Full Parameter Calibration And Distortion Correction In Fringe Projection Technique

Fringe projection profilometry is one of the mainstay optical three-dimensional(3D)measurement techniques.This technique,by taking advantage of being noncontacting,having high efficiency and accuracy,and providing whole-field information,has been widely used in industry,civil field,and so forth.With it,however,the exisiting 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.Fringe pattern analyses need to be improved for enhancing their accuracies,efficiencies,and computational simplicities.This dissertation focuses on the full-parameter calibration of the system,distortion correction,3D reconstruction,phase measurement and phase error compensation in fringe projection technique.As a result,novel techniques are proposed thus providing competitive solutions for the aforementioned issues.The main contents of this dissertation are as follows.(1)Full parameter calibration of the measurement systemEmulating the camera model,we derive the projector model and,further,establish the system model to determine the mapping relationship between the fringe pattern and the 3D coordinates of the measured object.The camera is calibrated by following the calibration method proposed by Zhang,to obtain its intrinsic and extrinsic parameters,as well as its lens distortion coefficients.However,it is difficult to calibrate projector parameters,since the projector cannot capture images,leading an obstacle to obtaining its pixel coordinates on the image plane.For solving this issue,we suggest an iterative calibration method for determining projector parameters.This method establishes the correspondence between camera pixels and projector pixels by using horizontal and vertical fringe phases of the calibration board.Fitting these fringe phases using rational functions in the least squares sense,allows us to determine the projector pixels accurately.An iterative strategy is used for optimizing the projector parameters thus improving the measurement accuracy.(2)Distortion correction and 3D reconstructionBased on the measurement system model and the camera and projector parameters,the mapping relationship between fringe phases and 3D coordinates is determined.With it,however,the projector lens distortion may decrease the measurement accuracy.For correcting the effects of the lens distortions on measurement,we propose two solutions.The pre-correction actively curves the fringes in computer when generating them;whereas when using the post-correction,the lens distortion correction is performed in the data processing stage.Both the methods are effective in restraining the effects of the projector lens distortion on the measurement results.(3)Temporal phase unwrapping based on Chebyshev polynomialsIn fringe projection profilometry,the phase measuring technique directly affects the measurement accuracy.Especially,phase-unwrapping is an important step for getting correct measurement results.In this dissertation,we propose a Chebyshev-code method,which is combined with the phase-shifting technique,aiming at calculating the absolute phase.To effectuate this idea,we apply Chebyshev polynomials as modulation functions to generate the fringe patterns,and suggest a nonlinear transformation to reshape the uneven curves of Chebyshev polynomials into uniformly sinusoidal ones.Using the recursive property of Chebyshev polynomials,combined with correction operation in the least-squares sense,allows us to estimate the fringe orders.In comparison with existing techniques,this method does not involve the operation of image segmentation,and hence its result is less sensitive to such factors as the color and texture of the measured surface,the nonuniformity of the illumination.Moreover,it is flexible in dealing with different SNRs of fringes by changing the number of capturing fringe patterns.(4)Research on compensation of nonlinear phase errorsIn fringe projection profilometry,the luminance nonlinearity of the projector has been recognized as one of the most crucial factors decreasing the measurement accuracy.It induces the ripple-like artifacts on the measured phase map.According to the analysis to captured patterns,we derive a phase error model and,further,suggest two compensation methods.The first method estimates error function coefficients from a couple of phase maps having different frequencies in an iterative least squares sense.The second one is to recognize and remove the nonlinearity-induced errors,directly from a calculated phase map.With this method,we estimate the phase error coefficients by exploting the dependence between the isolated artifacts and the smoothed phases under 3-sigma criterion.The two methods allow us to suppress the effect of the projector nonlinearity without a prior calibration for the projector intensities or phase errors,thus immuning the time-variance of the projector nonlinearity.