Research On Fringe Projection Profilometry Based On Epipolar Geometry

Fringe projection profilometry is one of the mainstay optical three-dimensional(3D)measurement techniques.This techinique,by taking advantages of whole-field,noncontacting,high-efficient,low-cost,and environment-insensitive,has great prospects for meeting demands from various applications in industry,civil field,and so forth.With it,however,the existing techniques have some shortcomings,which limit the improvements of measurement accuracy and efficiency.For example,the system calibration is complicated and its accuracy is not easy to control;The used devices have limitations in their capabilities,and their influences on the measurement results are hard to compensate for.In addition,fringe pattern analyses also need to be improved for enchancing their accuracies,efficiencies,and computational simplicaties.In this dissertation,we used the epipolar geometry to study the principle and method of fringe projection profilometry,and improved fringe pattern analysis methods by exploiting methematical tools.As a result,novel techniques were proposed thus providing competitive solutions for the aforementioned issues.The main contents of this dissertation are as follows.1.Geometric analysis and mathematical model of the measurement system.By use of the principle of epipolar geometric constraints,we analyzed the epipolar geometry of the fringe projection system,and derived the equations representing the epipolar lines of the projector and the camera.Based on these results,we eatablished a geometric and physical model for the measurement system,and determined the mapping relationship between the features of the fringe pattern and the depths of measured object.The analysis reveals that the epipole positions have important influence on the preformances of the measurement system.For this reason,we also suggested a calibration method for determining the system epipole coordinates.2.Research on the depth recovering method based on cross-ratio invariance.In fringe projection profilometry,the projector parameters are difficult to calibrate accurately thus inducing errors in measurement results.According to the analysis to the epipolar geometry of the fringe projection system,the depth variation along an incident ray and the pixel movement along the epipolar line on the image plane of the camera can be connected by using projective transformations.Under this condition,their crossratio keeps invariant.Based on this principle,we suggest a novel depth recovering method by use of cross-ratio invariance,which is immune to the errors associated with the projector,including its errors in geometry parameters,its lens distortions,and its luminance nonlinearity.Different from the traditional methods completely,this method provides a substantially new way to improve the measurement accuracy of fringe projection profilometry.3.Analyzing and optimizing the phase sensitivities.In fringe projection profilometry,the phase sensitivity is one of the important factors affecting the measurement accuracy.To gain insight into it,we performed a strict analysis to the epipolar geometry of the measurement system,revealing that the epipoles of the system have the key influence on in its phase sensitivity.We formularized the phase sensitivity as a function of the angle between the fringe direction and the epipolar line.Based on these results,we suggested the optimal fringes being circular-arc-shaped and centered at the epipole,which enable giving the best phase sensitivities over the whole fringe patterns;and the quasi-optimal fringes being straight and perpendicular to the connecting line between the fringe pattern center and the epipole,which can achieve satisfyingly high phase sensitivities over whole fringe patterns.these optimized fringes are effective in improving the phase sensitivities and further the measurement accuracies and resolutions.4.Research on frequency eatimating and phase recovering method of spatialcarrier fringe pattern.The deformed fringe pattern contains the 3D shape information of the measured object.Therefore,fringe pattern processing and analysis,aiming to extract the fringe phases,is one of the key steps in fringe projection profolometry.Spatial carrier fringe pattern is suitable for measuring dynamic events in real-time,because it involves only a single fringe pattern.In this dissertation,we proposed a new strategy for analyzing a spatial carrier fringe pattern.First,it eatimates the local phase gradients,i.e.,spatial frequency,at a pixel from its neighborhood,by use of statistics of the intensity gradients.Second,it recovers the phase map through the calculated phase gradients,and several fringe phase recovering methods,such as a numerical integration method based on 2D discrete cosine transform(DCT)and the adaptive least-squares spatial carrier phase shifting(SCPS)algorithm,were presented.Our proposed methods can be applied to a spatail carrier interferogram or a projected fringe pattern for phase analysis.Experimental results verified that these techniques can effectively improve the phase measuring accuracy and reduce the computational complexity simultaneously.