Measurement method, measurement apparatus, measurement program and computer readable recording medium in which measurement program has been recorded

A method for measuring a deformation of a surface of an object on which a two-dimensional grid is provided on the basis of a two-dimensional grid image of the surface of the object taken by a camera, comprising:

• taking the two-dimensional grid on the surface of the object with the camera to obtain the two-dimensional grid image in such a state that the directions of camera pixels are adjusted to the two-dimensional grid image of the surface of the object, and at the same time one period of said two-dimensional grid image in an x direction is adjusted to Nx pixels of the camera and one period in a y direction is adjusted to Ny pixels of the camera, where Nx and Ny are integers greater than 2 and smaller than the number of pixels in the x and y directions on an imaging surface of the camera;
• cutting out a pixel region of Nx×Ny which corresponds in the x direction and the y direction, from the two-dimensional grid image;
• sampling data on intensity of the Nx pixels in the x direction or that of the Ny pixels in the Y direction from the cut out pixel region, and obtaining phase θ of the component of the frequency, the period of which is N pixels through the following formula:
• ∑
• k
• =
• 0
• N
• -
• 1
• ⁢
• I
• k
• ⁢
• sin
• ⁡
• (
• k
• ⁢
• 2
• ⁢
• π
• N
• )
• ∑
• k
• =
• 0
• N
• -
• 1
• ⁢
• I
• k
• ⁢
• cos
• ⁡
• (
• k
• ⁢
• 2
• ⁢
• π
• N
• )
• =
• -
• tan
• ⁢
• ⁢
• θ
• wherein Ik is the intensity of light in the kth pixel in the x or y direction of the value gained from the pixel;
• and
• after the surface of the object is deformed, taking the two-dimensional grid image by the camera, the obtaining the phase θ being carried out on each pixel of the two-dimensional grid image, and identifying the deformation of the surface of the object on the basis of said phase θ.

A program stored on non-transitory computer-readable medium for measuring a deformation of a surface of an object on which a two-dimensional grid is provided on the basis of a two-dimensional grid image of the surface of the object taken by a camera and allowing a computer to perform:

• taking the two-dimensional grid on the surface of the object with a camera to obtain the two-dimensional grid image in such a state that the directions of camera pixels are adjusted to the two-dimensional grid image of the surface of the object, and at the same time one period of said two-dimensional grid image in;
• an x direction is adjusted to Nx pixels of the camera and one period in a y direction is adjusted to Ny pixels of the camera, where Nx and Ny are integers greater than 2 and smaller than the number of pixels in the x and y directions on an imaging surface of the camera;
• and
• cutting out a pixel region of Nx×Ny which corresponds in the x direction and the y direction from the two-dimensional grid image;
• carrying out the two dimensional Fourier transformation to the cut out pixel region, and sampling a set of components (1, 0) and (0, 1) or (−1, 0) and (0, −1) of the frequencies in the Fourier transform plane;
• finding the phases of either set of the frequencies in each pixel of the two-dimensional grid image;
• and
• after the surface of the object is deformed, the finding the phases on the two-dimensional grid image taken by the camera is carried out on each pixel of the image to obtain the deformation of the object on the basis of the phases of each pixel before and after the deformation of the surface of the object.

A program stored on a non-transitory computer-readable medium for measuring a deformation of a surface of an object on which a two-dimensional grid is provided on the basis of a two-dimensional grid image of the surface of the object taken by a camera and allowing a computer to perform:

• taking the two-dimensional grid on the surface of the object with the camera to obtain the two-dimensional grid image in such a state that the directions of camera pixels are adjusted to the two-dimensional grid image of the surface of the object, and at the same time one period of said two-dimensional grid image in an x direction is adjusted to Nx pixels of the camera and one period in a y direction is adjusted to Ny pixels of the camera, where Nx and Ny are integers greater than 2 and smaller than the number of pixels in the x and y directions on an imaging surface of the camera;
• cutting out a pixel region of Nx×Ny which corresponds to the x direction and the y direction of the two-dimensional grid image;
• sampling data on intensity of the Nx pixels in the x direction or that of the Ny pixels in the y direction from the cut out pixel region, and obtaining phase θ of the component of the frequency, the period of which is N pixels through the following formula:
• ∑
• k
• =
• 0
• N
• -
• 1
• ⁢
• I
• k
• ⁢
• sin
• ⁡
• (
• k
• ⁢
• 2
• ⁢
• π
• N
• )
• ∑
• k
• =
• 0
• N
• -
• 1
• ⁢
• I
• k
• ⁢
• cos
• ⁡
• (
• k
• ⁢
• 2
• ⁢
• π
• N
• )
• =
• -
• tan
• ⁢
• ⁢
• θ
• wherein Ik is the intensity of light in the kth pixel in the x or y direction of the value gained from the pixel;
• and
• after the surface of the object is deformed, taking the two-dimensional grid image by the camera, the obtaining the phase θ being carried out on each pixel of the two-dimensional grid image, and identifying the deformation of the surface of the object on the basis of said phase θ.