DE102019220174A1 - Method and device for determining an angle of rotation of an axis of rotation and target - Google Patents

Abstract

The invention relates to a method for determining an angle of rotation (W) of an axis of rotation (2), at least one image of a target (8) with at least one periodic pattern (9) being generated, the periodic pattern (9) along at least one dimension having periodic intensity profile, wherein at least one wave property of the periodic intensity profile is determined, wherein the angle of rotation (W) is determined as a function of the at least one wave property.

Description

Method and device for determining an angle of rotation of an axis of rotation and target

The invention relates to a method and a device for determining an angle of rotation of an axis of rotation and a target suitable for the determination.

Parts rotating about an axis of rotation are used in many industrial applications. For example, rotary tables or swivel joints are used in measurement technology, e.g. to rotate a test body arranged on the rotary table or a sensor to record measuring points.

However, rotational errors can occur in the rotary movements, as a result of which the rotating part rotates e.g. more or less than a desired angle of rotation. This incorrect movement can be recorded in a calibration process and then corrected during later operation on the basis of the incorrect movements recorded during the calibration. Such a calibration can generally achieve the required accuracy of the rotary movement with regard to the concentricity and axial run-out or wobble. The correction of explained rotation errors, however, generally requires a high level of computational effort, in particular the determination of the rotation angle at a large number of support points. Furthermore, such calibration processes are very time-consuming and can require a great deal of assembly and setup effort.

The EP 3 321 883 A1 describes a method and a system for determining a 6-DOF pose of an object in space with an optical marker which is arranged on the object. It is disclosed herein that the marker has an inner marker area which has a circular contour with a known radius and a marker pattern. It is further described that the marker pattern can have an intensity profile which varies substantially along a circular path around a center, which intensity values can vary in accordance with a function consisting of a linear combination of a limited number of sinusoidal components.

The technical problem arises of creating a method and a device for determining an angle of rotation of an axis of rotation, as well as a target for such a determination, which enable the angle of rotation to be determined easily and quickly and accurately. As a result, a rotational error of the axis of rotation can also be determined quickly, easily and precisely.

The solution to the technical problem results from the subjects with the features of the independent claims. Further advantageous refinements of the invention emerge from the subclaims.

A method for determining an angle of rotation of an axis of rotation is proposed. In the method, at least one image of a target is generated, the target comprising, having or forming at least one periodic pattern. The periodic pattern can be an optically detectable pattern. The image can in particular be a two-dimensional image.

The target can be mounted so that it can rotate about the axis of rotation. For example, the target can be attached to a part rotatable about the axis of rotation.

The periodic pattern of the target has a periodic intensity profile along at least one dimension. The periodic pattern preferably has a harmonic, in particular a sinusoidal, intensity profile along the at least one dimension. An intensity curve can denote a curve of gray values. Of course, however, it is also possible for the intensity profile to designate a profile of one color value or a sum of several color values.

The fact that the periodic pattern of the target has a periodic intensity profile along at least one dimension can mean that there is a periodic intensity profile along a line of the pattern. The line can be a straight line. The line can also be partially or fully circular. As will be explained in more detail below, the periodic pattern can also be formed in the form of a transverse wave with a direction of propagation, in particular a straight direction of propagation.

The periodic pattern can in particular be a printed pattern. Here, a maximum wavelength of the periodic pattern can be greater than twice the minimum pixel resolution in the detection area of an image detection device for generating the image. If such an image acquisition device has, for example, a minimum pixel resolution of 0.5 mm per pixel in the acquisition area, then the wavelength is preferably greater than 1 mm. However, the wavelength is particularly preferably distinct, in particular 10 times or more than 10 times greater than this minimum pixel resolution in the detection area.

According to the invention, there is at least one wave property of the periodic intensity profile certainly. This is done in particular on the basis of images. In particular, the wave property can thus be determined by evaluating the image of the periodic pattern, in particular by a suitable evaluation device. Exemplary wave properties are explained in more detail below.

The angle of rotation is also determined as a function of the 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 form an output variable of the determination method.

For example, there can be a known association between the angle of rotation and the shaft property, which can be determined, for example, in a calibration process. A functional or characteristic curve or map-based relationship between the shaft property and the angle of rotation can also be evaluated in order to determine the angle of rotation.

The angle of rotation can be an absolute angle of rotation or a relative angle of rotation, that is to say a change in the angle of rotation. If the method is used to determine a change in the angle of rotation, the proposed method can be used to determine both a first angle of rotation in a first rotational position of the axis of rotation and a further angle of rotation in a further angular position of the axis of rotation, the change in angle of rotation corresponding to the difference between the two angles of rotation. It is therefore necessary that at least two images are generated in different angular positions of the axis of rotation and thus of the target.

In known methods for determining angles of rotation, optical patterns with sharp, that is, abrupt, intensity transitions are often used. However, due to the limited resolution of an image acquisition device, these can only be mapped with limited accuracy, which in turn reduces the accuracy when determining the angle of rotation. By using a periodic pattern for determining the angle of rotation, this disadvantage can advantageously be avoided, which results in a more precise determination of the angle of rotation. A simple and quick determination of the angle of rotation also results in an advantageous manner, since no complex evaluation algorithms have to be carried out.

The method is particularly suitable for the detection of rotational errors, since such errors generally generate imaging errors in the area of fewer pixels and are therefore very difficult to detect.

The method can in particular be used to determine a residual rotation error. In this case, the axis of rotation can be rotated, for example, by a predetermined target angle of rotation, the actually resulting actual angle of rotation then being determined by the proposed method, the difference then forming the residual rotation error.

It is possible that at least one image of a plurality of targets is generated, each with at least one periodic pattern, it being possible for these to be arranged in different relative positions relative to the axis of rotation. This makes it possible to identify perspective distortions in the imaging of these targets and to compensate accordingly.

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 variable that is dependent on the phase value.

Alternatively, the wave property can be amplitude or frequency information of the periodic intensity profile, that is to say information about an amplitude or a frequency of the periodic intensity profile.

In this case, frequency information can be a frequency value or a variable that is dependent on the frequency value. As will be explained in more detail below, frequency information can also be a position in a two-dimensional frequency space or a variable that is dependent on it. Such a position can be determined, among other things, by using a two-dimensional Fourier transformation.

As explained in more detail below, a wave property can be determined by numerical methods for adapting a periodic, preferably harmonic, intensity profile to the mapped intensity profile or using a Fourier transformation and evaluation of the transformed profile.

This advantageously results in a computationally simple to implement and fast and accurate determination of the angle of rotation, since in particular established and thus already implemented methods for determining the shaft property can be used.

In a further embodiment, the periodic pattern has a harmonic intensity profile along at least one dimension. This advantageously results in a very reliable and thus precise determination of the wave property, since only properties of a single harmonic have to be determined.

In a preferred embodiment, the periodic pattern has a periodic intensity profile along at least one partially or fully circular line. A center point of this line can in particular be a center of the periodic pattern or a center of the target. In particular, the target can be arranged rotatably about the axis of rotation in such a way that the center of the circular course of the line is arranged on the axis of rotation. As explained below, with such a design of the periodic pattern, by determining phase information, a particularly simple determination of the angle of rotation that can be carried out quickly in terms of time can be achieved in an advantageous manner.

In a further embodiment, intensity values of a number of measurement points along at least one partially or fully circular line in the image are determined in the image, phase information or phase position of the course of the intensity values being determined as the wave property. The measuring points can be determined in particular in the image coordinate system of the image. If the coordinate of a measurement point does not deviate by more than a predetermined amount from the coordinate of an image point, the intensity value of the image point can be determined as the intensity value of the measurement point. If the coordinate of the measuring point deviates by more than a predetermined amount from the coordinate of an image point, the intensity value of the measuring point can be determined as a function of the intensity values of several image points, for example by interpolating intensity values of adjacent image points.

If the pattern is rotated with the partially or fully circular periodic intensity profile, then, depending on the angle of rotation, a phase position of the image-based profile of the intensity values will change. If, as explained above, the center of the partially or fully circular line lies exactly on the axis of rotation, then in particular the amplitude of the curve determined in the image and its frequency can remain unchanged, in which case only the phase position changes. If the said center point does not lie exactly on the axis of rotation, then in addition to the phase position, the amplitude of the course of the intensity values determined in the image can also change.

The determination of the phase information results in a simple and reliable determination of the angle of rotation in an advantageous manner.

In a further embodiment, the phase information is determined by a Fourier transformation of the course of the intensity values. In particular, a Fourier transformation of the course of the intensity values can be carried out, with an output variable of the Fourier transformation being the phase position. In particular, the phase position results from the imaginary part determined by the Fourier transformation. Alternatively, the phase information is determined by adapting a periodic, in particular harmonic, function to the course of the intensity values, one parameter of the periodic function being the phase information, in particular the phase position. Further parameters of the periodic function can be an amplitude and a frequency. For example, suitable optimization methods can be used to minimize a cost function by varying the parameters of the periodic function, the cost function being, for example, a deviation or a squared deviation between the image-based determined intensity values and the intensity values of the periodic function.

This advantageously results in a simple and reliable determination of the phase information, which in turn leads to a precise determination of the angle of rotation.

In a further preferred embodiment, intensity values of a number of measurement points along a plurality of partially or fully circular lines in the image are determined in the image, phase information or phase position of the courses of the intensity values being determined as the wave property. The multiple partially or fully circular lines can have a common center point, but radii different from one another. If the intensity values of these multiple lines are plotted over the angle in a polar coordinate system, then in the ideal case, with a harmonious intensity profile of the pattern, all intensity values are arranged on a sinusoidal curve. For this embodiment, the periodic pattern along a plurality of partially or fully circular lines can each have a periodic, preferably harmonic, intensity profile, these having / have a common center point and radii different from one another, but the same amplitudes. Such a pattern can also be referred to as a Siemens star with a harmonic intensity profile.

This advantageously increases the reliability and accuracy when determining the phase information and thus also the accuracy when determining the angle of rotation.

In a further embodiment, a center of the partially or fully circular lines is determined in the image. This center can be determined, for example, as the center of one or more partially or fully circular lines, the intensity values of the measurement points along the line (s) having a sinusoidal profile with a constant or have no more than a predetermined amount of varying frequency. If intensity values of measuring points are determined along a partially or fully circular line, the center of which does not correspond to the true center, then the course of the intensity values along these measuring points will be essentially sinusoidal, but a varying frequency, in particular varying more than a predetermined amount exhibit.

Furthermore, the center determined in this way can then form the center of the partially or fully circular lines, wherein, as explained above, these serve to determine the intensity values of a number of measurement points.

This advantageously results in a reliable and precise determination of the phase position and thus also of the angle of rotation.

In a further embodiment, the center in the image is determined as a function of a reference pattern. The reference pattern can in particular be a pattern of the target that is different from the periodic pattern. In particular, the reference pattern can enable an image-based, that is to say by evaluating the image, a reliable determination of the center. Such a reference pattern can be designed, for example, in the form of a QR code. Such a reference pattern can also be a so-called aruco pattern, this being used in known aruco markers. The center determined in this way can then also serve as a center for defining the partially or fully circular lines for determining the measurement points or their intensity values. As explained above, this advantageously results in a simple and precise determination of the angle of rotation.

In a further embodiment, the angle of rotation is additionally determined as a function of a further pattern of the target, the further pattern being different from the periodic pattern. The further pattern can be the explained reference pattern. However, the further pattern can be different both from the periodic pattern and from the reference pattern.

This advantageously results in an exact determination of the phase position and thus an exact determination of the angle of rotation, since depending on the number of periods of the intensity profile along the partially or fully circular line, the same phase position for different angles of rotation in the range from 0 ° (inclusive) to eg 360 ° (exclusively) can be present. The provision of a further pattern advantageously enables a phase position to be assigned to precisely one of these angles of rotation, in particular if the further pattern is arranged in a stationary manner relative to the periodic pattern.

In an alternative embodiment, the periodic pattern comprises at least a partial area with a transverse unweighted stripe or wave pattern or a transversal weighted stripe or wave pattern, with a Fourier transformation, in particular a two-dimensional Fourier transformation, being carried out on the image and the angle of rotation depending on a position of an intensity maximum in Frequency domain is determined. The intensity maximum can in particular be a local intensity maximum.

The transversal unweighted stripe or wave pattern can in particular be a two-dimensional wave pattern which in the image has a periodic intensity profile along a straight direction of propagation of the wave and has constant intensity values transversely, in particular perpendicular, to the direction of propagation. The transversely weighted stripe or wave pattern can have intensity values of the transversely constant stripe or wave pattern weighted with an, in particular two-dimensional, weighting function.

A stripe pattern can be a pattern with abrupt changes in intensity along the direction of propagation of the stripe pattern. A wave pattern can be a pattern with periodic, in particular harmonic, intensity changes along the direction of propagation. If such a transverse stripe or wave pattern is Fourier transformed, a local intensity maximum results in the two-dimensional frequency space with respect to the amount that is assigned to the various frequencies in the two-dimensional frequency space, with a radial distance of the local intensity maximum from an origin of the frequency space being a frequency of the stripe. or represents a wave pattern and an angle between the ordinate of a coordinate system of the two-dimensional frequency space and a connecting line between the origin of the coordinate system and the intensity maximum represents an orientation of the wave pattern. If such a pattern is rotated by an angle of rotation, the position of the intensity maximum and thus the previously explained angle in the frequency space also change. By determining the position, a current angle of rotation and thus also a change in the angle of rotation of the target can be determined. This advantageously results in an alternative, reliable and precise determination of the angle of rotation. If such a pattern is moved, that is, shifted, with a purely translational movement, the phase information that is assigned to the frequencies in the two-dimensional frequency space changes. By evaluating the Phase information can therefore also be used to reliably and precisely determine a translational movement.

In a further embodiment, the periodic pattern comprises a plurality of partial areas with stripe or wave patterns of different orientation. These different sub-areas can adjoin one another. Furthermore, a, in particular two-dimensional, Fourier transformation of the image is carried out and the angle of rotation is then determined as a function of the position of the multiple local intensity maxima in the frequency space. This advantageously improves the robustness and thus also the accuracy of the determination of the angle of rotation.

In a further embodiment, intensity values of a transversely weighted stripe or wave pattern of a sub-area are determined by weighting a transverse, unweighted stripe or wave pattern with a, in particular two-dimensional, Gaussian function. Here, a vertex of the Gaussian function can correspond to the center of the sub-area. As a result of the weighting, intensity values will decrease towards the edges of the partial area, with the wave properties of the stripe or wave pattern nevertheless being retained. This advantageously avoids a sharp, that is, abrupt, intensity transition from the sub-area to a further sub-area or to an edge area encompassing the sub-area, which enables better evaluation and determination of the position of an intensity maximum in the frequency domain.

In a further embodiment, frequencies of the stripe or wave pattern are different from one another in different subregions. In this way, a simpler identification and assignment of local intensity maxima in the frequency space to a sub-range and thus an improved determination of the angle of rotation can advantageously take place.

In a further embodiment, local intensity maxima are determined by adapting a previously known distribution of local intensity maxima. If frequencies and orientations or directions of propagation of the strip or wave patterns used are known, the relative position of the local intensity maxima in the frequency space can also be known in advance. For example, a cost function can then be minimized with known optimization methods by varying a rotation angle of a rotation of the arrangement of these intensity maxima with the known relative positions, which for example corresponds to the difference or the squared difference between the local intensity maxima or their intensity values determined in the image and the local intensity maxima of the corresponding corresponds to rotated arrangement. The rotation can be a rotation around the origin of the coordinate system of the two-dimensional frequency space.

This advantageously results in a robust determination of the position of the intensity maxima in the frequency space, which in turn increases the accuracy in determining the angle of rotation.

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, with cutoff frequencies of the bandpass being selected in such a way that frequencies of the periodic, in particular harmonic, intensity profile are not attenuated by more than a predetermined amount, but portions with frequencies different therefrom by more than the predetermined amount be weakened.

The filtering can also be used to convolve the at least one image with the Gaussian function explained above in order to achieve the advantages also explained above by means of an arithmetic operation. This can take place in particular when the periodic pattern comprises at least a partial area with a transverse, unweighted stripe or wave pattern.

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

A device is also proposed for determining an angle of rotation of an axis of rotation, the device comprising at least one image acquisition device and at least one evaluation device. The image acquisition device can in particular be designed as a camera, for example as a CMOS camera or CCD camera. The evaluation device can in particular be designed as a microcontroller or integrated circuit or comprise one (s).

The at least one image acquisition device generates at least one image of a target with at least one periodic pattern, the periodic pattern having a periodic intensity profile along at least one dimension.

According to the invention, the evaluation device provides at least one wave property of the (depicted) periodic intensity profile determined, wherein the angle of rotation is determined as a function of the at least one shaft property.

The device is thus configured in such a way 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 explained method to be carried out.

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.

A system with a device according to one of the embodiments described in this disclosure and with a target according to one of the embodiments described in this disclosure is described further. The system can further comprise at least one rotatable part, the target being arranged on the rotatable part, in particular rotatable about the axis of rotation of the movable part.

A target for determining an angle of rotation of an axis of rotation is also proposed. The target can have or form a marker. The target, in particular the marker, can have or form at least one periodic pattern, the periodic pattern having a periodic, preferably harmonic, intensity profile along at least one dimension. Furthermore, the target can have or form at least one fastening means for fastening to a part that can rotate about the axis of rotation. As explained above, the pattern is an optical pattern which can be imaged by an image acquisition device. Further aspects relating to the target and the periodic pattern have been explained above. The target advantageously enables the precise and timely determination of the angle of rotation of the axis of rotation.

In a further embodiment, the periodic pattern comprises at least a partial area with a transversely weighted or unweighted stripe or wave pattern. This and the corresponding advantages have been explained above. The sub-area can in particular be a rectangular, in particular square, sub-area.

In a further embodiment, the periodic pattern comprises a plurality of partial areas with stripe or wave patterns of different orientation. The subregions can be arranged adjacent to one another. All subregions can be designed to be rectangular, in particular square. The fact that the stripe or wave pattern have different orientations can mean that in a common reference coordinate system, for example in a two-dimensional target-fixed coordinate system, the axes of which span the plane in which the stripe or wave pattern is arranged, have different directions of propagation from one another. As explained above, such a target enables the angle of rotation to be determined reliably and quickly.

In a further embodiment, the target has at least one further pattern which is different from the periodic pattern. The further pattern can in particular be the reference pattern explained above, which can also be detected for determining the angle of rotation. The further pattern can also be used to determine a center of the periodic pattern.

In particular, the further pattern can be surrounded by the periodic pattern. In other words, the further pattern can be arranged in a partial area which is partially or completely surrounded by the periodic pattern. The further pattern can have a circular or a polygonal, in particular square, border.

Furthermore, intensity values of a transversely weighted stripe or wave pattern of a sub-area can be determined by weighting a transverse, unweighted stripe or wave pattern with constant amplitude with a Gaussian function. Furthermore, frequencies of the stripe or wave pattern can differ from one another in different partial areas. This and the corresponding advantages have already been explained above.

A program is also described which, when executed on or by a computer or an evaluation device, causes the computer to carry out one, several or all of the steps of the method for determining an angle of rotation of an axis of rotation shown in this disclosure. 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, for example in a permanent, form. Alternatively or cumulatively, a computer is described which comprises this program storage medium. Further alternatively or cumulatively, a signal is described, for example a digital signal which encodes information that represents the program and which comprises code means that are adapted, one, more or all of the steps of the method shown in this disclosure for determining an angle of rotation of a Axis of rotation perform. The signal can be a physical signal, for example an electrical signal, which in particular is generated technically or by machine. The program can also cause the computer to carry out the determination.

Furthermore, the method for determining an angle of rotation of an axis of rotation can be a computer-implemented method. For example, one, more or all of the steps of the method can be carried out by a computer. One embodiment for 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, for example, at least one storage device, in order to process the data, in particular 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.

• 1 ein schematisches Blockschaltbild einer erfindungsgemäßen Vorrichtung zur Bestimmung eines Drehwinkels einer Drehachse,
• 2 ein periodisches Muster eines Targets in einer ersten Ausführungsform,
• 3 ein periodisches Muster eines Targets in einer weiteren Ausführungsform,
• 4a ein abgebildetes periodisches Muster in einer ersten Drehstellung,
• 4b ein abgebildetes periodisches Muster in einer weiteren Drehstellung,
• 5a Messpunkte im abgebildeten Muster gemäß 4a,
• 5b Messpunkte im abgebildeten Muster gemäß 4b,
• 6a ein Verlauf von Intensitätswerten der in 5a dargestellten Messpunkte,
• 6b ein Verlauf von Intensitätswerten der in 5b dargestellten Messpunkte,
• 7 ein periodisches Muster eines Targets mit einem Referenzmuster,
• 8 ein periodisches Muster eines Targets mit einem weiteren Referenzmuster,
• 9a ein abgebildetes periodisches Muster mit mehreren Teilbereichen,
• 9b eine Betragsdarstellung einer zweidimensionalen Fouriertransformation des in 9a dargestellten periodischen Musters,
• 10a das in 9a dargestellte abgebildete periodische Muster mit mehreren Teilbereichen in einer weiteren Drehstellung,
• 10b eine Betragsdarstellung einer zweidimensionalen Fouriertransformation des in 10a dargestellten Musters,
• 11a ein abgebildetes periodisches Muster mit mehreren Teilbereichen gemäß einer weiteren Ausführungsform,
• 11b eine Betragsdarstellung einer zweidimensionalen Fouriertransformation des in 11a dargestellten Musters und
• 12 ein schematisches Flussdiagramm eines erfindungsgemäßen Verfahrens gemäß einer ersten Ausführungsform.

The invention is explained in more detail using exemplary embodiments. The figures show:

• 1 a schematic block diagram of a device according to the invention for determining an angle of rotation of an axis of rotation,
• 2 a periodic pattern of a target in a first embodiment,
• 3 a periodic pattern of a target in a further embodiment,
• 4a an imaged periodic pattern in a first rotational position,
• 4b an imaged periodic pattern in a further rotational position,
• 5a Measuring points in the pattern shown in accordance with 4a ,
• 5b Measuring points in the pattern shown in accordance with 4b ,
• 6a a course of intensity values of the in 5a shown measuring points,
• 6b a course of intensity values of the in 5b shown measuring points,
• 7th a periodic pattern of a target with a reference pattern,
• 8th a periodic pattern of a target with another reference pattern,
• 9a an imaged periodic pattern with several sub-areas,
• 9b a representation of the amount of a two-dimensional Fourier transformation of the in 9a depicted periodic pattern,
• 10a this in 9a depicted depicted periodic pattern with several partial areas in a further rotary position,
• 10b a representation of the amount of a two-dimensional Fourier transformation of the in 10a shown pattern,
• 11a an imaged periodic pattern with several partial areas according to a further embodiment,
• 11b a representation of the amount of a two-dimensional Fourier transformation of the in 11a illustrated pattern and
• 12th a schematic flow diagram of a method according to the invention according to a first embodiment.

In the following, the same reference symbols designate elements with the same or similar technical features.

1 shows a schematic block diagram of a device 1 for determining an angle of rotation W of an axis of rotation 2 . The device 1 in this case comprises an image acquisition device 3 which can be designed as a CMOS or CCD camera, for example. The device further comprises 1 an evaluation device 4th which, for example, is designed as a microcontroller or can include one.

A turntable is also shown 5 , the one static part 6th as well as one around the axis of rotation 2 rotatable part 7th includes. A target is also shown 8th , which is on the rotatable part 7th is attached. The target 8th is thus also around the axis of rotation 2 rotatably arranged.

As will be explained in more detail below, the target has at least one periodic pattern 9 on.

With the image capture device 3 becomes an image of the target 8th , especially the periodic pattern 9 or at least a part thereof. This image can in particular be a two-dimensional image.

The image, in particular intensity values of the image, can then be used by the evaluation device 4th be evaluated. In particular, the evaluation allows at least one wave property of the imaged periodic intensity profile of the pattern 9 can be determined, the angle of rotation W then being determined as a function of the at least one shaft property.

2 shows an exemplary periodic, in particular harmonic, pattern 9 of a target 8th . The pattern 9 points along circular lines around a center 10 of the pattern 9 a harmonic gray value curve, in particular a sinusoidal gray value curve. In other words, it is similar to in 2 illustrated pattern 9 a well-known Siemens star, although there are no sudden changes in gray value along the circular line from a white gray value to a dark gray value or vice versa, but rather a harmonic change between the white and dark gray value.

Here it is shown that the pattern 9 20 waves per revolution of the pattern 9 around the center 10 , so one perpendicular to the plane of the drawing through the center 10 extending axis of rotation.

The gray value gradient is in a polar coordinate system with an origin in the center 10 Plotted over the angle to a stationary reference line, a sinusoidal curve with a frequency of 20 oscillations results when the angle is changed by 360 °.

In 3 is another periodic pattern 9 shown, which can also be used to determine the angle of rotation W. In contrast to the in 2 illustrated pattern 9 shows that in 3 illustrated pattern 9 along a circular line around a center 10 40 waves per revolution.

4a shows an image of a periodic pattern 9 in a first rotary position. The pictured periodic pattern 9 shows in accordance with the in 2 and 3 illustrated embodiments along a circular line around a center 10 of the optical pattern has a sinusoidal gray value or intensity value curve, this 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 one another. It is shown that the origin of the image coordinate system is in the center 10 of the pattern shown 9 is arranged.

In 4b is that in 4a depicted depicted periodic pattern 9 shown in a further rotational position, the pattern shown 9 in the image coordinate system by 10 ° around the center 10 , so one perpendicular to the plane of the drawing through the center 10 running axis of rotation, is twisted in a mathematically positive sense.

5a shows schematically measuring points 11 along several circular lines in the in 4a shown image are arranged, the radii of these circular lines are different from each other. Intensity values of these measuring points are thereby used 11 certainly. For the sake of clarity, only one measuring point is provided with a reference number.

In 5b are also measuring points 11 which are also arranged along several circular lines with radii different from one another, with intensity values of these measuring points in the in 4b can be determined.

6a shows a course of the intensity values of the measuring points 11 in a polar coordinate system with its origin in the center 10 of the in 5a shown image is arranged, wherein the gray values of the measurement points over an angle between the longitudinal axis x and a connecting line between the center 10 and the respective measuring point 11 are applied. It can be seen that the intensity curves of the measuring points of different circular lines have the same sinusoidal curve. It can also be seen that a phase position of the sinusoidal curve is 0 °.

In 6b is the corresponding course of the intensity values for the measuring points 11 in the in 5b shown image. In contrast to 6a the phase position of the sinusoidal curve is approx. 100 °. Since the frequency of the periodic intensity profile along a circular line 10 Periods per full revolution of the pattern around its center 10 is, the rotation angle W can be determined as 10 °.

7th shows a target 8th with a periodic pattern 9 and a reference pattern 12th , where the reference pattern 12th is designed as a QR code (binary code). It is shown that the reference sample 12th in a sub-area 13th is arranged within the periodic pattern 9 is arranged. An edge area is also shown 14th of the target 8th , which is the periodic pattern 9 surrounds. Between the reference pattern 12th and the periodic pattern 9 can be a transition area 15th be arranged with a constant gray value.

The reference pattern 12th can determine the position of the center 10 of the periodic pattern 9 , in particular the circular lines with a periodic intensity profile along the circular line, in the image. The reference pattern can also be used 12th are also used to determine the angle of rotation W.

8th shows a plan view of a target 8th with a periodic pattern 9 and another reference pattern 12th . In contrast to the in 7th In the illustrated embodiment, the further reference pattern comprises several sub-areas with QR codes (binary codes) and several sub-areas with a constant gray value.

9a shows an image of a target 8th with another periodic pattern 9 , with this periodic pattern several sub-areas 16a , 16b , 16c , 16d having. Each sub-area comprises a transverse, unweighted stripe or wave pattern, each with a different orientation. The wave patterns here are transverse wave patterns, with one direction of propagation of the wave pattern in the various sub-areas 16a , ..., 16d by arrows 17th is shown. This is the direction of propagation, for example 17th of the wave pattern of the first sub-area 16a with an angle of -45 ° or + 315 ° to a longitudinal axis x of the target 8th oriented. The direction of propagation 17th of the wave pattern in the second sub-area 16b is oriented at an angle of - 270 ° or + 90 ° relative to the longitudinal axis x. The direction of propagation of the wave pattern in the third sub-area 16c is oriented parallel to the longitudinal axis x. The direction of propagation 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. Here this is in 9a depicted depicted periodic pattern 9 in a first rotational position of a target 8th around the axis of rotation 2 (please refer 1 ) shown. The wave patterns of the various sub-areas 16a , ...., 16d can in this case have the same, but preferably different, frequencies.

9b shows an intensity distribution of a two-dimensional Fourier transform of the in 9a shown image, with only the amounts assigned to the different frequencies, that is, the amounts of the power components of these different frequencies are shown. Also shown is a frequency coordinate system of the frequency space with a frequency longitudinal axis xf and a frequency transverse axis yf, which are oriented perpendicular to one another. Furthermore, an intersection of these axes xf, yf forms an origin of the frequency coordinate system. Local intensity maxima in the two-dimensional frequency space are also shown. The circled frequency maxima 18th are due to the wave pattern in the first sub-area 16a conditional, the two local intensity maxima forming a complex conjugate intensity maxima pair.

It can be seen that there is a radial distance between the local intensity maxima 18th 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 corresponds between the frequency longitudinal axis xf and a connecting line between the origin of the frequency coordinate system and the local intensity maximum 18th with the previously explained direction of propagation and thus orientation of the wave pattern. The explained angle thus corresponds to the local intensity maximum 18th , especially the first intensity maximum 18a and the frequency longitudinal axis xf, an angle of -45 ° (or + 315 °). The local intensity maxima shown further also form conjugate complex pairs and are due to the wave pattern of the further sub-areas 16b , 16c , 16d conditionally.

Since this position of the local intensity maxima in the illustrated arrangement of local intensity maxima is an untwisted target 8th corresponds to, the angle of 0 ° can be determined as the angle of rotation W.

10a shows a schematic image of a target 8th with several sub-areas each with different wave patterns, which, however, differs from the one in 9a shown image by 15 ° around the axis of rotation 2 (please refer 1 ) was twisted.

10b shows the corresponding two-dimensional Fourier transformation with the local intensity maxima already explained, which are caused by the wave patterns of the various sub-areas. It can be seen here that the first sub-area 16a corresponding local intensity maxima 18th have been rotated by 15 ° in the frequency coordinate system. The angle of rotation W of 15 ° can thus be determined as a function of a position of the corresponding intensity maxima in the frequency domain.

11a shows an image of a target 8th with an optical pattern 9 in a further embodiment. Here, the periodic pattern includes 9 several sub-areas 16a , 16b , 16c , 16d with wave patterns in different directions of propagation 17th represented by corresponding arrows.

Here are the intensity values of a sub-area 16a , ..., 16d by weighting a transversal unweighted wave pattern (see e.g. 9a) determined with a two-dimensional Gaussian function, with a maximum of the two-dimensional Gaussian or normal distribution in a center of the corresponding sub-area 16a , .. ., 16d is arranged. Co-variances of the corresponding distribution to one dimension of the sub-area can also be used 16a , ..., 16d be adapted, in particular selected such that an intensity of the weighted wave pattern in a sub-area at the transition edge to a further sub-area 16a , ..., 16d or to an outer edge region is smaller than a predetermined intensity value or is zero.

It is also shown that the frequencies of the wave patterns of the various sub-areas 17th are different from each other.

In 11b is then the two-dimensional Fourier transform of the in 11a periodic pattern shown 9 shown, whereby according to the in 9b and 10b Fourier transforms shown local intensity maxima are shown. Local intensity maxima are shown by circles 18th by the weighted wave pattern of the first sub-area 16a are conditional. Due to the different frequencies, the local intensity maxima are not along a circular line, as in 9b and 10b shown, but arranged along an elliptical course in the frequency coordinate system.

12th shows a schematic flow diagram of a method according to the invention in a first embodiment. The first step here is S1 , which can also be referred to as an imaging step, is an image of a target 8th with a periodic pattern 9 (please refer 1 and e.g. 2 ) generated. In a second step S2 , which can also be referred to as an evaluation step, at least one wave property of the depicted periodic intensity profile is determined. In one determination step S3 the angle of rotation W is then determined as a function of at least the shaft property.

A center can be used in a first sub-step of the evaluation step 10 of the depicted periodic pattern 9 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 12th (please refer 7th , 8th ) respectively. Furthermore, in a further sub-step, measuring points along circular lines around the center determined in this way and their intensity values can be determined. Furthermore, in a further partial step, a phase position of the periodic, in particular harmonic, curve formed by these intensity values can then be determined, the angle of rotation W then being determined as a function of the phase position.

Alternatively, in a first sub-step of the second step S2 a two-dimensional Fourier transformation of the image can be carried out. You can continue in a further sub-step of the second step S2 local intensity maxima can be determined in the two-dimensional frequency space. Furthermore, as explained above, the angle between the connecting line of 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 (see 9b) , are determined, a rotational position of the target as a function of this angle 8th can be determined. Here, for example, a previously known association between said angle and an angle of rotation W of the target can be used 8th be evaluated.

List of reference symbols

1

contraption

2

Axis of rotation

3

Image capture device

4th

Evaluation device

5

Turntable

6th

fixed part

7th

rotatable part

8th

Target

9

periodic pattern

10

center

11

Measuring point

12th

Reference sample

13th

Transition area

14th

Edge area

15th

Transition area

16a, ..., 16d

Sub-areas

17th

Direction of propagation

18th

local intensity maximum

18a, 18b

local intensity maxima

S1

first step

S2

second step

S3

Third step

QUOTES INCLUDED IN THE DESCRIPTION

This list of the documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent literature cited

• EP 3321883 A1 [0004]

Claims (21)

Method for determining an angle of rotation (W) of an axis of rotation (2), at least one image of a target (8) with at least one periodic pattern (9) being generated, the periodic pattern (9) having a periodic intensity profile along at least one dimension, characterized in that at least one wave property of the periodic intensity profile is determined, the angle of rotation (W) being determined as a function of the at least one wave property. Procedure according to Claim 1 , characterized in that a wave property is phase information or amplitude information or frequency information. Method according to one of the preceding claims, characterized in that the periodic pattern has a harmonic intensity profile along at least one dimension. Method according to one of the preceding claims, characterized in that the periodic pattern has a periodic intensity profile along at least one partially or fully circular line. Procedure according to Claim 4 , characterized in that intensity values of a number of measuring points (11) are determined in the image along at least one partially or fully circular line in the image, phase information of the course of the intensity values being determined as the wave property. Procedure according to Claim 5 , characterized in 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 adapting a periodic function to the course of the intensity values, one parameter of the periodic function being the phase information. Method according to one of the Claims 4 to 6th , characterized in that intensity values of a number of measurement points along a plurality of partially or fully circular lines in the image are determined in the image, phase information of the courses of the intensity values being determined as the wave property. Method according to one of the Claims 4 to 7th , characterized in that a center (10) of the partially or fully circular lines is determined in the image. Procedure according to Claim 8 , characterized in that the center (10) in the image is determined as a function of a reference pattern (12). Method according to one of the Claims 4 to 9 , characterized in that the angle of rotation (W) is additionally determined as a function of a further pattern of the target (8), the further pattern being different from the periodic pattern (9). Method according to one of the Claims 1 to 3 , characterized in that the periodic pattern (9) comprises at least a partial area (16a, ..., 16d) with a transversal unweighted or weighted stripe or wave pattern, a Fourier transformation of the image being carried out and the angle of rotation (W) depending on a Location of an intensity maximum (18, 18a, 18b) in the frequency space is determined. Procedure according to Claim 11 , characterized in that the periodic pattern (9) comprises several partial areas (16a, ..., 16d) with stripe or wave patterns of different orientation, a Fourier transformation of the image being carried out and the angle of rotation (W) depending on the position of several intensity maxima ( 18, 18a, 18b) is determined in the frequency domain. Procedure according to Claim 11 or 12th , characterized in that intensity values of a transversely weighted stripe or wave pattern of a sub-area (16a, ..., 16d) are determined by weighting a transversal unweighted stripe or wave pattern with a Gaussian function. Method according to one of the Claims 12 to 13th , characterized in that frequencies of the stripe or wave pattern in different sub-areas (16a, ..., 16d) are different. Method according to one of the Claims 12 to 14th , characterized in that intensity maxima (18, 18a, 18b) are determined by adapting a previously known distribution of intensity maxima. Method according to one of the preceding claims, characterized in that the at least one image is filtered, the at least one wave property of the periodic intensity profile being determined in the filtered image. Device for determining an angle of rotation (W) of an axis of rotation (2), wherein the device (1) comprises at least one image acquisition device (3) and at least one evaluation device (4), with at least one image of a target (3) being provided by the at least one image acquisition device (3). 8) with at least one periodic Pattern (9) is generated, the periodic pattern (9) having a periodic intensity profile along at least one dimension, characterized in that at least one wave property of the periodic intensity profile is determined by the evaluation device (4), the angle of rotation (W) as a function the at least one wave property is determined. Target for determining an angle of rotation of an axis of rotation, the target (8) having at least one periodic pattern (9), the periodic pattern (9) having a periodic intensity profile along at least one dimension. Target after Claim 18 , characterized in that the periodic pattern (9) comprises at least a partial area (16a, ..., 16d) with a transversal unweighted or weighted stripe or wave pattern. Target after one of the Claims 18 or 19th , characterized in that the periodic pattern (9) comprises several partial areas (16a, ..., 16d) with stripe or wave patterns of different orientation. Target after one of the Claims 18 to 20th , characterized in that the target (8) has at least one further pattern which is different from the periodic pattern (9).

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