Resharch On 2D Fast Generalized S Transform In Surface Measurement Of Optical 3D Objects

Optical three-dimensional measurement technology has an important role and broad application prospects in geological exploration,physical simulation,industrial automation detection and other fields.Fourier transform profilometry is a commonly utilized three-dimensional sensing technology of single-frame carrier-frequency.Classical Fourier transform is a processing method for stationary signals.Due to the lack of local analysis ability and time-domain positioning function,time-frequency analysis,as a non-stationary signal analysis method different from Fourier analysis,has gradually received widespread attention in recent years.Two-dimensional S-transform can realize the local analysis of signal in horizontal and vertical directions simultaneously,which improves the resolution of time-frequency transformation of signal.However,there are also problems with slower measurement speeds and high memory demand.Aiming at this problem,this paper introduces the x-f-k transform and the two-dimensional sparse S-transform into the frequency domain phase unwrapping of three-dimensional surface measurement for quickly realizing the three-dimensional surface measurement.The main works of this paper is as follows:1.Three-dimensional object shape measurement is realized by two-dimensional S-transform.It mainly includes the introduction of two-dimensional S-transform,the preparation of two-dimensional S-transform algorithm and the realization of frequency domain phase resolution method.Two-dimensional S-transform theory is introduced from continuous and discrete aspects respectively.The two-dimensional S-transform algorithm is written to deal with the distorted fringe image,and the specific implementation process and flow of the two-dimensional S-transform algorithm is given,and the algorithm is tested by the reconstruction of the deformation grating.The two-dimensional S-transform realizes the frequency domain decomposition,mainly by analyzing the frequency domain phase unwrapping principle to obtain the expression for calculating the phase value and the application of the two-dimensional S-transform algorithm in the three-dimensional shape measurement is verified by simulation experiment.2.To solve the problems of slow measurement speed and high memory demand in the three-dimensional shape measurement,the x-f-k transform is introduced to implement the frequency domain unwrapping method.By combining the S-transform with the Fourier transform,the coefficient matrix of the x-f-k transform is obtained,and the phase and height distribution information are obtained by analyzing the matrix.The method considers the change of the window function,generalizes the two-dimensional S-transform by changing the shape and width of the window function,and reduces the processing result from four-dimensional to three-dimensional,which improves the speed of the three-dimensional shape measurement and the required memory is also effectively reduced.The simulation experiment demonstrates the method by vertical stripe and diagonal stripe.The results show that the method has a good effect on three-dimensional shape measurement.3.The x-f-k transform reduces the dimension of the processing result in the three-dimensional shape measurement process,which makes the accuracy of the measurement result slightly affected.For the problem,the two-dimensional sparse S-transform is used to quickly realize the frequency domain phase unwrapping method.The number of sampling points is simultaneously reduced in the horizontal direction and the vertical direction by the binary frequency multiplication and the harmonic frequency multiplication,and the phase information is obtained according to the two-dimensional sparse S-transformation matrix,thereby obtaining the height distribution information.The method considers recovering the shape of the three-dimensional object with fewer points,which effectively reduces the amount of calculation.Simulation experiments show that the method quickly achieves frequency domain phase unwrapping and improves the accuracy of measurement results.