Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape, the influence of sampling on it was studied. First, on the basis of deriving spectra expressions through the Fourier transform, the generation of CCD pixels was analyzed, and its expression was given. Then, based on the discrete expression of deformation fringes obtained after sampling, its Fourier spectrum expression was derived, resulting in an infinitely repeated "spectra island" in the frequency domain. Finally, on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component, the inverse Fourier transform was used to reconstruct the signal strength. A method of reducing the sampling interval, i.e., reducing the number of sampling points per fringe, was proposed to increase the ratio $ m $ between the sampling frequency and the fundamental frequency of the grating. This was done to reconstruct the object’s surface shape more accurately under the condition of $m > 4$. The basic principle was verified through simulation and experiment. In the simulation, the sampling intervals were 8 pixels, 4 pixels, 2 pixels, and 1 pixel, the maximum absolute error values obtained in the last three situations were 88.80%, 38.38%, and 31.50% in the first situation, respectively, and the corresponding average absolute error values are 71.84%, 43.27%, and 32.26%. It is demonstrated that the smaller the sampling interval, the better the recovery effect. Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions. The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.