Non-contact apparatus and method for measuring surface profile

• US 20030007159A1
• Filed: 06/27/2002
• Published: 01/09/2003
• Est. Priority Date: 06/27/2001
• Status: Active Grant

• Current Assignee: Southwest Research Institute
• Original Assignee: Southwest Research Institute
• Inventors: Mitchell, Joseph N., Beeson, Robert J., Franke, Ernest A., Rigney, Michael P., Magee, Michael J.
• Granted Patent: US 7,061,628 B2
• Time in Patent Office: Days
• US Class Current: 356/604
• CPC Class Codes: G01B 11/25 by projecting a pattern, e.g. one or more lines, moiré fringes on the object G01B11/255 takes precedence ; image analysis for depth or shape recovery G06T7/50
• CPC Class Codes: G01B 11/2504 Calibration devices
• CPC Class Codes: G06T 7/521 from laser ranging, e.g. using interferometry; from the projection of structured light

Abstract

Embodiments of the invention provide a non-contact method for measuring the surface profile of an object that can include generating a point-type optical signal and projecting it on a rotatable precision optical grating, generating a rotating pattern of light and dark lines onto the object, recording a series of images of the rotating pattern moving across the object with an image receiving device and calculating the surface profile of the object. Other embodiments can include a method to calibrate the system and a non-contact apparatus that generally includes a point-type light source, a rotatably mounted optical grating being configured to project a moving grating image on the object, a processor in communication with the image capturing device and configured to receive image input from the image capturing device and generate a surface profile representation of the object therefrom.

Claims

1. A method for calibrating a dynamic structured light measuring system, comprising:

determining a focal length of an imaging device;

determining a transformation from an imaging device coordinate system to an absolute coordinate system;

determining absolute coordinates of a point in a plane, wherein a Z coordinate of the plane is known; and

determining at least one equation for at least one quadric surface containing projected grid line tracks.

2. The method of claim 1, wherein determining the focal length comprises:

acquiring a first image of a calibration object;

calculating a first calibration parameter for the calibration object from the first image;

adjusting the position of the object a first known distance;

acquiring a second image of the calibration object;

calculating a second calibration parameter for the calibration object from the second image; and

determining the focal length from the first and second calibration parameters.

3. The method of claim 2, wherein the calibration object comprises at least 3 circular markings having collinear centers such that a line joining the collinear centers is parallel with an X axis of the imaging device.

4. The method of claim 3, wherein the first and second calibration parameters comprise a distance between outer centers of the at least three circular markings.

5. The method of claim 2, further comprising:

adjusting the position of the object a second known distance;

acquiring a third image of the calibration object;

calculating a third calibration parameter for the calibration object from the third image; and

determining the focal length from the first, second, and third calibration parameters.

6. The method of claim 1, wherein determining a transformation from an imaging device coordinate system to an absolute coordinate system comprises:

positioning a calibration object such that a plane containing the calibration object is coplanar with an absolute coordinate system and contains an origin of the absolute coordinate system, and such that a line joining circles of the calibration object is collinear with an X axis of the absolute coordinate system; and

determining a distance between an optical center of the imaging device and the plane containing the calibration object using the focal length.

7. The method of claim 1, wherein each individual quadric surface of the at least one quadric surface is derived through curve fitting to the projected gridline tracks in three or more reference planes.

8. The method of claim 1, wherein each individual quadric surface of the at least one quadric surface is derived through a least squares fit method.

9. The method of claim 8, wherein the least squares fit method further comprises solving the equation C=U M^T (M M^T)⁻

1, wherein, C represents a nine element row vector of unknown coefficients, M represents a matrix having nine rows and a number of columns that corresponds to a number of projected points, and U represents a row vector of ones having a number of vector elements that corresponds to the number of projected points.

10. The method of claim 9, further comprising determining a set of coefficients associated with each projected grid line.

11. The method of claim 1, wherein determining at least one equation for at least one quadric surface containing projected grid line tracks further comprises independently determining an equation for each individual quadric surface.

13. The method of claim 12, wherein determining the focal length comprises:

orienting the optical imaging device;

positioning a planar calibration object having at least three markings having collinear centers above the reference measurement surface a first distance in a manner such that a plane of the calibration object is perpendicular to an optical axis of the optical imaging device and so that a line joining the centers is parallel with an X-axis of the optical imaging device;

calculating a first image plane distance between centroids of outer markings of the at least three markings for the first distance;

positioning the calibration object a second distance above the reference measurement surface, where the second distance is not equal to the first distance;

calculating a second image plane distance between centroids of outer markings of the at least three markings for the second distance; and

calculating the focal length from the first and second image plane distances.

14. The method of claim 12, wherein calculating a transformation from a camera coordinate system to an absolute coordinate system comprises:

positioning calibration markings such that a plane containing the calibration markings is coplanar with an absolute system, the plane containing the calibration markings contains an origin of the absolute coordinate system, and such that a line joining the calibration markings is collinear with an X-axis of the absolute coordinate system;

determining the distance between an optical center of the optical imaging device and a plane of a calibration object from the equation

$Z_0=f<br><br>\left(\frac{D}{d_0}\right)<br><br>\text{\hspace{1em}<br><br>},$

where Z₀ is the distance between an optical center of the optical imaging device and the plane of a calibration object, f is a focal length of the optical imaging device, D is a distance between centers of calibration markings, and d₀ is the distance between projections of the centers of the calibration markings; and

calculating the transformation from the optical imaging device coordinate system to the absolute coordinate system from the equation Z_Camera=Z_Absolute+Z₀.

15. The method of claim 12, wherein determining at least one representative equation for at least one surface containing projected grid line tracks comprises:

providing a point light source;

rotating a grid about a central point at a location between the point light source and the reference measurement surface such that the a line joining the point light source and a point on each grid line that is closest to the central point traces out a quadric cone; and

independently determining an equation for the quadric surface.

16. The method of claim 12, wherein each of the at least one quadric surfaces is through curve fitting to the projected gridline tracks in three or more reference planes.

17. The method of claim 12, wherein each of the at least one quadric surfaces is derived through a least squares fit method.

18. The method of claim 17 wherein the least squares fit method further comprises solving the equation C=U M^T (M M^T)⁻

1, wherein, C represents a nine element row vector of unknown coefficients, M represents a matrix having nine rows and a number of columns that corresponds to a number of projected points, and U represents a row vector of ones having a number of vector elements that corresponds to the number of projected points.

19. The method of claim 18, further comprising determining a set of coefficients associated with each projected grid line.

12. A method for calibrating a dynamic structured light measuring system, comprising:

determining a focal length of an optical imaging device positioned above a reference measurement surface;

calculating a transformation from a camera coordinate system to an absolute coordinate system;

determining absolute coordinates of a point in a first plane above the reference measurement surface using the transformation, wherein a distance from the reference measurement surface to the first plane is known; and

determining at least one representative equation for at least one quadric surface containing projected grid line tracks.

20. A non-contact method for measuring a surface of an object, comprising:

projecting a rotating grid onto the surface of the object;

capturing a plurality of images of the surface of the object having the rotating grid projected thereon with an imaging device;

determining at least one quadric surface above and at least one quadric surface below a point on the surface of the object where a pixel ray of the imaging device intersects the surface of the object.

21. The method of claim 20, wherein the at least one quadric surface above the point and the at least one quadric surface below the point are immediate the point on the surface of the object where the pixel ray intersects the surface.

22. The method of claim 20, wherein the at least one quadric surface above the point and the at least one quadric surface below the point further comprise the first two quadric surfaces immediately above the point and the first two quadric surfaces immediately below the point.

23. The method of claim 20, wherein determining the at least one quadric surface above and below the point further comprises:

determining a fractional gridline number corresponding to where a pixel ray intersects the surface of the object;

determining integer quadric surfaces above and below the fractional gridline number; and

calculating a three-dimensional point corresponding to a location where the pixel ray intersects the surface of the object.

24. The method of claim 23, wherein calculating the three-dimensional point further comprises interpolating between three-dimensional points determined by the pixel ray intersection with the quadric surfaces.

25. The method of claim 23, wherein calculating the three-dimensional point further comprises using quadric surfaces determined in a calibration process.

26. The method of claim 23, wherein the three-dimensional point where the pixel ray intersects the surface of the object corresponds to a fractional gridline number.

28. The method of claim 27, wherein generating a rotating pattern of light and dark lines onto the object to be measured further comprises rotating the rotatable precision optical grating at a known constant velocity while the point-type optical signal is projected thereon.

29. The method of claim 27, wherein calculating the surface profile of the object further comprises:

determining a fractional gridline number for each pixel where a measurement is desired;

determining the intersection of a line projected through an image plane of the image receiving device and a point on a quadric surface defined by the fractional gridline number; and

determining the three dimensional absolute coordinates of the point from camera rays.

30. The method of claim 29, wherein determining a fractional gridline number further comprises dividing a number of gridlines between a center of rotation and a specific pixel array by the cosine of the angle represented by one half of a tangential pulse.

31. The method of claim 30, wherein the fractional gridline is determined in accordance with the equation:

32. The method of claim 29, wherein determining the intersection of a line projected through an image plane of the image receiving device and a point on a quadric surface defined by the fractional gridline number further comprises:

determining a first point on the line;

determining a second point on the line; and

substituting an equation of the line into an equation for the quadric surface and solving by the quadratic formula.

33. The method of claim 29, wherein determining the three dimensional absolute coordinates further comprises:

determining a grid line number;

determining a rounded up grid line number and a rounded down grid line number between which a point represented by the absolute coordinates lies;

determining an intersection between two quadric surfaces representing the rounded up grid line number and the rounded down grid line number; and

calculating the three dimensional absolute coordinates of the point as a weighted sum of the intersection between the two quadric surfaces.

34. The method of claim 33, wherein calculating the surface profile of the object further comprises determining the distance from an axis of rotation of the rotatable precision optical grating from a number of light and dark transitions generated at a point.

35. The method of claim 29, wherein fractional gridline number corresponds to an intersection of a pixel ray, a quadric surface, and a surface of an object being measured.

36. The method of claim 27, wherein calculating the surface profile of the object further comprises:

determining a fractional gridline number corresponding to an intersection of a pixel array, a quadric surface, and a surface on an object being measured;

determining a pulse width of a series of contiguous black and white intensity values; and

determining a tangential pulse from the pulse width.

38. The apparatus of claim 37, wherein the point-type light source further comprises a high intensity optical source.

39. The apparatus of claim 37, wherein the point type light source further comprises a mercury vapor lamp.

40. The apparatus of claim 37, wherein the rotatably mounted optical grating further comprises a precision optical grid of a predetermined size and granularity.

41. The apparatus of claim 37, wherein the rotatably mounted optical grating further comprises a motor in mechanical communication with the rotatably mounted optical grating, the motor being configured to selectively impart rotational motion to the optical grating.

42. The apparatus of claim 37, further comprising a lens system for projecting an image of the grating illuminated by the point source onto the object that can be varied to alter the size of the projected grating.

43. The apparatus of claim 37, wherein the image capturing device further comprises a camera configured to record a sequence of images of the object and the moving grating image projected thereon, and generate a digital image representative of each image in the sequence of images.

44. The apparatus of claim 37, wherein the processor is further configured to determine a fractional gridline number at each pixel on the surface of the object, compute an intersection of a three dimensional line with a quadric surface, and determine three dimensional absolute coordinates from camera rays.

45. The apparatus of claim 37, wherein the rotatably mounted optical grating is configured to be rotated at a constant speed and to project a rotating pattern of light and dark lines onto the object to be measured.

46. The apparatus of claim 37, wherein the light generated by the point-type light source is at least partially transmitted to the a rotatably mounted optical grating in a fiber optic cable.

47. The apparatus of claim 37, wherein the apparatus is calibrated by measuring and calculating a fractional grid line distance back projected to at least three planar surfaces placed at known positions in an object space.

48. The non-contact apparatus of claim 37, wherein the apparatus is scalable to measure varying sizes of objects through correspondingly varying optical lenses of the apparatus and the granularity of the rotatably mounted optical grating.

50. The non-contact measuring apparatus of claim 49, wherein the point-type light source further comprises a high intensity optical source.

51. The non-contact measuring apparatus of claim 49, wherein the point type light source further comprises a mercury vapor lamp.

52. The non-contact measuring apparatus of claim 49 wherein the rotatably mounted optical grid further comprises a precision optical grating of a predetermined size and granularity.

53. The non-contact measuring apparatus of claim 49, wherein the rotatably mounted optical grid further comprises a stepping motor in mechanical communication with the rotatably mounted optical grid, the stepping motor being configured to selectively impart rotational motion to the optical grid.

54. The non-contact measuring apparatus of claim 49, further comprising a lens assembly positioned between the grid and the measuring surface, the lens assembly being configured to project an image of the grid illuminated by the point source onto an object to be measured that can be varied to alter the size of the projected grating.

55. The non-contact measuring apparatus of claim 49, wherein the microprocessor is further configured to determine a fractional gridline number at each pixel on the surface of an object being measured, compute an intersection of a three dimensional line with a quadric surface, and determine three dimensional absolute coordinates from camera rays.

27. A non-contact method for measuring the surface profile of an object, comprising:

generating a point-type optical signal;

projecting the point-type optical signal on a rotatable precision optical grating;

generating a rotating pattern of light and dark lines onto the object to be measured;

recording a series of images of the rotating pattern or light and dark lines moving across the object to be measured with an image receiving device; and

calculating the surface profile of the object to be measured from the series of images.

37. A non-contact apparatus for measuring the surface profile of an object, comprising:

a point-type light source;

a rotatably mounted optical grating positioned in an optical path of the point-type light source, the optical grating being configured to project a moving grating image on the object;

an image capturing device positioned to view the object and the moving grating image projected thereon; and

a processor in communication with the image capturing device, the processor being configured to receive image input from the image capturing device and generate a surface profile representation of the object therefrom.

49. A non-contact apparatus for measuring the surface profile of an object, comprising:

a point-type light source positioned above a measuring surface and at an acute angle to the measuring surface;

a rotatably mounted optical grid positioned between the point-type light source and the measuring surface;

a camera fixedly positioned above the measuring surface, the camera being configured to view the measuring surface; and

a microprocessor in communication with the camera, the microprocessor being configured to receive images from the camera and generate an electronic surface profile representation of the object.