Method for calibrating a laser profilometer with respect to a rotation axis and corresponding calibration system

Abstract

A method for calibrating a laser profilometer (2) with respect to a rotation axis (4) and presenting the steps of: arranging at least one spherical master body (5) of known radius r at a distance I from the rotation axis (4) in such a way that the laser profilometer (2) frames the master body (5) during a relative rotation, around the rotation axis (4) and with step σφ, between the laser profilometer (2) and the spherical master body (5); defining a reference system W with an axis Zw aligned with the rotation axis (4); defining a reference system S integral with the laser profilometer (2); generating a relative rotation in step and with angular step σφ around the rotation axis (4) between the master body (5) and the laser profilometer (2); acquiring, through the laser profilometer (2) and at each step of rotation, the coordinates in the reference system S of a line of points belonging to an external surface of the spherical master body (5); and determining the elements of a rotation matrix R and the elements of a translation matrix T which, when applied together, transform the coordinates Ps of a point in the reference system S into the coordinates Pw of the same point in the reference system W.

Description

[0001] METHOD FOR CALIBRATING A LASER PROFILOMETER WITH RESPECT TO A ROTATION

[0002] AXIS AND CORRESPONDING CALIBRATION SYSTEM

[0003] Cross-Reference to Related Patent Applications

[0004] This patent application claims priority from Italian patent applications No. 102024000005377 and No. 102024000005383 both filed on March 1 1 , 2024, the entire disclosure of which is incorporated herein by reference.

[0005] Technical Field

[0006] The present invention relates to a method for calibrating the orientation of the reference system of a laser profilometer with respect to the reference system of an arbitrary rotation axis and a corresponding calibration system.

[0007] Prior Art

[0008] A laser profilometer is used to acquire the shape of the outer surface of an object along a line generated by the intersection of the object's outer surface and a plane of light generated by a laser source (or similar).

[0009] In order to be able to reconstruct entire portions of the external surface of an object, it is necessary to move the object (or equivalently the laser profilometer) along a predefined trajectory comprising successive positions that determine different and possibly contiguous sections. Precise knowledge of the relative orientation of the laser profilometer with respect to each of the positions determines the accuracy of the overall reconstruction and is therefore the subject of numerous calibration techniques designed to determine it. Such methods are referred to in this context as 'calibration techniques' and generally depend on the characteristics of the predefined trajectory.

[0010] Patent application US2004141 187A1 describes calibration techniques for determining the rigid body coordinate transformation that accurately aligns the coordinate frame of a laser scanner with the coordinate frames of different axes of motion.

[0011] Patent application US2004141187A1 describes the calibration of an optical sensor using a rotatable mounted calibration body; in particular, the parameters describing the transformation of an optical sensor coordinate system into the machine coordinate system are calculated.

[0012] Description of the invention

[0013] The purpose of the present invention is to provide a method for calibrating a laser profilometer with respect to a rotational axis and a corresponding calibration system that enable calibration to be carried out accurately.

[0014] According to the present invention, a method for calibrating a laser profilometer with respect to a rotation axis and a corresponding calibration system are provided, as claimed in the attached claims. The claims describe preferred embodiments of this invention forming an integral part of the present specification.

[0015] Brief Description of the Drawings

[0016] The present invention will now be described with reference to the accompanying drawings, which illustrate non-limiting embodiments, wherein:

[0017] Figure 1 schematically illustrates an optical object control station equipped with a single laser profilometer and coupled with a calibration system to calibrate the laser profilometer against a rotation axis;

[0018] Figures 2 and 3 illustrate schematically and from two different viewpoints an optical object control station equipped with a plurality of laser profilometers: and

[0019] Figures 4 and 5 are respectively a perspective and side view of a support that is fitted with a plurality of spherical calibration bodies and is part of a calibration system used to calibrate the laser profilometers in Figures 2 and 3.

[0020] Preferred Embodiments of the Invention

[0021] In figure 1 , reference number 1 shows a control station in which a laser profilometer 2 can detect the external shape of an object (not shown).

[0022] Specifically, the object is attached to a support 3 that is motorised and is mounted rotatable around a vertical rotation axis 4; in use, the support 3 is rotated in step around the rotation axis 4 to show the laser profilometer 2 successive positions of the object on the support 3.

[0023] To perform the calibration of the laser profilometer 2, a spherical master body 5 of known radius r is attached to the support 3 in such a way that the spherical master body 5 can be rotated in step around the rotation axis 4. The spherical master body 5 is fixed to support 3 in such a way that its center C is at an unknown but constant distance I from the rotation axis 4.

[0024] It is important to note that the radius r of the spherical master body 5 is known as precisely as possible as any error in the knowledge of the radius r introduces an inaccuracy into the calibration. On the other hand, the distance I between the center C of the spherical master body 5 and the rotation axis 4 is not known a priori.

[0025] Calibrating the laser profilometer 2 involves positioning the spherical master body 5 so that its trajectory passes through the scanning area of the laser profilometer 2 and rotating the master body 5 in step (in particular by rotating the support 3) in small increments of the rotation angle (p with step 6cp >0.

[0026] A reference system W is defined on the support 3 comprising an axis Zwaligned with the rotation axis 4, an axis Xwaligned with the direction conventionally associated with the zero angle of rotation an axis Ywderived from the vector product between the axis Xwand the axis Zwand an origin Ow located on the rotation axis 4 at a point conventionally identified by a projection of the center C of the spherical master body 5. By construction, for each angle of rotation (p the coordinates Cw in the reference system W of the center C of the spherical master body 5 are: ~lcos<p~ Isinq)

[0027] . 0 .

[0028] The laser profilometer 2 has its own reference system S comprising an axis Zs, an axis Xs, an axis Ys, and an axis Os. The laser profilometer 2, with respect to its own reference system S, detects a point Ps= Pys, Pzs]Ton the surface of the spherical master body 5. Given R and T, respectively, the rotation matrix and the translation matrix carrying the points from the reference system S to the reference system W, the point Psis defined, in the reference system W, by the following equation [1]: 11r12r13 Pxs ^x

[0029]

[0001] Pw= RPs +T =r21r22r23 Pys + ty

[0030] .r31r32r33. .Pzs. - z-

[0031] Pw coordinates of the point in the reference system W;

[0032] Ps coordinates of the point in the reference system S;

[0033] R rotation matrix;

[0034] T translation matrix; rllr12 TL3 r21r22r23 elements of the rotation matrix R;

[0035] .r31r32r33. coordinates Ps; x ty elements of the translation matrix T. -tz-

[0036] In other words, the calibration of the laser profilometer 2 involves arranging the spherical master body 5 of known radius r at distance I from the rotation axis 4, in such a way that the laser profilometer 2, previously arranged in a fixed position, frames the spherical master body 5 during a rotation of the spherical master body 5 around the rotation axis 4, and then rotates the spherical master body 5 around the rotation axis 4 in step and with angular step Sep.

[0037] At each rotation step, the laser profilometer 2 acquires the coordinates in the reference system S of a line of points belonging to an external surface of the spherical master body 5; subsequently, using the coordinates in the reference system S of the points belonging to the external surface of the spherical master body 5, the elements of the rotation matrix R and the elements of the translation matrix T are determined which, when applied together, transform the coordinates Ps of a point in the reference system S into the coordinates Pw of the same point in the reference system W using equation

[0001] described above.

[0038] Calibrating the laser profilometer 2 consists precisely in determining the elements of the rotation matrix R and the elements of the translation matrix T, as these R and T matrices make it possible to establish the link between the position in space of the laser profilometer 2 and the position in space of the master body 5.

[0039] Specifically, the step of determining the elements of the rotation matrix R and the elements of the translation matrix T involves determining an objective function that performs a difference between a radius of the spherical master body 5 estimated using the coordinates in the reference system S of a point belonging to the outer surface of the spherical master body 5 and the known radius r of the spherical master body 5. Once the objective function has been determined, it is iteratively optimised for all points belonging to the outer surface of the spherical master body 5 and acquired by the laser profilometer 2. Specifically, the objective function theoretically provides a null result and the iterative optimisation minimises a summation of the errors of the objective function for all points belonging to the outer surface of the spherical master body 5 and acquired by the laser profilometer 2.

[0040] Since all the points on the surface of the spherical master body 5 are distant r from the center C of the spherical master body 5, we have II Pw- Cw||2=r2, i.e. the objective function consists of the following equation [2]: rllr12r13‘ r21r22r23 is the rotation matrix R relative to the rotation between the reference system

[0041] .r31r32r33.

[0042] W and the reference system S;

[0043] Pxs

[0044] Pys are the coordinates of point P on the surface of spherical master body 5 in .Pzs. reference system S; is the translation matrix T relating to the translation between the reference system W and the reference system S; lcos<p

[0045] Isinq) are the coordinates of the center C of the spherical master body 5 in the reference system W; is the distance of the center C of the spherical master body 5 from the rotation axis 4; p is the angle of rotation; and r is the radius of the spherical master body 5.

[0046] In equation [2], Pxs> Pys> Pzs , cp and r are known, while the nine rotation elements r7, the three translation elements and the distance I are unknown. Since the laser profilometer 2 can acquire millions of points for different angles at the same time r^, and I, it is easy to produce millions of equations [2],

[0047] However, the optimisation of equation [2] is problematic for two reasons: the non-linearity prevents the easy identification of a closed or otherwise deterministic form, and the need to optimise using orthonormal matrices for rotation would require continuous reprojections through exponential maps.

[0048] As the problem is non-linear, the calibration method involves strong initialisation so as to avoid local minima. To definitively solve the problem of the orthonormality of the rotation matrix R described above, the objective function preferably consists of a minimal Tait-Bryan form of equation [2] corresponding to the following equation [3] (where a, p, y are the three Tait-Bryan angles):

[0049] Equation [3] comprises seven unknowns (the three Tait-Bryan angles tx, ty, tzand I) and the rotation matrix R, which is orthonormal throughout the optimisation.

[0050] It should also be noted that since the laser profilometer 2 produces points only in its plane Xs- Zs, in practice pysit is constantly null, so equation [3] can be further simplified by assuming that the laser profilometer 2 produces points only in the Xs- Zsplane, thus deriving the following equation [4]:

[0051] Since the spherical master body 5 has no orientation characteristics (i.e. no surface references recognisable by laser profilometer 2), there is no way of knowing which points on the surface have actually been reconstructed by laser profilometer 2. Fortunately, it is possible to derive the center C of the spherical master body 5 from the reconstructed points in the reference system S that generated them, which is unambiguous in terms of correspondence in the reference system W. Considering the points Psi= [PXSP Pzsi]Tobserved by the laser profilometer 2 in a given frame (i.e. in a given profilometer acquisition) it is possible to estimate the center of intersection between a scanning plane and the spherical master body 5 by minimising the error defined by the following equation [6] using a least squares method and in particular one of either "Full Least Squares", "Reduced Least Square" or "Modified Least Square": . cxsis the coordinate of the center C of the spherical master body 5 along the axis xs; czsis the coordinate of the center C of the spherical master body 5 along the axis zs; r is the radius of the spherical master body 5 in the plane Xs- Zs; pxsiis a coordinate in the reference system S of an i-th point on the surface of the spherical master body 5 along the axis Xs; and pzsiis a coordinate in the reference system S of the i-th point on the surface of the spherical master body 5 along the axis Zs.

[0052] The coordinates in the reference system S of the center C of the spherical master body 5, given the radius r of the spherical master body 5, become:

[0053] The sign of the y-coordinate depends on the position of the real spherical master body 5 relative to a section plane of the laser profilometer 2. For each frame t (i.e. for each acquisition made at a certain instant t of time), the points acquired are filtered by an iterative method, e.g. with the RANSAC system, keeping only the frames t that have a sufficient number of valid points and with a radius r of the dominant circumference greater than a predetermined threshold rmin.

[0054] At this point, for each frame t, we have the valid points = [pxsi, PzSi]Tand the center C of the spherical master body 5 Cj = [c£s, CyS, czs] , where the coordinate of Cj along the axis Ysis:

[0055] CySis the coordinate of Cj along the axis Ysin the frame t.

[0056] All points Cg obtained are constrained to lie on the same plane, which is orthogonal from the rotation axis 4. Projecting all points Cj onto this plane, an optimisation identical to that used to estimate the Cj can be used to derive an estimate of distance I, denoted hereafter by t. At this point, thanks to the estimated distance / , for each pointe / in the reference system S, an estimate of the coordinates^ in the reference system W of the center C of the spherical master body 5 is obtained:

[0057] 8^ is the angular pitch of rotation and is always positive, i.e. greater than zero. With these estimates, it is possible to use Horn's method to obtain the rigid transformation between the reference system S and the reference system W, finally deriving the three Tait-Bryan angles and thus completing the set of initialisation values, i.e. a, p, y, tx, ty, tzand I.

[0058] Finally, given these initialisers, given a large number of points acquired in a large number of frames t, using all collected samples simultaneously and minimising, equation [4] becomes the following equation [5]:

[0059] It should be noted that the spherical master body 5 must be fixed in such a way that it does not deform, that it crosses the acquisition area of the laser profilometer 2 and that it rests without wobbling on the support 3 (or on any other support used to rotate the spherical master body 5 around the rotation axis 4.

[0060] The material and surface finish of the spherical master body 5 must be chosen to ensure adequate visibility by the laser profilometer 2.

[0061] According to a preferred embodiment, the radius r of the spherical master body 5 must be of a size to ensure a sufficiently large scanning area. The radius r is preferably between 10% and 150% of the distance I. In particular, the radius r is preferably between 50% and 120% of the distance I or preferably between 25% of the side of the scan area and 100% of the side of the scan area.

[0062] It should be noted that the root of the error in equation [4] divided by the collected samples indicates the accuracy of the measurement in the reference system W and is therefore an estimate of the accuracy of the alignment between different laser profilometers 2 and the overall alignment of the system elements after a complete rotation.

[0063] According to the embodiment shown in Figure 1 , there is a single laser profilometer 2 and a single spherical master body 5.

[0064] According to other not illustrated embodiments, multiple laser profilometers 2 and / or multiple spherical bodies 5 may be provided (i.e. two or more spherical master bodies 5 to calibrate a single laser profilometer 2, a single spherical master body 5 to calibrate two or more laser profilometers 2, or two or more spherical master bodies 5 to calibrate two or more laser profilometers 2.

[0065] According to an alternative embodiment, there are two or more (N) spherical master bodies 5 that are separated and distinct from each other in order to calibrate a single laser profilometer 2. In particular, the (N) spherical master bodies 5 are arranged in such a way that they have different angular positions with respect to the rotation axis 4 and different heights in the direction of the rotation axis 4 (i.e. they are arranged at different heights with respect to support 3). Preferably, the spherical master bodies 5 are arranged in such a way that they also have different radial distances to the rotation axis 4. The coordinates of the centers C of all (N) spherical master bodies 5 in a reference system common to them are known, so the actual distances between said centers C of all N spherical master bodies 5 can be determined. Specifically, among said N spherical master bodies 5, a spherical master body 5 is assumed to be the reference master body 5 to which the calibration method described above is applied (with reference to the use of a single spherical master body 5 in order to determine the relevant rotation matrices and translation matrices, i.e. to determine the elements of the rotation matrix R and the elements of the translation matrix T referring to the reference spherical master body 5. The position of a center C of each spherical master body 5 other than the reference spherical master body 5 can be defined as a function of a center C of the reference spherical master body 5: c0is the center of the reference spherical master body 5 ctis the center C of the spherical master body 5 whose position is to be calculated with respect to the center C of the reference spherical master body 5 a, b, c are the elements of a translation matrix referring to the spherical master body 5 other than the reference spherical master body 5.

[0066] The rotation and translation matrices determined for the reference spherical master body 5 are applied to the spherical master bodies 5 other than the reference spherical master body 5 with the aim of defining a new objective function to minimise the difference of the distances between the centers of the N spherical master bodies 5 from the actual distances between the centers C of the spherical master bodies 5 by modifying the translation and rotation matrices determined with respect to the reference spherical master body 5.

[0067] This new objective function is of this type: rx, rY, rzare the elements of the rotation matrix R with respect to the axes X, Y and Z tx, tY, tz are the elements of the translation matrix (T) with respect to the axes X, Y and

[0068] Z a, b, c are the elements of a translation matrix referring to the spherical master body 5 other than the reference spherical master body 5 described above.

[0069] An example of application of the laser profilometer 2 is to verify the conformity to the design specifications of objects with a complex shape (such as stators of electric motors, brake discs or components of mobile phones): using a coordinate measuring machine, an exhaustive control of an object with a complex shape would take a long time, while using the laser profilometer 2 (which provides millions of points which are then filtered to obtain the measurable surfaces of the object) the same control can take, for example, a time of between thirty seconds and one minute.

[0070] Figures 2 and 3 show, from two different viewpoints, a control station 1 used for the optical control of an object 6 of complex shape (schematically illustrated), which may for example be a stator of an electric motor. The control station 1 comprises an upper group of laser profilometers 2 which consists of five laser profilometers 2a, 2b, 2c, 2d and 2e and is configured to inspect an upper face 7 of the object 6 and a lower group of laser profilometers 2 which consists of five laser profilometers 2f, 2g, 2h, 2j and 2k and is configured to inspect a lower face 8 (opposite to the upper face 7) of the object 6.

[0071] Once the ten laser profilometers 2 are mounted and locked in a fixed position, a calibration system is used, which involves the use of a support 3 (illustrated in Figures 4 and 5) that is mounted swivelling around the rotation axis 4 (exactly with the support 3 illustrated in Figure 1 ) and houses a plurality of spherical master bodies 5. According to a preferred embodiment, the support 3 has a ring shape and a cylindrical symmetry around the rotation axis 4. However, the support 3 can have different shapes depending on space requirements or the specific application.

[0072] In the embodiment shown in Figures 4 and 5, the support 3 has an upper face 9 and a lower face 10 which are opposite to each other; the master bodies 5 are arranged both at the upper face 9 of the support 3 in order to be framed, during the rotation of the support 3 around the rotation axis 4, by the laser profilometers 2 of the upper group, and at the lower face 10 of the support 3 in order to be framed, during the rotation of the support 3 around the rotation axis 4, by the laser profilometers 2 of the lower group.

[0073] In the embodiment shown in Figures 4 and 5, four master bodies 5a, 5b, 5c and 5d are provided arranged at the lower face 10 of the support 3 to be framed, during the rotation of the support 3 about the rotation axis 4, by the laser profilometers 2 of the lower group, and five master bodies 5e, 5f, 5g, 5j and 5k are arranged at the upper face 9 of the support 3 to be framed, during the rotation of the support 3 around the rotation axis 4, by the laser profilometers 2 of the upper group.

[0074] According to a preferred embodiment, the support 3 comprises a series of columns 1 1 , each of which is cantilevered from the support 3, is oriented parallel to the rotation axis 4, and houses a respective master body 5 at its upper end. The columns 1 1 have different axial extensions (i.e. measured along the rotation axis 4) in order to arrange master bodies 5 at different positions (elevations) along the rotation axis 4.

[0075] The master bodies 5 are mounted on the one common support 3 in such a way that each laser profilometer 2 frames at least two master bodies 5 during relative rotation, around the rotation axis 4 and with step Ocp, between laser profilometers 2 and support 3, i.e. during step rotation of support 3 around the rotation axis 4. By way of example, in the embodiment shown in the attached figures, the following situation exists: the laser profilometer 2a frames the reference bodies 5f and 5g: the laser profilometer 2b frames the reference bodies 5f and 5g: the laser profilometer 2c frames the reference bodies 5f, 5j and 5k; the laser profilometer 2d frames the reference bodies 5e and 5k; the laser profilometer 2e frames the reference bodies 5j and 5k; the laser profilometer 2f frames the reference bodies 5a and 5d; the laser profilometer 2g frames the reference bodies 5b and 5c; the laser profilometer 2h frames the reference bodies 5a, 5b and 5c; the laser profilometer 2j frames the reference bodies 5b and 5c; and the laser profilometer 2k frames the reference bodies 5a and 5d.

[0076] Obviously, according to other embodiments not illustrated, a different number of laser profilometers 2, a different arrangement of laser profilometers 2, a different number of master bodies 5, and / or a different arrangement of master bodies 5 can be provided. In addition, according to other embodiments not illustrated, only the upper group of laser profilometers 2 is provided for or only the lower group of laser profilometers 2 is provided for.

[0077] The master bodies 5 are arranged in such a way that each laser profilometer 2 frames, during a complete rotation of the support 3 around the rotation axis 4, at least two master bodies 5 (i.e. not less than two master bodies 5 and possibly more than two master bodies 5). Preferably, an angular distance between the two master bodies 5 framed by the same laser profilometer 2 is 90°.

[0078] Preferably, the laser profilometers 2 share at least one common master body 5 in pairs, so that the same master body 5 is framed by two different laser profilometers 2. In addition, the two master bodies 5 framed by the same laser profilometer 2 have a different position along the rotation axis 4 in the measuring range of the laser profilometer 2.

[0079] Preferably, the projection of the distance between the two master bodies 5 framed by the same laser profilometer 2 along the rotation axis 4 is as large as possible in order to make the calibration more robust.

[0080] When calibrating the laser profilometers 2 with respect to the rotation axis 4 (around which support 3, which carries the spherical master bodies 5, rotates in step), the global reference system W is defined (as described above), which is unique to the support 3 and includes the axis Zwaligned to the rotation axis 4. A respective reference system S integral with laser profilometer 2 is defined (as described above) for each laser profilometer 2 and, through each laser profilometer 2 and at each rotation step, the coordinates in the respective reference system S of a line of points belonging to an external surface of each spherical master body 5 are acquired framed by laser profilometer 2.

[0081] Then, during the calibration of the laser profilometers 2 with respect to the rotation axis 4, for each reference system S and using the coordinates in the reference system S of the points belonging to the external surface of each respective spherical master body 5, the elements of a respective matrix of rotation R and the elements of a respective matrix of translation T are determined, which when applied together transform the coordinates Rs of a point in the reference system S into the coordinates Pw of the same point in the global reference system W.

[0082] That is, the purpose of calibrating laser profilometer 2 with respect to the rotation axis 4 is to derive the rototranslation matrices R and T that are able to place a generic point, whose coordinates Ps are expressed in the system of local reference S of the laser profilometer 2 that acquired it, in the system of global reference W common to all laser profilometers 2 whose Zwaxis coincides with the rotation axis 4.

[0083] According to a preferred embodiment, the radii r of each master body 5 are determined in advance and the mutual distances between the centers C of the master bodies 5 are determined in advance. As an example, it is possible to first determine the coordinates of the centers C of the master bodies 5 in the global reference system W and then calculate the mutual distances between the centers C of the master bodies 5 using the coordinates of the centers C of the master bodies 5.

[0084] The mutual distances between the centers C of the master bodies 5 are used, if and when known, to determine the elements of the rotation matrices R and the elements of the translation matrices T with greater accuracy and confidence. That is, the coordinates C of the master bodies 5 are used to utilise their distance from each other when calibrating; this artifice increases the accuracy of calibration if a single laser profilometer 2 sees several master bodies 5 relatively small in relation to their distance from the rotation axis 4.

[0085] In addition, the reciprocal distances between the centers C of the master bodies 5 are used, if and when known, to determine the relative position and thus with respect to the global reference system W of two laser profilometers 2 that do not frame any common master bodies 5.

[0086] That is, in the example illustrated in Figures 2 and 3, to determine the relative position and thus with respect to the global reference system W of the laser profilometer 2 of the upper group with respect to the laser profilometer 2 of the lower group.

[0087] In other words, the relative distance between the calibration bodies 5 is required to determine the relative position and thus with respect to the global reference system W of two or more laser profilometers 2 that do not share any calibration bodies 5 in common; this is the case for the upper group of laser profilometers 2 and the lower group of laser profilometers 2. In this situation, the laser profilometers 2 of each group are correctly referred to each other, but the two groups do not share any common master body 5. In this case, the distance along the direction of the rotation axis 4 of the gauge and the angular phase around the same rotation axis 4 of the two sets of laser profilometers 2 are unknown. Considering a system with multiple groups of laser profilometers 2, each observing a separate group of master bodies 5 in which all master bodies 5 are integral, to accurately record the different groups of laser profilometers 2, barring degenerate cases, it is sufficient to measure in the metrology room the distance between the center C of two master bodies 5 of each group and a master body 5 of the other groups. The phase and distance values along the rotation axis 4 between laser profilometer 2 groups that ensure that these two distances are maintained are unambiguous. Clearly, measuring all distances between master bodies 5 is better (i.e. increasing confidence and accuracy), but two distances are already sufficient in the case of two groups (in general, at least 2N-1 is needed in the case of N groups).

[0088] In this case, to make the calibration more robust, it is preferable (but not necessary) to certify the positions of the centers C of all master bodies 5 in order to be able to calculate all combinations of reciprocal distances.

[0089] As mentioned above, the W global reference system comprises: the axis Zwaligned with the rotation axis 4; the axis Xwaligned with a direction conventionally associated with the zero angle of rotation; the axis Ywderived from the vector product between the axis Xwand the axis

[0090] Zw; and the origin Ow located on the rotation axis 4.

[0091] An upper laser profilometer 2 (i.e. belonging to the upper group) and a lower laser profilometer 2 (i.e. belonging to the lower group) are spaced apart only by an offset in the Zwdirection and an angular phase; the coordinates of a point acquired by a lower laser profilometer

[0092] 2 seen in the reference system of an upper laser profilometer 2 are expressed by the following equation [1]:

[0093] X12, Y12, Z12 are the coordinates of a point acquired by the lower laser profilometer 2 seen in the reference system of the upper laser profilometer 2;

[0094] 11, ji , ki is the versor of an X2axis as seen from the reference system of the upper laser profilometer 2;

[0095] 12, J2, k2 is the direction of an axis Y2seen from the reference system of the upper laser profilometer 2; is, js, ks is the versor of an axis Z2as seen from the reference system of the upper laser profilometer 2;

[0096] X22, Y22, Z22 are the coordinates of a point acquired by the lower laser profilometer 2 seen in the reference system of the lower laser profilometer 2;

[0097] Ol 2X, Ol 2y, Ol 2Zare the coordinates of an origin in the lower laser profilometer 2 reference system seen in the upper laser profilometer 2 reference system.

[0098] After calibration of the two laser profilometers 2 (upper and lower respectively), equation [1] is written as follows:

[0099] Xi2, YI2, ZI2are the coordinates of a point acquired by the lower laser profilometer 2 seen in the reference system of the upper laser profilometer 2; ii, ji is the versor of an X2axis as seen from the reference system of the upper laser profilometer 2; x22, Y22, Z22are the coordinates of a point acquired by the lower laser profilometer 2 seen in the reference system of the lower laser profilometer 2;

[0100] Ol2zis the coordinate of an origin in the lower laser profilometer 2 reference system seen in the upper laser profilometer 2 reference system.

[0101] The coordinates of the centers C of the spherical master bodies 5 as seen from the reference system of the lower laser profilometer 2 in the reference system of the upper laser profilometer 2 in the unknowns ii, ji and Oi2zare described by equation [2]:

[0102] COS 0 = i- sin 6 = j

[0103] Bxj1, Byj1, Bzj1are the coordinates of a center of a j-th spherical master body 5 with j=1 ...m as seen by the lower laser profilometer 2 in the reference system of the upper laser profilometer 2 (expressed for example in [pm]);

[0104] Bxj2, Byj2, Bzj2are the coordinates of a center of a j-th spherical master body 5 with j=1 ...m as seen by the lower laser profilometer 2 in the reference system of the lower laser profilometer 2 expressed for example in [pm]).

[0105] The upper laser profilometer 2 and the lower laser profilometer 2 are linked by the following equation [3]:

[0106] Ax,1, Ay,1, Az,1are the coordinates of a center of an i-th spherical master body 5 with i=1 ...n as seen from the upper laser profilometer 2 in the reference system of the upper laser profilometer 2 expressed for example in [pm]);

[0107] Bxj1, Byj1, Bzj1are the coordinates of a center of a j-th spherical master body 5 with j=1 ...m as seen by the lower laser profilometer 2 in the reference system of the upper laser profilometer 2 expressed for example in [pm]); and

[0108] SMAiBjis a distance certified in the metrology room between the center of the spherical master body 5 Ai and the center of the spherical master body 5 Bj corresponding to the temperature of the current gauge expressed for example in [pm]).

[0109] According to a preferred embodiment, the certified distance in the metrology room between the center C of the spherical master body 5 Ai and the center C of the spherical master body 5 Bj corresponding to the current gauge temperature [pm] is expressed by the following equation [4]:

[0110] (SMAiBj0is the distance certified in the metrology room between the center of the spherical master body 5 Ai and the center of the spherical master body 5 Bj

[0111] KtMstis the coefficient of thermal expansion of the gauge material [1 / °C]; and

[0112] TMstis the current temperature value of the gauge during the calibration procedure

[0113] [°C].

[0114] The embodiments described herein may be combined with each other without departing from the scope of protection of the present invention.

[0115] The calibration method described above has many advantages.

[0116] Firstly, the calibration method described above allows calibration to be performed quickly and, at the same time, is also extremely accurate.

[0117] This is achieved by using spherical master bodies 5 that can be manufactured with a very high degree of precision; i.e. the spherical shape of the master bodies 5 makes it possible to manufacture master bodies 5 with a very high degree of precision (unlike other master bodies with more or less complex and therefore more or less asymmetrical shapes). By way of example, a spherical master body 5 can be manufactured (at reasonable cost and time) with an accuracy of the order of a tenth of a micron, whereas a master body with a more or less parallelepiped or pyramid shape can be manufactured (at reasonable cost and time) with an accuracy of the order of a micron at the most, and thus with an accuracy approximately ten times lower than a spherical master body 5.

[0118] This result is also obtained by determining the objective function (which performs a difference between a radius of each spherical master body 5 calculated using the coordinates in the reference system S of a point belonging to the external surface of the spherical master body 5 and the known radius r of the spherical master body 5 and iteratively optimising the objective function for all the points belonging to the external surface of the spherical master body 5 and acquired by each laser profilometer 2; In fact, operating in this manner, it is possible to accurately calculate the elements of the rotation matrix R and the elements of the translation matrix T even when using a spherical master body 5, which due to its spherical symmetry presents many ambiguities (a spherical master body 5 presents exactly the same appearance and dimensions from all possible points of view).

[0119] In other words, the calibration method described above makes it possible to use (against a higher computational load that is in any case manageable without too many problems) spherical master bodies 5 which allow very high accuracies to be achieved,

[0120] The calibration method described above makes it possible to calibrate multiple laser profilometers 2 in the same reference system W; in fact, the reference systems will be automatically consistent. This result is closely linked to the use of spherical master bodies 5 that present the same appearance regardless of the point of view of the laser profilometers 2 (i.e. a spherical master body 5 offers the same appearance to all possible laser profilometers 2 that frame it regardless of their position and orientation); thus, the same spherical master body 5 is usable with the exact same precision by all laser profilometers 2 that are able to frame it.

[0121] The calibration method described above may involve using several different spherical master bodies 5 in the event that it is not possible for all laser profilometers 2 to see the same spherical master body 5. In this case, the reference systems will still be coherent minus only one degree of freedom, namely the rotational one, which can be fixed using any known object that can appear in multiple laser profilometers 2; in fact, for a coherent system to be obtained during calibration, it is sufficient that the same spherical master body 5 is seen in at least in pairs of laser profilometers 2 and the intersection graph is connected.

[0122] Finally, the calibration method described above is relatively simple and inexpensive to implement, as a spherical master body 5 with the necessary precision is readily available on the market, and it is also easy to attach the spherical master body 5 to the support 3 in order to rotate the spherical master body 5 around the rotation axis 4.

[0123] LIST OF REFERENCE NUMBERS IN THE FIGURES

[0124] 1 control station

[0125] 2 laser profilometer

[0126] 3 support

[0127] 4 rotation axis

[0128] 5 spherical master body

[0129] 6 object

[0130] 7 upper face

[0131] 8 lower face

[0132] 9 upper face

[0133] 10 lower face

[0134] 11 columns

Claims

CLAIMS1 . A method for calibrating a laser profilometer (2) against a rotation axis (4) and comprising the steps of: arranging at least one spherical master body (5) of known radius r at a distance I from the rotation axis (4) in such a way that the laser profilometer (2) frames the master body (5) during a relative rotation, around the rotation axis (4) and with step Ocp, between the laser profilometer (2) and the spherical master body (5); defining a reference system W including an axis Zwaligned to the rotation axis (4); defining a reference system (S) integral with the laser profilometer (2); generating a relative rotation in step and with angular step Sep around the rotation axis (4) between the master body (5) and the laser profilometer (2); acquiring, by means of the laser profilometer (2) and at each rotation step, the coordinates in the reference system S of a line of points belonging to an external surface of the master body (5); and determining, using the coordinates in the system of reference S of the points belonging to the external surface of the spherical master body (5), the elements of a rotation matrix R and the elements of a translation matrix T which, when applied together, transform the coordinates Rs of a point in the system of reference S into the coordinates Pw of the same point in the system of reference W according to the following equation [1 ]: 11r12r13 Pxs ^X[1 ] Pw= RPs +T =r21r22r23 Pys + ty.r31r32r33. .Pzs. - z-Pw coordinates of the point in the reference system W;Ps coordinates of the point in the reference system S;R rotation matrix;T translation matrix; rllr12r13‘ r21r22r23 elements of the rotation matrix R;.r31r32r33. coordinates Ps;elements of the translation matrix T.the method is characterised by the fact that the step of determining the elements of the rotation matrix R and the elements of the translation matrix T comprises the further stepsof: determining an objective function that performs a difference between a radius of the spherical master body (5) calculated using the coordinates in the reference system S of a point belonging to the external surface of the spherical master body (5) and the known radius r of the spherical master body (5); and iteratively optimising the objective function for all points belonging to the outer surface of the spherical master body (5) and acquired by the laser profilometer (2).

2. Method according to claim 1 , in which: the objective function theoretically provides a null result; and the iterative optimisation minimises a summation of the errors of the objective function for all points belonging to the outer surface of the spherical master body (5) and acquired by the laser profilometer (2).

3. The method according to claim 1 or 2, in which the reference system W comprises: the axis Zw; an axis Xwaligned with a direction conventionally associated with the zero angle of rotation; an axis Ywobtained by the vector product between the axis Xwand the axis Zw; and an origin Ow located on the rotation axis (4) at a point conventionally identified by a projection of a center C of the spherical master body (5).The method according to claim 3, where the objective function consists of the following equation [2]:11r12r13r21r22r23 is the rotation matrix R relative to the rotation between the reference system W.r31r32r33. and the reference system S;PxsPys are the coordinates of point P on the surface of the spherical master body (5) in .Pzs. the reference system S;^X y is the translation matrix T relating to the translation between the reference -tz- system W and the reference system S;~lcos<p~ Isinq) are the coordinates of the center C of the spherical master body 5 in the. 0 .reference system W;I is the distance of the center C of the spherical master body (5) from the rotation axis (4);(p is the angle of rotation; and r is the radius of the spherical master body (5).

5. The method according to claim 4, wherein the objective function consists of the following equation [3], which is a Tait-Bryan minimum form of equation [2]:a, p, y are the three Tait-Bryan angles.

6. The method according to claim 5, wherein the objective function consists of the following equation [4], which is a simplification of equation [3] assuming that the laser profilometer(2) produces points only in the plane Xs- Zs:

7. The method according to claim 6, where the objective function consists of the folloE is the summation of the errors of the objective function for all points belonging to the outer surface of the spherical master body (5) and acquired by the laser profilometer (2); 8^ is the angular pitch of rotation.

8. The method according to claim 5, 6 or 7 and comprising the step of determining the initialisation values of the three Tait-Bryan angles a, p, y, the elements tx, ty, tzof the translation matrix T, and the distance I with which to start the iterative optimisation.

9. The method according to claim 8, in which the step of determining the initialisation values involves obtaining from the reconstructed points in the reference system S the center of the sphere that generated them, which is also unique in terms of correspondence in the reference system S.

10. the method according to claim 9, wherein an ambiguity due to the fact that two spheres of symmetrical centers with respect to the scanning plane are located on a planar variety of sampled points is resolved by taking into account the time domain defined by the step variation of the angle of rotation.1 1. The method according to claim 8, 9 or 10, wherein the step of determining theinitialisation values involves, considering the points observed by the laser profilometer (2) in a given frame, estimating the center of intersection between a scan plane and the spherical master body (5) by minimising the error of the following equation [6]:cxsis the coordinate of the center (C) of the spherical master body (5) along the axis Xs; czsis the coordinate of the center (C) of the spherical master body (5) along the axis Zs; r is the radius of the spherical master body (5) in the plane Xs- Zs; pxsiis a coordinate in the reference system S of an i-th point on the surface of the spherical master body (5) along the axis Xs; and pzsiis a coordinate in the reference system S of the i-th point on the surface of the spherical master body (5) along the axis Zs.

12. The method according to claim 11 , wherein the error of equation [6] is minimised using a method of least squares and in particular one of: "Full Least Squares", "Reduced Least Squares" or "Modified Least Squares".

13. The method according to claim 11 or 12, in which the coordinates Csin the reference system S of the center C of the spherical master body (5) are:± r2- r2is the coordinate of the center C of the spherical master body (5) along the axis Ys.

14. The method according to claim 13, wherein the sign of the coordinate ± r2- r2of the center C of the spherical master body (5) along the axis Ysis defined based on a relative position of the master body (5) with respect to the plane Xs- Zs.

15. The method according to claim 14, wherein, in a frame t, the sign of the coordinate ± r2- r2of the center C of the spherical master body (5) along the axis Ysis defined by the following conditions:£ is the radius of the master body (5) in the plane Xs- Zsin the frame t.

16. The method according to claim 13, 14 or 15, wherein an estimate of the coordinates in the reference system W of the center C of the spherical master body (5) are derived based on an estimate of the distance I of the center C of the spherical master body (5) from the rotation axis (4).

17. The method according to claim 16, in which the estimated coordinatesin the reference system W of the center C of the spherical master body (5) are:I is the estimated distance I of the center C of the spherical master body (5) from the rotation axis (4); t is the frame considered;S<p is the angular pitch of rotation and is always positive, i.e. greater than zero.

18. The method according to any one of the preceding claims, wherein the radius r of the spherical master body (5) is between 10% and 150% of the distance I of the center C of the master body (5) from the rotation axis (4) and preferably the radius r of the spherical master body (5) is between 50% and 120% of the distance I of the center C of the spherical master body (5) from the rotation axis (4).

19. The method according to any one of the preceding claims, wherein at least two spherical master bodies (5) are used which are separate and distinct from each other and are arranged to have different angular positions with respect to the rotation axis (4).

20. The method according to claim 19, wherein said at least two spherical master bodies (5) are arranged at different heights in the direction of the rotation axis (4).21 . The method according to claim 19 or 20, wherein said at least two spherical master bodies (5) are arranged to have different radial distances from the rotation axis (4).

22. The method according to claim 19, 20 or 21 , wherein the coordinates of the centers (C) of all spherical master bodies (5) in a reference system common to them are known and the effective distances between said centers (C) of the spherical master bodies (5) are determined.

23. The method according to claim 22 and comprising the steps of: assuming a reference spherical master body (5) between the at least two master bodies; and determining the elements of the rotation matrix R and the elements of the translation matrix T referred to said reference spherical master body (5) by applying the calibration method according to claims 1 to 18.

24. The method according to claim 23, further comprising the step of defining the position of a center (C) of each master body (5) other than the reference spherical master body (5) as a function of a center (C) of the reference spherical master body (5) as follows:c0is the center (C) of the reference spherical master body (5); ctis the center (C) of the spherical master body (5) whose position is to be calculated with respect to the center (C) of the reference spherical master body (5);a, b, c are the elements of a translation matrix referring to the spherical master body (5) different from the reference spherical master body (5).

25. The method according to claim 24, comprising the steps of: applying to spherical master bodies (5) other than the reference spherical master body (5) the elements of the rotation matrix R and the elements of the translation matrix T referred to said reference spherical master body (5); and defining a new objective function to minimise the difference of the distances between the centers (C) of all the spherical master bodies (5) from the actual distances between the centers (C) of the spherical master bodies (5) by modifying the elements of the rotation matrix R and the elements of the translation matrix T determined with respect to the reference spherical master body (5), said new objective function being of the type:rx, ry, rzare the elements of the rotation matrix R with respect to the axes X, Y and Z; tx, ty, tzare the elements of the translation matrix T with respect to the axes X, Y andZ; a, b, c are the elements of the translation matrix referring to the master body (5) other than the reference spherical master body (5) defined according to claim 14.

26. The method according to one of the previous claims, in which the laser profilometer(2) is arranged and held in a fixed position and the master body (5) is rotated in step around the rotation axis (4).

27. The calibration system to calibrate a laser profilometer (2) against a rotation axis (4) and comprising: at least one spherical master body (5) of known radius r arranged at a distance I from the rotation axis (4) in such a way that the laser profilometer (2) frames the master body (5) during a relative rotation, around the rotation axis (4) and with step Ocp, between the laser profilometer (2) and the spherical master body (5); an actuator device configured to generate a relative rotation with step Sep angular about the rotation axis (4) between the master body (5) and the laser profilometer (2); and a control unit configured to implement the calibration method according to one of the preceding claims.

28. The method for calibrating at least two laser profilometers (2) against a rotation axis (4) and comprising the steps of: attaching at least two spherical master bodies (5) to a common support (3) in such a way that each laser profilometer (2) frames at least two master bodies (5) during a relative rotation, around the rotation axis (4) and with Sep pitch, between the laser profilometers (2) and the support(3); and generating a relative rotation in step and with the angular step Sep around the rotation axis(4) between the support (3) and the laser profilometers (2); in which the laser profilometers (2) share at least one common master body (5) in pairs in such a way that the same master body (5) is framed by two different laser profilometers (2).

29. The method according to claim 28 and comprising the steps of: defining a global reference system W comprising an axis Zwaligned to the rotation axis (4); defining, for each laser profilometer (2), a respective reference system S integral with the laser profilometer (2); acquiring, through each laser profilometer (2) and at each rotation step, the coordinates in the respective reference system (S) of a line of points belonging to an external surface of each spherical master body (5) framed by the laser profilometer (2); and determining, for each reference system S and using the coordinates in the reference system S of the points belonging to the external surface of each respective spherical master body (5), the elements of a respective rotation matrix R and the elements of a respective translation matrix T that when applied together transform the coordinates Rs of a point in the reference system S into the coordinates Pw of the same point in the global reference system W.

30. The method according to claim 29 and comprising the steps of: determining in advance the radius r of each master body (5); determining in advance the mutual distances between the centers C of the master bodies(5); and using the mutual distances between the centers C of the master bodies (5) to determine the elements of the rotation matrices R and the elements of the translation matrices T.31 . The method according to claim 29 or 30 and comprising the steps of: determining in advance the coordinates of the centers C of the master bodies (5) in the global reference system W; and calculating the mutual distances between the C centers of the master bodies (5) using the coordinates of the C centers of the master bodies (5).

32. The method according to claim 30 or 31 and comprising the step of using the reciprocal distances between the centers C of the master bodies (5) to determine the relative position and thus with respect to the global reference system W of two laser profilometers (2) that do not frame any common master body (5).

33. The method according to one of claims 29 to 32, in which: the global reference system W comprises: an axis Zwaligned with the rotation axis (4); an axis Xwaligned with a direction conventionally associated with the zero angle of rotation; an axis Ywderived from the vector product between the axis Xwand the axis Zw; and an origin Ow located on the rotation axis (4); and the two laser profilometers (2) are only one offset apart in the direction Zwand one angular phase; andthe coordinates of a point acquired by a second laser profilometer (2) seen in the reference system of a first laser profilometer (2) are expressed by the following equation [1]:X12, Y12, Z12 are the coordinates of a point acquired by the second laser profilometer(2) seen in the reference system of the first laser profilometer (2); ii, ji, ki is the versor of an axis X2 as seen from the reference system of the first laser profilometer (2); i2, J2, k2 is the versor of an axis Y2 seen from the reference system of the first laser profilometer (2); is, js, ks is the versor of an axis Z2axis as seen from the reference system of the first laser profilometer (2);X22, Y22, Z22 are the coordinates of a point acquired by the second laser profilometer(2) seen in the reference system of the second laser profilometer (2);Oi2x, Oi2y, Oi2zare the coordinates of an origin in the reference system of the second laser profilometer (2) seen in the reference system of the first laser profilometer (2).

34. The method according to claim 33, in which, after calibration of the two laser profilometers (2), equation [1] is written as follows:X12, Y12, Z12 are the coordinates of a point acquired by the second laser profilometer (2) seen in the reference system of the first laser profilometer (2); ii , ji is the versor of an X-axiS2 as seen from the reference system of the first laser profilometer (2);X22, Y22, Z22 are the coordinates of a point acquired by the second laser profilometer (2) seen in the reference system of the second laser profilometer (2);Oi2zis the coordinate of an origin in the reference system of the second laser profilometer (2) seen in the reference system of the first laser profilometer (2).

35. The method according to claim 34, wherein the coordinates of the centers C of the spherical master bodies (5) as seen from the reference system of the second laser profilometer (2) in the reference system of the first laser profilometer (2) in the unknowns ii, ji and Oi2zare described by equation [2]:BXj1cos 6 — sin 6 0 BXj2■ 0By1— sin 0 cos 6 0 Byj2+ 0Bzj1. 0 0 1. Bzj2012Zcos 0 = irsin 6 = jBxj1, By , Bzj1are the coordinates of a center of a j-th spherical master body (5) (with j=1...m) as seen by the second laser profilometer (2) in the reference system of the first laser profilometer (2) [pm];Bxj2, Byj2, Bzj2are the coordinates of a center of a j-th spherical master body (5) (with j=1 ...m) as seen by the second laser profilometer (2) in the reference system of the second laser profilometer (2) [pm].

36. The method according to claim 35, in which the first laser profilometer (2) and the second laser profilometer (2) are linked by the following equation [3]:Ax1, Ay1, Az1are the coordinates of a center of an i-th spherical master body (5) (with i=1 ...n) as seen from the first laser profilometer (2) in the reference system of the first laser profilometer (2) [pm];Bxj1, Byj1, Bzj1are the coordinates of a center of a j-th spherical master body (5) (with j=1...m) as seen by the second laser profilometer (2) in the reference system of the first laser profilometer (2) [pm]; andSMAiBjis a distance certified in the metrology room between the center of the spherical master body (5) Ai and the center of the spherical master body (5) Bj corresponding to the current gauge temperature [pm],37. The method according to claim 36, in which the certified distance in the metrological room between the center of the spherical master body (5) Ai and the center of the spherical master body (5) Bj corresponding to the current gauge temperature [pm] is expressed by the following equation [4]:(SMAiBj~20is the certified distance in the metrology room between the center of the spherical master body (5) Ai and the center of the spherical master body (5) Bj [pm];KtMstis the coefficient of thermal expansion of the gauge material [1 / °C]; andTMstis the current temperature value of the gauge during the calibration procedure[°C].

38. The method according to any one of claims 28 to 37, wherein the laser profilometers (2) are arranged and held in a fixed position and the support (3) is rotated in steparound the rotation axis (4).

39. The method according to any one of claims 28 to 38, wherein the support (3) has a ring shape and a cylindrical symmetry about the rotation axis (4).

40. The method according to claim 39, wherein the support (3) comprises a series of columns (11 ), each of which is oriented parallel to the rotation axis (4), is cantilevered from the support (3), and houses at its upper end a respective master body (5).41 . The method according to any of claims 28 to 40, wherein the master bodies (5) are arranged at opposite faces (9, 10) of the support (3).

42. The method according to one of claims 28 to 41 , in which: more than two laser profilometers (2) are provided; more than two master bodies (5) are provided; and each laser profilometer (2) frames at least two master bodies (5) during relative rotation, around the rotation axis (4) and with step Ocp, between the laser profilometers (2) and the support (3).

43. The method according to one of claims 28 to 42, in which an angular distance between the two master bodies (5) framed by the same laser profilometer (2) is 90°.

44. The method according to any one of claims 28 to 43, wherein the two master bodies (5) framed by one and the same laser profilometer (2) have, within a measuring range of the laser profilometer (2), a different position along the rotation axis (4).

45. A calibration system for calibrating at least two laser profilometers (2) against one rotation axis (4) and comprising: at least two (5) spherical master bodies; a same common support (3) to which the two spherical master bodies (5) are fixed in such a way that each laser profilometer (2) frames at least two master bodies (5) during a relative rotation, around the rotation axis (4) and with step Ocp, between the laser profilometers (2) and the support (3); an actuator device configured to generate a relative rotation in step and with angular step dtp around the rotation axis (4) between the support (3) and the laser profilometers (2); and a control unit configured to implement the calibration method according to one of claims 18 to 29; in which the laser profilometers (2) share at least one common master body (5) in pairs in such a way that the same master body (5) is framed by two different laser profilometers (2).

46. The calibration system according to claim 45, in which the support (3) has a ring shape and a cylindrical symmetry about the rotation axis (4).

47. The calibration system according to claim 46, wherein the support (3) comprises a series of columns (1 1 ), each of which is cantilevered from the support (3) and houses a respective master body (5) at its upper end.

48. The calibration system according to claim 46 or 47, wherein the master bodies (5) are arranged at opposite faces (9, 10) of the support (3).

49. The calibration system according to any one of claims 45 to 48 for calibrating more than two laser profilometers (2) and comprising more than two master bodies (5) fixed to the support (3) such that the laser profilometers (2) share in pairs at least one common master body (5) such that the same master body (5) is framed by two different laser profilometers (2).

50. The calibration system according to any of claims 45 to 49, wherein an angular distance between the two calibration bodies (5) framed by the same laser profilometer (2) is 90°.

51. The calibration system according to any one of claims 45 to 50, wherein the two calibration bodies (5) framed by one and the same laser profilometer (2) have, within a measuring range of the laser profilometer (2), a different position along the rotation axis (4).

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