Apparatus for measuring three-dimensional curved surface shapes

Abstract: A three-dimensional curved surface shape measuring apparatus of the slit light linear scanning type. In accordance with a composite image u(x′, y′) produced by image composing means when a slit light is scanned over a surface of an object to be measured, a measured value or computed value u o (x′, y′) of a composite image with respect to a reference plane, a light projecting angle ϑ to the reference plane and a reference plane-television camera distance a , a necessary computational processing is performed to determine a three-dimensional curved surface shape f(x, y) of the surface of the object which is free of any distortions due to a perspective effect of the television camera.

Description: The present invention relates to an apparatus for measuring three-dimensional curved surface shapes in a non-contact manner and more particularly to the compensation for distortions due to the perspective effect of its television camera. Three-dimensional curved surface shape measuring apparatus have been proposed, for example, in EP-A-0335035 (published on 04/10/89). In these apparatus, the three-dimensional curved surface shape of an object to be measured is measured by scanning a linear slit light all over the surface of the object to form a composite image in which the value of each of the picture elements within the picture of a video signal produced by picking up the surface of the object is represented by information relating to the position of the slit light at the instant that the slit light passes one of the positions on the object surface corresponding to that picture element and subjecting the composite image to a computational processing. However, this shape computing method is based on the tacit assumption that the distance between the television camera and an object to be measured, is infinitely great or can be considered to be infinitely great. Where the distance between the television camera and the object to be measured is finite and the perspective effect cannot be ignored when observing the object from the television camera as in the actual measuring system, there is a disadvantage that if this shape computing method is applied as such, distortions due to the perspective effect are caused in the shape measurement result obtained. From WO 86/07443 another slit light scanning technique is known which involves scanning a known reference datum having a cross-section with at least four planar surfaces extending perpendicular to a measurement plane. The four lines formed by the intersection of these planar surfaces with the measurement plane define at least three non co-linear reference locations at the intersections of the lines. Any distortion caused by the viewing geometry of the apparatus is determined in this calibration step using this known reference datum, and a subsequent scan of an unknown profile is compensated accordingly. An apparatus according to the preamble of claim 1 is known from the Japanese laid-open application JP-A-60 196608. A scanning technique is disclosed which operates at different speeds according to whether the detector senses the presence or absence of curvature. High speed scanning takes place across planar portions of the object under scan, with more precise scanning in fine steps being performed in the vicinity of curved regions. It is an object of the present invention to provide a three-dimensional curved surface shape measuring apparatus which is capable of eliminating the distortions due to the perspective effect of a television camera. The invention is an apparatus for measuring the shape of a three-dimensional curved surface of an object, comprising: slit light projecting means for linearly scanning a linear slit light over the surface of said object placed on a measuring reference plane from a direction forming with said measuring reference plane an angle ϑ which is not perpendicular thereto; a television camera having its optical axis disposed at right angles to said measuring reference plane for picking up the surface of said object, position sensor means for measuring the position of the slit light source during scanning; image composing means for receiving an output of said television camera to compose in composite image memory means an image in which the value of each of a plurality of picture elements is represented by the position signal registered by said position sensor at each instant as said projected slit light passes through a respective measuring point corresponding to each said picture element, thereby forming a composite image of the surface of said object; characterised in that the apparatus comprises: shape computing means which includes: height computing means for computing height data z(x′, y′), in accordance with said composite image u(x′, y′) produced by said image composing means when said projected slit light is scanned over the surface of said object, a measured value or computed value u o (x′, y′) of a composite image with respect to said measuring reference plane, said light projecting angle ϑ relative to said measuring reference plane, and a distance a defined as the separation between said measuring reference plane and said television camera; distortion compensating means for compensating two-dimensional coordinates (x′, y′) of said height data z(x′, y′) produced by said height computing means in accordance with compensated height data z(x′, y′) and said distance a between said reference plane and said television camera; and memory means for storing said height data subjected to said two-dimensional coordinates compensated by said distortion compensating means as three-dimensional shape data of said object; wherein said shape computing means is adapted to determine the three-dimensional curved surface shape f(x,y) of the surface of said object in accordance with the following equations: f(x, y) = z(x′, y′) z(x′, y′) = u o (x′ y′) - u(x′, y′) 1+ u o (x′, y′) a . tanϑ . tanϑ In the drawings: Fig. 1 is a schematic diagram showing the measuring principle of a three-dimensional shape measuring apparatus of the slit light linear scanning type disclosed in EP-A-0 335 035. Fig. 2 is a diagram useful for explaining the measurement distortions in the shape measuring method of the slit light linear scanning type and the method of compensating for the distortions. Fig. 3 is a schematic block diagram showing the construction of a three-dimensional shape measuring apparatus of the slit light linear scanning type according to an embodiment of the present invention. In order to facilitate the understanding of embodiments of the present invention, the apparatus disclosed in EP-A-0 335 035 will be described briefly with reference to the drawings prior to the description of the present invention. Fig. 1 is a schematic diagram showing the measuring principle of the three-dimensional curved surface shape measuring apparatus of the slit light linear scanning type disclosed in EP-A-0 335 035. As shown in Figure 1, a slit light 3a spreading vertically to the paper plane is projected obliquely from above onto the surface of an object 2 to be measured which is placed on a reference plane 1. Then, while moving the slit light 3a transversely to the paper plane, the object 2 is picked up by a television camera 8 from, for example just above the object 2. At this time, the manner in which the linear reflected pattern of the slit light at the object surface is moved transversely to the picture is observed on a monitor television 18 connected to the television camera 8. The linear shape of the reflected pattern of the slit light 3a reflects the irregularity information of the object surface. In accordance with the video signal outputted from the television camera 8 picking up the manner in which the linear reflected pattern of the slit light 3a is moved over the surface of the object, a composite image is formed in which each of the picture elements within the picture has a value representing the moment at which the slit light passes through the position on the object surface corresponding to that picture element or the moment at which the brightness of that position becomes maximum. With the composite image produced in this way, the values of its respective picture elements represent a height profile of the object surface based on a plane A (hereinafter referred to as a virtual reference plane) shown by the dot-and-dash line in Fig. 1. In this way, the height profile of the object surface based on the virtual reference plane A is measured. However, generally the three-dimensional shape measurement of the object must measure the profile based on the reference plane 1 on which the object 2 to be measured is placed and not the profile with respect to the virtual reference plane A in Fig. 1. In order to satisfy this requirement the previously mentioned measurement is first made with respect to the object surface, thus measuring its height profile based on the virtual reference plane A. Then, after the object to be measured has been removed, the same measurement is made with respect to the reference plane 1, thus measuring a height profile based on the virtual reference plane A. Thereafter, the difference between each pair of corresponding picture element values of the two profile images, i.e., the object surface composite image u(x, y) and the reference plane composite image u o (x, y) is computed. As the result of this computation, a height profile image based on the reference plane 1 is produced. The value of each of the picture elements in this height profile image is proportional to the height of the corresponding position on the surface of the object to be measured which is based on the reference plane 1. However, where the perspective effect of the video camera is not negligible, the present shape computing method has the disadvantage of causing a height distortion and position distortion as mentioned previously. This disadvantage will now be explained with reference to Fig. 2. Fig. 2 is a diagram corresponding to the slit light linear scanning-type measuring method of Fig. 1. If the distance between the television camera 8 and the object 2 to be measured is infinitely great, the image of a point A to be measured on the reference plane 1 is observed at a point B. Then, considering the fact that the application of the shape computational expression disclosed in Japanese Laid-Open Patent No. 63-76389, f(x, y) = u o (x, y) - u(x, y) tan ϑ, results in u o (x, y) = x o , u(x, y) = x, we obtain f(x, y) =(x o - x)tan ϑ and this corresponds to the height z of the point A. However, where the distance between the television camera and the object to be measured is finite and the perspective effect of the camera is not negligible, the following two attributive distortions are caused. (1) The height distortion: While the height z of the point A should properly be measured, what is measured is the height z′ of a point A′ which is the intersecting point between the slit light plane and the perpendicular drawn from the reference plane at the image point B′ of the point A on the reference plane. (2) The position distortion: While the coordinate x of the point A on the reference plane should properly be the coordinate x of the point B, it is measured to be the coordinate x ′ of the point B′ and the coordinate x′ varies depending on the height of the point A. The background of the present invention has been made clear by the foregoing description and the distortion compensating method according to the present invention will now be described. (1) The height distortion compensation The height z of the point A in Fig. 2 is given by the following equation derived from Figure 2. z = (x - x o ) tan ϑ However, the point of projection of the point A on reference plane is the point B′ and therefore the height of the point A is outputted as follows in accordance with the previously mentioned conventional method : z′ = (x′ - x o )tan ϑ To compensate for this distortion, it is only necessary that the proper coordinate x of the point A on the reference plane be computed from the actually observed projective coordinate x of the point A on the reference plane. The relation between x ′ and x can be obtained in the form of the following equation (3) by a simple geometric calculation from Fig. 2 (a = the reference plane - television camera distance ): x = (1 - z a )x′ By substituting equation (3) in equation (1) and simplifying it, the height z of the point A can be given in the following form: z = x′ - x o l+ x′ a tan ϑ tan ϑ In equation (3), x o corresponds to the composite image u(x′, y′) produced by scanning the slit light over the surface of the object to be measured and x′ corresponds to the composite image u o (x′, y′) with respect to the reference plane. Therefore, equation (4) can be easily generalized and the shape computational expression compensated for the height distortion can be obtained in the form of the following equation: z(x′, y′) = u o (x′, y′) - u(x′, y′) l+ u o (x′, y′) a tan ϑ tan ϑ (2) The position distortion compensation Although the true height of the point A has been determined by equation (5), the position coordinates of the point A are the coordinates (x′, y′) of the projective point B′ of the point A on the reference plane centering the camera lens and not the coordinates (x,y) of the projective point B of the point A in the rectangular coordinate system. This coordinate distortion can be compensated for by the following equations as will be readily understood from Fig. 2: (3) The shape computing expression By using the above-mentioned height and position distortion compensation expressions (5), (6) and (7) and considering the compensation for the perspective effect of the camera, the shape computational expression for the three-dimensional shape f(x, y) of the surface of the object to be measured can be given by the following equations: f(x, y) = z(x′, y′) Fig. 3 is a schematic block diagram showing the construction of a three-dimensional shape measuring apparatus of the slit light linear scanning type according to an embodiment of the present invention. An object 2 to be measured is mounted on a reference plane 1 serving as a basis of measurement. A slit light source 3 is mounted on a linear stage 4 and it projects a slit light 3a at a projection angle ϑ onto the reference plane 1 and the object 2 to be measured. With the slit light source 3 mounted on it, the linear stage 4 is driven by a motor 6 which is controlled by a motor controller 5 and the slit light source 3 is moved in a direction parallel to the reference plane 1. At this time, the position of the slit light source 3 is measured by a position sensor 7 incorporated in the linear stage 4 and it is applied to a shape measuring apparatus 9 through the motor controller 5. The reference plane 1 and the object 2 to be measured are picked up by a television camera 8 arranged such that its optical axis crosses the reference plane 1 at right angles and the resulting video signal is applied to the shape measuring apparatus 9. The shape measuring apparatus 9 mainly comprises a shape computing circuit 10 serving as image computing means for performing a shape computation by image composing and a sequence controller 11 for generating commands for the motor controller 5 and performing a computation timing control for the shape computing circuit 10. During the shape measurement, the shape measuring apparatus 9 drives the linear stage 4 through the sequence controller 11 responsive to an externally applied start signal and the slit light source 3 is set in its initial position. Thereafter, the scanning of the slit light source 3 is started. The shape computing circuit 10 includes in its input section an image composing circuit 12 so that at the same time that the scanning of the slit light source 3 is started, the video signal applied from the television camera 8 is processed from moment to moment and an image composing computation is performed in which the value of each of the picture elements within the picture is represented by a stage position signal at the instant that the image of the slit light passes through that picture element. Then, upon the completion of one scanning of the slit light source 3, its result u(x′, y′) is transferred to an object plane composite image memory 13. Then, after the object 2 has been removed from the reference plane 1, the sequence controller 11 returns the slit light source 3 to the initial position and the scanning of the slit light source 3 is started again. The image composing circuit 12 performs the same composing computation as performed with respect to the object 2 but this time for the reference plane l so that upon completion of the slit light source scanning, the result u o (x′, y′) is transferred to a reference plane composite image memory 14. After these image composing computations have been completed, in response to the commands from the sequence controller 11 the shape computing circuit 10 causes a height computing circuit 15 and a distortion compensating circuit 16 to perform the following computations. The height computing circuit 15 computes a height z(x′, y′) from the image data stored in the object plane composite image memory 13 and the image data stored in the reference plane composite image memory 14 in accordance with equation (5). Thereafter, the distortion compensating circuit 16 provides compensation for the distortions in accordance with equations (6), (7) and (8) and the resulting height profile data f(x, y) is stored in a three-dimensional shape memory 17. In response to the command from a higher rank computer or CAD system, the height profile data stored in the three- dimensional shape memory 17 is suitably transferred to the computer or the CAD system. It is to be noted that while, in the above-described embodiment, the composite image of the reference plane 1 is produced during the measurement, it is necessary to produce the composite image of the reference plane 1 only once and therefore the initially produced composite image of the reference plane 1 can be used as such during the second and following measurements. Also, the composite image of the reference plane 1 is simple in construction so that the shape computing circuit 10 may be provided with an additional computing function such that a virtual reference plane is obtained by calculation in accordance with equation (5) to produce and store its composite image in the reference plane composite image memory 14. Further, while in the above-described embodiment the stage position signal is directly used as a composing signal in the image composing circuit 12, assuming for example that the stage is caused to make an uniform motion, any signal corresponding to the stage position, e.g., the elapsed time since the starting of the scanning of the stage, can be used and the stage position signal itself need not be used particularly. In this case, however, a stage position conversion circuit must be provided after the image composing circuit 12.

Claims: An apparatus (9) for measuring the shape of a three-dimensional curved surface of an object (2), comprising: slit light projecting means (3) for linearly scanning a linear slit light over the surface of said object placed on a measuring reference plane (1) from a direction forming with said measuring reference plane (1) an angle ϑ which is not perpendicular thereto; a television camera (8) having its optical axis disposed at right angles to said measuring reference plane (1) for picking up the surface of said object (2), position sensor means (7) for measuring the position of the slit light source (3) during scanning; image composing means (12) for receiving an output of said television camera (8) to compose in composite image memory means an image in which the value of each of a plurality of picture elements is represented by the position signal registered by said position sensor (7) at each instant as said projected slit light passes through a respective measuring point corresponding to each said picture element, thereby forming a composite image of the surface of said object (2); characterised in that the apparatus comprises: shape computing means (10) which includes: height computing means (15) for computing height data z(x′,y′), in accordance with said composite image u(x′, y′) produced by said image composing means (12) when said projected slit light is scanned over the surface of said object (2), a measured value or computed value u o (x′, y′) of a composite image with respect to said measuring reference plane (1), said light projecting angle ϑ relative to said measuring reference plane, and a distance a defined as the separation between said measuring reference plane (1) and said television camera (8); distortion compensating means (16) for compensating two-dimensional coordinates (x′, y′) of said height data z(x′, y′) produced by said height computing means (15) in accordance with compensated height data z(x′, y′) and said distance a between said reference plane (1) and said television camera (8); and memory means (17) for storing said height data subjected to said two-dimensional coordinates compensated by said distortion compensating means as three-dimensional shape data of said object; wherein said shape computing means (10) is adapted to determine the three-dimensional curved surface shape f(x,y) of the surface of said object (2) in accordance with the following equations: f(x, y) = z(x′, y′) z(x′, y′) = u o (x′ y′) - u(x′, y′) 1+ u o (x′, y′) a . tanϑ . tanϑ A measuring apparatus (9) according to Claim 1, characterised in that said shape computing means (10) includes height computing means (15) for computing a height z(x′, y′) in accordance with said composite image u(x′, y′) of the surface of said object (2) and said measured value or computed value u o (x′, y′) of a composite image with respect to said reference plane(l), and distortion compensating means (16) for compensating for distortions in an output of said height computing means (15). A measuring apparatus (9) according to claim 2, wherein said shape computing means (10) further includes first memory means (13) for storing said composite image u(x′, y′) of the surface of said object, and second memory means (14) for storing said measured value or computed value u o (x′, y′) of a composite image with respect to said reference plane (1).

Inventors: INOMATA MASAICHI, UESUGI MITSUAKI, INOMATA, MASAICHI, UESUGI, MITSUAKI
Applicants: NIPPON KOKAN KK, NKK CORPORATION
Application year: 1990
Main classification: G01B11
IPC codes: G01B11, H04N7, G06T15