwell times τ: ℝ ⊃ S → ℝ _≥0 is described. A two-dimensional stock removal prediction g(x) with the tool function k: ℝ ² → ℝ ² can be described by a curve integral along c as $$G\left(x\right)={\displaystyle {\int }_{s}k\left(x-c\left(s\right)\right)\tau \left(s\right)\text{d}s}$$

The removal prediction g(x) in 1 represents a prediction of the surface change that can be generated by means of the control command 34 and is designated by the reference numeral 48. In an embodiment in which the processing means effects a material application, g(x) accordingly represents an order prediction. As can be seen from (1), the term representing the removal prediction g(x) is ∫ _S k(x - c(s)) τ(s) ds, , which in 1 is designated by the reference number 50, depends on the processing path c(s).

The processing path 36 runs in a processing area Ω' ⊂ ℝ ² , while the useful area Ω is decisive for the evaluation of the surface roughness, which indicates the area actually used in the later operation of the object 14 in a projection exposure system for microlithography.

The control device 30 is configured to carry out a two-stage optimization to determine the dwell time 32E specified in the control command 34 from the specified target change 28. In a first stage 52 of the optimization, also referred to as the first optimization in this text, an approximation τ _N (s) of the dwell time, designated by the reference number 32N, is determined by minimizing a target function 54 or quality function: $$\underset{\tau }{\text{argmin}}\rho {\left(H-G\right)}^2+\lambda {\displaystyle {\int }_s{\left|\dot{\tau }\left(s\right)\right|}^2\text{d}s}$$

Here (h-g) denotes the deviation 56 of the prediction g(x) from the target change h(x) and ρ denotes the standard deviation of (h-g). As is known to those skilled in the art, the standard deviation of a quantity is formed by subtracting the individual values of the quantity from their mean, adding their squares and taking the root from the result.

The objective function 54 is minimized under a secondary condition 58: $$\text{NB:}\tau \in T$$

As an optimization method for minimizing the objective function 54, a standard convex optimization method can be used. For example, the (linearized) ADMM algorithm (see Neal Parikh & Stephen Boyd, "Proximal algorithms, Foundations and Trends in Optimization, 1 (3):127-239, 2014) or the Chambolle-Pock algorithm (see Antonin Chambolle and Thomas Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40(1): 120-145, May 2011) are used if norms other than the 2 norms should be used. In the specific form (2) with quadratic norms, the method of conjugate gradients can preferably be used. In this case, the secondary condition is implemented by subsequently shifting the dwell time 32. For small problem sizes, e.g. if the removal prediction is in a basis is shown, a direct solution of the resulting linear system of equations can also be used.

besteht aus zwei Termen. Der erste Term ist der Datenterm. Er misst die RMS-Rauheit der bearbeiteten Oberfläche 12. Der zweite Term dient als Bestrafungsterm und erzwingt eine Glattheit der Lösung, d.h. er definiert ein Limit auf der Ableitung von τ und somit auf der Beschleunigung der Formmanipulationseinrichtung 16. Ein Gewichtungsfaktor in Form eines skalaren Wertes λ dient der Regulierung der Glattheit der Lösung.The objective function 38 in the form shown under (2). $$\rho {\left(H-G\right)}^2+\lambda {\displaystyle {\int }_s{\left|\dot{\tau }\left(s\right)\right|}^2\text{d}s}$$

consists of two terms. The first term is the data term. It measures the RMS roughness of the machined surface 12. The second term serves as a penalty term and enforces smoothness of the solution, i.e. it defines a limit on the derivative of τ and thus on the acceleration of the shape manipulation device 16. A weighting factor in the form of a scalar value λ is used to regulate the smoothness of the solution.

The constraint 48 according to expression (3) dictates that the solution of the residence time τ agrees with a residence time function given by a set T of residence time functions. The quantity T specifies all dwell time functions that can be implemented with the shape manipulation device 16.

In an optional second stage 60 of the optimization, also referred to as further optimization in this text, the dwell time 32E, ie a final result of the dwell time of the particle beam 18, is determined by minimizing a further objective function 62: $$\underset{\tau }{\text{argmin}}{\displaystyle {\int }_s\tau \left(s\right)+\lambda {\left|\dot{\tau }\left(s\right)\right|}^2\text{d}s}$$

wobei ρ die Standardabweichung von (h-g) bildet, sowie einer zweiten Nebenbedingung 70: $$\text{NB2: }\tau \in T$$

The objective function 62 is minimized under a first secondary condition 68: $$\rho \left(H-G\right)<{\text{RMS}}_{\text{spec}}$$

where ρ is the standard deviation of (hg), as well as a second constraint 70: $$\text{NB2:}\tau \in T$$

When optimizing the second stage 50, the approximation 32N of the specification for the control variable determined in the first stage is used as the starting point for the control variable τ(x). This means that the optimization of the second stage 50 is based on the value distribution of the approximation τ _N (x) determined in the first stage for the length of stay τ (x). For those in 1 Not specifically illustrated embodiment, according to which the second stage 60 of the optimization is dispensed with, the dwell time 32N determined in the first stage 52 of the optimization is included in the control command 34 as the final result 32E of the dwell time.

As an optimization method for minimizing the objective function 52, a standard method for convex optimization designed as an interior point method can also be used here, i.e. an admissible solution that satisfies the secondary conditions 68 and 70 is required. This can be ensured, for example, by solving the problem according to expression (6) with a feasible user specification. The initial solution comes from the first optimization 52, i.e. the approximation 32N is used as the initial solution. The condition according to expression (7) can then be realized using a logarithmic barrier and, for example, with the help of the generalized forward-backward splitting method (cf. Hugo Raguet, Jalal Fadili, and Gabriel Peyre, “A generalized forward-backward splitting”, SIAM Journal on Imaging Sciences, 6(3): 1199-1226, 2013).

umfasst ein Integral über die Streckenposition s der Bearbeitungsbahn 36. Die Zielfunktion 62 ist, wie auch die Zielfunktion 54, ein Funktional. Der Integrand der Zielfunktion 62 umfasst zwei Terme in Form von zwei Summanden. Der erste Term 64 minimiert die Gesamtbearbeitungszeit τ_Total, während der zweite Term 66 die Glattheit der Lösung kontrolliert. Das Integral des ersten Terms 64 über die Verweildauer τ(s) entspricht der Gesamtzeit, welche zur Erzeugung der mit der Verweildauer 32E definierten Oberflächenänderung mittels der Formmanipulationseinrichtung 16 benötigt wird. Aufgrund des ersten Terms der Zielfunktion 62 wird daher in der zweiten Stufe 60 der Optimierung die Verweildauer 32E durch Minimierung der Gesamtzeit ermittelt. Der zweite Term des Integranden der Zielfunktion 52 entspricht dem bereits in der Zielfunktion 54 der ersten Stufe 52 enthaltenen Bestrafungsterm, mit dem ein Ortsgradient der Aufenthaltsdauer τ gering gehalten wird. Der Gewichtungsfaktor λ kann in beiden Stufen 52 und 60 der Optimierung unterschiedlich gewählt werden.The objective function 62 in the form shown under (6). $${\displaystyle {\int }_s\tau \left(s\right)+\lambda {\left|\dot{\tau }\left(s\right)\right|}^2\text{d}s}$$

comprises an integral over the distance position s of the processing path 36. The target function 62, like the target function 54, is a functional. The integrand of the objective function 62 includes two terms in the form of two summands. The first term 64 minimizes the total processing time τ _Total , while the second term 66 controls the smoothness of the solution. The integral of the first term 64 over the dwell time τ(s) corresponds to the total time required to produce the surface change defined with the dwell time 32E by means of the shape manipulation device 16. Based on the first term of the objective function 62, the dwell time 32E is determined in the second stage 60 of the optimization by minimizing the total time. The second term of the integrand of the objective function 52 corresponds to the punishment term already contained in the objective function 54 of the first stage 52, with which a spatial gradient of the length of stay τ is kept low. The weighting factor λ can be chosen differently in both stages 52 and 60 of the optimization.

The first secondary condition 68 limits the deviation 56 of the surface change generated by the shape manipulation device 16, ie the removal prediction g, from the target change h. For this purpose, a designated limit value RMS _spec is defined for a mean value of the squared deviation of g with respect to h, calculated over the useful area Ω, to which the target change 28 relates. This mean value is formed in the first secondary condition 68 using the standard deviation ρ. This means that a certain error budget RMS _spec is available. This should be achieved using a processing rule τ _E (s) that has the shortest possible total processing time. The second secondary condition 70 corresponds to the secondary condition according to expression (3) already explained above with reference to the first stage 52 of the optimization.

In the embodiment already mentioned above, in which different configurations of the processing path 36 are specified, the control device 30 carries out both stages 52 and 60 of the optimization for each of the predetermined processing paths 36 and thereby determines a respective preliminary control command with a respective preliminary dwell time τ _V ( s) for processing the surface 12 along the respective configuration of the processing path 36. From the determined preliminary control commands with the respective preliminary dwell time τ _V (s), the control device 30 then selects the final control command 34 with the final dwell time 32E. The control command 34 is preferably selected based on a suitable quality criterion, which is determined, for example, from a combination of the total processing time and the approximation to the target change 28 that can be achieved using the control command 34.

The 7 and 8th serve to illustrate an embodiment according to which the control device 30 configures the control command 34 in such a way that a so-called block change time is adapted to a respective section of the processing path 36. The set change time is to be understood as the time that is required to upload a changed control data set 72 or a changed control-related minimum dwell time in the mold manipulation device 16. A changed control data set 72 is to be understood as meaning the control data that is required to change the beam control of the shape manipulation device 16, ie in particular the deflection unit 26, to a changed position-dependent dwell time, ie a changed processing speed of the processing means in the form of a changed scanning speed of the particle beam 18.

The set change time is adapted to the respective section of the processing path 36 in such a way that the period of time required for the particle beam 18 to process the relevant section of the route corresponds to that of the set change time. Since the set change time generally remains the same, the relevant section of the route is dimensioned longer at a higher scanning speed of the particle beam 18 than at a lower scanning speed. This ensures that at the time of changing the scanning speed, the control data set 72 required to operate the following route section with the changed scanning speed is already uploaded to the shape manipulation device 16. According to the in 7 In the exemplary embodiment shown, the control data record 72 is uploaded to a control signal generator 76.

7 shows an example of the processing of the dwell time 34E depending on the route position s in the mold manipulation device 16 according to 1 . The processing instruction of the processing path 36 specified by the dwell time 34E is stored in a storage unit 74. During operation of the shape manipulation device 16 during the processing of a section of the processing path 36, the control data record 72 for the following section of the processing path 36 is then uploaded from the storage unit 74 into the control signal generator 76 in real time. The relevant control data set 72 relates to a respective scanning speed v _n . The control signal generator 76 then regulates the beam control of the shape manipulation device 16, in particular the deflection unit 26.

8th shows, by way of example, the division of a processing path 36 into a plurality of sections 78 between two successive support points S ₁ to S ₇ . The processing path 36 is thus divided into six successive route sections 78, namely the route section 78-1 between s ₁ and s ₂ , the route section 78-2 between s ₂ and s ₃ , the route section 78-3 between s ₃ and s ₄ , the route section 78-4 between s ₄ and s ₅ , the route section 78-5 between s ₅ and s ₆ and the route section 78-6 between s ₆ and s ₇ .

Each of the route sections 78 is assigned a scanning speed v _n , for example the route section 78-4 being longer than the route section 78-3 and thus the scanning speed v ₄ being greater than the scanning speed v ₃ . The respective scanning speed v _n is uniform in the relevant section 78. This means that the position-dependent residence time τ ₁ to τ ₆ (reference numbers 32 ₁ - 32 ₆ ) of the particle beam 18 in the relevant section 78 is also uniform. The black dots on the processing path 36 according to 8th are used when executing the optimization 52 by means of the control device 30 to determine the removal prediction 48.

As explained above, according to the 7 and 8th illustrated embodiment, the position-dependent residence time τ _E (s) of the particle beam 18 at the positions of respective sections of the processing path is uniform, the section sections 78 being adapted to the respective residence time in such a way that the residence time of the processing agent in each section 78 is the same length. The length of stay then corresponds to the set change time.

Below we will do this in 8th illustrated exemplary embodiment explained in other words and in addition. In practice, the residence times on the processing path 36 are subject to certain restrictions which ensure practical feasibility by the processing means or the tool. In the previous optimization problems, the set of feasible curves was denoted as T. A possible limitation is that the machining path c for execution is divided into intervals on which the shape manipulation device 16 moves at a constant speed. At each of these intervals the tool has a minimum dwell time, which results from the maximum speed of the tool and the block change time. Let C {c(s _i ) | s ₁ , ..., s _N ∈ S} is the set of points (also called support points) at which the speed of the tool is changed, then the dwell time between these support points must be constant, i.e. τ(s) = τ(s _i ) ∀s ∈ [s _i , s _i+1 ) ∀ _i . The dwell time on one of these intervals is then $$t_i={\displaystyle {\int }_{s_i}^{s_{i+1}}\tau \left(s\right)\text{d}s}.$$

erhält. Da c auf Bogenlänge parametrisiert ist entspricht hierbei S_i+1 - s_i der Länge des Kurvenabschnitts zwischen c(s_i) und c(s_i+1). Wir fassen die Menge der diesbezüglich zulässigen Verweilzeiten zusammen als $$\begin{array}{c}T=\{\tau :S\to ℝ\ge |\tau \left(s\right)=\tau \left(s_i\right)\forall \text{s}\in \left[s_i,s_{i+1}\right)\forall i,\\ t_i\ge \text{max}\left(\frac{s_{i+1}-s_i}{v_{\text{max}}},t_{\text{sw}}\right)\}.\end{array}$$

The block change time t _sw results in the restriction t _i ≥ t _sw , while the maximum speed of the tool v _max results in the restriction $t_i\ge \frac{s_{i+1}-s_i}{v_{\text{Max}}}$

receives. Since c is parameterized to arc length, S _i+1 - s _i corresponds to the length of the curve section between c(s _i ) and c(s _i+1 ). We summarize the amount of permissible dwell times in this regard as: $$\begin{array}{c}T=\{\tau :S\to ℝ\ge |\tau \left(s\right)=\tau \left(s_i\right)\forall \text{s}\in \left[s_i,s_{i+1}\right)\forall i,\\ t_i\ge \text{Max}\left(\frac{s_{i+1}-s_i}{v_{\text{Max}}},t_{\text{sw}}\right)\}.\end{array}$$

The quality of the removal prediction 48 depends largely on the selected discretization of expression (1) in conjunction with the curve model. Due to the piecewise constant dwell times, in order to accurately model the movement of the tool, only the dwell time t _i in this interval needs to be determined for each interval. The residence times τ(s), s ∈ [s _i , s _i+1 ) are then given as $\tau \left(s\right)=\frac{t_i}{s_{i+1}-s_i}\forall s\in \left[s_i,s_{i+1}\right).$

Accordingly, in the numerical optimization, the t _i can be optimized, while for the removal prediction 48 according to expression (1), the curve c is sampled with any precision and the time t _i is distributed over the points of fine discretization of the respective interval. This means that the accuracy remains high regardless of the choice of support points C. An illustration of this is in 8th to find. The dwell times t _i refer to the intervals delimited by lines; the finely scanned points are given in black. In the implementation, for example, a maximum distance dmax from points on the curve can be specified. We have ||c(s _i+1 ) - c(s _i ) || ₂ > d _max , so many points are added in the corresponding interval for the removal prediction that the maximum distance between them is below the limit value. In order to represent the constant speed of the tool on each interval, a linear upsampling operator is integrated into the functional, which distributes the dwell time in each interval evenly across the points in this interval.

The inventive approach of representing the removal prediction 48 contained in the target function 54 by the term 50, which is dependent on the processing path 46, can also be referred to as a 1-dimensional optimization approach, which differs from a 2-dimensional optimization approach of alternative optimization methods in which the removal prediction is represented in a relevant target function as a two-dimensional function depending on the coordinates of the surface to be machined.

The 1-dimensional approach according to the invention has the particular advantages over the alternative 2-dimensional approaches that a more precise calculation of the removal can be carried out, that the distances along and between the processing trajectories 44 of the processing path 36 can be varied and that the gradient of the dwell times along the processing path 36 can be taken into account.

In the 2-dimensional optimization, the accuracy of the removal prediction depends on the selected grid of the dwell time field. In contrast, the 1-dimensional approach considers the continuous tool path to calculate the material removal. The tool path can be accurately represented between the support points by adding points with appropriate dwell times. A sufficiently fine discretization leads to an arbitrarily accurate representation of the tool path. The removal calculated from this corresponds better to the actual removal.

When specifying the tool trajectories, the models described provide new degrees of freedom compared to the 2-dimensional optimization approach, which have a positive effect on the overall machining time. Since the sampling points of the curve no longer have to lie on a regular grid, the course of the curve c can be changed, and the sampling points C on the trajectory can be freely selected.

The tool must spend at least the minimum dwell time in each interval between two sampling points on the curve, see expression (11), before it can continue machining in the next interval. The minimum dwell time in each interval creates a basic removal rate of the tool, which can be reduced by the additional degrees of freedom. In general, the goal here is to keep the number of sampling points C low in order to minimize the basic removal caused by the block change time in (11).

A frequently used processing path 36 is the one in the 3 until 5 Meander shown, in which the processing area is covered by long, straight, parallel paths connected at the edge. In addition, the distance between the path points must be chosen to be small in order to ensure a certain level of accuracy in the removal prediction. This restriction no longer applies to the 1D models.

The distance between the tracks can be changed without reducing the accuracy of the removal prediction 48. Increasing the distance reduces the overall length of the curve and therefore the overall machining time. The paths can have different distances, i.e. they can be shifted relative to one another, in order to adapt the curve to local properties of the measured surface deviations h. Each individual point of the curve can be moved, also for local adaptation to the surface deviations h.

These advantages apply similarly to other types of curves, such as a spiral. Increasing the spacing of the sampling points along the tool path reduces the number of sampling points. This can also have a positive effect on the base removal and the overall processing time.

Another advantage of the 1-dimensional approach arises from the calculation of the gradient of the dwell times in the web direction. The smoothness of the dwell times (and thus the speed) on the trajectory has a strong impact on the feasibility on the production system - arbitrarily high accelerations and changes in acceleration may not be possible. In 2D approaches, the smoothness of the residence time field is treated isotropically, that is, no distinction is made between the smoothness along the trajectory and between the trajectory.

By explicitly modeling the 1-dimensional nature of the processing path 36, only the smoothness along the processing path is taken into account in the optimizations 52 and 60 described above. This results in fewer restrictions on the residence time distribution, which leads to smaller base removal and lower overall processing time.

The above description of exemplary embodiments, embodiments or embodiment variants is to be understood as an example. The resulting disclosure, on the one hand, enables the person skilled in the art to understand the present invention and the associated advantages, and on the other hand, in the understanding of the person skilled in the art, also includes obvious changes and modifications to the structures and methods described. Therefore, all such alterations and modifications to the extent that they come within the scope of the invention as defined in the appended claims, and equivalents, are intended to be covered by the protection of the claims.

Reference symbol list

10

Device for changing the shape of a surface

12

surface

14

object

16

Mold manipulation device

18

particle beam

20

electron source

22

Acceleration unit

24

Focusing unit

26

Distraction unit

28

specified target change

30

Control device

32

Dwell time of the particle beam τ(s)

32N

Approximation of a residence time of the particle beam τ _N (s)

32E

Final result of a dwell time of the particle beam τ _E (s)

321-326

Position-dependent duration of stay on different route sections

33

location on the surface

34

Control command

36

Processing path

37

Route position s of the processing path

38E

Final result of at least one path parameter

BP1, BP2, BP3

Orbit parameters

40

Processing surface

42

Usable area

44, 44M

Machining trajectories

46

Tool function

48

Removal prediction

50

term

52

first stage of optimization

54

Objective function

56

Deviation of the forecast from the target change

58

Additional condition

60

second stage of optimization

62

another objective function

64

first term

66

second term

68

first secondary condition

70

second secondary condition

72

Control data set

74

Storage unit

76

Control signal generator

78

Route sections

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102012212199 A1 [0002]

Claims (15)

Device (10) for changing a shape of a surface (12) of an object (14) with: - a shape manipulation device (16), which is configured to scan the surface along a processing path (36) by means of a processing means (18) configured to process the surface and thereby change the surface shape, - a control device (30), which is configured to determine a control command (34) for the shape manipulation device from a predetermined target change (28) in the surface shape of the object by optimizing a target function (54), in which a deviation (56) of a prediction (48) the surface change that can be generated by means of the control command is minimized from the target change, the prediction (48) being represented in the target function by a term (50), which is dependent on the processing path (36). Device according to Claim 1 , wherein the term (50) representing the prediction comprises a function which represents a position-dependent dwell time (32) of the processing means (18) when scanning the surface and is configured as a one-dimensional function with an independent variable (37), the independent variable being a Route position on the processing path (36) is defined. Device according to Claim 1 or 2 , wherein in the term (50) of the target function, the prediction (48) is represented along a predetermined configuration of the processing path (36). Device according to one of the preceding claims, in which the control device (30) is configured to carry out the optimization for different configurations of the processing path (36) and thereby to issue a respective preliminary control command for the processing of the surface (12) along the respective configuration of the processing path determine, and select the control command (44) for the shape manipulation device (16) from the determined preliminary control commands. Device according to Claim 4 , wherein at least two of the different configurations of the processing path differ by a distance (BP1) between parallel arranged sections (44) of the processing path. Device according to Claim 4 or 5 , whereby at least two of the different configurations of the processing path differ by a change in direction (BP2) of the processing path. Device according to Claim 1 or 2 , wherein at least one path parameter (38) relating to a design of the processing path (36) serves as a variable of the optimization and the control command comprises a specification determined by the optimization for the at least one path parameter. Device according to Claim 7 , wherein the at least one path parameter comprises a distance (BP1) between parallel arranged sections of the processing path. Device according to Claim 7 or 8th , wherein the at least one path parameter includes a change in direction (BP2) of the processing path. Device according to one of the Claims 7 until 9 , wherein the at least one path parameter comprises a course characterization (BP3) of the processing path in at least a section of the processing path. Device according to one of the preceding claims, wherein the control command (34) comprises a position-dependent dwell time (32E) of the processing means (18) along the processing path (36), the dwell time (32 ₁ -32 ₆ ) at the positions of respective route sections (78). the processing path is uniform and the route sections are adapted to the respective residence time in such a way that a residence time of the processing means is the same length in each route section. Device according to one of the preceding claims, wherein the control device is configured to determine an approximation (32N) of the control command during the optimization (52) and then to carry out a further optimization (60), in which, based on the approximation, a final result (32E ) of the control command (34) is determined by minimizing a total time required to generate the surface change using the shape manipulation device. Device according to Claim 12 , wherein the control device (30) is configured to carry out the further optimization (60) under a secondary condition (68) that limits the deviation of the surface change from the target change. Device according to one of the preceding claims, in which the shape manipulation device device comprises a particle irradiation device (16) or a mechanical removal device, which is configured to bring about local changes in the surface (12) of the object by means of a spatially resolved effect distribution depending on the control command (34). Method for changing a shape of a surface (12) of an object (14), in which: from a predetermined target change (28) in the surface shape of the object by means of an optimization of a target function (54), a control command (34) for a shape manipulation device (16) is determined, which is configured to use a processing means (18) configured to process the surface to scan the surface along a processing path (36) and thereby change the surface shape, wherein during the optimization, a deviation of a prediction (48) of the surface change that can be generated by means of the control command from the target change is minimized and wherein in the target function the prediction is represented by a term (50), which depends on the processing path.

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