WO2023160946A1

WO2023160946A1 - Line-generating optical system

Info

Publication number: WO2023160946A1
Application number: PCT/EP2023/052136
Authority: WO
Inventors: Andreas Heimes; Christoph Irion; Tim Hieronymus
Original assignee: Trumpf Laser- Und Systemtechnik Gmbh
Priority date: 2022-02-22
Filing date: 2023-01-30
Publication date: 2023-08-31
Also published as: DE102022104082A1

Abstract

The invention relates to a line-generating optical system (10) for generating a defined laser line (24) on a working plane (26), comprising at least one laser light source (12) for generating at least one laser beam (20); an optical assembly (14) which is designed to generate an illumination beam (22) from the at least one laser beam (20) along a beam path, wherein the illumination beam (22) defines a beam direction which intersects the working plane (26), the illumination beam (22) forms the defined laser line (24) in the region of the working plane (26), the optical assembly (14) has a focusing unit (18) with a focusing lens (28) in the beam path for focusing the illumination beam (22), and the focusing lens (28) can move parallel to the beam direction; a camera system (36) which is designed to monitor the illumination beam (22) at at least three defined positions downstream of the focusing lens (28), said illumination beam (22) having a focus state at each of the at least three defined positions; and a controller (44) which is designed to determine the position of the focus of the focusing lens (28) on the basis of the focus states at the at least three defined positions and to control the position of the focusing lens (28) parallel to the beam direction such that the focus position is arranged on the working plane (26).

Description

line optics system

The present invention relates to a line optics system for generating a defined laser line on a working plane.

Such a line optical system is basically known from US 2006/182155 A1.

[0003] The linear laser illumination of such a linear optical system can advantageously be used to thermally process a workpiece. The workpiece can be, for example, a plastic material on a glass plate, which serves as a carrier material. The plastic material can in particular be a film on which organic light-emitting diodes, so-called OLEDs, and/or thin-film transistors are produced. OLED films are increasingly being used for displays in smartphones, tablets, televisions and other screen display devices. After the electronic structures have been produced, the film must be detached from the glass carrier.

This can be done with laser illumination in the form of a thin laser line, which is moved at a defined speed relative to the glass plate and in doing so detaches the adhesive bond of the film through the glass plate. In practice, such an application is often referred to as LLO or Laser Lift Off.

Another widely used application for the sequential illumination of a workpiece with a defined laser line can be the line-by-line melting of amorphous be silicon on a carrier plate. Here, too, the laser line is moved at a defined speed relative to the workpiece surface. The comparatively inexpensive amorphous silicon can be converted into higher-quality polycrystalline silicon by melting it and then cooling it down. In practice, such an application is often referred to as Solid State Laser Annealing SLA, Sequential Lateral Solidification (SLS) or Excimer Laser Annealing (ELA).

For such applications, a laser line is required on the work plane, which is as long as possible in one direction in order to cover the widest possible work area, and which is very short in comparison to this in the other direction, in order to provide a suitable for the respective process provide the required energy density. Accordingly, a long, thin laser line with a very large aspect ratio of line length to line width is desirable. For typical applications, a line length of 100mm or more with a linewidth of the order of 20pm may be desirable. The direction in which the laser line runs is usually referred to as the long axis (LA) and the line width as the short axis (SA) of the so-called beam profile. As a rule, the laser line should have a defined intensity curve in both axes. It is often desirable for the laser line to have an intensity profile that is as rectangular or trapezoidal as possible in the long axis, with the latter being advantageous if several laser lines are to be joined together to form a longer overall line. Depending on the application, a rectangular intensity profile (so-called top hat profile) or a Gaussian profile is often desired in the short axis.

WO 2018/019374 A1 discloses a device for generating such a laser line with numerous details relating to the elements of the optical arrangement. The optical arrangement here includes a collimator that collimates a raw laser beam, as well as a beam transformer, a homogenizer and a focusing stage. The beam transformer takes the collimated raw beam and expands it in the long axis. In principle, the beam transformer can also accept several raw laser beams from several laser sources and combine them into an expanded laser beam with higher power. The homogenizer produces the desired beam profile in the long axis. The focusing stage focuses the reshaped laser beam on a defined position in the area of the working plane. The known device is suitable for LLO and SLA applications and can be implemented using laser radiation with wavelengths ranging from the infrared (IR) to the ultraviolet (UV) range.

[0007] At high laser power, the optical properties can change in line focus systems. Reasons for this are, for example, thermal lenses of the optics or mechanical expansion due to temperature changes. This can lead to a shift in the focal position of the laser line.

This problem is known in cutting optics and line focus systems. To compensate, a focusing optics of the line focus system was previously controlled on the basis of a characteristic. This characteristic indicates the position of the focusing optics as a function of time. The characteristic curve is determined in advance, for example in a calibration process, and can be used, for example in the form of control data, by a control unit of the line optics system in order to regulate the focusing optics during operation.

[0009] For example, the document DE 10 2018 200 078 A1 shows an optical system for generating an illumination line. The optical system includes a laser beam source for generating a laser beam along an optical axis. Furthermore, the optical system comprises a beam shaping device, which is set up to shape the laser beam in such a way that a beam profile of the laser beam has a long axis and a short axis, and an imaging device (e.g. a focusing lens) arranged downstream of the beam shaping device in the beam path of the laser beam is set up to image the laser beam thus shaped as an illumination line. The beam shaping device comprises at least one telescope arrangement, which comprises a first lens group and a second lens group, the first lens group and the second lens group having an optical refractive power at least with respect to the short axis. The optical system includes first moving means for moving at least one of the first and second lens groups along the optical axis. The optical system includes a second moving device for moving the imaging device along the optical axis. The optical system also includes a control unit which is set up to control the first and second movement device in such a way that the at least one of the first and second lens groups and the imaging device are moved while the laser Beam source generates the laser beam. To control the first and second movement device, control data are stored in a memory of the control unit.

However, the known line optics systems still leave room for improvement, in particular with regard to the regulation of the focusing optics.

Against this background, it is an object of the present invention to provide a line optics system that has improved control of the focusing optics.

[0012] According to one aspect, this object is achieved by a line optics system for generating a defined laser line on a working plane. The line optics system has at least one laser light source for generating at least one laser beam, an optical arrangement, a camera system and a control device. The optical arrangement is set up to generate an illumination beam from the at least one laser beam along a beam path, with the illumination beam defining a beam direction that intersects the working plane, with the illumination beam forming the defined laser line in the area of the working plane, with the optical arrangement in the Beam path has a focusing unit with a focusing lens for focusing the illumination beam, wherein the focusing lens is movable parallel to the beam direction. The camera system is set up to observe the illumination beam at at least three defined positions downstream of the focusing lens, with the illumination beam having a focus state at each of the at least three defined positions. The control device is set up to determine a focus position of the focus of the focusing lens on the basis of the focus states at the at least three defined positions and to regulate a position of the focusing lens parallel to the beam direction in such a way that the focus position is arranged in the working plane.

The at least one laser light source can be a UV laser light source for generating a UV laser beam or an IR laser light source for generating an IR laser beam. The at least one laser light source can be set up to generate more than one laser to generate a beam. In particular, a plurality of laser light sources can be provided, each laser light source being set up to generate a respective laser beam.

The optical arrangement is set up to generate the illumination beam from the at least one laser beam along a beam path. The illumination beam has a linear beam profile in the area of the working plane. The illumination beam thus generates the defined laser line in the working plane. In other words, the illumination beam has a beam profile in the region of the working plane which has a long axis with a long-axis beam width and a short axis with a short-axis beam width perpendicular to the beam direction. To generate the illumination beam from the at least one laser beam, the optical system can have a series of beam-guiding and beam-shaping optics along the beam path. In addition, the optical arrangement can be movable relative to the working plane along a direction of movement, preferably parallel to the working plane, in order to process a workpiece with the aid of the illumination beam.

The optical arrangement has the focusing unit. The focusing unit is set up to focus the illumination beam. In particular, the focusing unit can focus the illumination beam in the short-axis direction. In other words, the focusing unit serves to focus the short axis of the laser line. The focusing unit is preferably arranged in the beam path after the beam-guiding and beam-shaping optics.

[0016] In order to focus the illumination beam, the focussing unit has a focussing lens. The focusing lens can have one or more optics. The focus of the focusing lens is at a focus position downstream of the focusing lens. In other words, the focal position of the focus of the focusing lens is the position downstream of the focusing lens at which the focusing lens focuses the illumination beam. The focus position thus defines a distance down the beam from the focusing objective, at which the focus of the focusing objective lies. The term "beam down" is to be understood in relation to the beam path and the beam direction of the illumination beam and means that something in the beam path or in Beam direction is arranged below. In other words, the focal position of the focus of the focusing objective is in the beam path or in the beam direction of the illumination beam, ie behind the focusing objective.

[0017] The focusing lens can also be moved parallel to the beam direction. In other words, the focusing objective is mounted in such a way that it can be moved parallel to the direction of the beam. To move the focusing lens, the focusing unit can have a movement device, for example. By moving the focusing lens, the position of the focus of the focusing lens can be adjusted.

The line optics system can also have other optics downstream of the focusing unit, such as protective glasses, deflection mirrors and the like. The other optics preferably have no beam-shaping or focusing function.

The camera system is set up to observe the illumination beam at at least three defined positions downstream of the focusing lens. Observing means that the camera system records, for example, one or more images of the illumination beam in which the illumination beam is imaged at the respective defined positions. The at least three positions are arranged after the focusing lens in the beam direction of the illumination beam. In one embodiment, the camera system can be set up to observe the illumination beam at three defined positions downstream of the focusing objective. In other embodiments, the camera system can be set up to observe the illumination beam at more than three, in particular four, five or six, defined positions downstream of the focusing lens. The defined positions are different. The defined positions can preferably be arranged consecutively in the beam direction with the same spacing.

The focusing lens has a different distance in the beam direction from each of the defined positions. A focus state of the illumination beam also varies with the distance from the focusing lens. The focus state describes the focusing at a specific position relative to the focusing lens. In particular, the focus state how strongly the illumination beam is focused at the respective position. In other words, the focus state indicates a degree of focus at the respective position. Focusing is at its maximum at the focus position, i.e. in the focus of the focusing lens. The further one moves away from the focus position parallel to the beam direction, the lower the focusing becomes. A specific focal state of the illumination beam is therefore assigned to each of the defined positions.

The control device is set up to determine the focus position of the focus of the focusing lens on the basis of the focus states of at least three of the defined positions and to regulate a position of the focusing lens parallel to the beam direction in such a way that the focus position is arranged in the working plane. The control device preferably analyzes the focus states at the defined positions observed by means of the camera system in order to determine the focus position on the basis thereof. The control device can then regulate the position of the focusing lens accordingly on the basis of the determined focus position. In particular, the position of the focusing lens is adjusted in such a way that the focus position is shifted into the working plane. In this way, the short axis of the laser line is focused in the working plane.

[0022] For this purpose, the control device can in particular have a control unit and a data processing unit. The data processing unit can, for example, carry out calculation steps to determine the focus position. The control unit can, for example, generate control commands by means of which the position of the focusing objective is controlled. For example, the control commands can be used to control a movement device that is set up to move the focusing lens.

The line optics system according to the invention is designed in such a way that the focus position can be determined online, ie during operation, and tracked accordingly, ie regulated. A few positions along the beam direction are observed using the camera system. For example, the few positions can be imaged on a camera using a suitable optical system. Recordings of the illumination beam at these positions can then be processed via an algorithm and the exact focus position can be determined. The position of the focusing lens can be adjusted accordingly.

The line optics system according to the invention thus makes it possible to determine the focus position of the focusing lens during operation and to regulate it accordingly, so that the illumination beam, in particular the laser line, is focused in the working plane.

[0025] The task set at the outset is thus achieved in its entirety.

In a first embodiment of the line optics system, the camera system is arranged downstream of the working plane.

The illumination beam is thus observed in the beam path after the working plane. For this purpose, the illuminating beam can be observed either after it has passed the working plane or after it has been reflected at the working plane.

In particular, the camera system can be arranged in such a way that it can observe a reflected beam of the illumination beam at the working plane. The reflected beam is a back reflection of the illuminating beam at the work plane. In particular, during operation the illumination beam can be reflected on a surface of a workpiece to be machined with the laser line, which is arranged in the working plane. The back reflection can then be observed using the camera system. In this way, in addition to the focus shift, a variation in the working plane can also be compensated.

Alternatively, the camera system can also be arranged behind the working plane. The working plane lies between the camera system and the focusing unit. The camera system can thus observe an illumination beam that passes the work plane. With this arrangement of the camera system, the focus position can be determined and adjusted when no workpiece is arranged in the working plane or when the laser line has been used to cut completely through the workpiece that the laser line can pass the working plane and reach the camera system.

In a further configuration, the line optics system has further optics which are arranged downstream of the focusing unit, the further optics being set up to split the illumination beam, with part of the illumination beam pointing in the direction of the working plane and another part of the illumination beam pointing in direction of the camera system.

As already explained above, further optics, such as a deflection mirror or a protective glass, can be arranged in the beam length after the focusing unit, via which the illumination beam reaches the working plane. The additional optics can, for example, split the illumination beam into two parts. In particular, the additional optics can be constructed in such a way that they reflect part of the illumination beam and allow another part of the illumination beam to pass through, that is to say transmit it. Either the transmitted or the reflected part runs in the direction of the working plane, whereas the corresponding other part runs in the direction of the camera system and is observed by it. The reflected part of the illuminating beam can be referred to as a back reflection of the illuminating beam at the additional optics.

In particular, the camera system can be set up to observe the back reflection of the illumination beam on the further optics. This is particularly advantageous when the further optics have a protective glass through which the illumination beam runs in the direction of the working plane, with a back reflection being observed on the protective glass by means of the camera system.

Alternatively, the camera system can also be set up to observe the transmitted part of the illumination beam. For this purpose, for example, the further optics can have a partially transparent, in particular semi-transparent, deflection mirror. The deflection mirror can deflect, i.e. reflect, the illumination beam in the direction of the working plane, in which case the transmitted part of the illumination beam that has passed through the deflection mirror can be observed by means of the camera system. In a further embodiment of the line optics system, the camera system has at least one camera for recording at least one image, the at least one image having images of the illumination beam at the at least three defined positions.

In other words, the at least one image has an image for each defined position. Each of these images thus forms the illumination beam at the respective defined position in the respective focus state. The illumination beam is thus shown in the images with different degrees of focus. On the basis of these images, the control device can determine the corresponding focus states at the corresponding defined positions.

In particular, the camera system can have a camera for recording an image, this image having images of the illumination beam at the at least three defined positions. These images are preferably imaged spaced from each other in the image. This means that the images in the image do not overlap. In particular, the images in the image are offset from each other in the short axis direction. In this way, all focus states can be mapped at the at least three defined positions in one image.

Alternatively, the camera system can also have a plurality of cameras, with each camera taking a respective image. Each image has an image of the illumination beam at one of the at least three defined positions. In other words, a corresponding image is recorded by the cameras for each defined position. The number of cameras and the number of images correspond to the number of defined positions, with each image depicting the illumination beam in a corresponding focus state.

In a further refinement of the line optics system, the camera system has a beam splitter which is designed to split the illumination beam into partial beams, the at least one camera being designed to display the partial beams in the to form at least one image, the images of the partial beams corresponding to the images of the illumination beam at the at least three defined positions.

The number of partial beams corresponds to the number of defined positions. In particular, the partial beams are spaced apart from one another. This means that the partial beams run side by side, in particular parallel to one another, and do not overlap in the image. The sub-beams can be offset from each other in the direction of the short axis. In the embodiment in which the camera system has a camera, the partial beams are recorded with this camera. In this way, the partial beams can be imaged together in one image, preferably next to one another. In the alternative embodiment, in which the camera system has a plurality of cameras, each partial beam can be recorded with one of the cameras. In particular, the number of partial beams corresponds to the number of cameras and the number of images recorded. In this way, each partial beam can be displayed in its own image. The imaging of a partial beam corresponds to the imaging of the illumination beam at a defined position. In other words, each partial beam is used to image the illumination beam at one of the at least three defined positions. Preferably, the paths or transit times of the partial beams up to the camera in which they are recorded are different. Due to the different lengths of travel, imaging is achieved at different defined positions. The images of the partial beams therefore form the illumination beam at different distances from the focusing objective and thus also in different focus states. For example, the beam splitter can be constructed in such a way that the partial beams pass through the beam splitter with paths of different lengths. This can be implemented in particular by means of one or more deflection mirrors in the beam splitter. In particular, the beam splitter can be set up to lengthen the travel paths of the partial beams in such a way that the at least three defined positions in the beam direction are arranged one after the other with the same spacing. The beam splitter thus makes it possible in a simple manner to observe the illumination beam at at least three defined positions using a camera system.

In a further refinement of the line optics system, the control device is set up to determine a focus value of each focus state at the at least three positions based on the at least one image, wherein the focus position of the focus of the focusing lens is determined based on the determined focus values.

[0041] A focus value indicates a measure of the focussing, ie the sharpness of the image, at a defined position of the illumination beam in the direction of the beam. The focus value has a global extremum at the focus position of the focus of the focusing lens. In particular, the progression of the focus values in the beam direction can be modeled as a parabola-like progression, with the position of the extremum corresponding to the focus position. By determining the focus values at at least three positions in the beam direction, the course of the parabola and thus also the position of the extremum can be determined. If the focus value is determined at more than three defined positions, an overdetermined system of equations is obtained, which can be solved, for example, by means of a regression calculation, in particular the least squares method, in order to determine the position of the extremum. Alternatively, another function that has a global extremum, in particular a Gaussian function or an even polynomial function with degree four or higher, can also be used to model the course of the focus values. The number of defined positions to be observed by means of the camera system is preferably greater than or equal to the degree of the polynomial function plus one.

In a further refinement of the line optics system, a beam profile of the illumination beam in the direction of the short axis is determined for each image of the illumination beam in the at least one image, with each focus value being determined on the basis of the beam profile of the corresponding image.

The beam profile is an intensity profile that represents the intensity profile of the illumination beam in the direction of the short axis at the respective defined position. The respective beam profile can be determined in particular on the basis of a projection of the pixels of the corresponding image in the at least one image along the direction of the long axis onto the direction of the short axis. The beam profile can preferably be a rectangular intensity profile (a so-called top hat profile) or a Gaussian profile. The focus value can be a steepness (also called edge steepness) of the beam profile, for example. The steepness describes the gradient in the edge area of the beam profile, i.e. on a flank of the beam profile. The smaller the value, the slope is, the steeper the slope. The focus value can also be the inverse of the slope, for example. The focus value is then the smaller, the steeper the edge is. Alternatively, the focus value can also be the width of the beam profile. In particular, the width of the beam profile can be taken to be the width of the region of the beam profile in which the intensity values are equal to or greater than 1/e ² , 50% or 90% of the maximum of the beam profile. At the focus position, the slope of the beam profile is at a maximum and the inverse of the slope and the width of the beam profile are at a minimum. In order to determine the focus position, the position in the beam direction can thus be determined at which the steepness of the beam profile of the illumination beam is minimal in the direction of the short axis. Alternatively, the position in the beam direction can also be determined at which the inverse of the steepness or the width of the beam profile of the illumination beam is minimal in the direction of the short axis. In particular, the steepness and the width in the beam direction follow a parabolic curve, with the position of the extremum, in particular the minimum or maximum, corresponding to the focus position of the focus of the focusing objective. By determining the steepness or width at three positions in the direction of the beam, the course of the parabola and thus also the position of the extremum can be determined.

In a further configuration of the line optics system, a position of the working plane downstream of the focusing lens is predetermined, with the control device being set up to regulate the position of the focusing lens parallel to the beam direction in such a way that the focus position of the focus of the focusing lens varies from the determined focus position to the predetermined position of the working plane is moved.

The position of the working plane is thus a target position of the focus position and the focus position determined by means of the control device is an actual position of the focus position. The position of the focusing lens parallel to the beam direction is thus regulated in such a way that the focus position is shifted from the actual position to the desired position. For example, a displacement vector can be formed from a difference between the desired position and the actual position, according to which the focusing lens is moved. For example, the position of the working plane can be determined in advance, in particular by the user. In a preferred embodiment, the camera system is arranged in such a way that one of the defined positions is the target position of the focus position corresponds. For example, the illumination beam can be observed via the additional optics described above. The control device can then regulate the position of the focusing objective in such a way that the focus position is shifted to the corresponding, defined position.

In a further refinement, the line optics system has a movement device for moving the focusing lens parallel to the beam direction, the control device being set up to control the movement device in order to regulate the position of the focusing lens.

[0047] For example, the control device can send control commands to the movement device, with the movement device then moving the focusing lens in accordance with these control commands. The movement device can have a linear guide, for example, along which the focusing lens can be moved parallel to the beam direction. The linear guide thus provides a guide for the focusing lens parallel to the beam direction. The movement device can also have a drive device that can move the focusing objective parallel to the beam direction, in particular along the linear guide. In particular, the control device can control the drive device.

In a further configuration of the line optics system, the optical arrangement also has beam-guiding and beam-shaping optics which are set up to generate the illumination beam from the at least one laser beam.

The optical arrangement preferably has a row of beam-guiding and beam-shaping optics along the beam path, by means of which the illumination beam is generated. These optics are preferably arranged in the beam path in front of the focusing unit. The illumination beam generated by the beam-guiding and beam-shaping optics is focused by the focusing unit in the working plane. The optical arrangement can have, for example, a beam transformer, a homogenizer and large optics as beam-guiding and beam-shaping optics. The beam transformer can be arranged in the beam path after the laser light source. The The beam transformer is set up to expand the at least one laser beam in a direction transverse to the beam direction, in particular in the direction of the long axis. In particular, the beam transformer serves to optimize the aspect ratio of the illumination beam even further and/or even more efficiently with regard to the desired laser line. The homogenizer can be arranged in the beam path after the beam transformer. The homogenizer is set up to distribute the at least one, preferably expanded, laser beam homogeneously in the long axis. The homogenizer thus serves to achieve a homogeneous intensity distribution of the illumination beam along the long axis. The large optics are preferably arranged in the beam path after the homogenizer. The large optics are used to shape the beam profile in the working plane. The large optics can have, for example, one or more optical elements (e.g. Fourier lenses) along the beam path, which generate the linear beam profile in the area of the working plane.

It goes without saying that the features mentioned above and those yet to be explained below can be used not only in the combination specified in each case, but also in other combinations or on their own, without departing from the scope of the present invention.

Embodiments of the invention are shown in the drawing and are explained in more detail in the following description. Show it:

1 shows a schematic representation of an exemplary embodiment of a new line optical system;

2 representations of the imaging of the illumination beam by means of a focusing objective and different beam profiles of the illumination beam;

3 shows two representations of the displacement of the focus position of a focusing lens; 4 shows four representations of different arrangements of a camera system in the beam path of a line optics system;

5 shows two representations of two different embodiments of a camera system;

6 shows three diagrams for representing a focus value distribution for three different focus positions;

7 shows a representation of a further embodiment of a camera system for recording an image and a diagram of an intensity profile of the image;

8 several diagrams for the representation of beam profiles and focus value distributions at different focus positions;

FIG. 9 shows two diagrams for representing a beam profile and a focus value distribution at a specific focus position; FIG.

FIG. 10 shows a diagram that shows the course of the focus shift over time and the corresponding readjustment of the focusing objective; FIG. and

11 shows a representation of a further embodiment of a camera system for recording an image as well as a diagram of an intensity profile of the image and the corresponding focus value distribution.

In FIG. 1, an exemplary embodiment of the new line optical system is denoted by the reference number 10 in its entirety. The line optics system 10 generates a laser line 24 in the area of a working plane 26 in order to machine a workpiece (not shown here) that is placed in the area of the working plane 26 . The laser line 24 runs in a direction that is referred to below as the x-axis. The laser line has a line width that is viewed here in the direction of a y-axis running orthogonally to the x-axis. Accordingly, the x-axis below corresponds to the long axis and the The y-axis corresponds to the short axis of the beam profile formed on the working plane 26 . In other words, the beam profile has a long axis with a long-axis beamwidth in the x-direction and a short axis with a short-axis beamwidth in the y-direction. The respective beam width can, for example, be defined as the width of the intensity profile I (x, y) at 50% of the maximum intensity (FWHM, Full Width at Half Maximum) or, for example, as the width between the 90% intensity values (Full Width at 90% Maximum, FW@90% ) or defined in some other way.

In some embodiments, the workpiece may include a surface layer of amorphous silicon that is converted to polycrystalline silicon using the laser line 24 . For processing, the laser line 24 can be moved in a direction of movement relative to the working plane 26 . In other exemplary embodiments, the workpiece can be a transparent carrier plate from which an adhering film, for example an OLED film, is to be detached.

The line optics system 10 has at least one laser light source 12 . In preferred exemplary embodiments, the laser light source 12 can be a solid-state laser. Laser light source 12 generates at least one laser beam 20. In preferred embodiments, laser light source 12 can generate a plurality of laser beams. In alternative exemplary embodiments, the line optics system 10 has a plurality of laser light sources 12, with each laser light source 12 generating at least one laser beam 20.

The line optics system 10 also has an optical arrangement 14 . The optical arrangement 14 is set up to generate an illumination beam 22 from the at least one laser beam 20 along a beam path. The illumination beam 22 defines a beam direction that intersects the working plane 26 . In the region of the working plane 26, the illumination beam 22 has a beam profile which, perpendicular to the beam direction, has a long axis with a long-axis beam width and a short axis with a short-axis beam width. In other words, the illumination beam 22 has a linear beam profile in the area of the working plane 26 . The illumination beam 22 thus generates the laser line 24 in the working plane 26. The optical arrangement has a row of beam-guiding and beam-shaping optics 16 and a focusing unit 18 along the beam path. The focusing unit 18 is arranged downstream of the beam-guiding and beam-shaping optics 16 .

The beam-guiding and beam-shaping optics 16 are set up to generate the illumination beam 22 from the at least one laser beam 20 . The optical arrangement can have, for example, a beam transformer, a homogenizer and large optics as beam-guiding and beam-shaping optics 16 . The focusing unit 18 is set up to focus the illumination beam 22 . In particular, the focusing unit 18 focuses the illumination beam 22 in the short-axis direction.

The focusing unit 18 has a focusing lens 28 for focusing the illumination beam 22 . The focusing lens 28 may include one or more optics. The focusing lens 28 can be moved parallel to the beam direction. The focusing unit 18 has a movement device 30 which is set up to move the focusing lens 28 parallel to the beam direction. The movement device 30 has a linear guide 32 and a drive device 34 . The linear guide 32 thus provides a guide for the focusing lens 28 parallel to the beam direction. The focusing lens 28 can be moved along the linear guide 32 . The drive device 34 is set up to move the focusing objective 28 parallel to the beam direction, in particular along the linear guide 32 .

The line optics system 10 also has a camera system 36 . The camera system 36 is set up to observe the illumination beam 22 downstream of the focusing lens 28 . In particular, the camera system 36 is set up to observe the illumination beam 22 at a defined position downstream of the focusing lens 28 . The illumination beam 22 has a specific focus state at this defined position. The camera system 36 has an imaging system 38 and a camera 40 . The imaging system 38 images the illumination beam 22 onto the camera 40 . The camera 40 is set up to record an image of the illumination beam 22 . In particular, the camera 40 is arranged in such a way that it takes an image of the illumination beam 22 at the defined position downstream of the beam of the focusing lens 28 receives. The image thus has an image of the illumination beam 22 at the defined position.

The camera system 36 is set up in particular to observe the illumination beam 22 at at least three defined positions downstream of the focusing lens 28, the illumination beam 22 having a specific focus state at each of the defined positions. For this purpose, the camera system 36 has at least one camera 40 that records at least one image that has images of the illumination beam 22 at the at least three defined positions. In a preferred embodiment, the camera system 36 has only one camera 40 for recording an image, this image having the images of the illumination beam 22 at the at least three defined positions. In an alternative embodiment, the camera system 36 can also have a plurality of cameras 40, with each camera 40 recording an image and each image having an image of the illumination beam 22 at one of the defined positions.

The camera system 36 can have a beam splitter 42 . The beam splitter 42 can be arranged in the beam path between the imaging system 38 and the camera 40 . The beam splitter 42 is set up to split the illumination beam 22 to be observed into partial beams. The at least one camera 40 is set up to image the partial beams in the at least one image, with the images of the partial beams corresponding to the images of the illumination beam 22 at the at least three defined positions. In particular, the beam splitter 42 is constructed in such a way that the partial beams pass through the beam splitter 42 with paths of different lengths. The partial beams can be recorded with a camera 40 and displayed together in one image, preferably side by side. Alternatively, the partial beams can be recorded with a plurality of cameras 40 and each imaged in separate images.

The line optics system 10 also has a control device 44 . The control device 44 is set up to regulate the position of the focusing lens 28 parallel to the beam direction. For this purpose, the control device 44 can, for example, send corresponding control commands to the movement device 30 . The movement equipment Device 30 can then be moved by means of the drive device 34, the focusing lens 28 according to the control commands along the linear guide 32. Furthermore, the control device 44 can receive data from the camera system 36 . The data may include one or more captured images. The control device 44 regulates the position of the focusing lens based on the data from the camera system 36.

In order to regulate the position of the focusing lens 28, the control device 26 can have various sub-units, for example, which each control a component of the line optics system 10 and/or process data. For this purpose, the control device 44 can have, for example, a control unit and a data processing unit. The control unit can, for example, generate control commands by means of which the position of the focusing objective is controlled. The data processing unit can, for example, carry out calculation steps based on which the data received from the camera system 36 are analyzed. On the basis of this analysis, the position of the focusing objective 28 is then regulated accordingly, in particular the corresponding control commands are generated.

The control device 44 can be connected to or have a non-volatile data memory in which a computer program is stored. In some embodiments, controller 4 is a general purpose computer, such as a commercially available personal computer running Windows®, Linux, or MacOS, and the computer program from memory includes program code designed and configured to implement control of focusing lens 28 . In an alternative embodiment, the controller 44 is a logic circuit such as a Field Programmable Gate Array (FPGA), an Application-Specific Integrated Circuit (ASIC), a microcontroller, or any other appropriate programmable electrical circuit. Therein, the regulation of the focusing objective 28, in particular control and determination steps, can be implemented with the logic circuit, so that the logic circuit for implementing the regulation of the focusing objective 28 is designed and constructed. To implement the control of the focusing lens 28 in the logic circuit, any measured programming language or hardware description language can be used, such as C, VHDL and the like.

The control device 44 is set up to determine a focus position of the focus of the focusing lens 28 on the basis of the focus states at the at least three defined positions and to regulate a position of the focusing lens 28 parallel to the beam direction in such a way that the focus position is arranged in the working plane 26 is. For example, the control device 44 can analyze the focus states at the defined positions observed by means of the camera system 36 in order to determine the focus position on the basis thereof. The control device 44 can then regulate the position of the focusing lens 28 accordingly on the basis of the determined focus position. In particular, the position of the focusing objective 28 is adjusted in such a way that the focus position is shifted into the working plane 26 .

In FIG. 2(A) a focusing lens 28 is shown as an example that focuses an illumination beam at a focus position 46 . Two beam profiles of the illumination beam 22 in the direction of the short axis are shown in FIGS. 2(B) and 2(C). 2(B) shows a Gaussian profile. 2(C) shows a rectangular beam profile, a so-called top hat profile.

Both beam profiles from FIGS. 2(B) and (C) have a steepness in the edge area or edge area of the beam profile. The steepness suppresses the drop in intensity y over the path x on the edge, i.e. in the edge area of the beam profile. The flank is the edge area of the profile where the gradient is greatest. The slope is thus defined by the quotient y/x. Correspondingly, the inverse of the slope is defined as the quotient x/y.

Both beam profiles of Figures 2(B) and (C) also have a width. In particular, the width of the beam profile can be taken to be the width of the region of the beam profile in which the intensity values are equal to or greater than 1/e ² , 50% or 90% of the maximum value of the intensity of the beam profile. In the focus position 46, the beam profile of the illumination beam has a minimum width and a maximum steepness in the direction of the short axis. The further one moves away from the focus position 46 parallel to the beam direction, the smaller the steepness of the beam profile becomes and the larger the width and the inverse of the steepness of the beam profile become.

The slope, the inverse of the slope or the width of the beam profile can thus be used to describe the focus state of the illumination beam at a specific position in the beam direction. In other words, the slope, the inverse of the slope or the width of the beam profile can be a focus value of the focus state.

In Fig. 3 (A) is shown as an example of how the focus position 46 of the focusing lens 28 can shift during operation due to thermal effects, while the position of the focusing lens 28 does not change. The original focus position is denoted by reference number 46 . The shifted focus position is denoted by reference numeral 46'.

In Fig. 3 (B) is shown as an example of how the focus position 46 of the focusing lens 28 can be regulated. The focusing lens 28 can be moved along the linear guide 32 . In the representation of Fig. 3(B), the focusing lens is shifted in the direction of the focus position, for example, with the position of the shifted focusing lens being denoted by the reference numeral 28". Correspondingly, the shifting of the focusing lens 28 also shifts the focus position 46 accordingly, with the shifted focus position is denoted by reference numeral 46''.

4 shows four exemplary arrangements of the camera system 36 in the beam path of the line optics system 10, on which the camera system 36 can observe the illumination beam 22. In FIG. 4(A), the camera system 36 is arranged behind the working plane 26. In FIG. In this arrangement, the camera system 36 observes the illumination beam 22 as it passes through the working plane.

In FIG. 4(B), a deflection mirror 48 is arranged in the beam path between the focusing lens 28 and the working plane 26, which deflects the illumination beam 22 in the direction of the working plane 26. The deflection mirror 48 is partially transparent. The camera system 36 is arranged in such a way that the part let through by the deflection mirror 48 runs in the direction of the camera system 36 . In this arrangement, the camera system 36 observes the part of the illumination beam 22 that is allowed to pass through the deflection mirror 48.

In FIG. 4(C), the illumination beam 22 is reflected at the working plane 26. In FIG. The camera system 36 is arranged in such a way that the illumination beam reflected at the working plane 26 runs in the direction of the camera system 36 . In this arrangement, the camera system 36 observes the illumination beam 22 reflected at the working plane.

In FIG. 4(D), further optics 50, for example a protective glass, are arranged in the beam path between the focusing lens 28 and the working plane 26, through which the illumination beam 22 passes in the direction of the working plane 26. A part of the illumination beam 22 is reflected at the additional optics 50 . The camera system 36 is arranged in such a way that the part of the illumination beam 22 reflected on the further optics 50 runs in the direction of the camera system 36 . In this arrangement, the camera system 36 observes the part of the illumination beam 22 reflected by the further optics 50.

5(A) shows an exemplary embodiment of a camera system 36 of the line optics system 10 from FIG. 1, with which the illumination beam 22 of the line optics system 10 can be observed at a defined position. In the camera system 36, the illumination beam 22, in particular the working plane 26, is imaged onto the camera 40 by means of the imaging system 38. The mapping plane the imaging of the illumination beam 22 in the camera is denoted by the reference numeral 52 . The camera system 36 and the camera 40 are preferably arranged in such a way that the imaging plane 52 lies at a target position of the focus position 46 . However, the imaging plane 52 can also be arranged at any desired position in the beam direction.

5(B) shows a further exemplary embodiment of the camera system 36 of the line optics system 10 from FIG. 1, with which the illumination beam 22 of the line optics system 10 can be observed at three defined positions. In the camera system 36 the illumination beam 22 is imaged on the camera 40 by means of the imaging system 38 . In this embodiment, the camera system 36 additionally has the beam splitter 42 . The beam splitter 42 divides the illumination beam 22 into three partial beams. The partial beams run parallel to one another from the beam splitter 42 to the camera 40 and are imaged on the camera 40 . The partial beams are spaced apart and do not overlap. In an image recorded by the camera 40, the partial beams are thus displayed next to one another, that is to say at a distance from one another.

The partial beams have paths of different lengths within the beam splitter 42 . Due to the different lengths of travel of the partial beams, the partial beams are imaged in different imaging planes 52, 52', 52" in the camera. A first partial beam is in plane 52', a second partial beam in plane 52 and a third partial beam in plane 52 " pictured. The paths of the partial beams in the beam splitter 42 are such that the imaging planes 52, 52', 52" are consecutive and offset from one another at the same distance. In particular, the imaging plane 52 is arranged between the imaging planes 52' and 52" and points to the same distance up. By means of the beam splitter 42, the partial beams of the illumination beam 22 are thus imaged on the camera 40 at different defined positions downstream of the focusing lens 28 and thus also with different focus states. The three images of the partial beams of the illumination beam 22 on the camera 40 are thus three images of the illumination beam 22 at three defined positions zi, Z2, Z3 downstream of the focusing lens 28. The first partial beam is at position zi, the second partial beam at position Z2 and the third partial beam is imaged at position Z3. The camera system 36 and the camera 40 are preferably arranged in such a way that the imaging plane 52 of the second partial beam lies at a target position of the focus position 46 . In the representation of FIG. 5(B), the imaging plane 52 of the second partial beam is arranged at the focal position 46 . Correspondingly, the imaging plane 52' is arranged in front of the focus position 46 and the imaging plane 52" behind the focus position 46. In this case, the camera 40 takes the beam profiles (image at position zi), at (image at position Z2) and behind (image at Position Z3) of the focus position 46 on.

As explained above with reference to FIGS. 2(B) and (C), the beam profile of the illumination beam 22 can be a Gaussian profile or a rectangular intensity profile, a so-called top hat profile. The control device 44 can analyze the corresponding imaged beam profile for each image of the partial beams, ie at each of the three defined positions zi, Z2, Z3, in order to determine the focus state at the respective position zi, Z2, Z3. For this purpose, for example the slope, the inverse of the slope or the width of the beam profile can be determined as the focus value Si, S2, S3 of the focus state.

6 shows how the focus values Si, S2, S3 determined at the three defined positions zi, Z2, Z3 change when the focus position 46 of the focus of the focusing lens 28 changes, in particular due to heating of the optics , shifts. The inverse of the steepness is used as the focus value in FIG. In the diagrams of FIGS. 6(A) to (C), the focus value distribution 56, 56', 56" is plotted in the beam direction (z-direction) for different positions of the focus position 46. The focus value distributions 56, 56', 56" have a parabola-shaped course, the minimum of the parabola being at the location of the focus position 46 .

A focus value distribution 56 is shown in FIG. 6(A), the focus position 46 being at position Z2. The focus value distribution 56 thus has its minimum at position Z2.

In Fig. 6(B) is a focus value distribution 56', wherein the focus position 46 is shifted in the beam direction (z-direction) from the illustration in Fig. 6(A). The minimum of Focus value distribution 56′ lies downstream of positions zi, Z2, Z3 in the vicinity of position Z3. The beam profile 56 is drawn in with a dashed line for comparison.

In Fig. 6(C) there is a focus value distribution 56", the focus position 46 being shifted further in the beam direction (z-direction) compared to the representations in Fig. 6(A) and (B). The minimum of the focus value distribution 56 ' is located further downstream of the position Z1, Z2, Z3 in from the position Z3 compared to Fig. 6(B).The beam profile 56 is drawn in dashed line for comparison.

Instead of the steepness or the inverse of the steepness, the width of the respective beam profiles at positions zi, Z2, Z3 can also be used as the focus value, with the width changing in the same way at the respective positions.

A further embodiment of the camera system 36 of the line optics system from FIG. 1 is shown in FIG. 7(A). The camera system 36 has basically the same structure as the camera system 36 shown in FIG. 5(B). The imaging system 38 is designed as a telescope arrangement. The telescope arrangement enlarges the image of the illumination beam 22 by a factor k. The enlargement thus leads to a change in scale.

The illumination beam 22 is reflected multiple times in the beam splitter 42 between two mirrors. The mirrors are arranged parallel to one another and have a distance d from one another. One of the mirrors is partially transparent, with the partial beams being transmitted through this mirror in the direction of the camera 40 . Due to the different number of reflections between the mirrors, the partial beams have paths of different lengths. The path difference between two adjacent partial beams is 2d. The offset öz of the positions zi, Z2, Z3 in the direction of the beam then results from the formula öz=2d×g(k) due to the change in scale, where g(k) describes a functional relationship to the enlargement k. For a Gaussian beam, for example, g(k)=1/k ^A 2 applies. In other words, δz is the distance between the three imaging planes 52, 52', 52". FIG. 7(B) shows an intensity profile of an image taken with the camera 40 of the camera system 36 of FIG. 7(A) along the short axis direction (y-direction). The illumination beam 22 has a rectangular beam profile. The intensity profile has the images of the beam profiles of the three partial beams of the illumination beam 22 . In this case, the beam profiles are arranged next to one another in the intensity profile, ie spaced apart from one another in the direction of the short axis.

FIGS. 8(A) to (E) show five measurements of the beam profiles at positions zi, Z2, Z3 and the corresponding focus value distributions at different focus positions. From Fig. 8A) to Fig. 8(E), the focus position was shifted by 250 pm each time. In Fig. 8(C), the focus position is approximately at position Z2. Assuming that the focus position is 0 pm in Fig. 8(C), the focus position is -500 pm in Fig. 8(A), -250 pm in Fig. 8(B), in 8(C) at 0 pm, in Fig. 8(D) at 250 pm and in Fig. 8(E) at 500 pm. The position of the focus values Si, S2, S3 at the respective positions zi, Z2, Z3 also changes in accordance with the shift in the focus position.

[0092] An example of a method is described below, with which the focus position of the focus of the focusing lens 28 can be determined on the basis of the determined focus values Si , S2 , S3 at the positions zi , Z2 , Z3 .

For this purpose, it is initially assumed that the focus value distribution follows a parabola, as shown in FIG. 6, for example. This is the case, for example, for a Gaussian beam. As explained above, the gradient, the inverse of the gradient or the width of the beam profile at each position zi, Z2, Z3 can be determined as the focus value.

The course of the parabola in the beam direction (z-direction) can be described with the formula f(Z)=a(Z−Z′) ² +β. Here, Z' indicates the position of the extremum of the parabola. The discrete derivation of this formula using the positions zi, Z2, Z3 is given by

The discrete derivative on the left is given by:

A = _s3 -Si

The second derivative is given by:

B — = 2a öz ^z

where B is given by:

B = _s3 - _2S2 + Si

From this, the focus position at the time of image recording can be determined using the formula:

As previously explained, δz is the distance between positions zi, Z2, Z3.

An example of a control process for controlling the position of the focusing lens 28 will be described below. Initially, the focusing lens 28 is at a position Pi. In a first step, the camera system 36 carries out a measurement at a point in time h. For the measurement, the camera system 36 observes the illumination beam 22 at at least three defined positions. In particular, the camera system 36 observes the illumination beam 22 at the positions zi, Z2, Z3 by means of the camera 40, as previously described.

In a further step, the control device 44 determines a focus value of the focus state at the corresponding defined position. For this purpose, the control device 44 analyzes the beam profile at each defined position in order to determine the focus value of the focus state at the corresponding defined position. In particular, the focus values Si, S2, S3 are determined at the positions zi, Z2, Z3. This is shown again as an example in FIGS. 9(A) and (B). Fig. 9(A) shows the beam profiles at positions zi, Z2, Z3. 9(B) shows the corresponding focus value distribution of the focus values Si , S2, S3. For example, the slope, the inverse of the slope or the width of the beam profile can be determined as focus values.

In a further step, the control device 44 then determines the focus position on the basis of the focus values determined. In particular, the method described above can be used for this purpose, in which case the quantities A and B are first determined, and the focusing position can then be determined on the basis of the quantities A and B.

In a further step, the control device 44 then regulates the position of the focusing lens 28 in such a way that the focal position of the focus of the focusing lens 28 is arranged in the working plane 26 . The position of the working plane is predetermined and gives a target position for the focus position. The focus position determined by the controller 44 is an actual position of the focus position. The control device 44 regulates the position of the focusing lens 28 in such a way that the focus position moves from the actual position to the desired position at a predetermined speed vo. In particular, the focusing lens 28 is moved between the desired and actual position according to the difference, in particular the difference vector. The speed vo can, for example, be specified in advance, in particular by a user. In a preferred embodiment, the target position of the focus position at the

Position S2 lie. In this case, the focusing lens 28 becomes the position

proceed with the speed vo.

The control steps can then be repeated at a later point in time t2, with the focusing lens 28 then being moved further starting from the position P2.

In particular, the control steps mentioned above can be repeated at regular time intervals in order to regularly readjust the focus position of the focus of the focusing lens during operation of the line optics system.

Such a regular readjustment is shown in FIG. 10 by way of example. Fig. 10 shows simulation results in which the run-in behavior of the focus position according to equation

was modulated in time.

The representation also contains the focus position determined by the method described and corresponding compensation δz _CO m _P by moving the lens. The simulation shows that the measuring principle and the proposed method for tracking the focus during operation, i.e. for so-called online tracking of the focus, is sufficient.

Another embodiment of a camera system for capturing an image is described in FIG. 11(A). This embodiment differs from the embodiment of FIG. 7(A) in that the beam splitter 42 is set up to split the illumination beam 22 into more than three partial beams. In this way, the camera system 36 can observe more than three defined positions downstream of the focusing lens 28 . The number of positions to be observed corresponds to the number of partial beams. The number of defined positions to be observed can be, for example, between four and 20, preferably between five and 15, in particular seven or ten. In the present embodiment of FIG. 11, seven defined positions are observed. The defined positions are preferably arranged one after the other at equal intervals in the beam direction (z-direction).

The camera 40 of the camera system 36 can record an image in which the partial beams are imaged. In Fig. 11(B), an intensity profile of the image picked up by the camera 40 along the short axis direction (y-direction) is shown. The beam profiles of the partial beams are arranged next to one another in the intensity profile.

The controller 44 can then determine a focus value for each of the defined positions based on the beam profiles. The focus value history of the determined focus values is shown in Fig. 11(C). On the basis of the determined focus values, the focus position can then be determined using a correspondingly adapted method.

[00114] If a parabola is assumed to model the course of the focus values, an overdetermined system of equations is obtained when considering more than three defined positions, which system can be solved, for example, by means of a best fit calculation, in order to determine the focus position.

[00115] Alternatively, another function can also be used for modeling the course of the focus values, which has a global extremum, in particular a Gaussian function or an even polynomial function with degree four or higher. The number of defined positions to be observed by means of the camera system 36 is preferably greater than or equal to the degree of the polynomial function plus one. [00116] By observing more than three defined positions, the focus position can be calculated more precisely. In addition, there is direct access to parameters such as depth of field, which is possible online in this measurement.

Claims

Line optics system (10) for generating a defined laser line (24) on a working plane (26), with: at least one laser light source (12) for generating at least one laser beam (20); an optical arrangement (14) which is set up to generate an illumination beam (22) from the at least one laser beam (20) along a beam path, the illumination beam (22) defining a beam direction which intersects the working plane (26), wherein the illumination beam (22) forms the defined laser line (24) in the area of the working plane (26), the optical arrangement (14) in the beam path having a focusing unit (18) with a focusing objective (28) for focusing the illumination beam (22), wherein the focusing lens (28) is movable parallel to the beam direction; a camera system (36) configured to observe the illumination beam (22) at at least three defined positions downstream of the focusing lens (28), the illumination beam (22) having a focus state at each of the at least three defined positions; and a control device (44), which is set up to determine a focus position of the focus of the focusing lens (28) on the basis of the focus states at the at least three defined positions and to regulate a position of the focusing lens (28) parallel to the beam direction in such a way that the Focus position is arranged in the working plane (26). Line optics system (10) according to claim 1, wherein the camera system (36) is arranged downstream of the working plane (26). Line optics system (10) according to Claim 1, in which the line optics system (10) has further optics (48, 50) which are arranged downstream of the focusing unit (18), the further optics (48, 50) being set up to focus the illumination beam ( 22), with part of the illumination beam (22) running in the direction of the working plane (26) and another part of the illumination beam (22) running in the direction of the camera system (36). Line optics system (10) according to one of Claims 1 to 3, the camera system (36) having at least one camera (40) for recording at least one image, the at least one image having images of the illumination beam (22) at the at least three defined positions. Line optics system (10) according to Claim 4, in which the camera system (36) has a beam splitter (42) which is set up to split the illumination beam (22) into partial beams, the at least one camera (40) being set up to convert the partial beams into to form the at least one image, the images of the partial beams corresponding to the images of the illumination beam (22) at the at least three defined positions. Line optics system (10) according to Claim 4 or 5, wherein the control device (44) is set up to determine a focus value of each focus state at the at least three positions based on the at least one image, the focus position of the focus of the focusing lens (28) being based on of the determined focus values is determined. The line optics system (10) of claim 6, wherein for each image of the illumination beam (22) in the at least one image, a beam profile of the illumination beam (22) in the short axis direction is determined, each focus value being determined based on the beam profile of the corresponding image . Line optics system (10) according to one of Claims 1 to 7, in which a position of the working plane (26) is predetermined downstream of the focusing objective, the control device (44) being set up to regulate the position of the focusing objective (28) parallel to the beam direction in such a way that that the focus position of the focus of the focusing lens (28) is shifted from the determined focus position to the position of the working plane (26). Line optics system (10) according to one of Claims 1 to 8, the line optics system (10) having a movement device (30) for moving the focusing lens (28) parallel to the beam direction, the control device (44) being set up to move the movement device (30 ) to regulate the position of the focusing lens (28). Line optics system (10) according to one of Claims 1 to 9, the optical arrangement (14) also having beam-guiding and beam-shaping optics (16) which are set up to generate the illumination beam (22) from the at least one laser beam (20). .