# US 2021/0241437 A1 · Method and arrangement for determining a position of an object > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2021/0241437 A1 - Document ID: US20210241437A1 - Status: Published application - Kind: A1 - Application number: 17/163,543 - Filed: 2021-01-31 - Published: 2021-08-05 - Earliest claimed: 2020-01-31 - Assignees: Carl Zeiss Industrielle Messtechnik GmbH - Applicants: Carl Zeiss Industrielle Messtechnik GmbH - Inventors: Wolfgang Hoegele - Web page: https://patentgrep.com/patent/US20210241437A1 ## CPC - G06T 7/001: {using an image reference approach} - G06T 7/70: Determining position or orientation of objects or cameras (camera calibration G06T7/80) - G01N 21/8806: {Specially adapted optical and illumination features} - G06T 7/11: Region-based segmentation - G01N 2021/8845: {Multiple wavelengths of illumination or detection} - G06T 2207/10004: Still image; Photographic image - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) ## Abstract A position of an object is determined by optically capturing at least one capture structure arranged at the object or at a reference object captured from the object and thereby obtaining capture information, the at least one capture structure having a point-symmetrical profile of an optical property that varies along a surface of the capture structure, transforming a location-dependent mathematical function corresponding to the point-symmetrical profile of the optical property into a frequency domain, forming a second frequency-dependent mathematical function from a first frequency-dependent mathematical function, wherein the second mathematical function is formed from a relationship of in each case a real part and an imaginary part of complex function values of the first frequency-dependent mathematical function, and forming at least one function value of the second frequency-dependent mathematical function and determining the same as location information about a location of a point of symmetry of the location-dependent mathematical function. ## Claims ### Claim 1 A method for determining a position of an object, the method comprising: optically capturing at least one capture structure arranged at the object or at a reference object captured from the object and thereby obtaining capture information; the at least one capture structure having a point-symmetrical profile of an optical property that varies along a surface of the at least one capture structure; transforming a location-dependent mathematical function corresponding to the point-symmetrical profile of the optical property that is captured with the capture information into a frequency domain, such that a first frequency-dependent mathematical function is obtained; forming a second frequency-dependent mathematical function from the first frequency-dependent mathematical function, wherein the second frequency-dependent mathematical function is formed from a relationship of in each case a real part and an imaginary part of complex function values of the first frequency-dependent mathematical function; and forming at least one function value of the second frequency-dependent mathematical function and determining the at least one function value as location information about a location of a point of symmetry of the location-dependent mathematical function. ### Claim 2 (depends on 1) The method according to claim 1, wherein the object is a component of an arrangement of components. ### Claim 3 (depends on 1) The method according to claim 1, wherein the location-dependent mathematical function is a function of discrete values of the location, and wherein the location-dependent mathematical function is transformed into the frequency domain with a discrete Fourier transformation. ### Claim 4 (depends on 1) The method according to claim 1, wherein the at least one function value of the second frequency-dependent mathematical function is formed for a plurality of frequency values, and wherein a weighted value obtained by weighting the function values is determined as a measure of the location of the point of symmetry. ### Claim 5 (depends on 4) The method according to claim 4, further comprising: weighting function values of the second frequency-dependent mathematical function higher for low frequency values than for higher frequency values. ### Claim 6 (depends on 5) Method according to claim 5, wherein all function values which are assigned to a frequency value which is larger than a limit frequency value or which is larger than or equal to the limit frequency value: are weighted such that a weighted value of zero arises, and/or are not taken into account in a determination of the location of the point of symmetry. ### Claim 7 (depends on 1) The method according to claim 1, further comprising: forming the first frequency-dependent mathematical function, in the case of a two-dimensional location-dependent mathematical function, as a two-dimensional frequency-dependent mathematical function; forming, from the first frequency-dependent mathematical function, two second frequency-dependent mathematical functions, for each of which the at least one function value is determined as the location information about the location of the point of symmetry, and wherein the two second frequency-dependent mathematical functions respectively correspond to a location coordinate axis of the two-dimensional location-dependent mathematical function and the function values therefore have in each case the location information regarding the corresponding location coordinate axis. ### Claim 8 An arrangement for determining a position of an object, the arrangement comprising: at least one capture structure arrangeable at the object or at a reference object captured from the object; a capturing device configured to optically capture the at least one capture structure and to thereby obtain capture information; the at least one capture structure having a point-symmetrical profile of an optical property that varies along a surface of the at least one capture structure; an evaluation device, wherein the evaluation device and/or the capturing device are/is configured to generate a location-dependent mathematical function corresponding to the point-symmetrical profile of the optical property that is captured with the capture information; and the evaluation device being configured to: transform the location-dependent mathematical function into a frequency domain, such that a first frequency-dependent mathematical function is obtained, form a second frequency-dependent mathematical function from the first frequency-dependent mathematical function, wherein the second frequency-dependent mathematical function is formed from a relationship of in each case a real part and an imaginary part of complex function values of the first frequency-dependent mathematical function, and form at least one function value of the second frequency-dependent mathematical function and to determine it as location information about a location of a point of symmetry of the location-dependent mathematical function. ### Claim 9 (depends on 8) The arrangement according to claim 8, wherein the object is a component of an arrangement of components. ### Claim 10 (depends on 8) The arrangement according to claim 8, wherein the location-dependent mathematical function is a function of discrete values of the location, and wherein the evaluation device is configured to transform the location-dependent mathematical function into the frequency domain with a discrete Fourier transformation. ### Claim 11 (depends on 8) The arrangement according to claim 8, wherein the evaluation device is configured to form the at least one function value of the second frequency-dependent mathematical function for a plurality of frequency values and to determine a weighted value obtained by weighting the function values as a measure of the location of the point of symmetry. ### Claim 12 (depends on 11) The arrangement according to claim 11, wherein the evaluation device is configured to weight function values of the second frequency-dependent mathematical function higher for low frequency values than for higher frequency values. ### Claim 13 (depends on 12) The arrangement according to claim 12, wherein the evaluation device is configured such that all function values which are assigned to a frequency value which is larger than a limit frequency value or which is larger than or equal to the limit frequency value: are weighted such that a weighted value of zero arises, and/or are not taken into account in a determination of the location of the point of symmetry. ### Claim 14 (depends on 8) The arrangement according to claim 8, wherein the evaluation device is configured to form the first frequency-dependent mathematical function, in the case of a two-dimensional location-dependent mathematical function, as a two-dimensional frequency-dependent mathematical function and to form, from the first frequency-dependent mathematical function, two second frequency-dependent mathematical functions, for each of which the at least one function value is determined as the location information about the location of the point of symmetry, and wherein the two second frequency-dependent mathematical functions respectively correspond to a location coordinate axis of the two-dimensional location-dependent mathematical function and the function values therefore have in each case the location information regarding the corresponding location coordinate axis.