Abstract
The number of phase wraps that result from the carrier component can be completely eliminated or reduced by first applying a fast Fourier transform (FFT) to the image and then shifting the spectrum to the origin. However, because the spectrum can only be shifted by an integer number, the phase wraps of the carrier component cannot be completely reduced. In this paper, an improved carrier frequency-shifting algorithm based on 2-FFT for phase wrap reduction is proposed which allows the spectrum to be shifted by a rational number. Firstly, the phase wraps are reduced by the conventional FFT frequency shift method. Secondly, the wrapped phase with residual carrier components is filtered and magnified sequentially; the amplified phase is transformed into the frequency domain using an FFT, and then, the wrapped phase with the residual carrier components can be further reduced by shifting the spectrum by a rational number. Simulations and experiments were conducted to validate the efficiency of the proposed method.
Highlights
In optical metrology, two-dimensional (2D) phase-based techniques have been widely used in various measurement applications, such as deformation and vibration measurement and three-dimensional (3D) surface measurement [1,2,3]
Because the spectrum can only be shifted by an integer number in a conventional fast Fourier transform (FFT), while the carrier frequency is always a fraction in a practical application, the carrier phase cannot be reduced completely, thereby resulting in a measurement error
We presented an improved carrier frequencyshifting algorithm based on 2-FFT for phase wrap reduction
Summary
Two-dimensional (2D) phase-based techniques have been widely used in various measurement applications, such as deformation and vibration measurement and three-dimensional (3D) surface measurement [1,2,3]. Phase unwrapping can be avoided or the phase wraps can be significantly reduced, for example, in fringe projection or off-axis holographic profilometry [12,13,14] In these techniques, a carrier signal is included in the extracted phase information. Because the spectrum can only be shifted by an integer number in a conventional fast Fourier transform (FFT), while the carrier frequency is always a fraction in a practical application, the carrier phase cannot be reduced completely, thereby resulting in a measurement error. The wrapped phase that results from the residual carrier components is further reduced by shifting the spectrum by a rational number
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