Study On The Techniques For Phase Retrieval In Fringe Projection Profilometry

Fringe Projection Profilometry(FPP) successfully realized its application in many fields such as national security, industrial production, flexible manufacturing, space exploratory and medical examinations. Fourier Transform Profilometry (FTP)and its continuations, which can recover the instantaneous phase through only single fringe pattern, have becoming the main methods in FPP, as they have many merits such as large data density, high accuracy, friendly environment, non-contact, no-injury and suit for dynamic object measurement.For the slow-rate of the phase recover problem, we proposed to use discrete Meyer wavelet in projection profilometry, which can increase the speed of phase retrieval. For the carrier wave component in distored fringe pattern, the inherent feature is detailed analyzed and then a cost function is constructed. The optimal discrete Meyer wavelet decomposition level is corresponding to the minimal value of the cost function. The main advantage of this method is it speedability, and also, which can avoid the detrimental effects of the phase jump and frequency overlap when the background component is sample enough.Traditionally, Mexican Hat wavelet profilometry has high accuracy and speed for phase retrieval when the outline of the measure element is slow varying, but the robustness of the Mexican Hat wavelet profilometry is poor because the scale which used is fixed and invariant. Based on the differential property of the Fourier transform, a new cost function is constructed, which is robust and stable for signals with noises, has very sample expression and has a clear interpretation in theory. The optimal discrete Meyer decomposition level is corresponding to the minimal value of the new cost function, and the optimal continue Mexican Hat wavelet scale can be adaptive determined through the new cost function. The proposed method is very useful when the outline’s gradient of the measurement object has a little vaiation range. And more study illustrates that the new cost function has ability to find the optimal carrier wave component form the Empirical Mode Decomposition (EMD) of the distorted fringe pattern. To increase the accuracy of the phase retrieval, the pattern should be de-noised ahead of the processing of phase recover. In this paper, we lucubrate the wavelet de-noising methods, and, based on the Orthogonal Wavelet Transform Stein Unbiased error Estimate Linear Extend Transform(OWT_SURE_LET) wavelet de-noising method, we introduces an improved wavelet de-noising, which adopt redundancy wavelet transform and need no the knowledge of the wavelet coefficients prior distribution. The step and process of the noised pattern’s wavelet coefficients optimal estimate for the improved method is made in detail in this manuscript. Peaks Signal Noise Radio (PSNR) and the Root Square Mean Error (RSME) of the phase retrieval for the distorted pattern are used to verify the effectiveness of the proposed improved wavelet de-noising method.A large error will occur when phase jump exist for the traditional wavelet profilometry, for which use dynamic programming and cost funcition to find the optimal wavelet ridge. To overcome this problem, this paper proposed to use dynadic wavelet transform for phase recover, and this algorithm uses OTSU to adaptive choose the larger wavelet coefficients from the the wavelet ridge and its neighbourhood coefficients to reconstruct the carrier wave component. This method can decrease the effect of the phase jump when noise is very little and is ignored.Band pass filter is offen used in fourier transform profilometry to eliminate the nosie and the back-component, but the center frequency and width of bandpass are hard to determine in practice. Bsed on the research of the dynadic wavelet transform, we found that the carrier wave compnent of the distorted fringe pattern can be reconstructed accurately using the dyadic wavelet sub-signal and its neighborhoods, and then an empirical formula is introduced in this algorithm to adaptive choose the child-signals form the results of the dyadic wavelet transform. Theory analysis show the new algorithm is an adaptive band-pass wavelet filter banks in essential, the band-width and center frequency are variant with types changing of the measurement objects,and this method is very useful when spectra overlap can be ignored.Adaptability and robustness are very important for object3D measurement in practice. These phase retrieval algorithms presented in this paper are all self-adaptive, data driven, needing no manual intervation, and even for different types of measured object, all the proposed methods in this manuscript need not parameters adjusting at all and need not paremeters presetting at all. More important is that all the methods introduced in this paper are all realtime and have a little calculation, which guarantee that these methods can be used with high effective in3D measurement in practice.