Method and device for determining the angle of rotation of a rotation axis

Abstract

Method for determining a rotation angle (W) of a rotation axis (2), wherein at least one image of a target (8) with at least one periodic pattern (9) is generated, wherein the periodic pattern (9) has a periodic intensity profile along at least one dimension, wherein the periodic pattern (9) has a periodic intensity profile along at least one partial or full circular line, wherein at least one wave property of the periodic intensity profile is determined, wherein the rotation angle (W) is determined as a function of the at least one wave property, characterized in that a center of the periodic pattern (9) is determined in the image as the center (10) of the at least one partial or full circular line.

Description

[0001] The invention relates to a method and a device for determining an angle of rotation of a rotational axis.

[0002] Many industrial applications utilize parts that rotate around a rotary axis. For example, in metrology, rotary tables or swivel joints are used to rotate a test specimen or a sensor for capturing measurement points.

[0003] However, rotational errors can occur during rotary movements, causing the rotating part to rotate more or less than the desired angle. This error can be detected during a calibration process and then corrected during subsequent operation based on the errors recorded during calibration. Such calibration typically achieves the required accuracy of the rotational movement with regard to concentricity, axial runout, and wobble. However, correcting these rotational errors generally requires significant computational effort, particularly determining the angle of rotation at a large number of points. Furthermore, such calibration processes are very time-consuming and can require considerable assembly and setup time.

[0004] EP 3 321 883 A1 describes a method and a system for determining a 6-DOF pose of an object in space using an optical marker attached to the object. It is disclosed that the marker has an inner marker region with a circular contour of known radius and a marker pattern. It is further described that the marker pattern can have an intensity profile that varies essentially along a circular path around a center, with these intensity values ​​varying according to a function consisting of a linear combination of a finite number of sine components.

[0005] US 2009 / 0231574A1 refers generally to a method and system for measuring angles.

[0006] DE 10 2010 063 804 A1 relates to the determination of the angular position of a part rotatable about an axis of rotation using an optical image sensor, in particular the determination of the angular position of a rotor of an electric drive in a motor vehicle.

[0007] DE 101 63 027 A1 relates to an object position determination method by which an inclination of an object is determined and to a device applying this method.

[0008] CN 1 02 799 080 A belongs to the technical field of proximity contact lithography and relates in particular to a method for eliminating alignment errors between mask grids.

[0009] WO 2019 / 139 685 A1 relates to the field of measurement technology and in particular to the design of targets.

[0010] JP 2003-97930 A discloses a method for determining a rotation angle that corresponds to a deviation from a reference position of an image recognition object.

[0011] US Patent 8,625,107 B2 discloses devices and methods for producing an orientation-dependent radiation source (ODR) for use in systems employing such methods and devices.

[0012] The technical problem is to create a method and a device for determining the rotation angle of a rotary axis that enables a simple, fast, and accurate determination of the rotation angle. This would then also allow for a fast, simple, and accurate determination of the rotation error of the rotary axis.

[0013] The solution to the technical problem is provided by the articles with the features of the independent claims. Further advantageous embodiments of the invention are described in the dependent claims.

[0014] A method for determining the rotation angle of a rotation axis is proposed. In this method, at least one image of a target is generated, wherein the target comprises, exhibits, or forms at least one periodic pattern. The periodic pattern can be an optically detectable pattern. The image can, in particular, be a two-dimensional image.

[0015] The target can be mounted so that it can rotate around the axis of rotation. For example, the target can be attached to a part that can rotate around the axis of rotation.

[0016] The target's periodic pattern exhibits a periodic intensity profile along at least one dimension. Preferably, the periodic pattern exhibits a harmonic, and in particular a sinusoidal, intensity profile along the at least one dimension. An intensity profile can denote a progression of grayscale values. However, it is also possible for the intensity profile to denote a progression of a single color value or a sum of several color values.

[0017] The fact that the target's periodic pattern exhibits a periodic intensity profile along at least one dimension can mean that a periodic intensity profile exists along a line of the pattern. This line can be straight. It can also be partial or full circles. As explained in more detail below, the periodic pattern can also take the form of a transverse wave with a propagation direction, particularly a straight propagation direction.

[0018] The periodic pattern can, in particular, be a printed pattern. The maximum wavelength of the periodic pattern can be greater than twice the minimum pixel resolution in the detection area of ​​an image acquisition device used to generate the image. If, for example, such an image acquisition device has a minimum pixel resolution of 0.5 mm per pixel in the detection area, the wavelength is preferably greater than 1 mm. However, it is particularly preferred that the wavelength be significantly, in particular 10 times or more than 10 times, greater than this minimum pixel resolution in the detection area.

[0019] Furthermore, at least one wave property of the periodic intensity profile is determined. This is done primarily using image analysis. Specifically, the wave property can be determined by evaluating the image of the periodic pattern, particularly using a suitable evaluation device. Exemplary wave properties are explained in more detail below.

[0020] Furthermore, the angle of rotation is determined as a function of at least one shaft property. This can mean that the shaft property forms an input variable for determining the angle of rotation. The angle of rotation can also form an output variable of the determination process.

[0021] For example, a known relationship between the angle of rotation and the shaft property may exist, which can be determined, for instance, during a calibration process. Alternatively, a functional, characteristic curve, or map-based relationship between the shaft property and the angle of rotation can be evaluated to determine the angle of rotation.

[0022] The rotation angle can be an absolute angle or a relative angle, i.e., a change in the rotation angle. If the method is used to determine a change in the rotation angle, the proposed method can determine both a first rotation angle in a first rotation position of the axis of rotation and a further rotation angle in a further angular position of the axis of rotation, where the change in the rotation angle corresponds to the difference between the two rotation angles. Therefore, it is necessary that at least two images are generated in different angular positions of the axis of rotation and thus of the target.

[0023] Known methods for determining rotation angles often employ optical patterns with sharp, i.e., abrupt, intensity transitions. However, due to the limited resolution of an image acquisition device, these patterns can only be reproduced with limited accuracy, which in turn reduces the accuracy of the rotation angle determination. Using a periodic pattern to determine the rotation angle advantageously avoids this disadvantage, resulting in a more precise determination. Furthermore, this method allows for a simple and rapid determination of the rotation angle, as no complex evaluation algorithms are required.

[0024] The method is particularly suitable for detecting rotational errors, as these usually produce imaging errors in the range of a few pixels and are therefore very difficult to detect.

[0025] The method can be used in particular to determine a residual rotation error. For example, the axis of rotation can be rotated by a predetermined target rotation angle, and the actual resulting rotation angle is then determined using the proposed method, with the difference representing the residual rotation error.

[0026] It is possible to generate at least one image of multiple targets, each with at least one periodic pattern, where these targets can be arranged in different relative positions to the axis of rotation. This makes it possible to identify and compensate for perspective distortions in the imaging of these targets.

[0027] In a preferred embodiment, the wave property is phase information of the periodic intensity profile. The phase information can be a phase value or a quantity dependent on the phase value.

[0028] Alternatively, the wave property can be amplitude or frequency information of the periodic intensity profile, i.e., information about an amplitude or a frequency of the periodic intensity profile.

[0029] Frequency information can be a frequency value or a quantity dependent on that frequency value. As explained in more detail below, frequency information can also be a position in a two-dimensional frequency space or a quantity dependent on it. Such a position can be determined, among other things, by applying a two-dimensional Fourier transform.

[0030] As explained in more detail below, a wave property can be determined by numerical methods for fitting a periodic, preferably harmonic, intensity profile to the depicted intensity profile, or by applying a Fourier transform and evaluating the transformed profile.

[0031] This advantageously results in a computationally simple, fast and accurate determination of the rotation angle, since established and therefore already implemented methods for determining the wave properties can be used.

[0032] In another embodiment, the periodic pattern exhibits a harmonic intensity profile along at least one dimension. This advantageously results in a very reliable and therefore accurate determination of the wave properties, since only the properties of a single harmonic need to be determined.

[0033] Furthermore, the periodic pattern exhibits a periodic intensity profile along at least one partial or full circular line. A midpoint of this line can, in particular, be the center of the periodic pattern or the center of the target. Specifically, the target can be rotatably arranged around the axis of rotation such that the midpoint of the circular path of the line is located on the axis of rotation. As explained below, with such a configuration of the periodic pattern, determining phase information advantageously allows for a particularly simple and rapid determination of the rotation angle.

[0034] In a further embodiment, intensity values ​​of a number of measurement points along at least one partial or full circular line in the image are determined, whereby a phase information or position of the intensity value progression is determined as a wave property. The measurement points can be determined, in particular, within the image's coordinate system. If the coordinate of a measurement point deviates from the coordinate of an image point by no more than a predetermined amount, the intensity value of the image point can be determined as the intensity value of the measurement point. If the coordinate of the measurement point deviates from the coordinate of an image point by more than a predetermined amount, the intensity value of the measurement point can be determined as a function of the intensity values ​​of several image points, for example, by interpolating the intensity values ​​of neighboring image points.

[0035] If the pattern with the partial or full circular periodic intensity curve is rotated, the phase of the image-based intensity values ​​will change, depending on the angle of rotation. If, as explained previously, the center point of the partial or full circular line lies exactly on the axis of rotation, then the amplitude and frequency of the curve determined in the image can remain unchanged; in this case, only the phase changes. If the center point does not lie exactly on the axis of rotation, then both the phase and the amplitude of the intensity values ​​determined in the image can change.

[0036] Determining the phase information advantageously results in a simple and reliable determination of the rotation angle.

[0037] In another embodiment, the phase information is determined by a Fourier transform of the intensity values. In particular, a Fourier transform of the intensity values ​​can be performed, with the phase as an output variable of the Fourier transform. Specifically, the phase is derived from the imaginary part determined by the Fourier transform. Alternatively, the phase information is determined by fitting a periodic, particularly harmonic, function to the intensity values, with one parameter of the periodic function being the phase information, specifically the phase. Further parameters of the periodic function can be an amplitude and a frequency.For example, by suitable optimization procedures a cost function can be minimized by varying the parameters of the periodic function, where the cost function can be, for example, a deviation or a squared deviation between the image-based determined intensity values ​​and the intensity values ​​of the periodic function.

[0038] This advantageously results in a simple and reliable determination of the phase information, which in turn leads to an accurate determination of the rotation angle.

[0039] In a further preferred embodiment, intensity values ​​of a number of measurement points along several partial or full circular lines in the image are determined, wherein the wave property is the phase information or position of the intensity value profiles. The several partial or full circular lines can have a common center point but different radii. If the intensity values ​​of these several lines are plotted against the angle in a polar coordinate system, then, ideally, with a harmonic intensity profile of the pattern, all intensity values ​​lie on a sinusoidal curve.In this embodiment, the periodic pattern along several partial or full circular lines can exhibit a periodic, preferably harmonic, intensity profile, wherein these lines have a common center point and different radii, but the same amplitudes. Such a pattern can also be referred to as a Siemens star with a harmonic intensity profile.

[0040] This advantageously increases the reliability and accuracy in determining the phase information and thus also the accuracy in determining the rotation angle.

[0041] According to the invention, a center point of at least one partial or full circular line is determined in the image. This center point can, for example, be determined as the center of one or more partial or full circular lines, wherein the intensity values ​​of the measurement points along the line(s) exhibit a sinusoidal profile with a constant frequency or a frequency that varies by no more than a predetermined amount. Specifically, if intensity values ​​of measurement points are determined along a partial or full circular line whose center point does not correspond to the true center, the profile of the intensity values ​​along these measurement points will indeed be essentially sinusoidal, but will exhibit a varying frequency, in particular one that varies by more than a predetermined amount.

[0042] Furthermore, the center determined in this way can then form the center of the partial or full circular lines, which, as explained above, serve to determine the intensity values ​​of a number of measuring points.

[0043] This advantageously results in a reliable and accurate determination of the phase position and thus also of the rotation angle.

[0044] In a further embodiment, the center in the image is determined based on a reference pattern. The reference pattern can, in particular, be a pattern of the target that differs from the periodic pattern. Specifically, the reference pattern can enable image-based, i.e., reliable, determination of the center by evaluating the image. Such a reference pattern can, for example, be in the form of a QR code. It can also be a so-called Aruco pattern, which are used in known Aruco markers. The center determined in this way can then also serve as the center for defining the partial or full circular lines for determining the measurement points or their intensity values. This advantageously results, as explained above, in a simple and accurate determination of the rotation angle.

[0045] In a further embodiment, the rotation angle is additionally determined depending on a further pattern of the target, wherein the further pattern differs from the periodic pattern. This further pattern can be the reference pattern described above. However, the further pattern can differ from both the periodic pattern and the reference pattern.

[0046] This advantageously results in a precise determination of the phase and thus a precise determination of the rotation angle, since, depending on the number of periods of the intensity profile along the partial or full circular line, the same phase can occur for different rotation angles in the range from 0° (inclusive) to, for example, 360° (exclusive). The inclusion of a further pattern advantageously allows a phase to be assigned precisely to one of these rotation angles, particularly if the further pattern is fixed relative to the periodic pattern.

[0047] A further embodiment is described in which the periodic pattern comprises at least one sub-region with a transverse unweighted stripe or wave pattern or a transverse weighted stripe or wave pattern, wherein a Fourier transform, in particular a two-dimensional Fourier transform, of the image is performed and the rotation angle is determined as a function of the position of an intensity maximum in the frequency domain. The intensity maximum can in particular be a local intensity maximum.

[0048] The transverse unweighted stripe or wave pattern can, in particular, be a two-dimensional wave pattern which, in the image, exhibits a periodic intensity profile along a straight wave propagation direction and constant intensity values ​​transversely, and especially perpendicularly, to the propagation direction. The transversely weighted stripe or wave pattern can exhibit intensity values ​​of the transversely constant stripe or wave pattern weighted by a weighting function, in particular a two-dimensional one.

[0049] A striped pattern can be a pattern with abrupt changes in intensity along the direction of propagation. A wave pattern can be a pattern with periodic, especially harmonic, changes in intensity along the direction of propagation. If such a transverse striped or wave pattern is Fourier-transformed, a local intensity maximum is obtained in the two-dimensional frequency space with respect to the magnitude assigned to the various frequencies in the two-dimensional frequency space. A radial distance of the local intensity maximum from an origin of the frequency space represents a frequency of the striped or wave pattern, and an angle between the ordinate of a coordinate system of the two-dimensional frequency space and a line connecting the origin of the coordinate system and the intensity maximum represents an orientation of the wave pattern.If such a pattern is rotated by a certain angle, the position of the intensity maximum also changes, and thus the previously described angle in the frequency domain. By determining the position, the current rotation angle, and therefore the change in the target's rotation angle, can be determined. This advantageously provides an alternative, reliable, and accurate method for determining the rotation angle. If such a pattern is moved, i.e., shifted, using a purely translational motion, the phase information associated with the frequencies in the two-dimensional frequency domain changes. By evaluating this phase information, a reliable and accurate determination of the translational motion can also be achieved.

[0050] In another embodiment, the periodic pattern comprises several sub-regions with stripe or wave patterns of different orientations. These different sub-regions can be adjacent to one another. Furthermore, a Fourier transform, particularly a two-dimensional one, is performed on the image, and the rotation angle is then determined as a function of the position of the multiple local intensity maxima in the frequency domain. This advantageously improves the robustness and thus also the accuracy of the rotation angle determination.

[0051] In a further embodiment, the intensity values ​​of a transverse weighted stripe or wave pattern of a sub-region are determined by weighting a transverse unweighted stripe or wave pattern with a Gaussian function, particularly a two-dimensional one. Here, a vertex of the Gaussian function can correspond to the center of the sub-region. Due to the weighting, intensity values ​​decrease towards the edges of the sub-region, while the wave characteristics of the stripe or wave pattern are nevertheless preserved. This advantageously avoids a sharp, i.e., abrupt, intensity transition from the sub-region to another sub-region or to a boundary region encompassing the sub-region, thereby enabling better evaluation and determination of the location of an intensity maximum in the frequency domain.

[0052] In another embodiment, the frequencies of the stripe or wave pattern differ from each other in different sub-regions. This advantageously allows for simpler identification and assignment of local intensity maxima in the frequency domain to a sub-region, and thus an improved determination of the rotation angle.

[0053] In another embodiment, local intensity maxima are determined by fitting a known distribution of local intensity maxima. If the frequencies and orientations or propagation directions of the stripe or wave patterns used are known, the relative positions of the local intensity maxima in the frequency domain can also be known. For example, using known optimization methods, a cost function can be minimized by varying the rotation angle of a rotation of the arrangement of these intensity maxima with the known relative positions. This cost function corresponds, for example, to the difference or the squared difference between the local intensity maxima determined in the image or their intensity values ​​and the local intensity maxima of the correspondingly rotated arrangement. The rotation can be a rotation about the origin of the coordinate system of the two-dimensional frequency domain.

[0054] This advantageously results in a robust determination of the location of the intensity maxima in the frequency domain, which in turn increases the accuracy in determining the rotation angle.

[0055] In a further embodiment, the at least one image is filtered. For example, the at least one image can be filtered with a bandpass filter, wherein the cutoff frequencies of the bandpass are selected such that frequencies of the periodic, in particular harmonic, intensity profile are attenuated by no more than a predetermined amount, while components with different frequencies are attenuated by more than the predetermined amount.

[0056] Filtering can also be used to convolve at least one image with the previously explained Gaussian function, in order to achieve the previously explained advantages through a single calculation. This is particularly useful if the periodic pattern includes at least one sub-area with a transverse unweighted stripe or wave pattern.

[0057] Furthermore, at least one wave property of the periodic intensity profile in the filtered image is determined. This advantageously results in a more precise determination of the rotation angle.

[0058] A further proposal is for a device for determining the rotation angle of a rotational axis, wherein the device comprises at least one image acquisition device and at least one evaluation device. The image acquisition device can, in particular, be configured as a camera, for example as a CMOS camera or CCD camera. The evaluation device can, in particular, be configured as a microcontroller or integrated circuit, or comprise one or more such.

[0059] The at least one image acquisition device generates at least one image of a target with at least one periodic pattern, wherein the periodic pattern has a periodic intensity profile along at least one dimension.

[0060] Furthermore, the evaluation device determines at least one wave property of the (imaged) periodic intensity profile, whereby the rotation angle is determined as a function of the at least one wave property.

[0061] The device is thus configured such that a method according to one of the embodiments described in this disclosure can be carried out with the device. The device thus advantageously enables the execution of the described method.

[0062] The device, in particular the image acquisition device and the evaluation device, can be part of a measuring device, in particular a coordinate measuring device.

[0063] A system comprising a device according to one of the embodiments described in this disclosure and a target according to one of the embodiments described in this disclosure is further described. The system may further comprise at least one rotatable part, wherein the target is arranged on the rotatable part, in particular rotatably about the axis of rotation of the movable part.

[0064] A target for determining the angle of rotation of a rotational axis is further described. The target can include or form a marker. The target, and in particular the marker, can have or form at least one periodic pattern, wherein the periodic pattern exhibits a periodic, preferably harmonic, intensity profile along at least one dimension. Furthermore, the target can have or form at least one fastening means for attachment to a part rotatable about the rotational axis. The pattern is, as previously explained, an optical pattern that can be imaged by an image acquisition device. Further aspects regarding the target and the periodic pattern have been explained previously. The target advantageously enables the precise and rapid determination of the angle of rotation of the rotational axis.

[0065] A further embodiment is described in which the periodic pattern comprises at least one sub-area with a transverse weighted or unweighted stripe or wave pattern. This and its corresponding advantages have been explained above. The sub-area can, in particular, be rectangular, especially square.

[0066] In another embodiment, the periodic pattern comprises several sub-areas with stripe or wave patterns of different orientations. These sub-areas can be arranged adjacent to one another. All sub-areas can be rectangular, particularly square. The fact that the stripe or wave patterns have different orientations can mean that, in a common reference coordinate system, for example, a two-dimensional target-fixed coordinate system whose axes span the plane in which the stripe or wave pattern is arranged, they exhibit different directions of propagation. As explained above, such a target enables a reliable and rapid determination of the rotation angle.

[0067] In a further embodiment, the target has at least one additional pattern that differs from the periodic pattern. This additional pattern can, in particular, be the reference pattern described above, which can be detected in addition to determining the angle of rotation. The additional pattern can also serve to determine the center of the periodic pattern.

[0068] In particular, the additional pattern can be surrounded by the periodic pattern. In other words, the additional pattern can be arranged in a sub-area that is partially or completely surrounded by the periodic pattern. The additional pattern can have a circular or polygonal, especially quadrilateral, border.

[0069] Furthermore, the intensity values ​​of a transverse weighted stripe or wave pattern in a sub-area can be determined by weighting a transverse unweighted stripe or wave pattern with constant amplitude using a Gaussian function. Additionally, the frequencies of the stripe or wave pattern can differ between different sub-areas. This and its corresponding advantages have already been explained.

[0070] A program is further described which, when executed on or by a computer or evaluation device, causes the computer to perform one, several, or all steps of the method described in this disclosure for determining the angle of rotation of a rotational axis. Alternatively or cumulatively, a program storage medium or computer program product is described on or in which the program is stored, in particular in a non-temporary, e.g., permanent, form. Alternatively or cumulatively, a computer comprising this program storage medium is described. Furthermore, alternatively or cumulatively, a signal is described, for example, a digital signal, which encodes information representing the program and which includes code means adapted to perform one, several, or all steps of the method described in this disclosure for determining the angle of rotation of a rotational axis.The signal can be a physical signal, for example an electrical signal, which is generated technically or mechanically. The program can also instruct the computer to perform the determination.

[0071] Furthermore, the method for determining the angle of rotation of a rotational axis can be a computer-implemented method. For example, one, several, or all steps of the method can be performed by a computer. One embodiment of the computer-implemented method is the use of the computer to carry out a data processing method. The computer can, for example, comprise at least one computing device, in particular a processor, and at least one storage device to process the data, particularly technically, for example, electronically and / or optically. A computer can be any type of data processing device. A processor can be a semiconductor-based processor.

[0072] The invention is explained in more detail using exemplary embodiments. The figures show: Fig. 1 a schematic block diagram of a device according to the invention for determining a rotation angle of a rotation axis, Fig. 2 a periodic pattern of a target in a first embodiment, Fig. 3 a periodic pattern of a target in a further embodiment, Fig. 4a a depicted periodic pattern in a first rotation position, Fig. 4b a depicted periodic pattern in another rotation position, Fig. 5a Measuring points in the illustrated pattern according to Fig. 4a, Fig. 5b Measuring points in the illustrated pattern according to Fig. 4b, Fig. 6a a progression of intensity values ​​of the in Fig. 5a shown measuring points, Fig. 6b a progression of intensity values ​​of the in Fig. 5b shown measurement points, Fig. 7 a periodic pattern of a target with a reference pattern, Fig. 8 a periodic pattern of a target with another reference pattern, Fig. 9a a depicted periodic pattern with several sub-areas, Fig. 9b a magnitude representation of a two-dimensional Fourier transform of the in Fig. 9a depicted periodic pattern, Fig. 10a the in Fig. 9a shows a periodic pattern with several sub-areas in a further rotation position, Fig. 10b a magnitude representation of a two-dimensional Fourier transform of the in Fig. 10a of the pattern shown, Fig. 11a a depicted periodic pattern with several sub-areas according to a further embodiment, Fig. 11b a magnitude representation of a two-dimensional Fourier transform of the in Fig. 11a pattern shown and Fig. 12 a schematic flowchart of a method according to the invention in a first embodiment.

[0073] In the following, identical reference symbols denote elements with the same or similar technical characteristics.

[0074] Fig. Figure 1 shows a schematic block diagram of a device 1 for determining a rotation angle W of a rotation axis 2. The device 1 includes an image acquisition device 3, which can be, for example, a CMOS or CCD camera. The device 1 also includes an evaluation device 4, which can be, for example, a microcontroller or include one.

[0075] The figure shows a rotary table 5, which comprises a static, i.e., fixedly arranged, part 6 and a part 7 that is rotatable about the axis of rotation 2. Also shown is a target 8, which is attached to the rotatable part 7. The target 8 is thus also rotatable about the axis of rotation 2.

[0076] As explained in more detail below, the target exhibits at least one periodic pattern 9.

[0077] The image acquisition device 3 generates an image of the target 8, in particular of the periodic pattern 9 or at least a part thereof. This image can, in particular, be a two-dimensional image.

[0078] The image, in particular its intensity values, can then be evaluated by the evaluation unit 4. Specifically, at least one wave property of the depicted periodic intensity profile of pattern 9 can be determined by the evaluation, whereby the rotation angle W is then determined as a function of this at least one wave property.

[0079] Fig. Figure 2 shows an exemplary periodic, in particular harmonic, pattern 9 of a target 8. The pattern 9 exhibits a harmonic gray value gradient, in particular a sinusoidal gray value gradient, along circular lines around a center 10 of the pattern 9. In other words, the pattern resembles the pattern shown in Figure 2. Fig. 2. The pattern shown is a well-known Siemens star, but there are no abrupt changes in the gray value along the circle from a white gray value to a dark gray value or vice versa, but rather a harmonious change between the white and the dark gray value.

[0080] This shows that pattern 9 has 20 waves per revolution of pattern 9 around the center 10, i.e., a rotation axis perpendicular to the plane of the drawing through the center 10.

[0081] If the gray value profile is plotted in a polar coordinate system with an origin at center 10 over the angle to a stationary reference line, a sinusoidal profile with a frequency of 20 oscillations results when the angle is changed by 360°.

[0082] In Fig. Figure 3 shows another periodic pattern 9, which can also be used to determine the rotation angle W. Unlike the one in Fig. The pattern shown in 2, number 9, indicates that in Fig. 3 depicted patterns 9 along a circular line around a center 10 40 waves per revolution.

[0083] Fig. Figure 4a shows an image of a periodic pattern 9 in a first rotational position. The depicted periodic pattern 9 exhibits, according to the in Fig. 2 and Fig. In the three illustrated embodiments, a sinusoidal gray value or intensity value profile is displayed along a circular path around a center 10 of the optical pattern, with this profile having 10 waves per revolution. Also shown is an image coordinate system with a longitudinal axis x and a transverse axis y, which are oriented perpendicular to each other. It is shown that the origin of the image coordinate system is located at the center 10 of the depicted pattern 9.

[0084] In Fig. 4b is the one in Fig. 4a shows the depicted periodic pattern 9 in a further rotation position, wherein the depicted pattern 9 is rotated in the image coordinate system by 10° around the center 10, i.e. a rotation axis perpendicular to the drawing plane through the center 10, in a mathematically positive sense.

[0085] Fig. 5a schematically shows measuring points 11, which are located along several circular lines in the area shown in Fig. The points are arranged in the diagram shown in 4a, with the radii of these circles differing from one another. Intensity values ​​of these measurement points 11 are determined. For clarity, only one measurement point is marked with a reference symbol.

[0086] In Fig. 5b also shows measurement points 11, which are also arranged along several circular lines with different radii, with intensity values ​​of these measurement points in the Fig. The image shown in 4b can be determined.

[0087] Fig. Figure 6a shows a progression of the intensity values ​​of the measurement points 11 in a polar coordinate system, the origin of which is in the center 10 of the in Fig. The diagram shown in Figure 5a is arranged, with the gray values ​​of the measurement points plotted over an angle between the longitudinal axis x and a connecting line between the center 10 and the respective measurement point 11. It is evident that the intensity profiles of the measurement points on different circular lines exhibit the same sinusoidal shape. It is also evident that the phase of the sinusoidal shape is 0°.

[0088] In Fig. 6b is the corresponding progression of intensity values ​​for measuring points 11 in the in Fig. The image shown in 5b is depicted. In contrast to Fig. 6a The phase angle of the sinusoidal waveform is approximately 100°. Since the frequency of the periodic intensity profile along a circle is 10 periods per full rotation of the pattern around its center, the rotation angle W can be determined to be 10°.

[0089] Fig. Figure 7 shows a target 8 with a periodic pattern 9 and a reference pattern 12, where the reference pattern 12 is a QR code (binary code). The reference pattern 12 is shown to be located in a sub-area 13 that is within the periodic pattern 9. Also shown is a border region 14 of the target 8 that surrounds the periodic pattern 9. A transition region 15 with a constant gray value can be located between the reference pattern 12 and the periodic pattern 9.

[0090] The reference pattern 12 can enable the determination of the position of the center 10 of the periodic pattern 9, in particular the circles with a periodic intensity profile along the circle, in the image. Furthermore, the reference pattern 12 can also be used to determine the rotation angle W.

[0091] Fig. Figure 8 shows a top view of a target 8 with a periodic pattern 9 and another reference pattern 12. In contrast to the one in Fig. In the embodiment shown in Figure 7, the further reference pattern comprises several sub-areas with QR codes (binary codes) and several sub-areas with a constant grey value.

[0092] Fig. Figure 9a shows an image of a target 8 with a further periodic pattern 9, wherein this periodic pattern has several sub-regions 16a, 16b, 16c, 16d. Each sub-region comprises a transverse unweighted stripe or wave pattern, each with a different orientation. The wave patterns are transverse wave patterns, with the propagation direction of the wave patterns in the different sub-regions 16a, ..., 16d being represented by arrows 17. For example, the propagation direction 17 of the wave pattern of the first sub-region 16a is oriented at an angle of -45° or +315° to a longitudinal axis x of the target 8. The propagation direction 17 of the wave pattern in the second sub-region 16b is oriented at an angle of -270° or +90° relative to the longitudinal axis x. The propagation direction of the wave pattern in the third sub-region 16c is oriented parallel to the longitudinal axis x.The propagation direction of the wave pattern in the fourth sub-area 16d is oriented at an angle of +225° (or -135°) relative to the longitudinal axis x. This is in . Fig. 9a depicted periodic pattern 9 in a first rotational position of a target 8 about the axis of rotation 2 (see Fig. 1) shown. The wave patterns of the different sub-areas 16a, ..., 16d can have the same frequencies, but preferably different frequencies from each other.

[0093] Fig. Figure 9b shows an intensity distribution of a two-dimensional Fourier transform of the in Fig. Figure 9a shows only the magnitudes assigned to the different frequencies, i.e., the magnitudes of the power components of these different frequencies. Also shown is a frequency coordinate system of the frequency space with a longitudinal frequency axis xf and a transverse frequency axis yf, which are oriented perpendicular to each other. Furthermore, the intersection of these axes xf and yf forms the origin of the frequency coordinate system. Also shown are local intensity maxima in the two-dimensional frequency space. The circled frequency maxima 18 are caused by the wave pattern in the first sub-region 16a, with the two local intensity maxima forming a complex conjugate intensity maximum pair.

[0094] It is evident that the radial distance between the local intensity maxima 18 and the origin of the frequency coordinate system is proportional to the frequency of the wave pattern. The higher the frequency of the wave pattern, the greater the radial distance. Furthermore, an angle between the frequency axis xf and a line connecting the origin of the frequency coordinate system and the local intensity maximum 18 corresponds to the previously explained propagation direction and thus orientation of the wave pattern. The explained angle between the local intensity maximum 18, in particular the first intensity maximum 18a, and the frequency axis xf corresponds to an angle of -45° (or +315°). The subsequently depicted local intensity maxima also form complex conjugate pairs and are caused by the wave patterns of the further sub-regions 16b, 16c, and 16d.

[0095] Since this position of the local intensity maxima in the illustrated arrangement of local intensity maxima corresponds to an unrotated target 8, the angle of rotation W can be determined to be 0°.

[0096] Fig. Figure 10a shows a schematic representation of a target 8 with several sub-areas, each with different wave patterns, which, however, differs from the one in Fig. Image 9a shown rotated 15° around the axis of rotation 2 (see Fig. 1) was twisted.

[0097] Fig. Figure 10b shows the corresponding two-dimensional Fourier transform with the previously explained local intensity maxima, which are caused by the wave patterns of the different sub-domains. It can be seen that the local intensity maxima 18 corresponding to the first sub-domain 16a have also been rotated by 15° in the frequency coordinate system. Thus, the rotation angle W of 15° can be determined depending on the position of the corresponding intensity maxima in the frequency domain.

[0098] Fig. Figure 11a shows an image of a target 8 with an optical pattern 9 in a further embodiment. Here, the periodic pattern 9 comprises several sub-areas 16a, 16b, 16c, 16d with wave patterns of different propagation directions 17, which are represented by corresponding arrows.

[0099] Here, the intensity values ​​of a sub-area 16a, ..., 16d are determined by weighting a transverse unweighted wave pattern (see e.g. Fig. 9a) determined with a two-dimensional Gaussian function, wherein a maximum of the two-dimensional Gaussian or normal distribution is located at the center of the corresponding sub-region 16a, ..., 16d. Furthermore, co-variances of the corresponding distribution can be adapted to a dimension of the sub-region 16a, ..., 16d, in particular chosen such that an intensity of the weighted wave pattern in a sub-region at the transition edge to another sub-region 16a, ..., 16d or to an outer boundary region is less than a predetermined intensity value or is zero.

[0100] It is further shown that the frequencies of the wave patterns of the different sub-areas 17 are different from each other.

[0101] In Fig. 11b is then the two-dimensional Fourier transform of the in Fig. The periodic pattern 9 shown in 11a is represented, in accordance with the Fig. 9b and Fig. The Fourier transforms shown in Figure 10b depict local intensity maxima. Local intensity maxima 18, caused by the weighted wave pattern of the first sub-region 16a, are shown in circles. Due to the different frequencies, the local intensity maxima are not along a circular path, as shown in Figure 10b. Fig. 9b and Fig. 10b is shown, but arranged along an elliptical path in the frequency coordinate system.

[0102] Fig. Figure 12 shows a schematic flowchart of a method according to the invention in a first embodiment. In a first step S1, which can also be referred to as the imaging step, an image of a target 8 with a periodic pattern 9 is created (see Figure 12). Fig. 1 and e.g. Fig. 2) generated. In a second step S2, which can also be called the evaluation step, at least one wave property of the depicted periodic intensity profile is determined. In a determination step S3, the rotation angle W is then determined as a function of at least one of the wave properties.

[0103] In a first sub-step of the evaluation step, a center 10 of the depicted periodic pattern 9 can be determined, i.e., a center of the periodic pattern 9 in the image coordinate system. This can be done by detecting and evaluating a reference pattern 12 (see Fig. 7, Fig. 8) are carried out. In a further step, measurement points along circles around the center thus determined and their intensity values ​​can be determined. In a further step, the phase of the periodic, in particular harmonic, curve formed by these intensity values ​​can then be determined, whereby the rotation angle W is then determined as a function of the phase.

[0104] Alternatively, in a first sub-step of the second step S2, a two-dimensional Fourier transform of the image can be performed. Furthermore, in a further sub-step of the second step S2, local intensity maxima in the two-dimensional frequency space can be determined. Finally, as explained previously, the angle between the line connecting the origin of the frequency coordinate system and the local intensity maximum, as well as a reference axis in the frequency coordinate system, for example, a frequency longitudinal axis xf, can be determined (see Fig. 9b), whereby a rotational position of the target 8 can be determined as a function of this angle. For example, a previously known relationship between the aforementioned angle and a rotational angle W of the target 8 can be evaluated. Reference symbol list 1 Device 2. Axis of rotation 3 Image capture device 4 Evaluation unit 5 Turntable 6 fixed part 7 rotating part 8 Target 9 periodic pattern 10 Center 11 measuring point 12 reference patterns 13 Transition area 14 Edge area 15 Transition area 16a, ..., 16d Sub-areas 17 Direction of spread 18 local intensity maximum 18a, 18b local intensity maxima S1 first step S2 second step S3 third step

Claims

[1] Method for determining a rotation angle (W) of a rotation axis (2), wherein at least one image of a target (8) with at least one periodic pattern (9) is generated, wherein the periodic pattern (9) has a periodic intensity profile along at least one dimension, wherein the periodic pattern (9) has a periodic intensity profile along at least one partial or full circular line, wherein at least one wave property of the periodic intensity profile is determined, wherein the rotation angle (W) is determined as a function of the at least one wave property, characterized by , that in the image a center of the periodic pattern (9) is determined as the center (10) of the at least one partial or full circular line. [2] Method according to claim 1, characterized by, that intensity values ​​of a number of measurement points (11) along at least one partial or full circular line in the image are determined, wherein a phase information of the course of the intensity values ​​is determined as a wave property. [3] Method according to claim 2, characterized by that the phase information is determined by a Fourier transformation of the course of the intensity values ​​or that the phase information is determined by fitting a periodic function to the course of the intensity values, where one parameter of the periodic function is the phase information. [4] Method according to any of the preceding claims, characterized by , that intensity values ​​of a number of measurement points along several partial or full circular lines in the image are determined, whereby phase information of the progressions of the intensity values ​​is determined as a wave property. [5] Method according to any of the preceding claims, characterized by , that the center (10) in the image is determined depending on a reference pattern (12). [6] Method according to any of the preceding claims, characterized by , that the rotation angle (W) is additionally determined depending on a further pattern of the target (8), wherein the further pattern is different from the periodic pattern (9). [7] Method according to any of the preceding claims, characterized by , that the periodic pattern (9) exhibits a harmonic intensity profile along at least one dimension. [8] Method according to any of the preceding claims, characterized by that a wave property is phase information, amplitude information, or frequency information. [9] Method according to any of the preceding claims, characterized by, that the at least one image is filtered, whereby the at least one wave property of the periodic intensity profile in the filtered image is determined. [10] Device for determining a rotation angle (W) of a rotation axis (2), wherein the device (1) comprises at least one image acquisition device (3) for generating an image and at least one evaluation device (4) for evaluating the image, wherein the at least one image acquisition device (3) is configured to generate at least one image of a target (8) with at least one periodic pattern (9), wherein the periodic pattern (9) has a periodic intensity profile along at least one dimension, wherein the periodic pattern (9) has a periodic intensity profile along at least one partial or full circular line, wherein the evaluation device (4) is configured to determine at least one wave property of the periodic intensity profile, wherein the evaluation device (4) is further configured to determine the rotation angle (W) as a function of the at least one wave property, characterized by , that the evaluation device (4) is further developed to determine in the image a center of the periodic pattern (9) as the center (10) of the at least one partial or full circular line.

Images