Dynamic 3D Shape Measurement Based On Fiber-optic Interferometric Fringe Projection Profilometry

Fringe projection profilometry(FPP)is an important method for high-precision 3D shape measurement of small and medium-sized objects(0.01?0.5m),because with this technique 3D data can be directly recovered from two-dimensional coded images without the need for any scanning devices.Fiber-optic interferometric fringe projection profilometry(FoFPP)in the family of FPP uses a miniaturized fiber-optic interferometer as the projector,and is capable of projecting high-density fringe patterns with infinite depth of focus.Unlike digital FPP,it doesn't have a frame rate limit and therefore is a promising technique for high-speed and dynamic 3D shape measurement.In FoFPP,the profile measurement is based on phase measurement,which is the same as digital FPP,so FoFPP needs to first realize high-precision,high-speed phase demodulation in order to be used in high-precision dynamic topography measurement.On one hand,however,initial phase of the fringe pattern projected by a fiber interferometer is prone to drift owing to environmental disturbances such as temperature variation and vibration.On the other hand,when phase shifting technique is used to demodulate the phase map of the fringe pattern,traditional step phase shifting and linear phase shifting is not applicable to high-speed phase measurement because they may cause distortion or ringing effect;sinusoidal phase shifting can be used for high-speed measurement,but the result it obtains has low signal-to-noise ratio.It is difficult to achieve both high accuracy and high speed for the phase measurement.Besides,the fringe pattern projected by FoFPP is inherently distorted,and if not considered in system calibration,it may induce error to the conversion of phase map to three-dimensional coordinates.Therefore,this paper intends to study the dynamic 3D shape measurement based on fiber interferometric fringe projection,and to develop a high-speed and high-precision dynamic 3D shape measurement method for small and medium-sized objects from the aspects of phase shifting method,phase shifting accuracy and system calibration.The main research contents are summarized as follows:(1)A phase stabilization method based on synchronous integration was developed.Firstly,the Michaelson interference signal reflected by fiber endfaces is integrated in N(N?3)episodes of the modulation period;then,the integration results are manipulated to calculate the phase drift by add and arctangent;finally,a feedback control is utilized to compensate for the phase drift.Phase stabilization system based on the proposed method was built,and phase drift was reduced to 15 mrad within 5minutes for both linear phase shifting and sinusoidal phase shifting fringe demodulation.Experimental results showed that compared with traditional AC phase tracking(PTAC)stabilization method,the proposed method doesn't need extra AC phase modulation,and therefore will not affect fringe contrast.It is efficient and simple in calculation,occupies less resources of Micro controller unit(MCU),and can obtain the same phase stability performance as PTAC.(2)An improved algorithm for 1/4 period sinusoidal phase shifting integrating-bucket phase demodulation method was proposed.The phase demodulation model was built and the optimized modulation amplitude and initial integration phase were calculated.With the improved algorithm,a 3D shape measurement can be completed within a sinusoidal modulation cycle.It improves the measurement speed,and alleviates the contrast reduction problem caused by sinusoidal phase shift.In addition,it makes the setting of various system parameters,such as light source power,modulation frequency and integral time,more flexible.Simulation and experimental results showed that sinusoidal phase-shift phase demodulation with integral time less than 1/4 period can improve SNR by about 2.5dB.(3)A scale factor calibration method was proposed for sinusoidal phase shifting integrating-bucket phase demodulation method.Firstly,an image variable is produced by linearly combining the phase-shifted fringe patterns.Then,the scale factor can be calibrated by minimizing the second-order harmonic amplitude of fringe frequency in the spectrum of the aforementioned image variable.The proposed method avoids the need to calibrate sinusoidal phase-shift modulation amplitude and initial phase,and therefore is simple and fast.Besides,it avoids the need to acquire the Michaelson interference signal reflected by the fiber ends.The method was verified by MATLAB simulation,and the results showed that it has high calibration accuracy and good robustness against random noise of fringe image.(4)A phase shift estimation method based on small amplitude sinusoidal phase modulation was proposed for Fo FPP.Firstly,a small amplitude sinusoidal modulation is introduced to the interference phase.Then,the phase shift of the fringe pattern can be estimated by integrating the real-time interference phase obtained with phase generated carrier(PGC)technique.The estimated phase shifts are utilized to calculate the phase map with the least square method,and noise model for the demodulation of the phase map is deduced considering circuit noise,light intensity noise and CMOS noise.The optimized modulation amplitude can be found with the noise model.Experimental results showed that this method can obtain the same phase shift estimation accuracy and phase demodulation accuracy as the modified Fourier transform algorithm,but the time consumed is only one-sixth of the latter.The proposed method is suitable for real-time and high-speed fringe phase demodulation.(5)A blockwise calibration method is proposed to calibrate the parameters of phase-to-height conversion model.The phase map used in the calibration is divided to some small blocks;for each block,the height,phase and pixel coordinates are fitted to a pre-defined function.Only 2?3 phase maps are needed in the calibration.Considering fringe distortion generated by the fiber-optic interferometer,this method and the pixel-by-pixel calibration method were simulated,and results showed that the two were comparative in terms of robustness for distortion and the former is superior to the latter regarding noise performance.This method was used to calibrate Fo FPP system we built,and the heights of a 4mm and a 7mm gauge blocks were measured with the calibrated system.Results showed that the measurement accuracy was better than 0.05 mm.Dynamic 3D shape measurement experiment was carried out with the calibrated system,and the 3D shapes of a deforming toy and moving fingers were measured at a rate of 30Hz.