WO2014044505A1 - Method for aligning two laser sensors in relation to each other - Google Patents

Description

"Method for aligning two laser sensors to each other" Description

The invention relates to a method for aligning at least two laser distance sensors to each other, wherein the laser distance sensors each having a laser and a sensor.

The invention also relates to a method for measuring the thickness of a body or a coating of a coated body in a measuring setup, which are used in the measurement of the two laser distance sensors. Finally, the invention also relates to a device for carrying out such a method.

Laser distance sensors are used, inter alia, when the thickness of a body or a coating is to be measured precisely. In this case, the light reflected from the object to be measured is measured and the thickness determined therefrom.

Such a method is known, for example, from EP 2 031 347 A1, in which the temperature of the object to be coated is also measured during the measurement in order to obtain a more accurate estimate of the thickness of a coating in the case of a thickness measurement.

A method for measuring the coating thickness by means of laser triangulation is known from EP 2 312 267 A1. The measurement is measured before and during or after coating and can be carried out selectively. A similar method is used in DE 103 13 888 A1. In the method, a distance is determined by a laser triangulation method and compared with a reference value in order to be able to estimate the thickness of a coating.

For all these methods, it is important to precisely set the position of the lasers for the measurement to allow a reliable determination of the thicknesses. An error in the positioning affects the accuracy of the thickness measurement and therefore leads to errors in determining the thickness.

When using two lasers to determine the thickness of a body or coating, the data measured with the two lasers may be one compensate for possible uncertainty in the positioning of the object to be measured. For this it is important that these lasers are aligned with each other as accurately as possible in order to determine a reliable and accurate determination of the layer thickness of a coating can.

The object of the invention is therefore to provide a method for positioning two lasers to one another, which is as simple as possible to carry out and leads to the most accurate adjustment and positioning of the laser distance sensors to each other.

Other tasks not explicitly mentioned arise from the overall context of the following description, examples and claims.

These are solved as well as other tasks that are not explicitly mentioned, but which are readily derivable or deducible from the contexts discussed herein by way of a method having all the features of claim 1 and by a method having all the features of claim 15. Advantageous modifications of the method according to the invention according to claim 1 are provided in the dependent claims 2 to 14 under protection. Likewise, a useful modification of the method according to claim 15 is provided in dependent claim 16 under protection. A solution of the objects of the invention is also provided by an apparatus for implementing such a method according to claim 17. The subclaims 18 and 19 claim appropriate modifications of the device.

The present invention is accordingly realized by a method for aligning at least two laser distance sensors to one another, the laser distance sensors each having a laser and a sensor, comprising the following chronological steps A) to D):

A) coarse alignment of both laser distance sensors to one another and introduction of a calibration body with a defined geometry into a measurement setup comprising the laser distance sensors; B) distance measurements of a plurality of measurement points or a continuous course on the surface of the calibration body by the laser distance sensors, wherein the calibration body is moved in the measurement setup relative to the laser distance sensors to allow the laser of the laser distance sensors, the irradiation of the different measurement points or the continuous course for the distance measurements;

C) determining the position and orientation of the two laser distance sensors to each other on the basis of the distance measurements and the known geometry and position of the calibration body in the measurement setup; and

D) adjustment of at least one of the laser distance sensors based on the thus determined position and orientation of the laser distance sensors to each other, so that a desired position and a desired orientation of the laser distance sensors to each other is sought.

By the method according to the invention, among others, the following advantages can be achieved:

The method is simple to implement and therefore inexpensive to implement. In addition, with the method, a high accuracy of a subsequent measurement can be achieved. By determining and adjusting the orientation and position of the laser distance sensors with each other, errors in the calibration body and its storage are compensated, so that only small demands on the calibration body must be made and possible errors in carrying out the process are avoided from the outset.

Adjusting the position and orientation of at least two laser distance sensors to each other is the same when only the positions and the orientations of the laser of the laser distance sensors are adjusted when the lasers and the sensors of the laser distance sensors are not fixed to each other.

According to the invention, it can preferably be provided that the desired alignment of the laser distance sensors with respect to one another is aimed at an oppositely directed alignment of the laser beams produced and as the desired position the laser distance sensors is aimed at a position in which the laser beams generated by the lasers of the laser distance sensors meet without calibration body in one point, wherein the coarse alignment of the laser distance sensors is preferably oriented to the desired orientation and the desired position of the laser distance sensors to each other.

This orientation promotes an improvement in the accuracy of the subsequent measurement of the thickness of a body or coating.

A further embodiment of a method according to the invention can provide that the distance measurements are carried out on at least five measuring points on the surface of the calibration body by the laser distance sensors.

A higher number of measuring points leads to a smaller error in the subsequent evaluation of the results. At the same time, however, a small number of measuring points accelerate the entire process.

According to a further, particularly preferred embodiment of the invention can be provided that the calibration body is rotatably mounted in the measurement setup and the measurement points are driven by rotating the calibration body in the measurement setup about the axis of rotation or the continuous course is driven by rotating the calibration body in the measurement setup about the axis of rotation , wherein preferably the laser distance sensors are aligned on the axis of rotation, particularly preferably, the orientation of the laser distance sensors to the axis of rotation with an angle (Γ) of less than 20 °, most preferably with an angle (Γ) of less than 5 °.

A rotatable calibration body, in particular a turntable as calibration body, simplifies the entire structure. In addition, the structure can be made much more compact with a rotating calibration body.

It can be provided that the angular velocity (co) of the calibration body about the axis of rotation in determining the position and orientation of the two Laser distance sensors to each other is taken into account mathematically, especially in the distance measurement of the continuous course.

By this method, there are possibilities for a simple evaluation of the signal periodic by the rotation.

Furthermore, it can be provided that the angle of rotation (.phi.) Of the calibration body is determined, the time (t) preferably being measured at known angular velocity (co) in order to determine the angle of rotation (.phi.) Of the calibration body, with a marker being particularly preferred the calibration body is measured with the laser distance sensors to determine a full revolution.

As a result, an additional direct measurement of the rotation angle (φ) of the calibration body can be avoided.

Most preferably, it can be provided that a turntable is used as the calibration body, wherein preferably the turntable is inclined against the rotation axis, particularly preferably a tilt angle (δ) between 5 ° and 60 °, very particularly preferably a tilt angle (δ) between 15 ° and 30 ° is inclined.

Due to the inclination or tilting of the turntable increases in a periodic measurement of the swept value range of the signal of the distance measurement. This leads to a better evaluable signal and thus to a more accurate determination of the orientation and optionally also the position of the at least two laser distance sensors to each other.

It can be provided that the tilt angle (δ) of the turntable against the axis of rotation when determining the position and orientation of the two laser distance sensors to each other mathematically is taken into account.

By this measure, a further simplification of the calculation of the sought parameters can be achieved. It applies to the determination of the orientation and the position of the laser distance sensors to each other that the tilt angle (δ) of the turntable against the axis of rotation must be known approximately.

It can also be provided that the laser beams generated by the lasers of the laser distance sensors always strike the same side of the turntable during the distance measurement.

This measure also serves to simplify the arithmetic evaluation for determining the position and orientation of the laser distance sensors to one another.

A particularly preferred embodiment of the invention can provide that the position and orientation of the laser distance sensors to each other by parameter fits of, ■,, - δ,), _Λ i _,,, no (d - b),

Equations l _x = ----- · + ₀₁ and / ₂ = - - · +> 2 are determined n ° c ₁ ^'n ° c ₂

or are determined by a Taylor series expansion of these equations, preferably determined by a Fourier analysis of a Taylor series expansion of these equations, where / _? and h are the measured values of the two laser distance sensors when hitting the turntable, n is the normal vector of the turntable, di and c / 2 are the position vectors of the points of intersection of the surface of the turntable facing the respective laser 1 or laser 2 with the axis of rotation, bi and Ö2 the position vectors of the virtual intersection point of the first and second laser beam with the associated xy planes E ₁ and E ₂ through the points di and c / 2, Cj and c _2, the direction vectors normalized in the z direction to the amount of 1 of the incident on the turntable Laser beams of laser 1 and laser 2 in the direction of increasing measured values and k, i and h, 2, the measured values of the respective laser distance sensors, which would result in measuring the respective points bi and 62.

An evaluation of the above formula with the specified means is mathematically feasible and therefore suitable for calculatory evaluation.

It can also be provided that in the calculation of the data for the determination of the position and orientation of the two laser distance sensors from each other a periodic distance measurement, the amplitudes of a fundamental wave (F _{1 1} ), in particular the amplitudes of a fundamental wave (Fi, i) and at least the first harmonic wave (F ₂ , i) are used, wherein preferably the fundamental wave (Fi, i) and / or at least the first harmonic (F ₂ , i) are calculated by a Fourier analysis of the periodic distance measurement, particularly preferably calculated by a Taylor series development and a Fourier analysis of the periodic distance measurement.

The evaluation of a fundamental wave (Fi, i) and at least the first harmonic wave (F ₂ , i) of the periodic signal leads, with high accuracy of the result, to a simple implementability of the method. Details on this can be found in the mathematical derivation of FIGS. 3 to 5 below.

It may be provided that, in the calculation of the fundamental wave (Fi _, i) and / or at least the first harmonic (F ₂ , i), it is assumed that the amplitudes of the fundamental wave (Fi _, i) and / or at least the first harmonic wave ( F _{2 /} i) is greater than or equal to zero.

This assumption also leads to a simplification of the arithmetic evaluation of the signals.

In a very particularly preferred embodiment of the method according to the invention can be provided that the angles i and γι and the amplitudes C _l and the representation of the vectors in

 Cylindrical coordinates to determine the position and orientation of the first laser distance sensor using the equations

F _{2 l} 1

β ₁ = μ, - π - (c _zl - l) / 2; 7ι = Πι ^C i = 2 - cot (<5) - -; B _l = cot (<5) - _u be calculated, where μ? the phase angle of the fundamental wave of Ι _λ (φ) and η _ί the phase position of the 1. _Harmonic wave of Ι _λ (φ), c _zl = sign (c _zl ) indicates the z-orientation of the laser to the turntable, δ is the tilt angle of the turntable against the rotation axis and F _{1t 1 is} the measured amplitude of the fundamental wave and F ₂ , i is the measured amplitude of the first harmonic, preferably the angles j0 ₂ and 7 ₂ and the and position

and the orientation of the second laser distance sensor are used and from the position and orientation of the two laser distance sensors are calculated from each other.

These formulas, with high accuracy, greatly simplify the formulas for evaluating a signal from a rotating tilted or tilted turntable.

Furthermore, provision can be made for the distance measurements to be carried out using a laser triangulation method and / or for the laser distance sensors to be calibrated in the course of alignment on the basis of the measured data and / or the variables calculated therefrom.

The calibration is particularly preferably carried out by the calculation of the additive components k, i and k, 2 of the respective measurement signal by / _{0 1} = F _{0 l} - _{2 1} ^■ cos (y _l - or / _{0 2} = F _{0 2} - F _{2 2} - cos (7 ₂ - ß ₂ ).

Laser triangulation methods are simple and inexpensive to implement and particularly suitable for the implementation of methods according to the invention. The objects of the invention are also achieved by a method for measuring the thickness of a body or a coating of a coated body in a measurement setup, wherein the measurement of the thickness two laser distance sensors are used, previously in the measurement setup with a method according to any one of the preceding claims to each other were aligned.

The advantages of methods according to the invention, in which at least two laser distance sensors are adjusted exactly to one another, are particularly pronounced in a measurement of the thickness of a body or a coating of a coated body.

Such methods may preferably also include the following chronological steps:

E) removing the calibration body from the measurement setup;

F) inserting the body to be measured into the measurement setup; and

G) measuring the thickness of the body or its coating by means of the mutually aligned and positioned laser distance sensors.

As indicated by the alphabetical order of the letters, said steps are carried out in chronological order and according to steps A) to D) of alignment methods according to the invention.

The objects of the invention are also achieved by an apparatus for carrying out such a method, in which the apparatus comprises at least two laser distance sensors and a bearing for a body to be measured, each laser distance sensor having a laser and a sensor, the bearing for supporting a calibration body with defined surface is designed and the calibration body is defined in the device movable.

It can be provided that the calibration body is rotatably mounted in the device or can be stored and the calibration body by defined angle (φ) about an axis of rotation is rotatable and / or with at least one defined angular velocity (co) is rotatable.

It can be provided in turn that the calibration body is a disc which is inclined against the axis of rotation, preferably tilted by a Verkippungswinkel (δ) between 5 ° and 60 °, more preferably by a Verkippungswinkel (δ) between 15 ° and 30 ° is inclined, most preferably inclined by a tilt angle (δ) between 20 ° to 25 °.

The aim of a measurement setup according to the invention and an evaluation procedure or a method according to the invention is to determine the position and tilt of a plurality of laser distance sensors relative to one another and relative to a rotation axis defined by the measurement setup. The process is very robust because it does not necessarily use the absolute value of the laser distance sensor. In addition, the test setup is characterized by a low height.

The position parameters determined in this way can be used in particular to a) align one or more laser distance sensors parallel to a rotation axis defined by the measurement setup,

b) align two or more laser sensors parallel to each other, and / or c) to place the laser beams of two counter-rotating laser distance sensors exactly to each other.

Exemplary embodiments of the invention and calculations relating to the invention are explained below with reference to five schematically illustrated figures, without, however, limiting the invention. Showing:

Figure 1 is a schematic side view of a structure for implementing a method according to the invention in a desired position;

Figure 2 is a schematic side view of a structure for implementing a method according to the invention with coarse alignment at the beginning of the process; FIG. 3 shows a schematic perspective illustration for clarifying the angular relationships in a structure for implementing a method according to the invention in an initial situation;

FIG. 4 shows two schematic side views of a turntable as shown in FIG. 3; and

FIG. 5: a perspective diagram for clarifying the geometric relationships.

FIG. 1 shows a schematic side view of a measurement setup for implementing a method according to the invention in a desired position. The measurement setup comprises two laser distance sensors 1, 2, both of which each have a laser 4, 8 and its sensor 6, 10. The lasers 4, 8 and the sensors 6, 10 are arranged at a fixed angle to each other. Between the laser distance sensors 1, 2, a disc is arranged as a calibration body 12 and rotatably supported about a rotation axis z. The axis of rotation z does not have to be a material axis, as suggested by the drawing, for example when the calibration body 12 is held in a rotatable frame. The laser beams from the lasers 4, 8 hit the calibration body 12 on opposite surfaces. As sensors 6, 10 conventional CCD chips with an upstream lens can be used. Such sensors 6, 10 for measuring the reflected laser light are known from laser triangulation methods for determining the layer thickness of a coated body.

In the view shown in Figure 1, the lasers 4, 8 are oriented and positioned in a desired orientation relative to each other. The laser distance sensors 1, 2 are arranged in the desired orientation and position such that the laser beams generated by the lasers 4, 8 could meet in opposite directions at a point if the calibration body 12 were not arranged between the laser distance sensors 1, 2. If the laser beams are understood as vectors in the same coordinate system, one laser beam is equal to the other laser beam with a negative sign. With the method according to the invention, the alignment and positioning of the laser distance sensors 1, 2 shown in FIG. 1 is to be achieved relative to one another. First, the laser distance sensors 1, 2 are only roughly aligned in the measurement setup. This arrangement is shown in Figure 2 as a schematic side view. The laser distance sensors 1, 2 are not exactly opposite arranged and also tilted against each other. The aim of the method is to align the laser distance sensors 1, 2 against each other so that the arrangement comes as close as possible to the state shown in Figure 1.

For this purpose, the calibration body 12 is introduced into the measurement setup and rotatably mounted there. With the laser distance sensors 1, 2 a plurality of measuring points are recorded on the upper and the lower surface of the calibration body 12. For this purpose, the calibration body 12 is rotated in construction. Preferably not only discrete measuring points are recorded on the surface of the calibration body 12, but a continuous course of the distances between the two laser distance sensors 1, 2 is recorded by the two surfaces of the rotating calibration body 12. At known angular velocity ω and at least roughly known geometry of the calibration body 12, information can be obtained from the periodic signal of the laser distance sensors 1, 2, which allow precise conclusions about the arrangement and alignment of the lasers 4, 8 and thereby the laser distance sensors 1, 2 to each other. The information thus obtained can be used to adjust the laser distance sensors 1, 2 in order to achieve the desired state in FIG. 1 or to come as close as possible to this.

In a preferred embodiment, a turntable 12 is rotatably mounted as a calibration body 12 in the measurement setup. The turntable 12 is inclined from the rotation axis z by an angle. The turntable 12 is placed in the laser beams of the laser distance sensors 1, 2 and the distance of the laser 4, 8 measured to the point of impact of the laser beams on the turntable 12 during its rotation.

Optionally, the absolute angle (or at least its zero crossing) of the rotary disk 12 is measured on the rotation axis z.

From the measurement signal tilting and positioning of the laser 4, 8 and thus the laser distance sensors 1, 2 are mutually determined mathematically. FIG. 3 shows a schematic perspective illustration for clarifying the angular relationships in a structure for implementing a method according to the invention in an initial situation with coarsely adjusted lasers 24, 28 of two laser distance sensors. In a real design, the laser beams of the lasers 24, 28 must of course hit the turntable 32. The displacement of the lasers 24, 28 in the xy plane is used here only for a clearer representation of the angular relationships.

For the derivation of the geometric equations and the description of the setting algorithm, the definition of a coordinate system and of variables is necessary.

The z-axis of the Cartesian coordinate system is placed in the axis of rotation of a turntable 32. The turntable 32 is used as a calibration body in the measurement setup. The x- and y-axis is not determined geometrically, but should be based on the adjustment possibilities of the laser sensors. The first laser 28 radiates (in this representation from below) onto the turntable 32. The second laser 24 strikes the turntable 32 in the coarse alignment of the lasers 24, 28 or the laser distance sensors in approximately the same area.

The position and orientation of the laser sensor are by the Richtun svektor ^c \ des

festgelegt, wobei die parallel zur x-y-Ebene verläuft und die Drehachse senkrecht im Laser beam and the puncture point

set, which runs parallel to the xy plane and the axis of rotation perpendicular to

Point intersects, in which also the side facing the laser 28 of the turntable 32, the axis of rotation, ie the z-axis intersects.

FIG. 4 shows two schematic side views of the turntable 32 according to the illustration according to FIG. 3 in order to be able to vividly discuss the mathematical derivation of a solution according to the invention of the problem.

Within the coordinate system, the position of the rotary disk 32 is determined by the relevant axis _sections on the z-axis (d _zl and d _z2 ) and the normal vector n. Because of the choice of b _x , b _zl = d _zl . The normal vector n of the turntable 32 is tilted from the z-axis by the angle δ, with 0 <<5 <TT / 2, SO that also the angle between the surface of the rotary disk 32 and the x / y-plane is δ. The current rotation angle φ of the rotary disk 32 is the angle between the x-axis and the projected into the x / y plane negative gradient of the rotary disk 32 of the surface with base in the axis of rotation z. After this

Definition, the normal vector is parameterized by n.

FIG. 5 shows a perspective diagram for clarifying the geometric relationships. The vectors of a first laser beam of a first laser (for example of the laser 28 according to FIG. 3) and the vectors and angles used for the calculation are shown in relation to the coordinate system and the laser beam. For a second laser or other lasers, analogous diagrams result, which in the following lead to analogous considerations.

For the position b _x , the following Cartesian coordinates or cylindrical coordinates are used: cosCβ)

with B ₁ > 0.

 b.

The direction of the laser is described by two equivalent vectors: the

Unit vector ^{1 1 11} , which points in the direction of the first laser beam and in

dessen z-Komponente normiert ist. Diese Vektoren sind wie folgt parametrisiert: Direction of increasing readings, and

whose z-component is normalized. These vectors are parameterized as follows:

° . Dann ist ^{Czl C}*A^CA ""^^und ^¹' ^{1 + Ci2}. Der Winkel zwischen Laserstrahl und Parallelen zur Drehachse beträgt dann ^Γι ^{= arctan}(Ci)-

°. Then ^{Czl C} * A ^C A "" ^^ and ^ ¹ ' ^{1 + Ci2} . The angle between the laser beam and parallels to the axis of rotation is then ^Γ ι ^{= arctan} (Ci) -

The parameters _γ ι, _ϋ ι, _α Λ are selected from the measurement at the end _β ι, _Β ι determined, from which emerge all representations of ^ ^c i, and thus the position and tilt, the first laser.

The following is the geometry and measurement equation derived:

The points ^ on the laser beam of the first laser are parameterized by the corresponding measured value ^ as follows: p _l (l _l ) = b _l + (l _l -l _0l ) -c _l where ^ ⁰ ' ^{1 is} the measured value in point ⁼ ^ is.

In addition, all points on the side of the turntable facing the first laser satisfy the equation no (p ₁ - <i _j ) = 0, where here the sign "°" denotes the scalar product.

At the point of intersection between the beam of the laser and the turntable both equations are satisfied and one can eliminate the variable P ^ and obtain the following condition for the measured value ^ at the point of intersection: n ° (b _l + (l _l -l _ol ) -c _l -d _l ) = 0

If we solve the equation for ^, we get h ^{~ l} o, i ^~ r

no In the following, a Taylor series development and a Fourier analysis of the measurement signal are carried out in order to obtain easily accessible measurement quantities:

To prepare the Taylor development of the measurement signal of ^ becomes the relationship

into the above equation for Ί. You get

This equation can already be used according to the invention to calculate the position and orientation of the lasers with respect to one another by means of the distance measurements and the known ones. For this purpose, the equation can be solved mathematically using parameter fits. However, further mathematical simplifications lead to a preferred embodiment of the invention with much simpler calculation.

For this purpose, the definitions of the vectors ^c i and ⁿ are used first, taking advantage of the fact that = v The result is

_{/ = / |} - Β _λ cos (ß ₁ ) cos (<p) sin (5) - B ₁ sin (ß ₁ ) sin (<p) sin (5) Jl ä ^

C _j cos (7 _j ) cos (<p) sin ((5) + C ₁ sin ^) sin (<p) sin ((5) + c _zl cos ((5)

= cos(<p - /3_j) und erhält

Now we extend the numerator and denominator with c _zl / cos (ö) and use that c _z ² _l = 1 and the addition theorem cosijß

= cos (<p - / 3 _j ) and receives

Hereinafter, it is assumed for the Taylor series development that the first laser 28 and the rotation axis z have already been roughly aligned with each other, that is, that

C _l «cot (<5), for example C _l « 1 at δ <π 14. Then the amount of ε: = c _zl C _l tan (ö) ^■ cos (<p - γ _γ ) in the denominator of l _x for every angle φ very much smaller than 1 and a Taylor expansion

- = 1-ε + ε ² -ε ³ + 0 (ά ⁴ ) = (1-ε) · (1 + 0 (ά ² ))

£ +1 of the denominator from Ι to ε justified. With this Taylor development k = Ό _, ι + ("tan (5) · cos (<p - β)) - (l - c _z A tan (5) · cos (<p - _7ι )) · (1 + 0 (C ² )) ^■ JÜÖ ² and after dissolving the product terms of the cosine functions = l ₀ + (-B tan ² (ö) · cos ( _7l -β) · (1 + 0 (C ² )) - o _ζ Β tan (c5) · cos (<p - &) · (1 + 0 (C, ² )) +

From this representation, the Fourier development of _Ι λ (φ) can be in the form of k (<P) = ^F o, i + ^F i, i cos (<p _-μ ι) + _{2> 1} cos (2 <p - η ,) + ... with _u > 0, ₂₁ > 0. In order to obtain always positive amplitudes F _u > 0, irrespective of whether the laser beam scans the turntable 32 on the upper side or from the lower side, the sign of the prefactor, that is to say _{c zl} , must be replaced by an angle shifted by π in the argument of the cos terms. One obtains _μ λ = ß _l + n- (c _zl - \) ll,

wobei die Fourier-Koeffizienten F_0l, F beziehungsweise ₂₁ bis auf Restterme der Ordnung 0(C^), 0(C_X ²) beziehungsweise 0(C_X ) stimmen.

wherein the Fourier coefficients F _0l , F and ₂₁ , respectively, to residual terms of the order 0 (C ^), 0 (C _X ² ) or 0 (C _X ) vote.

With this preparatory work can now be with knowledge of the tilt angle δ of the hub 32, the z-orientation of the first laser 28, that is c _zl = sign (c _zl ), and the first terms of the Fourier series k (<P) = ^F o _, i + ^F i _, i cos (<p -μ _ι ) + _{2> 1} cos (2 <p - η,) + ... the above five (nonlinear) equations according to the five unknowns ⁱ '^' ^ ⁱ '^ ⁱ resolve with the following result:

 C, = 2-cot (5) - ^ -,

1

 1.1

'ο, ι ⁼ o, i-2, ^cos (7i-A) -

From the first four quantities, it is simply possible to determine the physical setting parameters, for example c _xl = C ₁ -cos (/ ₁ ),

b _yi = B, -sin (βJ, which are required when using linear tables and tilting tables in the x and y directions.

On the tilt angle δ of the hub 32 can be closed from the storage of the hub 32, which is defined by the measurement setup. The z-alignment of the lasers 24, 28 determines whether the turntable 32 is from above or below

 F

is irradiated. It should be noted that the constant term of the Fourier series, ie ⁰¹ , is not required for this calculation step and thus the measured value may also be offset.

With knowledge of all five sizes, each point on the laser beam of the first can be

Lasers (in the measuring range) unambiguously assign the measured value ^ by + h ^{, \) 'c \} , in particular also determine the zero point P ^ ^~ ^ ^ ^{' Cl} in space. For the zero point calibration of the laser, in turn, the offset in the measured value can be determined as the difference between the current measured value and the desired measured value, and the offset can then be taken into account in the evaluation of the later measured values.

In practice, the tilt angle δ is defined and known by the structure of the turntable 32. In a parallel alignment of multiple lasers 24, 28 with each other even the exact value is not necessary: The angle δ scales the amplitude value of the normalized tilting C _l and the derived values c _xl , c _yl , C _l , c _xl , c _yl only. The same applies to B _x and derived values b _xl , b _yl , if it has already been ensured that C _l «1. In the parallel alignment of multiple lasers 24, 28 with each other one seeks zeros of such derived quantities, which are independent of the scaling effect of δ.

F F F

The Fourier coefficients ⁰¹ , ^{1 1} , ^{2 1} and the phases μ _λ , η _λ of Ι _λ (φ) can be obtained in practice in various ways, as the following cases show:

1) The measurement signal is measured at predefined, discrete angular positions (spatial discrete on the turntable 32) and the parameters of Ι _λ (φ), for example, determined by a discrete Fourier transform. According to the invention, continuous measurements are preferred for ease of handling.

2) Instead of the angle-dependent measurement signal Ι _λ (φ), the time signal l _x (t) and the matching angle φ (ί) is measured and from this Ι _λ (φ) and its parameters determined. At possibly unknown, but constant rotational speed ω of the rotary disk 32, a time signal l _x (t) is measured and the times, t ₀ and t _x , two successive zero crossings φ (ί _λ ) = φ (ί ₀ ) = 0. Then you can with the

2TF tt angular velocity co = the angle signal φ (ί) = ω · (ί - ί ₀ ) = 2π - tt ₀ tt _{0 are} reconstructed. Together with the time signal l _x (t) again Ι _λ (φ) and its parameters can be determined. A constant angular velocity ω thus leads to a simplification of the calculation of the parameters and is therefore particularly preferred according to the invention.

It is also possible to do without direct angle measurement. Assume that the angle β _x between the first laser 28 and the turntable 32 is approximately known, for example due to a prefabricated measuring attachment. Thus, μ _{λ is} known. A time signal l _x (t) is recorded at a constant rotational speed ω of the rotary disk 32. If then the lasers 24, 28 are already quite well aligned, that is, if C _l «cot (<5), then the fundamental wave dominates the harmonic, that is F _u » 2 ^■ F _v , and it can be very simple successive times t _m0 and t _{ml are} found, in

 2K

which the signal assumes the maximum. Then ω =. With the knowledge of the rotational speed ω, the Fourier coefficients F _{0 l} , F _ll , F _{2 l can be determined} from the time signal l _x (t). In order to obtain the missing phase position η _λ , one first determines times ί _μ1 and ί _η1 at which the maxima of the fundamental wave and the harmonic are to be expected, for which μ _ι = ω - ί _μ1 and η _ι = 2ω - ί _η1 ,

 2 (t - 1)

Then η ₁ - 2μ ₁ = 2ω · (ί _η1 - ί _μ1 ) = 2π - and thus

2 (t - t,)

η _λ = 2π- + 2μ ₁ . Then all parameters of Ι _λ (φ) are known for the evaluation. For an estimation of the setting accuracy, a construction with the following parameters is considered below by way of example:

<5 _{= 7r} / 6 (= 30 °) => tan (c5) = 0.58;

j _j = 2.5 mm;

Ä _jj = \ μιη;

With respect to F _u , this means that at approximately parallel to the axis of rotation of

Turntable 1 2, 32 aligned laser 8, 28 and aligned laser 4, 8, 24, 28, the amplitude of the then approximately sinusoidal distance measurements is 2.5 mm and the Fourier coefficients F _U , F _{2 1 were determined} with an uncertainty of 1 μηη ,

It applies to the normalized tilt

Q = 2 - cot (<5) has a setting accuracy of

AC, ~ 2 · cot (c5) ^ = 1.3 - 1 (Γ ³ .

The uncertainty in the angle = arctan (Q) between a laser 8, 28 and a parallel to the axis of rotation z is then at these small values of C _l

ΔΓ = 1 / (1 + Q ² ) · AC _l = 1, 3mrad (= 0.079 °).

For the distance B _{x of} the laser point from the rotation axis z to z height d _zl holds

B _x = cot (c5) · F _j ! - «cot (ö) · F _j !

 Ί I

and thus an inaccuracy of inequality of "cot (5) - ÄF _n = 1, 72 / m. In the following, the effects on the uncertainty of a thickness measurement are shown.

The setting accuracy of the laser 4, 8, 24, 28 directly determines the uncertainty of a thickness measurement.

For an estimation we use the above numerical values.

The uncertainty Ad of the measured value in determining the thickness of a plate tilted by a maximum of <5 '= 5 ° in a measuring gap with a positioning accuracy in the z-axis direction of h = 2.5 mm by the two setting errors AC ₁ and AB _{1 of} the first

Lasers 8, 28 is then

The second laser 4, 24 provides an analogous contribution.

In order to keep the uncertainty low, the following points should be noted:

1) When adjusting the position and tilt of the sensors 6, 10, the largest possible angle δ should be selected and the full measuring range should be used as far as possible so that F can be as large as possible. However, this is limited by the real dimensions of the measurement setup, such as the dimensions of the laser distance sensors 1, 2, optionally the thickness of the turntable and the axis of rotation or the diameter of the laser beam. For real structures with commercially available laser distance sensors 1, 2, an angle δ between 15 ° and 35 ° is particularly preferred since it can be easily implemented with these components.

2) The resolution of the laser distance sensors 1, 2 should be as high as possible so that AF and AF _{V are} as small as possible. The resolution of the laser distance sensors

1, 2 may for example be limited by a measurement noise to 1 μιτι.

3) In the actual measurement of the object to be measured this should be as little as possible tilted, that is, the angle δ 'be as small as possible, and lie as quiet as possible in the direction of the z-axis, that is, h should be as low as possible. An inclination of the object to be measured of 0 ° can preferably be provided.

Two exemplary setting algorithms for methods according to the invention are presented below.

When constructing a suitable measuring device, the restrictions for its use must be taken into account. In particular, care must be taken that the measuring range of the laser distance sensors 1, 2 is both maintained during the measurement, and therefore also very well utilized.

The constructed measuring device is inserted into the beam path of the lasers 4, 8, 24, 28.

In order to align several lasers 4, 8, 24, 28 in parallel, it is preferable to proceed as follows:

1) Align axes of the lasers 4, 24, laser 8, 28 and axis of rotation z roughly parallel

«Cot (<5), => C ₂ « cot (<5));

2) measure signals Ι _λ , l ₂ ;

3) determine Fourier coefficients F _U , F _{2; 1} and the phases μ ₁ , η ₁ of Ι _λ (φ) and Fourier coefficients F _{1; 2} , F _{2; 2} and the phases μ ₂ , η ₂ of FIG ₂ φ);

4) position and tilt of the first laser 8, 28 by β _ι , γ _ι , 0 _ι , Β _ι determine and position and tilt of the second laser 4, 24 by β ₂ , γ ₂ , 0 ₂ , Β ₂ determine;

5) determine adjustment parameters of lasers 4, 24 and lasers 8, 28;

6) Tilt laser 4, 24 and / or laser 8, 28 until 8 _X = ± 8 ₂ .

Equivalent conditions are 8 _xA = 8 _z2 8 _x2 -8 _zl 8 _xl = 0 and c _y = c _z2 c _y2 -c _yl = 0.

In order to position two lasers 4, 8, 24, 28 exactly in opposite directions, it is preferred according to the invention to proceed as follows: 1) Make sure the lasers 4, 8, 24, 28 are roughly opposite, that is

^C zl ^{- ~ C} z \ '

 2) align lasers 4, 24 and lasers 8, 28 in parallel (see above);

3) ^Readjust position of laser 4, 24 and / or laser 8, 28 until i + ^{dz2 ~ dzl} c _zl c _xl = b _x2 + ^d * ^{~ d} c _z2 c _x2 and b _yi + ^{dz2 ~ dzl} c _yl = b _y2 + ^ ^{zl ~ z2} c _z2 c _y2 .

In the following, the effects of tumbling axes of rotation z are discussed.

So far, it has been assumed that the surfaces of the turntable 12, 32 are absolutely parallel and that the rotation axis z is exactly positioned during the measurement and does not wobble.

In test experiments, it was surprisingly found in the context of the present invention that a tumbling turntable 12, 32 cause massive measurement errors in the determination of the tilting of the lasers 4, 8, 24, 28 with respect to the turntable 12, 32, but the determination of the relative tilt of the Lasers 4, 8, 24, 28 are virtually unaffected.

The following shows why this is so.

The inclination of the turntable to the z-axis always appears in the form of the expression tan (<5) in the derivation equations. This expression must be at a staggering

Rotational axis to be replaced by a φ-dependent expression. Since only the Fourier components of the measurement signal are evaluated, it is sufficient to take into account the effect of the Taumein by the first terms of its Fourier evolution, ie by tan (<5) - (l + i cos (<p - p)) ,

Thus, replacing tan (<5) by tan (<5) - (l + i cos (<p - p)) in the equation for Ι _λ (φ), develops the terms in a Fourier series and considers the first Approximation, it follows Ι _λ = (const - c _zX B _x tan (<5) · cos (<p - β _λ ) +

+ B ₁ - tan ² (<5) · (C _j cos (2 <p - _7l - ft) - c _zl R cos (2 <p - p - ß,))) - ^ l + C ^.

In contrast to the original equation, only the Fourier term of the first harmonic changes.

If one uses these (falsified or modified and adapted to the tumbling axes of rotation) equation in the evaluation, one interprets

C _x cos (2 <p ^~ Y _i ^~ ß _i ) ^~ c _zl R cos (2 <p - p - ß _l ) = C cos (2 <p - γ (- β _γ ) and thus obtains a falsified tilt C {and tilt direction γ {instead of the true values C _l and γ _λ .

The measurement errors c _xl = c _x ^f _l -c _xl and c _yl = c _y ^f _l -c _yl in the x and y coordinates of the tilt of the first laser 8, 28 due to the tumbling axis of rotation are then c * i = - c _z iR cos (p); c _yl = -c _zl R sin (p), which becomes clear from the following subaccount: Firstly

C {cos (2cp - ß _j -γ ^f) - C _j cos (2cp - ß _j -γ)

= -c _zl i? - cos (2 (p - ß _j - p)

= -c _zl R cos (p) · cos (2cp - ß _j ) - c _zl R sin (p) · sin (2cp - ß _j ), and the other applies to the same expression

C {cos (2 <p - _j ß _j - y ^f) - C _j cos (2 <p - _β λ - γ)

= C {cos (/ ^f ) * cos (2 <p -β ₁ ) + C {sin (/ ^f ) ^■ sin (2 <p -β _x )

C _j COS (/) cos (2 <p-jβ _j ) -C _j sin (/) x sin (2 <p -β _λ )

= c _x ^f _l · cos (2 <p - ß _x ) + c _y ^f _l - sin (2 <p - β _λ ) - c _xl ^■ cos (2 <p - _βλ ) - c _xl ^■ sin (2 <p - _βλ )

= ci ^■ cos (2 <p _-βj ) + c * ^■ sin (2 <p -β,), whereby the sought relationship from the comparison of the result terms of the transformations, ie

C _zl R cos (p) * cos (2 <p - _j ß _j) - - c _zl R sin (p) * sin (2 <p - _β λ) = c _xl ■ cos (2 <p - _β λ) + c _yl · sin (2 <p - _βλ ), it follows that the equation must be satisfied for all possible angles φ. Similarly, for the measurement error in the tilt of the second laser 4, 24 c * 2 = -c _z2 ^R cos (p); c _y2 = -c _z2 R sin (p).

Calculating now the expected measurement error in the x and y component of the relative tilting of the second laser 4, 24 to the first laser 8, 28, the result for the x-component

= c _z2 (c »2 -c _x2 ) ^~ c _zl ic {i -c _xl ) = c _z2 ci ₂ - ci, = -R cos (p) + R cos (p) = 0. Similarly, for the y - component cy ^f A - CyA = (c ( ₂ c ₂ - c { _x c _y ^f _X ) - (c _z2 c _y2 - c _yl ) = ... = C _z2 c _y2 - c _yl = -R sin ( p) + R sin (p) = 0.

Thus, wobbling of the rotational axis causes each measurement errors in the values of the tilt of the laser 4, 8, 24, 28 with respect to the coordinate axis z, that is, ci ^ c _xl, c _y ^f _l * c _yl, Ο _{{2 Φ} Ο Χ2 and c _y ^f ₂ ^ c _y2 . However, the relative tilt is not affected, that is, _A = c _xA and _A = c _xA , since the error components in the

Cancel tilting when calculating the relative tilting exactly.

Thus, in general, methods according to the invention have the advantage that a tumbling of the axis of rotation, as well as a not exactly known axis of rotation and geometry of the calibration body 12, 32 by determining the position and orientation of the laser 4, 8, 24, 28 to each other in good Approximation can be compensated. This means that less attention must be paid to the storage of the calibration body 12, 32 in the measurement setup and that the calibration body 12, 32 must be made less accurate than if only the position and orientation of a laser to a calibration object is determined and set. The same applies to an unwanted slight deformation of the calibration body 12, 32nd

The features of the invention disclosed in the foregoing description, as well as the claims, figures and embodiments may be essential both individually and in any combination for the realization of the invention in its various embodiments.

LIST OF REFERENCE NUMBERS

1, 2 laser distance sensor

 4, 8, 24, 28 lasers

 6, 10 sensor

 12, 32 calibration bodies

Geometric variables δ Tilt angle between turntable (12, 32) and axis of rotation

 (Z)

φ angle between projection of the gradient of the turntable (12,

 32) in x-y plane and x-axis

n normal vector of the turntable (12, 32) (with positive z-component)

 Position vectors of the points of intersection of the surface of the turntable (12, 32) facing the first laser or second laser with the axis of rotation (z)

 z-components of the position vectors ^, ^ 2

Ε E ₂ virtual planes perpendicular to the axis of rotation at z-height of, ^ 2

Position vector of the virtual intersection of the first laser beam (8, 28) with plane ^E ^

x, y, z component of the position vector b _x

Distance of position vector b _x of rotation axis (z) ßi Angle between projection of position vector b _x in xy-plane and x-axis (= direction of virtual intersection b _x )

 Direction vector of the first laser beam (8, 28) in the direction of increasing measured values

^C x \ ^'C yl' ^C z \ x, y, z component of the direction vector c ₁

^C l on | c _zl | normalized direction vector c ₁ , ie c ₁ = _1/1 c _zl | ^• c ₁

^C x \ ^C y \ ' ^C z \ x, y, z component of the normalized direction vector Cj with c _zl = sign (c _zl )

Amplitude of normalized tilt c ₁ projected in xy plane

Angle between projection of the direction vector c ₁ in xy-plane and x-axis (= direction of tilting)

^C xA ' ^C yA x, y component of the relative tilt of second laser (4, 24) to the first laser (8, 28) defined by c _xA = c _z2 c _x2 - c _zl c _xl and

^C yA ^{~ C} z2 ^C y2 ^{~ C} z \ ^C y \

T _j = arctan (C ₁ ) Angle between first laser beam (8, 28) and parallel to

 Rotation axis (z)

 X x axis perpendicular to the z axis of the Cartesian

 coordinate system

y y axis perpendicular to the z axis and x axis of the Cartesian

 coordinate system

z axis of rotation of the calibration body and z-axis of the Cartesian

 coordinate system

Measured values and parameters k Measured value of the first laser sensor 1 when hitting the

 Turntable (12, 32)

Measurement of the first laser sensor 1 when measuring the point b _x

^F o, i constant term in Fourier evolution of 1 _λ (φ)

^F n amplitude of the fundamental wave of 1 _λ (φ)

^F 2, l amplitude of the 1. Harmonic of 1 _λ (φ)

Phase angle of the fundamental wave of 1 _λ (φ)

Phase position of the 1. Harmonic of 1 _λ (φ)

ω (constant) angular velocity d <p / df of the rotary disc (12, 32)

Claims

claims 1 . Method for aligning at least two laser distance sensors (1, 2) to one another, the laser distance sensors (1, 2) each having a laser (4, 8, 24, 28) and a sensor (6, 10) comprising the following chronological steps A) to D):  A) coarse alignment of the two laser distance sensors (1, 2) to one another and introducing a calibration body (12, 32) with a defined geometry into a measurement setup comprising the laser distance sensors (1, 2);  B) distance measurements of a plurality of measurement points or a continuous course on the surface of the calibration body (12, 32) by the laser distance sensors (1, 2), wherein the calibration body (12, 32) is moved in the measurement setup relative to the laser distance sensors (1, 2), to allow the lasers (4, 8, 24, 28) of the laser distance sensors (1, 2) to irradiate the different measuring points or the continuous course for the distance measurements;  C) determining the position and the orientation of the two laser distance sensors (1, 2) to one another based on the distance measurements and the known geometry and position of the calibration body (12, 32) in the measurement setup; and  D) adjustment of at least one of the laser distance sensors (1, 2) on the basis of the thus determined position and orientation of the laser distance sensors (1, 2) to each other, so that a desired position and a desired orientation of the laser distance sensors (1, 2) is sought each other. 2. The method according to claim 1, characterized in that as desired alignment of the laser distance sensors (1, 2) to each other an oppositely directed alignment of the laser beams is sought and desired position of the laser distance sensors (1, 2) a position is sought, in which the laser beams from the lasers (4, 8, 24, 28) of the laser distance sensors (1, 2) are produced without calibration bodies (12, 32) meet at a point, wherein preferably the coarse alignment of the laser distance sensors (1, 2) at the desired orientation and the desired position of the laser distance sensors (1, 2) is oriented to each other. 3. The method according to claim 1 or 2, characterized in that  the distance measurements at at least five measuring points on the surface of the calibration body (12, 32) are performed by the laser distance sensors (1, 2). 4. The method according to any one of the preceding claims, characterized in that  the calibration body (12, 32) is rotatably mounted in the measurement setup and the measurement points are controlled by rotating the calibration body (12, 32) in the measurement setup about the rotation axis (z) or the continuous course by rotating the calibration body (12, 32) in the measurement setup the axis of rotation (z) is traversed, wherein preferably the laser distance sensors (1, 2) are aligned on the axis of rotation (z), particularly preferably, the orientation of the laser distance sensors (1, 2) to the axis of rotation (z) with an angle (Γ) of less than 20 °, most preferably with an angle (Γ) of less than 5 °. 5. The method according to claims 4, characterized in that  the angular velocity (co) of the calibration body (12, 32) about the axis of rotation (z) in determining the position and orientation of the two laser distance sensors (1, 2) is mathematically taken into account, in particular in the distance measurement of the continuous course. 6. The method according to any one of claims 4 or 5, characterized in that the rotation angle (φ) of the calibration body (12, 32) is determined, wherein preferably the time (t) at a known angular velocity (co) is measured to the Rotation angle (φ) of the calibration body (12, 32) to determine, more preferably, a marker on the calibration body (12, 32) with the laser distance sensors (1, 2) is measured to determine a full revolution. 7. The method according to any one of claims 4 to 6, characterized in that as calibrating body (12, 32) a turntable is used, wherein preferably the turntable against the rotation axis (z) is inclined, more preferably by a Verkippungswinkel (δ) between 5 ° and 60 °, most preferably inclined by a tilt angle (δ) between 15 ° and 30 °. A method according to claim 7, characterized in that  the tilt angle (δ) of the turntable against the rotation axis (z) in determining the position and the orientation of the two laser distance sensors (1, 2) to each other mathematically taken into account. A method according to claim 7 or 8, characterized in that  the laser beams generated by the lasers (4, 8, 24, 28) of the laser distance sensors (1, 2) always strike the same side of the turntable during the distance measurement. A method according to any one of claims 7 to 9, characterized in that the position and the orientation of the laser distance sensors (1, 2) to each other by _λ Parameterfits equations Ι = ^η _^ ^ ^• | c ₁ | + / _{0 1} and no Cj l ₂ = ⁿ - ^■ \ c ₂ \ + l _{0 2} or with a n ° c ₂ Taylor series development of these equations are determined, preferably determined by a Fourier analysis of a Taylor series development of these equations, where /? and h are the measured values of the two laser distance sensors (1, 2) when they strike the turntable (12, 32), n the normal vector of the turntable (12, 32), di and c / _2, the position vectors of the intersections of the respective laser 1 (8, 28) and laser 2 (4, 24) facing surface of the turntable (12, 32) with the axis of rotation , bi and £> 2 the position vectors of the virtual intersection of the first and second laser beam with the associated xy planes E ₁ and E ₂ through the points di and c / ₂ , C _j and c ₂ in the z direction on the amount of 1 normalized direction vectors of the laser beams incident on the turntable (12, 32) of laser 1 (8, 28) or laser 2 (4, 24) in the direction of increasing measured values and k, i and k, 2 the measured values of the respective laser distance sensors (1 , 2), which would result in measuring the respective points bi and. 1 1. Method according to one of the preceding claims, characterized in that in the calculation of the data for the determination of the position and the orientation of the two laser distance sensors (1, 2) to each other from a periodic distance measurement, the amplitudes of a fundamental wave (Fi _, i), in particular the amplitudes of a fundamental wave (Fi, i) and at least the first Harmonic wave (F ₂ , i), wherein preferably the fundamental wave (Fi, i) and / or at least the first harmonic wave (F ₂ , i) are calculated by a Fourier analysis of the periodic distance measurement, more preferably by a Taylor series expansion and a Fourier analysis of the periodic distance measurement can be calculated. 12. The method according to claim 1 1, characterized in that in the calculation of the fundamental wave (Fi _, i) and / or at least the first harmonic wave (F ₂ , i), it is assumed that the amplitudes of the fundamental wave (Fi, i) and / or at least the first harmonic wave (F _2, i) are greater or equal to zero. 13. The method according to any one of claims 7 to 12, characterized in that the angles ßi and γι and the amplitudes Q and Bi for determining the position r ^ cosoß ^  and the orientation described by the vector the at least one laser distance sensor (1) with the

 equations βι = μι - π - (£ _ζ1

 2.1  Q = 2 - cot (<5) - F 1,1

be calculated, where μ? the phase angle of the fundamental wave of Ι _λ (φ) and η _ί the phase position of the 1. _Harmonic wave of Ι _λ (φ), c _zl = sign (c _zl ) _indicates the z-orientation of the laser (8, 28) to the turntable, <5 is the tilt angle of the turntable against the rotation axis (z) and F _{1t 1} the measured amplitude of the fundamental wave and F _2, i is the measured amplitude of the first harmonic, preferably the Angle j0 ₂ and 72 and the amplitudes C ₂ and B ₂ in the same way to Determination of the position and orientation through the vector c second laser distance sensor (2)

are used and from the position and orientation of the two laser distance sensors (1, 2) are calculated to each other. 14. The method according to any one of the preceding claims, characterized in that  the distance measurements are carried out with a laser triangulation method and / or that the laser distance sensors (1, 2) are calibrated in the course of the alignment on the basis of the measured data and / or the variables calculated therefrom. 15. A method for measuring the thickness of a body or a coating of a coated body in a measurement setup, wherein the measurement of the thickness of two laser distance sensors (1, 2) are used, which were previously aligned in the measurement setup with a method according to one of the preceding claims to each other , 16. The method according to claim 15, characterized by the chronological steps E) removing the calibration body (12, 32) from the measurement setup;  F) inserting the body to be measured into the measurement setup; and  G) measuring the thickness of the body or its coating by means of the mutually aligned and positioned laser distance sensors (1, 2). 17. An apparatus for carrying out a method according to one of the preceding claims, in which the apparatus comprises at least two laser distance sensors (1, 2) and a bearing for a body to be measured, each laser distance sensor (1, 2) comprising a laser (4, 8, 24, 28) and a sensor (6, 10), the bearing for holding a calibration body (12, 32) is designed with a defined surface and the calibration body (12, 32) is defined in the device movable. 18. The apparatus according to claim 17, characterized in that the calibration body (12, 32) is rotatably mounted in the device or can be stored, and the calibration body (12, 32) is rotated by defined angles (φ) around a rotation axis (z) is rotatable and / or with at least one defined angular velocity (co) is rotatable. Apparatus according to claim 18, characterized in that the calibration body (12, 32) is a disc which is inclined against the axis of rotation (z), preferably inclined by a tilt angle (δ) between 5 ° and 60 °, particularly preferably by a tilt angle (δ) between 15 ° and 30 ° °, very particularly preferably inclined by a tilt angle (δ) between 20 ° to 25 °.