Research On Fringe Projection Measurement Method Based On Cross Ratio Invariance

As one of the three-dimensional optical measurement technologies,fringe projection profilometry has a wide range of applications and development prospects in various fields of production and life due to its advantages of non-contact,simplicity,convenience and low cost.Although there are many researches about fringe projection technologies,numerous unsolved problems still exist.Because of the equipment itself,fringe projection systems will inevitably have errors in the measurement process,which will affect the measurement accuracy.In this paper,according to the geometric relationship of the fringe projection system,some new and practical depth measurement methods are put forward in view of the factors that limit the measurement accuracy.The research of this paper mainly includes the following aspects:In this paper,we analyze the epipolar geometry in the fringe projection system,and conclude that there is the invariance between the projector and the camera.Based on this,according to the feature that the epipolar lines converges on the epipoles,we deduce the calculation method of the epipole positions.According to the invariance of cross ratio in projective transformations,we establish the expression of the relationship between the depth and phase maps of the object at the side of reflected light,and analyze the influence of the phase errors caused by the projector on the measurement accuracy,which is also one of the important factors restricting the measurement accuracy.The paper presents a fast reconstruction method of depth map based on the invariance of pixel cross ratio.Although the existing pixel coordinate cross ratio measurement technologies can theoretically eliminate the influence of projector errors,there are still some constraints on the accuracy and speed.Therefore,according to the invariance of the cross ratio of the pixel coordinates,we deduce the general function of the relationship between the object depth and the pixel coordinates,and calibrate the parameters by the reference phase maps of different positions in advance.The parameters obtained by this method are only determined by the measurement system,but not related to the measured objects,which improve the measurement accuracy,especially the measurement speed.In addition,the average phase maps are used instead of the reference phase maps to calculate the depth.The average phase maps calculated by more reference planes can reduce the impact of random errors in measurement and further improve the accuracy of measurement.We verify the feasibility of the proposed method through experiments,and compare the results with several existing methods,the experimental results show that this method is not affected by the projector errors including lens distortions and nonlinearity,and have a good compromise in measurement accuracy and efficiency.