Research On Key Issues In 3D Measurement Of Micro-scale Objects With Fringe Projection Profilometry Systems

As one of the structured light projection based three-dimensional measurement methods,the fringe projection profilometry(FPP)technique has received popular applications and in-depth research in many industries such as advanced manufacturing,virtual reality,industrial testing,cultural relics protection and so forth because of its merits such as high measurement speed,high measurement accuracy,large amount of acquired data,simple measurement equipment and robustness to ambient light and so on.Recently,as the development of advanced manufacturing and the increasing use of micro devices in the fields of machinery,electronics,biomedical and new materials,precise 3D measurement for objects in small scale(less than 50 mm)has become more and more important.The main content of this paper is to apply the traditional FPP measurement technology into the 3D measurement tasks of small-sized objects,and deeply study some key problems in the two main aspects of the whole measurement system:calibration and phase quality improvement.The details of this paper are described as follows:(1)A new calibration algorithm for FPP measurement system which is based on the telecentric imaging system is proposed.The similarities and differences between the telecentric imaging system and the small hole imaging system are theoretically analyzed.Then the telecentric system is calibrated with the aid of the traditional 2D planar calibration method which is designed for pinhole model.In addition,a two-step optimization algorithm is proposed to further improve the system calibration accuracy.The affine camera can be well calibrated with a re-projection error of 0.07 pixels using the proposed algorithm.Once a projector with a small field of view(FOV)is also calibrated with this method,a complete FPP measurement system can be realized.The experimental results demonstrate the robustness and accuracy of the proposed calibration algorithm using a measurement system prototype.The measurement system can achieve a measurement accuracy of 5?m when the FOV is 28.43 mm x 21.33 mm and the working distance is 110 mm.(2)A high dynamic range(HDR)3D measurement method based on fully automatic multi-exposure is proposed.When measuring objects in small sizes,the texture of the objects' surface and the random noise of the camera will negatively affect the phase quality calculated by the captured fringe images.The multi-exposure based high dynamic range FPP measurement technique has been proved to be an effective method for the 3D measurement of objects with complex surface reflection variations.In the existing methods,however,it is usually required to select different shutter times manually and empirically,which makes the whole measurement process complicated and laborious.Moreover,sometimes the manually selected shutter time is difficult to ensure a high-quality phase information.This paper proposes an automatic multi-exposure based HDR FPP technique.Two major contributions of this approach are:First,the entire measurement process is fully automated,no human intervention is required,which greatly simplifies the entire measurement process.Second,all shutter times in this method follow rigorous mathematical calculations.It is mathematically proved that once the fringe modulation of an image pixel is greater than a certain threshold,the phase quality of this pixel is then less affected by random noises.This threshold can be used for the calculation of the required shutter times.The proposed algorithm then automatically adjusts the camera's shutter time and takes the desired fringe images.Experiments show that with these captured images,3D measurements with a high dynamic range can be easily obtained.(3)A phase error correction algorithm for image local blurring phenomenon is proposed.When measuring small-sized objects,local blur caused by various types of global light transfer,such as camera defocus,projector defocus,and subsurface scattering,is prone to occur in the acquired images.These local blurring phenomena will cause significant systematic errors in the FPP system.In this paper,the influence of local blur on phase quality is deeply analyzed and a simple error correction algorithm is proposed to compensate the phase errors.The method relies on a point spread function(PSF)and a local frontal plane assumption.For the defocus phenomenon caused by small depth of field(DOF)of the imaging system,the method can be directly applied for error compensation.For the subsurface scattering scenario,if the translucent object is dominated by multiple scattering phenomena,the proposed error correction method can also be applied once the bidirectional scattering-surface reflectance distribution function(BSSRDF)of the object material is measured.(4)A color decoupling algorithm based on neural network is proposed.In some 3D measurement applications,a color camera is required to get the color information of the objects.However,the inherent color coupling phenomenon of color cameras can significantly affect the phase information and the accuracy of FPP measurement systems.By deeply analyzing the formation principle of color coupling phenomenon,the color coupling phenomenon is described as a nonlinear process.And then the generalization and interpolation ability of feedforward back propagation neural network is used to fit the nonlinear function and realize the color decoupling in real measurements.The experimental results fully prove that the proposed method can effectively compensate the sinusoidal property of the captured fringe images and the final calculated phase quality.(5)A robust calibration algorithm for stereo light microscope(SLM)based FPP system is proposed.In order to improve the stability of the calibration method based on single parallel plane,a new robust calibration method based on the calculation of traditional homography matrix and Gaussian imaging model is proposed.This method first uses a convenient and accurate method to calculate the physical focal length F of the entire microscope optical system,and then uses the Gaussian imaging model to calculate the effective focal length f of the microscope.Once f is calculated,the initial value of the camera's internal matrix is obtained,and then the camera's external parameters can be easily calculated from the homography matrix.Finally,all internal and external parameters can be optimized along with the lens distortion through a nonlinear optimization process,so as to complete the microscope calibration.In this method only two images of the parallel calibration plate need to be captured to complete the calibration.Although it is required to additionally calculate the physical focal length of the optical system,this method also overcomes the problem of instablility of the existing calibration method,and significantly improves the robustness and accuracy of the whole calibration process.Therefore,this proposed method is very suitable for the calibration of the microscopic optical measurement system.Experiments show that once applying this calibration method into the SLM based FPP system,objects in micro-scale can be well reconstructed.