The Fourier transform method is an analytical method for interferograms with a spatial linear carrier. Interferograms
with a spatial linear carrier are analyzed to obtain the phase, by eliminating the noise from the shape components of the
interferograms in the Fourier domain. However, when the noise and shape components overlap in the Fourier domain, it
is difficult to eliminate only the overlapped noise components using conventional filtering techniques, such as bandpass
filtering. Accordingly, a method is proposed to solve this problem using two interferograms with slightly different
carrier frequencies. In this method, the Fourier transforms of two interferograms with slightly different carrier
frequencies are separately calculated. Both of the spectra resulting from the Fourier transforms of the interferograms
contain the same noise components; however, the locations of these components differ slightly for the two spectra. By
subtracting the two Fourier spectra, the noise components are removed, and the main components are generated, because
the frequency difference between the two components is small. We have named the proposed method the “two-step
Fourier transpose method”. The validity of the proposed filtering method is confirmed by experiments in which two
color fringes are projected simultaneously onto a scatter object. Images of the color fringes are acquired via a CCD
camera under the slow deformation of the scatter object. The images are then analyzed via the proposed method.
The generation theory of interference fringes patterns considering the aberration of the focusing lens is proposed in a position-sensing grating interferometer for a specular object. The proposed theory is based on the assumption that the deformation of the wavefront passing the interferometer is limited by the symmetry of the interferometer and that the wavefront can be expressed by Zernike polynomials. The simulation and experimental results are presented. The interference fringes pattern of the form of a barrel and a spool were obtained by the simulation. The experimental results agreed well with the simulation results.
In the method for obtaining an error in a shape under test using the integration from a lateral shearing interferogram, it is assumed that the lateral shear of the shape is so small that the interferogram pattern is considered to be representative of the wavefront slope. To obtain the shape, the slope is analyzed by integration. When the lateral shear of the wavefront is not small, an accurate shape cannot be obtained. Furthermore, the analyzed area of the wavefront is limited by the amount of shear, and the whole area cannot be obtained by this method. A method for reconstructing the whole accurate shape from the wavefront analyzed using the integration process is presented in this paper. In a computer simulation to investigate the efficacy of the method, the reconstructed shape agreed with the original shape error.
Fringe scanning for analyzing shape error of a test surface is performed by fringe shift of interference images with different phases. The method of proposed fringe shift is carried out by a zone-plate, which has fan-shaped sections of four different initial phases of 0, (pi) /4, (pi) /2, and 3(pi) /4. Experimental results agree with the theory.
The zone-plate interference fringe pattern is analyzed by FFT. The spectrum obtained by FFT contains information on the shape error. To select the information on the shape error from the spectrum of the fringe pattern is difficult, because the resolution of the spectrum is low. An FFT with over-sampling is applied to increase the spectrum resolution. A method is proposed to select the necessary information from the spectrum of the fringe pattern. Experimental results obtained by the proposed method agree well with those obtained by Fizeau interferometer.
This paper presents the technique of an on-machine precision profile measurement, through a kind of common-path interferometer using a zone-plate. We could analyze profile errors of a spherical mirror on the machine turning at a speed of 900 rpm. The results of experiments are evaluated.