Research On The Two Dimensional Phase Unwrapping Algorithms

Phase measurement technology takes the phase as the measurement informationcarrier.However,because of the cycle-changing quality of phase, phase can only berecorded in the cycles of2,therefore,the two mainstream phase extractionalgorithms i.e. Fourier transform method and phase shifting method, can only get thewrapped phase.Any phase measurement technology can not avoid the problem ofphase unwrapping.Itoh condition points out the root of phase unwrapping errors:the difference of theadjacent phase values in the real phase map exceeds the range of. In order toreduce the influence of the unreliable phase,the path-following algorithms choose theappropriate unwrapping paths via branch-cuts or quality maps,while the least-squaremehtod directly solves the objective function,to get the unwrapped phase map throughcurve fitting.The advantages of these two algorithms are that the former ones onlychange the wrapped phase by integer cycles of2,and will not distort the originalphase data,while the latter one can guarantee the unwrapped phase map to be globallycontinuous.However,for the phase maps with high noise level,the branch-cuts andquality maps fail to guide the unwrapping path accurately,then there will occur someregions which can not be unwrapped correctly,that is to say,the unwrapped phase isnot globally continuous.While fitting the final unwrapped phase,the least squaremethod will distort and compress the original phase data,namely, will not guaranteethe phase consistency. The high noise resistance unwrapping algorithm designed bythis thesis combines the advantages of the two kinds of aforesaid algorithms,whichare only altering the wrapped phase by cycles of2and guaranteeing the globalcontinuity.This thesis models the phase field with the Markov random field. Firstly,build anobservation model of the wrapped phase,and then under the constraint of altering thewrapped phase by cycles of2,and the guarantee of global continuity,derive theenergy function of phase estimates.Minimizing this energy function utilizing theGraph-Cuts optimizaion technology.After the introduction of the novel unwrappingalgorithm,the analysis to the noise resistance properties of the new unwrappingalgorithm is conducted,and a conclusion is achieved that the smoother the potential function is,the better the noise resistance will be.However the promotion of anti-noisecapability is at the expense of longer processing time.In the shearography experimental system,in order to obtain the strain field andthe out-of-plane displacement of the tyre deformation,this thesis proposes thefollowing processing flow: firstly unwrap the speckle wrapped phase map directlywithout any filtering, secondly reduce the noise of the obtained strain field by averagefiltering,finally restore the out-of-plane displacement of the tyre deformation throughthe accumulation of the filtered strain field. Owning to the fact that the true strainfield and out-of-plane displacement of the tyre deformation is unknowable,we mustvalidate the processing flow through numerical simulation.This thesis simulates thegeneration of the speckle wrapped phase map,then restores the strain field and theout-of-plane displacement according to the above-mentioned processingflow.Comparision between the numerical simulation results and the true values provesthat the proposed processing flow can accurately restore the strain field and theout-of-plane displacement. Finally,this thesis processes the wrapped phase obtained inthe shearography measurement experiment following the exact processing flow,andobtains the the strain field and the out-of-plane displacement of the tyre deformation.