Apparatus and method for measuring 3D form or deformation of an object surface using a grid pattern and reference plane

A method for measuring a 3D form of an object on a reference plane of a moire topographic optical system wherein a height of a center of a lens of a digital camera and that of a light source of a projector are the same relative to the reference plane, an imaging plane of the camera and a grid plane of the projector on which a pattern of equally spaced parallel grid lines is drawn are parallel to the reference plane, an x direction of the system is defined as that vertical to those of the grid lines and a y direction of the system is defined as that vertical to the x direction, and hence coordinates (i, j) of pixels on the imaging plane are defined to be aligned in an i direction parallel to the x direction and in a j direction parallel to the y direction, and a z direction is a height direction orthogonal to both of the x and y directions, the method comprising:

• adjusting the grid plane so as to be projected on the reference plane as a diagonal grid pattern with respect to the x direction,
• extracting a rectangular region including Nx pixels in the x direction and Ny pixels in the y direction (Nx and Ny are integers larger than or equal to 2) from a grid image taken in the imaging plane of the digital camera from the diagonal grid pattern projected on the reference plane, so that the phase of the projected grid is gained by dividing 2π by Nx×Ny within the rectangular region,
• extracting a rectangular region including Nx pixels in the x direction and Ny pixels in the y direction (Nx and Ny are integers larger than or equal to 2) from a grid image taken in the imaging plane of the digital camera from the diagonal grid pattern projected on the object laid on the reference plane, so that all phases included in one pitch of the grid pattern are covered within the region including Nx×Ny pixels,
• taking M=Nx×Ny pieces of brightness data out from the region including Nx×Ny pixels, and
• carrying out a phase analyzing process on each pixel on the basis of the taken pieces of brightness data.

A method for measuring a deformation of a surface of an object laid on a reference plane of a moire topographic optical system, wherein a height of a center of a lens of a digital camera and that of a light source of a projector are the same relative to the reference plane, an imaging plane of the camera is parallel to the reference plane, a pattern of equally spaced parallel grid lines is drawn preliminary on the surface of the object, an x direction of the system is defined as that vertical to those of the grid lines and a y direction of the system is defined as that vertical to the x direction, and hence coordinates (i, j) of pixels on the imaging plane are defined to be aligned in an i direction parallel to the x direction and in a j direction parallel to the y direction, and a z direction is a height direction orthogonal to both of the x and y directions, the method comprising:

• adjusting the direction of the grid lines on the object laid on the reference plane with respect the x direction of the system in order to extract a rectangular region including Nx pixels in the x direction and Ny pixels in the y direction (Nx and Ny are integers larger than or equal to 2) from a grid image taken in the imaging plane of the digital camera from a diagonal grid pattern projected on the reference plane, so that the phase of the projected grid is gained by dividing 2π by Nx×Ny within the rectangular region, and to extract a rectangular region including Nx pixels in the x direction and Ny pixels in the y direction (Nx and Ny are integers larger than or equal to 2) from a grid image taken in the imaging plane of the digital camera from the grid pattern on the object laid on the reference plane so that all phases included in one pitch of the grid pattern are covered within the region including Nx×Ny pixels,
• taking the image of the grid pattern on the object before deformation, taking out M=Nx×Ny pieces of brightness data before deformation from the rectangular region,
• taking the image of the grid pattern on the object after deformation and taking out M=Nx×Ny pieces of brightness data after deformation from the rectangular region,
• carrying out a phase analyzing process on each pixel on the basis of the pieces of brightness data before and after deformation, and
• calculating a displacement of the object on the basis of the differences between phases before and after deformation.