Application of Two-dimensional Wavelet Transformation to Analysis of Deformed Gratings

Abstract

Many methods of measuring the three-dimensional shape of objects have been proposed. For noncontact measurement optical techniques, moire and grating projection methods are desired. Their measurement sensitivity depends on grating pitch and illumination angle. Therefore, the accuracy of measurement is low. To raise the accuracy, a suitable analytical method is necessary. The phase shift, FFT and wavelet methods are used for the analysis of fringes or modulated gratings. The phase shift method is suitable for a static analysis because several images recorded at different times are used. The FFT and wavelet methods are suitable for dynamic analysis because only one image is used. In the FFT method, the spatial resolving power is low. On the other hand, the spatial resolving power in the wavelet method is chosen automatically according to the pattern of the image. When the image pattern is used for analysis by the one-dimensional wavelet method, the pattern is analyzed along many lines. The shape of the whole surface of the object is analyzed by connecting the phase between adjacent lines. Therefore, the analytical process is difficult.In this study, we focus on the grating projection method, and the analysis by a two-dimensional wavelet method is proposed. In this analytical method, the frequency, direction and phase of the modulated grating were obtained continuously, and the phase connection in the two-dimensional image analysis could be realized.