Methods and systems for measuring base elements of a construction cylinder arrangement

Abstract

The disclosure provides methods and systems for measuring a base element of a construction cylinder arrangement in machines for the additive manufacture of 3D objects using a high-energy beam, wherein a measurement pattern is produced from laser light that illuminates the base element, and sites of incidence of the laser light are monitored and evaluated with a camera to produce measuring data about the base element, e.g., position information, orientation information, and/or information about the shape of the surface of the base element. The measurement patterns are produced by deflecting measuring laser beams by an optical scanner system towards the base element, and the camera is arranged laterally offset from the deflected laser beams. The new methods and systems enable measuring base elements in a simple and flexible manner, and require only a small amount of space in the processing chamber.

Claims

1. A method for measuring a base element of a construction cylinder arrangement, wherein the construction cylinder arrangement including a base element, a piston, and a substantially cylindrical base body, is arranged on a machine for additive manufacturing of three-dimensional objects by sintering or melting a powdery material using a high-energy beam, and the base element can be moved by the piston in the substantially cylindrical base body of the construction cylinder arrangement, the method comprising producing a measurement pattern from laser light that illuminates at least part of the base element, wherein the measurement pattern is produced by deflection of a laser beam of a measuring laser by a scanner optical system such that differently deflected laser beams are produced and the deflected laser beams are oriented at least towards the part of the base element; illuminating the base element with the laser light; and monitoring sites of incidence of the laser light on the base element with a camera to produce measuring data about the base element, wherein the measuring data comprises information about a three-dimensional shape of at least a part of a surface of the base element and one or both of position information and orientation information, wherein the camera is arranged in a laterally offset manner in relation to the deflected laser beams, and wherein the measurement pattern is used to determine at least the three-dimensional shape of at least the part of the surface of the base element.

2. The method of claim 1, wherein the piston has an upper piston part, on which the base element is arranged, and a lower piston part, against which the upper piston part can be aligned by at least two adjusting elements.

3. The method of claim 2, wherein the measurement pattern is produced by illuminating at least a part of the base element in three different zones.

4. The method of claim 3, wherein locations of at least two of the three different zones substantially correspond to locations of the at least two adjusting elements with which the base element can be tilted with respect to a reference structure.

5. The method of claim 3, wherein the measurement pattern in each of the three zones comprises a plurality of laser points.

6. The method of claim 1, wherein measuring the base element further provides information relating to a tilting of the base element relative to a reference structure.

7. The method of claim 1, wherein the measurement pattern comprises a line-by-line scan of at least the part of the surface of the base element, wherein a plurality of individual images are taken with the camera during the line-by-line scan.

8. The method of claim 1, wherein the measurement pattern is further used to determine a height of the base element relative to a reference structure.

9. The method of claim 1, further comprising comparing the sites of incidence of the laser light on the base element monitored with the camera with expected sites of incidence of the laser light on the base element for measuring the base element.

10. The method of claim 9, wherein the measurement pattern illuminates only the base element or wherein only sites of incidence of the laser light on the base element are evaluated, or both.

11. The method of claim 1, wherein the machine further comprises a machining laser, and after the measuring of the base element, then for manufacturing layers of at least one three-dimensional object on the base element, at least parts of layers of powdery material on the base element are illuminated with machining patterns made of laser light, wherein the machining patterns are generated by deflecting a laser beam of the machining laser by the scanner optical system.

12. The method of claim 1, wherein after the measuring of the base element then layers of powdery material are applied on the base element for manufacturing layers of at least one three-dimensional object on the base element, wherein the layers of powdery material are optically checked with the camera before the high-energy beam is used.

13. The method of claim 1, wherein the measurement pattern comprises at least one triangulation point, in a measurement sequence sites of incidence of the at least one triangulation point are monitored at different travel positions of the base element in the base body using the camera and associated measurement sequence data are obtained, wherein the triangulation point is generated by a deflected laser beam which is directed at the base element at a fixed angle during the measurement sequence, the measurement sequence data are compared with reference measurement sequence data from a reference measurement sequence, wherein the sites of incidence of the at least one triangulation point were also monitored within a scope of the reference measurement sequence at different travel positions of a reference base element in the base body using the camera and the associated reference measurement sequence data were obtained, wherein the triangulation point was generated by a deflected laser beam, which was directed at the reference base element at a reference angle fixed during the reference measurement sequence, and correction information for the measuring of the base element is derived from the comparison of the measurement sequence data and the reference measurement sequence data.

14. The method of claim 13, wherein the measurement pattern comprises at least three triangulation points, and the triangulation points are formed as corner points of the measurement pattern, to which straight portions of the measurement pattern adjoin.

15. The method of claim 13, wherein one or more curve parameters are each determined from the measurement sequence data and the reference measurement sequence data, which in each case describe a fitted curve, which is fitted to the sites of incidence monitored as a function of the travel position of the base element in the base body.

16. The method of claim 15, wherein the correction information is determined from an offset of the curves of the measurement sequence data and the reference measurement sequence data.

17. The method of claim 15, wherein each fitted curve is a hyperbolic curve and the curve parameters are hyperbolic parameters, a position of a pole point of the fitted hyperbolic curve is determined from the one or more hyperbolic parameters, and the correction information is determined from a comparison of the positions determined of the pole points of the fitted hyperbolic curve of the measurement sequence data and the reference measurement sequence data.

18. The method of claim 13, wherein the fixed angle extends obliquely to a direction of travel of the base element in the base body.

Description

DESCRIPTION OF DRAWINGS

(1) The machines and methods described herein are illustrated in the drawing and are explained in more detail below.

(2) FIG. 1 is a schematic view of an embodiment of a machine as described herein for the additive manufacturing of three-dimensional objects for carrying out the methods disclosed herein.

(3) FIG. 2 is a schematic longitudinal section of a construction cylinder arrangement.

(4) FIG. 3 is an illustration of a triangulation measurement.

(5) FIG. 4 is a schematic plan view of a base element, to which a measurement pattern is directed, without tilting and with tilting of the base element, as used in the methods described herein.

(6) FIG. 5 is a schematic side view when scanning a preform line by line, as disclosed herein.

(7) FIG. 6 is a schematic overview for the detection of a triangulation point of a measurement pattern, with different travel positions of a base element.

(8) FIG. 7 is a schematic overview of a measurement pattern for four triangulation points.

(9) FIG. 8 is a schematic overview of the image recognition in the measurement pattern from FIG. 7.

(10) FIG. 9 is a graph that illustrates a set of reference measurement sequence data.

(11) FIG. 10 is a graph that illustrates a set of measurement sequence data and a fit curve of the reference measurement sequence data of FIG. 9, for a calibration via a curve offset.

(12) FIG. 11 is a graph that schematically illustrates calibration via the offset of pole points, based on fitted hyperbolic curves as shown in FIG. 10 and FIG. 11.

DETAILED DESCRIPTION

(13) FIG. 1 shows a schematic side view of an embodiment of a machine 1 for the additive manufacturing of a three-dimensional object 2 (or also a plurality of three-dimensional objects), also called a 3D printing machine.

(14) The machine 1 includes a gas-tight processing chamber 3, which can be filled and/or flushed in a manner not shown with an inert gas (protective gas), such as nitrogen or a noble gas such as argon.

(15) Connected to the processing chamber 3 is a powder cylinder arrangement 4 with a powder cylinder (storage cylinder) 5 for a powdery material 6 (shown with dots), from which the three-dimensional object 2 is manufactured here by sintering or melting. The powdery material 6 can, for example, include or consist of metal particles with an average grain size (D50) of 25-100 μm; in other applications, plastics material particles or ceramic particles of similar size can also be used. By gradually raising a powder piston 7 with a first lifting device (powder lifting device) 8, a small amount of the powdery material 6 is raised above the level of the bottom 9 of the processing chamber 3, so that using a motor-operated slider 10 this small amount can be brought to a construction cylinder arrangement 11.

(16) The construction cylinder arrangement 11, which is also connected to the processing chamber 3, has the piston 12, on the top of which a base element 13, here a substrate 13a, is arranged. The three-dimensional object 2 is built on the base element 13. The base element 13 can be moved vertically with the piston 12 in a base body 14. The piston 12 is constructed in multiple parts and is provided with adjusting elements in order to be able to correct a tilting of the base element 13 in the construction cylinder arrangement 11 (not shown in more detail, but see FIG. 2).

(17) Each time before the manufacturing of a new layer of the three-dimensional object 2, the piston 12 is lowered by one step using a second lifting device (lifting device) 15, and a small amount of the powdery material 6 is spread into the construction cylinder arrangement 11 with the slider 10. The applied layer of the powdery material 6 is checked with a camera 21 and a test device 28 connected to the camera (operating an image evaluation software); if necessary, the applied layer can be corrected with the slider 10 and/or with further powdery material 6. For example, a damaged slider 10 can be identified on the basis of a faulty powder application and subsequently exchanged in order to correct the applied layer. The camera 21 is preferably provided with a shifted optical system (not shown in detail). The camera 21 is arranged here behind a window 21a outside the processing chamber 3.

(18) Then the newly applied powder layer is illuminated locally and thus locally strongly heated from above using a high-energy beam 16, here a machining laser beam 16a, from a high-energy beam source 17, here a machining laser 17a, at locations which are intended for local solidification (melting, sintering) of the powdery material 6.

(19) The machining laser beam 16a is guided through a beam splitter 18 via a scanner optical system 19, containing one or more mirrors, which can be pivoted in total about at least two axes, via a focusing optical system 29 and through a window 20. The scanner optical system 19 and the focusing optical system 29 are located centrally above the base element 13 here. By means of the scanner optical system 19, the machining laser beam 16a can scan the base element 13 or the uppermost powder layer thereon in accordance with the intended shape of the three-dimensional object 2 (“machining pattern”).

(20) After that, further layers are manufactured until the three-dimensional object 2 is completed. Excess powdery material 6 can be spread with the slider 10 in a collection container 6a.

(21) As described herein, the machine 1 has a measuring system 22 for measuring the base element 13, e.g., before the start of the manufacture process, in order to be able to detect any deformations (such as tilting) on the base element 13 and, if necessary, to correct them.

(22) The measuring system 22 includes its own measuring laser 23, the laser beam 24 of which can be coupled via the beam splitter 18 into the scanner optical system 19 also used by the machining laser beam 16a or the beam path thereof, so that laser beams 24a of the measuring laser 23 deflected by the scanner optical system 19 can be directed at least onto parts of the base element 13 according to a measurement pattern. The deflected laser beams 24a spread downwards in the vertical direction or at a small angle (usually ≤30°, preferably 20°) with respect to the vertical. The scanner optical system 19 is connected to a control device 25, in which one or more measurement patterns or corresponding control commands for controlling the scanner optical system 19 for measuring the base element 13 are programmed.

(23) The measuring system 22 also includes the camera 21, which is also used for checking the powder bed. The surface of the base element 13 can be recorded with the camera 21, so that the actual sites of incidence of the deflected laser beams 24a of the measuring laser 23 can be recorded in accordance with the measurement pattern. The camera 21 is connected to an evaluation device 26 with which the observed sites of incidence are evaluated and converted into measuring data about the base element 13, for example a tilt of the base element. Here, the evaluation device typically uses reference information (“target images”). These measuring data can then be used to correct the position or orientation of the base element 13, possibly also iteratively.

(24) The camera 21 is offset from the base element 13 in the horizontal direction, cf. offset 27 (shown here between the edge of the base element 13 and the center of the camera lens of the camera 21; note that in practice the camera lens is usually much smaller than the offset 27). It is thereby achieved that the camera 21 “looks at” the deflected laser beams 24a at an angle (usually >20°).

(25) FIG. 2 shows a construction cylinder arrangement 11, such as can be used in the machine of FIG. 1, in a schematic longitudinal sectional view.

(26) In the approximately cylindrical base body 14, the piston 12 can be moved along the vertical cylinder axis with the second lifting device 15.

(27) The piston 12 has an upper piston part 12a on which the base element 13, here a substrate 13a, is arranged and fastened on the upper side. The upper piston part 12 has a powder seal 30, with which a gap to the base body 14 is closed, so that powdery material cannot penetrate, or can penetrate only in very small quantities, further downward into the construction cylinder arrangement 11. The upper piston part 12a typically has a heater with which the base element 13 and powdery material located thereon can be heated (not shown in more detail).

(28) The upper piston part 12a is arranged on a middle piston part 12b, a ceramic insulation plate 31 being arranged between the upper piston part 12a and the middle piston part 12b.

(29) The middle piston part 12b is mounted here on a lower piston part 12c via three adjusting elements 32. The adjusting elements 32 can for example be designed as piezo actuators. The adjusting elements 32 allow to set a tilting of the middle piston part 12b (and thus also the upper piston part 12a) with respect to the lower piston part 12c relative to two horizontal axes. The lower piston part 12c has a gas seal 33, which seals the gap to the base body 14 and prevents the penetration of atmospheric oxygen into the interior of the construction cylinder arrangement 11 during the manufacturing of a three-dimensional object. The lower piston part 12c typically has cooling (not shown in more detail).

(30) FIG. 3 explains the principle of measuring a base element, for example determining the local height position of a part of the base element, within the scope of the present disclosure. The base element is measured, e.g., by means of triangulation. Thereby, a measurement pattern is projected onto the base element, the target position of the measurement pattern (or the sites of incidence of the laser beam) on the base element being known on the basis of the scanner optical system control and the (target) geometry of the base element, and position or orientation information is obtained from the deviation of the actual, current measurement pattern (or the sites of incidence of the laser beam) on the base element, monitored, e.g., observed or imaged, by a laterally offset camera.

(31) The laser beam 24 of the measuring laser 23 is deflected at the scanner optical system 19, cf. the deflected laser beam 24a. The deflected laser beam 24a has an angle β with respect to the vertical which is parallel to a z-axis; typically β is in a range of +/−30° or less, or +/−20° or less.

(32) The deflected laser beam 24a strikes a surface O1 of the base element at a site of incidence A1. A camera, with the camera lens 40 which is laterally offset in the horizontal x-direction, observes the site of incidence A1. The site of incidence A1 is imaged as the site of projection P1 on a camera sensor 41 or a corresponding image plane.

(33) If the surface of the base element is lower in the vertical z-direction by the height difference dz (cf. the surface O2), the camera, on the other hand, recognizes the site of incidence A2, which strikes the camera sensor 41 at the site of projection P2. The sites of projection P1 and P2 differ by the projection offset dp in the x direction.

(34) The site of projection P.sub.1 on the camera sensor 41 can be used as a reference variable for which the height position z1 of the site of incidence A1 is known. By means of the projection offset dp of the site of projection P2 relative to the site of projection P1 (with knowledge of the angle β and the focal length f0 of the camera lens 40), the height position z2 of the site of incidence A2 can then be easily determined using the laws of geometric optics. If desired, the horizontal position x2 of the site of incidence A2 can be determined correspondingly if the horizontal position x1 of the site of incidence A1 is known.

(35) To determine the tilt of a base element 13, a measurement pattern 50 typically comprises illumination of the base element 13 in three different zones 51a, 51b, 51c, as can be seen in the top view of the base element 13 in FIG. 4. The measurement pattern 50 here includes a laser line 52a, 52b, 52c (shown in solid lines) in each zone 51a, 51b, 51c (shown in dashed lines); each laser line 52a, 52b, 52c consists of a multiplicity of laser points (not resolved in FIG. 4). The laser lines 52a-52c are generated here by a measuring laser and scanner optical system centrally above the base element 13 (not shown).

(36) If the base element 13 is tilted, for example with the upper section in FIG. 4 down into the plane of the drawing, the laser lines shift on the surface of the base element, cf. the dashed laser lines 53a, 53b, 53c, which can be easily detected with a laterally offset camera (not shown). A separate local height position of the base element 13 can be determined for each of the zones 51a, 51b, 51c; typically, height position information of the different laser points of a respective laser line is averaged. The tilting of the base element 13 results from the three local height positions.

(37) Adjusting elements (not shown) for adjusting the orientation of the base element 13 relative to a fixed reference structure 54, which is for example part of the bottom of the processing chamber, are preferably located directly under the zones 51a, 51b, 51c.

(38) FIG. 5 schematically illustrates the measurement of a base element 13, which is designed as a preform 13b. The preform 13b already has a complex three-dimensional shape on which the actual three-dimensional object (not shown) to be manufactured in an additive manner is to be built. Before the manufacturing of the three-dimensional object begins, the surface (contour) O3 of the preform 13b can be scanned (limited by any shadowing) using deflected laser beams 24a, which are generated from the laser beam 24 of a measuring laser with the scanner optical system 19. FIG. 5 shows the scanning of a line of the preform 13b in an angular range a; the entire measurement comprises further lines in front of and behind the drawing plane of FIG. 5, for each of which a separate image recording is carried out.

(39) The method according to the present disclosure can also be used to calibrate a measuring system. For this purpose, FIG. 6 illustrates, by way of example, a simple measurement setup (cf. upper partial image) with a base element 13, which can be moved along a (here vertical) direction of travel (z-direction). A deflected laser beam 24a of a measuring laser creates a so-called triangulation point 60 on the base element 13, corresponding to a site of incidence of the laser beam 24a on the surface of the base element 13. The camera 21, here comprising a lens 61, which simultaneously forms an entrance pupil of the camera 21, and a CMOS sensor 62, captures an image 63 of the triangulation point on the CMOS sensor 62. Depending on the travel position z of the base element 13, there is a different site of incidence, also called position signal x, from the image 63 of the triangulation point on the CMOS sensor 62. Depending on the travel position z of the base element 13, the position signal x obeys a hyperbolic curve, with x=P.sub.0/(P.sub.1+z)+P.sub.2, with P.sub.0, P.sub.1, P.sub.2: Hyperbolic parameters. The position signal x diverges on the CMOS sensor 62 when the base element 13 reaches the height of the entrance pupil or here the lens 61, regardless of the angle of the laser beam 24a with respect to the vertical or the direction of travel (z direction). This can be used for a calibration (cf. FIG. 11).

(40) FIG. 6 shows, by way of example, three different travel positions of the base element 13, which is designed here as a construction platform; the base element 13 is moved upward in the partial images from top to bottom. As described herein, position signals x at different travel positions z of a reference base element or of the base element are measured both in a reference measurement sequence and in later measurement sequences for individual construction jobs.

(41) It should be noted that in FIG. 6 the laser beam is directed parallel to the (vertical) direction of travel of the base element 13, which represents a possible design. However, it is preferred that the laser beam 24a extends obliquely to the direction of travel z, that is to say with an angle β>0°, as shown, for example, in FIG. 3, preferably with β≥5°. Then, speckle errors can be minimized.

(42) FIG. 7 shows, by way of example, a measurement pattern 50 in the shape of the edges of a rectangle, on which four triangulation points 60 are formed at the corners of a the rectangle; typically all triangulation points 60 are considered separately in the scope of (reference) measurement sequences. The straight portions of the rectangle can be easily recognized by image recognition software, cf. FIG. 8, in which the recognized straight sections are marked in bold, so that the position of the corner points or triangulation points 60 can easily be determined by extrapolation.

(43) FIG. 9 is a graph that illustrates the raw data (drawn in as circles) of a reference measurement sequence, in which the position signal (x), i.e. the location of the image of a triangulation point (plotted upwards), is shown as a function of the travel position (z) of the reference base element (plotted to the right). The individual measurement points lie on a fitted hyperbolic curve 91, which is drawn in as a solid line. The behavior of the reference base element is described by the fitted hyperbolic curve 91 (or another fitted curve, for example a polynomial curve), and speckle errors are averaged out.

(44) The location (with respect to z) of a pole point (z.sub.P.sup.R) of the hyperbolic curve, which represents the location of the entrance pupil of the camera, can also be determined from the fitted hyperbolic curve 91. The pole point lies outside the measured area and is determined by calculation from the hyperbolic parameter P.sub.1 of the fitted hyperbola (cf. FIG. 11 for this).

(45) FIG. 10 is a graph that shows the raw data of a measurement sequence (drawn in as circles), again with position signal x (upwards) against the travel position (z) of the base element (to the right). A hyperbolic curve 92 (or another curve) can again be fitted to these measuring points. In addition, the hyperbolic curve 91 of the reference measurement sequence is shown again.

(46) If it is ensured that the reference angle and the angle at which the laser beam was directed onto the reference base element or base element were practically identical for the reference measurement sequence and the measurement sequence, a height difference between the reference base element that was used in the reference measurement sequence and the base element that was used in the measurement sequence can be directly concluded from an offset 93 of the fitted curves 91, 92. Such a height difference can result, for example, from the manufacturing tolerances of construction platforms, or from thermal expansion, or simply from different types of construction platforms. This determined height difference can be taken into account as a correction term for setting the travel position of the base element in the subsequent additive manufacturing of a three-dimensional object. In the present case, under the boundary conditions of the measurement sequence (cf. hyperbolic curve 92), the travel position z must be set lower by the offset 93 in order to obtain the positions of the surface of the base element (relative to the camera) in accordance with the boundary conditions of the reference measurement sequence. The offset 93 can be determined relatively precisely even with comparatively small travel paths in the z direction.

(47) If it cannot or should not be assumed that the reference angle and angle are identical, in particular for a higher calibration accuracy, the position of the pole point (z.sub.P.sup.M) can also be determined for the fitted hyperbolic curve 92 of the measuring points of the measurement sequence. The pole point is again outside the measured area of FIG. 10 and is determined by calculation from the hyperbolic parameter P.sub.1 of the fitted hyperbolic curve 92 (cf. FIG. 11).

(48) FIG. 11 is a graph that schematically shows the hyperbolic curve 91 of the reference measurement sequence and the hyperbolic curve 92 of the measurement sequence in a larger area, in particular also in the area of the pole points. The position of the pole points of the reference measurement sequence and measurement sequence are independent of the reference angle and angle of the laser beam in the reference measurement sequence and the measurement sequence, and each corresponds to the (always the same) location of the entrance pupil of the camera, for example, the lens thereof. By comparing the pole point positions, the measuring system can also be calibrated, regardless of interfering influences such as pointing instabilities of the laser. A desired z position of the surface of a base element that was reached in the reference measurement sequence (with a reference base element) at a travel position z.sub.B.sup.R, wherein the pole point was determined in the reference measurement sequence at z.sub.P.sup.R and the pole point was determined in the measurement sequence at z.sub.P.sup.M, can be obtained (with the boundary conditions of the measurement sequence) by setting a travel position z.sub.B.sup.M=z.sub.P.sup.M+(z.sub.B.sup.R−z.sub.P.sup.R)=z.sub.B.sup.R+(z.sub.P.sup.M−z.sub.P.sup.R). The difference 94 of the pole point positions can therefore be used as the correction term 95.

Other Embodiments

(49) It is to be understood that while the new methods, machines, and systems disclosed herein have been described in conjunction with the detailed description thereof, the foregoing description is intended to illustrate and not limit the scope of the machines, methods, and systems disclosed herein, which are defined by the scope of the appended claims. Other aspects, advantages, and modifications are within the scope of the following claims.

LIST OF REFERENCE NUMERALS

(50) 1 machine 2 three-dimensional object 3 processing chamber 4 powder cylinder arrangement 5 powder cylinder 6 powdery material 6a collection container 7 powder piston 8 first lifting device 9 bottom 10 slider 11 construction cylinder arrangement 12 piston of the construction cylinder arrangement 12a upper piston part 12b middle piston part 12c lower piston part 13 base element 13a substrate 13b preform 14 base body 15 second lifting device 16 high-energy beam 16a machining laser beam 17 high-energy beam source 17a machining laser 18 beam splitter 19 scanner optical system 20 window of the scanner optical system 21 camera 21a window of the camera 22 measuring system 23 measuring laser 24 laser beam from the measuring laser 24a deflected laser beam of the measuring laser 25 control device 26 evaluation device 27 offset 28 test device 29 focusing optical system 30 powder seal 31 insulation plate 32 adjusting element 33 gas seal 40 camera lens 41 camera sensor 50 measurement pattern 51a-51c zones 52a-52c laser lines with the base element not tilted 53a-53c laser lines with tilted base element 54 reference structure 60 triangulation point 61 lens 62 CMOS sensor 63 image of the triangulation point 91 hyperbolic curve (measurement sequence) 92 hyperbolic curve (reference measurement sequence) 93 offset 94 difference in pole point positions 95 correction term A1, A2 sites of incidence dx horizontal offset dp projection offset dz height offset f0 focal length O1-O3 surface of the base element P1, P2 sites of projection P.sub.0, P.sub.1; P.sub.2 hyperbolic parameters x horizontal direction/position signal x1, x2 horizontal positions z vertical direction/direction of travel z1, z2 height positions z.sub.B.sup.M desired z position of the base element in the measurement sequence z.sub.B.sup.R desired z position of the base element in the reference measurement sequence z.sub.P.sup.M z position of the pole point in the measurement sequence z.sub.P.sup.R z position of the pole point in the reference measurement sequence β angle of the deflected laser beam relative to the vertical σ angular range of the deflected laser beams of a scanning line