Dynamic measurements by color gratings projection method using a two-step Fourier transform method

Abstract

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.