Fourier transform profilometry based on composite structured light pattern
Introduction
The Fourier transform profilometry (FTP), method based on fringe projection has several advantages including its high-resolution, one frame capture, and whole-field depth reconstruction. Since Takeda and Motoh [1] proposed the FTP method, it has been extensively studied [2], [3], [4], [5], [6], [7], [8], [9], [10], focusing on improving the measurement range and precision. FTP is one of the most widely used 3-D sensing methods, in which a fringe pattern is projected onto an object. The deformed fringe pattern formed by imaging the object onto a CCD camera is Fourier transformed and processed in the spatial frequency domain. The fundamental frequency component, which includes information on the height information of the measured object, is filtered in the frequency domain. This is followed by an inverse Fourier transform to determine the reconstruction depth. So the influence of frequency spectrum aliasing on the performance of this technique cannot be neglected. A sinusoidal grating projection combined with a π phase shifting technique has been used to eliminate zero and higher order components and improve the measured precision and range. However, to facilitate this two images of the fringe patterns must be captured, which influences the instantaneous characteristic of FTP.
Recently, a new phase measurement profilometry called composite phase measurement profilometry has been reported [11], in which only one composite fringe pattern is used to recover the object surface. This method uses at least three carrier frequencies, which increase the problems associated with aliasing and reduce the measuring precision. The literature [12] presents a novel method, in which a bicolor sinusoid fringe pattern (that consists of two interlaced RGB format base color fringe patterns with π phase difference) is projected onto the object via a digital light projector and the deformed color pattern is captured by a color digital camera.
In this paper, a novel method is proposed, in which a composite structured light pattern is projected to recover the object surface. The method eliminates the zero frequency by using only one fringe pattern. Theoretical analysis, numerical simulation and experimental results obtained by employing the new method are presented in this paper. The experimental results indicate that there is no perceivable decrease in the precision of this method compared with the traditional π phase shifting technique. The new method allows for practical real time, high-speed implementation.
Section snippets
Traditional π phase shifting FTP
In π phase shifting FTP, sinusoid patterns are projected as:where Ap and Bp are the projection constants and is the projector coordinate. The yp dimension is in the direction of the depth distortion and is called as the phase dimension. The xp dimension is perpendicular to the phase dimension, and is called as the orthogonal dimension. denotes the frequency of the sinusoid wave in the phase direction. The frequency of the fringe pattern is named as the
Numerical simulation
In numerical simulation, the two carrier frequencies f1 and f2 of CFTP are separately three lines per 20 pixels, four lines per 20 pixels, and fringe frequency in the phase direction is 512 lines per 20 pixels. The simulated image is shown in Fig. 3(a). The deformation is controlled by h(x, y), which is expressed asThe deformed fringe pattern is shown in Fig. 3(b). According to the above process of phase decoding, the
Experiments
Fig. 4 shows the block diagram of the experimental set-up. The composite fringe pattern is produced by a computer and projected by a digital light projector (DLP, PLUS U3-880). The image size is 800*600 pixels. The deformed fringe pattern is captured by a digital camera (Cannon A80). The two carrier frequencies f1 and f2 of CFTP are separately three lines per 40 pixels, six lines 40 pixels. The Fringe frequency in the phase direction is 600 lines per 32 pixels. To verify the method, we apply
Conclusions
In this paper a novel method called as composite FTP, is proposed, in which a composite fringe pattern is used. The composite structured light pattern is formed by modulating two separate fringe patterns with π phase difference along the orthogonal direction of the two distinct carrier frequencies. The theoretical analysis and experimental results show that the CFTP method can eliminate the zero frequency component by using only one fringe pattern. The ultimate advantage of the proposed method
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