US 7,457,721 B2
Method and apparatus for measuring small displacement
Mitsuo Takeda, Hachioji (Japan); Wei Wang, Kodaira (Japan); Nobuo Ishii, Chofu (Japan); and Yoko Miyamoto, Chofu (Japan)
Assigned to The University of Electro-Communications, Tokyo (Japan)
Appl. No. 11/587,142
PCT Filed Apr. 22, 2005, PCT No. PCT/JP2005/007683
§ 371(c)(1), (2), (4) Date Feb. 14, 2007,
PCT Pub. No. WO2005/103610, PCT Pub. Date Nov. 03, 2005.
Claims priority of provisional application 60/564433, filed on Apr. 22, 2004.
Prior Publication US 2007/0219745 A1, Sep. 20, 2007
Int. Cl. G01B 11/00 (2006.01); G06F 19/00 (2006.01)
U.S. Cl. 702—158  [356/300; 356/302; 356/303; 356/450; 356/451; 356/496; 356/498; 382/100; 702/127; 702/155; 702/189] 6 Claims
OG exemplary drawing
 
1. A method for measuring small displacement to measure small displacement of an object in a non-contact manner, the method comprising:
a first taking image step for taking a first image of a surface of a measuring object;
a first Fourier transform step for transforming the first image taken by the first take image step by using an N-dimensional Fourier transform (where N=1 or 2);
a first Hilbert transform step for replacing an amplitude of frequency spectrum of half or a part of in-plane including zero first frequency of the frequency spectrum transformed by the first Fourier transform step with zero;
a first frequency extraction step for extracting a first frequency component from the first frequency spectrum after the first Hilbert transform step;
a first inverse Fourier transform step for transforming the first frequency component by using an N-dimension inverse Fourier transform (where N=1 or 2) and then obtaining a first complex analytic signal;
a first amplitude correction step for correcting an amplitude value of the first complex analytic signal as being a constant value;
a first phase-only signal recording step for recording a first phase-only analytic signal to which the amplitude is corrected;
a second take image step for taking a second image of the surface of the measuring object, on the other hand, after the first taking image step;
a second Fourier transform step for transforming the second image taken by the second taking image step by using the N-dimensional Fourier transform (where N=1 or 2);
a second Hilbert transform step for replacing an amplitude of frequency spectrum of half or a part of in-plane including zero frequency of the second frequency spectrum transformed by the second Fourier transform step with zero;
a second frequency extraction step for extracting a second frequency component from the frequency spectrum after the second Hilbert transform step;
a second inverse Fourier transform step for transforming the second frequency component by using an N-dimension inverse Fourier transform (where N=1 or 2) and then obtaining a second complex analytic signal;
a second amplitude correction step for correcting an amplitude value of the second complex analytic signal as being a constant value;
a second phase-only signal recording step for recording a second phase-only analytic signal to which the amplitude is corrected;
a phase-only correlation processing step for obtaining a phase-only cross-correlation function to entire region or a part of region of the first phase-only analytic signal and the second phase-only analytic signal; and
a displacement magnitude calculation step for calculating displacement magnitude from a location of correlation peak to which the phase-only cross-correlation function shows a maximum modulus.