This structured light projection technique has been developed for the inspection of holes and tubes. In contrast to others, the triangulation base is parallel to the line of sight. The features of systems using this measurement method are the following: high accuracy in the wide-angle region, minimal diameter, symmetry of the measurements to the line of sight, and simplified coordinate calculation. the prototype application is the optics of the sewer pipe inspection robot KARO. Application fields are medical or technical wide-angle inspection systems (e.g., endoscopes). @1997 Optical Society of America
Key words: structured light projection, hollow spaces, tube inspection, endoscopes.
introduction
image formation a two-dimensional picture of the three-dimensional (3d) world is generated in the image plane of an objective lens. each element of the image corresponds to a pyramidal volume element of the 3d scene.thus an image alone permits only through estimations of the 3d coordinates of an object when the depth of focus is used.
one method often used to measure the 3d coordinates is the projection of structured light:the measurement object is illuminated with structured light with well-defined and known beams. the coordinate calculation is based on the parallax between camera and illumination and the principle of triangulation.
in the commonly used structured light measurement systems , the detector and the projector are lolized side by side (perpendicular to the line of light ).in these arrangements the measurements increases with the distance between the optical systems. the best accuracy is achable in the area in front of the systems (where the beam angles are nearly equal ),for many technical applications. the is also the most interesting region.
But this system property is not ideal for the spection of tubes,pipes,and hollow spaces,i.e.,for systems such as sewer pipe inspection robots and endoscopes,where there are almost no objects directly in front of the inspection heads and where wide-angle objective lenses are used to inspect the walls of the hollow space while the system moves through it. For these applications a modification of the structured light measurement principle was developed at the Fraunhofer-Institut fur informations-und Datenverarbeitung. in this modification the illumination and the objective lens are located(virtually) on the same optical axis, and the triangulation baseline (the distance between the object -side principal plane of the lens and the source of the illumination) is located on this common optical axis. After sketching the measurement principle and comparing it with a standard structured light system, we show that this modification has significant advantages for wide-angle measurement problems:
The measurement accuracy is not affected by the distance between illumination and camera perpendicular to the line of sight.
These systems are ideal for applications in which a minimal diameter of the inspection system is necessary.
They measure with higher accuracy in the wideangle region.
They provide rotationally symmetric measurements and measurement accuracies perpendicular to the optical axis.
when this symmetry is used, coordinate calculation is simplified.
These advantages show that the measurement principle is ideal for wide-angle inspection problem, i.e., endoscopic measurement systems and tube and hole inspection systems. Shown further in the sequel is the application of this measurement principle in an optical system for sewer pipe inspection.
2.Basic Principle of Structured Light Projection Techniques
Figure 1 illustrates the principle of optical 3D measurements by structured light projection: Point P, the center of lens L(focal length f), and a laser determine the trangle for the measurement of P. Angle w and the distance of the laser to the optical axis are system parameters(determined by calibration of the system). The angle of the central ray from the object through the lens is calculated from image point B. Thus the triangle laser-lens-P is completely determined.
From the basic equations of image formation follows
The second equation for determining object coordinates is given by the condition of illumination; i.e., point P is illuminated by the laser beam, whose ray is described by
An alternative point of view, that of this measurement principle ,is also shown in Fig.1 Equivalent to regarding the baseline b as the reference for the calculation is the use of the intersection of the laser beam with the optical axis at a . The laser beam is then described by
The object coordinates are calculated by
respectively. By the projection of a light pattern corresponding to that of the sketched laser,rotated around the potical axis, a completely rotationally symmetric measurement system is derived:a system for optical 3D measurements by a tadially symmetric structured light projection.
3.Mesurement principle
With a beam splitter it is possible to obtain virtually identical optical axes of a camera and a structured light projector.When radially symmetric structured(light cones) are projected, such a system measures radially symmetric light intersections, when move d centrically through a cylinder.
Because of the symmetry to the optical axis, the calculation of the object coordinates is simplified. To derive the formulas for calculating the coordinates, it is sufficient to regard one point P with cootdinates(R,Z) perpendicular in the direction of the potical axis. The origin of the coordinate system is the center of the object-side principal plane the source of the projected pattern is at(0,a)(see Figs.2 and 3).
Using the equations of image formation and illumination, we derive the equations for the object coordinate calculation:
The measurement errors @ @ of the calculated coordinates, resulting from the error @ of the measurement of r in the image plane,areFig.2. Principle of operation of optical 3D measurements by radially symmetric structured light projection.
The diagrams (Fig. 4 and 5) of the relative measurement accuracy versus the distance perpendicular in the direction of the optical axis show the symmetry of the measurements to the optical axis (R=0).
Fig.3. Typical pattern of the light intersection of a system using a radially symmetric structured light projection; a rectangular solid is observed lying on a plane.
Fig.4. Relative measurement accuracy of an optical 3D measurement system using radially symmetric structured light projection: The radial coordinate is shown.
4. Standard Arrangement of a Structured Light Projection System
To show the properties and possible applications of the proposed measurement principle, we compare it with a standard arrangement where the camera and the structured light projector are located side by side at a distance (baseline) b. In the standard arrangement the projector is emitting a light cone whose axis is parallel to the optical axis of the camera. The origin of the coordinate system id the center of the object-side principle plane of the objective lens.
The differences between such an arrangement and the new system become obvious by comparison of Fig.2 and 6, the sketch of the standard arrangement in the plane given by the optical axes and the distance b between the projector and the camera. Because of the asymmetric arrangement, the light sections with the asymmetric arrangement, the light sections with a cylinder wall are also asymmetric. One side is measured at a short distance with relatively high accuracy, whereas the other is measured at a much larger distance with reduced accuracy. The different distances of the measurement points to the projector and the camera lead to large variations in the intensity of the imaged light sections . Further on the limited depth of focus of the image formation leads to a partially unsharp image.
The formulas for coordinate calculation in the Y=0 plane are
Fig.5 Relative measurement accuracy of an optical 3D measurement system using radially symmetric structured light projection: The Z coordinate is shown.
Fig.6. Example of a standard arrangement for an optical 3D measurement system by structured light projection.
The measurement error @x of the determination of X in that plane is given by (10)
where @x is the error of the measurement of coordinate x (in the image plane).
The measurement error @z of the determination of Z is given by (13)
A comparison of the measurement accuracy with thar of the proposed system shows that standard arrangements provide better accuracy in the area in front of the optics, whereas they have significantly reduced accuracy in the outer regions (see Fig.7). the area of minimal measurement errors of a standard arrangement, when one looks into the tube.
Fig.7. Comparison of the measurement accuracies of the standard arrangement of Fig.6 (solid curve) with that of the propose system (see Fig.2) (dotted curve): The accuracy of measurement of the X coordinate is shown.
Because standard arrangements provide better measurement accuracies only in this region, the proposed measurement principle is better suited for hole-and tube-inspection systems.
In addition to the reduced measurement accuracy of the standard arrangement in the outer regions, because of problems mentioned above owing to intensity variations and depth of focus, the measurement accuracy is asymmetric (see Figs.7 and 8) either in the X coordinate and between the X and Y coordinates. Further on the formulas for the calculation of object coordinates are much more complex [see Eqs.(14)-(16)]; e.g. the computation takes longer:
Fig.8. Comparison of the measurement accuracy of the Z-coordinate measurement is shown.
5.applications of optical 3d measurement systems by using radially symmetric structured light projection
the main advantage of the measurement method outline above is the independence of the illumination and the camera perpendicular to the optical axis. thus measurement systems with minimal diameter can be designed.the principle is ideally suited for endoscopes and other inspection systems with limited diameters.
advantageous structured light projectors use a laser that illuminates a holographic grating. such projectors are able to project structures with a wide depth of focus. a projector of minimal dimensions may consist of a laser diode or a monomode fiber and a small holographic grating. further essential components of such a system are a beam splitter, the optics for image formation (see the sketch of a minimal configuration,fig 9), and a camera, an image conduit, or a fiber bundle.
in the system developed here (e.g.,fig.10),the light structure selected consists of seven concentric circles. when the inspection robot is guided centrically through a cylindrical sewer pipe, it measures one complete section perpendicular to the pipe axis per measurement interval . by comparison of measured and tolerable radii,defects in the pipe are automatically detected
the visual inspection of the sewer pipe should not be affected by the 3d measurements. thus the solution for the tube inspection robot was an optical system consisting of the following elements with virtually the same optical axis (see fig.11)
a structured light projector consisting of a semiconductor laser, a holographic grating, and optics for beam expansion.
a color tv camera for visual inspection.
a monochrome camera for measurements.
both cameras use the same zoom-objective lens and are combined with an erecting prism to compensate for image rotation, occurring when the optics is rotated and/or directed to the wall of the pipe , they observe the same object segment but are completely separated by wavelength (by the use of a dichroic beam splitter for a laser wavelength of 780 nm ). this system allows comfortable visual inspections of sewer pipes: detected defects (automatically) are precisely measurable by directing the optics on the defects and zooming, whereas the horizontal orientation of the image is controlled by the erecting prism. interesting points of the defects are marked by the operator in the color tv image and automatically measured by the 3d system. becase the 3d system is observing exactly the same scene, this is performed without further action of the operator. thus the operator works only on the basis of the color tv image, and the 3d measurement system automatically extracts the interesting object structures, without the need of special attention from the operator.
the authors acknowledge the support of the german ministry of education and research (formerly the ministry of research and technology).
Key words: structured light projection, hollow spaces, tube inspection, endoscopes.
introduction
image formation a two-dimensional picture of the three-dimensional (3d) world is generated in the image plane of an objective lens. each element of the image corresponds to a pyramidal volume element of the 3d scene.thus an image alone permits only through estimations of the 3d coordinates of an object when the depth of focus is used.
one method often used to measure the 3d coordinates is the projection of structured light:the measurement object is illuminated with structured light with well-defined and known beams. the coordinate calculation is based on the parallax between camera and illumination and the principle of triangulation.
in the commonly used structured light measurement systems , the detector and the projector are lolized side by side (perpendicular to the line of light ).in these arrangements the measurements increases with the distance between the optical systems. the best accuracy is achable in the area in front of the systems (where the beam angles are nearly equal ),for many technical applications. the is also the most interesting region.
But this system property is not ideal for the spection of tubes,pipes,and hollow spaces,i.e.,for systems such as sewer pipe inspection robots and endoscopes,where there are almost no objects directly in front of the inspection heads and where wide-angle objective lenses are used to inspect the walls of the hollow space while the system moves through it. For these applications a modification of the structured light measurement principle was developed at the Fraunhofer-Institut fur informations-und Datenverarbeitung. in this modification the illumination and the objective lens are located(virtually) on the same optical axis, and the triangulation baseline (the distance between the object -side principal plane of the lens and the source of the illumination) is located on this common optical axis. After sketching the measurement principle and comparing it with a standard structured light system, we show that this modification has significant advantages for wide-angle measurement problems:
The measurement accuracy is not affected by the distance between illumination and camera perpendicular to the line of sight.
These systems are ideal for applications in which a minimal diameter of the inspection system is necessary.
They measure with higher accuracy in the wideangle region.
They provide rotationally symmetric measurements and measurement accuracies perpendicular to the optical axis.
when this symmetry is used, coordinate calculation is simplified.
These advantages show that the measurement principle is ideal for wide-angle inspection problem, i.e., endoscopic measurement systems and tube and hole inspection systems. Shown further in the sequel is the application of this measurement principle in an optical system for sewer pipe inspection.
2.Basic Principle of Structured Light Projection Techniques
Figure 1 illustrates the principle of optical 3D measurements by structured light projection: Point P, the center of lens L(focal length f), and a laser determine the trangle for the measurement of P. Angle w and the distance of the laser to the optical axis are system parameters(determined by calibration of the system). The angle of the central ray from the object through the lens is calculated from image point B. Thus the triangle laser-lens-P is completely determined.
From the basic equations of image formation follows
The second equation for determining object coordinates is given by the condition of illumination; i.e., point P is illuminated by the laser beam, whose ray is described by
An alternative point of view, that of this measurement principle ,is also shown in Fig.1 Equivalent to regarding the baseline b as the reference for the calculation is the use of the intersection of the laser beam with the optical axis at a . The laser beam is then described by
The object coordinates are calculated by
respectively. By the projection of a light pattern corresponding to that of the sketched laser,rotated around the potical axis, a completely rotationally symmetric measurement system is derived:a system for optical 3D measurements by a tadially symmetric structured light projection.
3.Mesurement principle
With a beam splitter it is possible to obtain virtually identical optical axes of a camera and a structured light projector.When radially symmetric structured(light cones) are projected, such a system measures radially symmetric light intersections, when move d centrically through a cylinder.
Because of the symmetry to the optical axis, the calculation of the object coordinates is simplified. To derive the formulas for calculating the coordinates, it is sufficient to regard one point P with cootdinates(R,Z) perpendicular in the direction of the potical axis. The origin of the coordinate system is the center of the object-side principal plane the source of the projected pattern is at(0,a)(see Figs.2 and 3).
Using the equations of image formation and illumination, we derive the equations for the object coordinate calculation:
The measurement errors @ @ of the calculated coordinates, resulting from the error @ of the measurement of r in the image plane,areFig.2. Principle of operation of optical 3D measurements by radially symmetric structured light projection.
The diagrams (Fig. 4 and 5) of the relative measurement accuracy versus the distance perpendicular in the direction of the optical axis show the symmetry of the measurements to the optical axis (R=0).
Fig.3. Typical pattern of the light intersection of a system using a radially symmetric structured light projection; a rectangular solid is observed lying on a plane.
Fig.4. Relative measurement accuracy of an optical 3D measurement system using radially symmetric structured light projection: The radial coordinate is shown.
4. Standard Arrangement of a Structured Light Projection System
To show the properties and possible applications of the proposed measurement principle, we compare it with a standard arrangement where the camera and the structured light projector are located side by side at a distance (baseline) b. In the standard arrangement the projector is emitting a light cone whose axis is parallel to the optical axis of the camera. The origin of the coordinate system id the center of the object-side principle plane of the objective lens.
The differences between such an arrangement and the new system become obvious by comparison of Fig.2 and 6, the sketch of the standard arrangement in the plane given by the optical axes and the distance b between the projector and the camera. Because of the asymmetric arrangement, the light sections with the asymmetric arrangement, the light sections with a cylinder wall are also asymmetric. One side is measured at a short distance with relatively high accuracy, whereas the other is measured at a much larger distance with reduced accuracy. The different distances of the measurement points to the projector and the camera lead to large variations in the intensity of the imaged light sections . Further on the limited depth of focus of the image formation leads to a partially unsharp image.
The formulas for coordinate calculation in the Y=0 plane are
Fig.5 Relative measurement accuracy of an optical 3D measurement system using radially symmetric structured light projection: The Z coordinate is shown.
Fig.6. Example of a standard arrangement for an optical 3D measurement system by structured light projection.
The measurement error @x of the determination of X in that plane is given by (10)
where @x is the error of the measurement of coordinate x (in the image plane).
The measurement error @z of the determination of Z is given by (13)
A comparison of the measurement accuracy with thar of the proposed system shows that standard arrangements provide better accuracy in the area in front of the optics, whereas they have significantly reduced accuracy in the outer regions (see Fig.7). the area of minimal measurement errors of a standard arrangement, when one looks into the tube.
Fig.7. Comparison of the measurement accuracies of the standard arrangement of Fig.6 (solid curve) with that of the propose system (see Fig.2) (dotted curve): The accuracy of measurement of the X coordinate is shown.
Because standard arrangements provide better measurement accuracies only in this region, the proposed measurement principle is better suited for hole-and tube-inspection systems.
In addition to the reduced measurement accuracy of the standard arrangement in the outer regions, because of problems mentioned above owing to intensity variations and depth of focus, the measurement accuracy is asymmetric (see Figs.7 and 8) either in the X coordinate and between the X and Y coordinates. Further on the formulas for the calculation of object coordinates are much more complex [see Eqs.(14)-(16)]; e.g. the computation takes longer:
Fig.8. Comparison of the measurement accuracy of the Z-coordinate measurement is shown.
5.applications of optical 3d measurement systems by using radially symmetric structured light projection
the main advantage of the measurement method outline above is the independence of the illumination and the camera perpendicular to the optical axis. thus measurement systems with minimal diameter can be designed.the principle is ideally suited for endoscopes and other inspection systems with limited diameters.
advantageous structured light projectors use a laser that illuminates a holographic grating. such projectors are able to project structures with a wide depth of focus. a projector of minimal dimensions may consist of a laser diode or a monomode fiber and a small holographic grating. further essential components of such a system are a beam splitter, the optics for image formation (see the sketch of a minimal configuration,fig 9), and a camera, an image conduit, or a fiber bundle.
in the system developed here (e.g.,fig.10),the light structure selected consists of seven concentric circles. when the inspection robot is guided centrically through a cylindrical sewer pipe, it measures one complete section perpendicular to the pipe axis per measurement interval . by comparison of measured and tolerable radii,defects in the pipe are automatically detected
the visual inspection of the sewer pipe should not be affected by the 3d measurements. thus the solution for the tube inspection robot was an optical system consisting of the following elements with virtually the same optical axis (see fig.11)
a structured light projector consisting of a semiconductor laser, a holographic grating, and optics for beam expansion.
a color tv camera for visual inspection.
a monochrome camera for measurements.
both cameras use the same zoom-objective lens and are combined with an erecting prism to compensate for image rotation, occurring when the optics is rotated and/or directed to the wall of the pipe , they observe the same object segment but are completely separated by wavelength (by the use of a dichroic beam splitter for a laser wavelength of 780 nm ). this system allows comfortable visual inspections of sewer pipes: detected defects (automatically) are precisely measurable by directing the optics on the defects and zooming, whereas the horizontal orientation of the image is controlled by the erecting prism. interesting points of the defects are marked by the operator in the color tv image and automatically measured by the 3d system. becase the 3d system is observing exactly the same scene, this is performed without further action of the operator. thus the operator works only on the basis of the color tv image, and the 3d measurement system automatically extracts the interesting object structures, without the need of special attention from the operator.
the authors acknowledge the support of the german ministry of education and research (formerly the ministry of research and technology).
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