29 Bulgarian Chemical Communications, Volume 48, Special Issue G (pp. 29-32) 2016 Phase recovery from fringe patterns with global carriers: approach based on Hilbert transform and wavelet de-noising techniques P. Sharlandjiev*, N. Berberova, D. Nazarova and G. Stoilov 1 Institute for Optical Materials and Technologies “Acad. J. Malinowski”, Bulgarian Academy of Sciences, “Acad. G. Bonchev” str. Bl. 109, 1113 Sofia, Bulgaria 1 Institute of Mechanics, Bulgarian Academy of Sciences „Akad. G. Bonchev“ Str., block 4, Sofia PS-1113, Bulgaria, Received October 10, 2016; Revised November 10, 2016 Fringe pattern analysis is an important task in optical metrology. Fringe patterns can be formed by optical interference, by projection techniques, by overlapping two similar wave structures, etc. Patterns with constant global angular carriers represent straight lines in the field-of-view. The presence of an object under investigation distorts the fringes. Analysis of these distortions is called also phase recovery and it is widely used in many applications of science and engineering, i.e. for retrieval of surface topography of 3D objects. Usually, three steps are discerned: pre-processing (noise reduction, background zeroing), phase retrieval (extraction of the phase distribution), and post-processing (unwrapping, smoothing and ‘cleaning’). Herein we present an approach based on a combination of Hilbert transform for phase recovery and different wavelet techniques for de-noising and smoothing. By numeric simulations we show that this technique is effective and robust. Different types of noise are considered: Gaussian additive noise, multiplicative intensity dependent (speckle) noise, high frequency environmental noise, jitter, fringe distortion due to non-sinusoidal modulation (presence of second and third harmonics in the fringes). Each type of noise can be considered separately or all of them – cumulatively. Keywords: Optical metrology; Fringe projection; Numeric filter techniques INTRODUCTION Fringe pattern analysis is an important task in optical metrology. Fringe patterns can be formed by optical interference, by projection techniques, by overlapping two similar wave structures, etc. [1]. Patterns with constant global angular carriers represent straight lines in the field-of-view. The presence of an object under investigation distorts the fringes. Analysis of these distortions is called also phase recovery and it is widely used in many applications of science and engineering, i.e. for retrieval of surface topography of 3D objects [1,2]. Usually, three steps are discerned: pre-processing (noise reduction, background zeroing), phase retrieval (extraction of the phase distribution), and post-processing (unwrapping, smoothing and ‘cleaning’). Herein we present an approach based on a combination of Hilbert transform [2] for phase recovery and different wavelet techniques for de- noising and smoothing. Different types of noise are considered: Gaussian additive noise, multiplicative intensity dependent (speckle) noise, high frequency environmental noise, jitter, fringe distortion due to non-sinusoidal modulation (presence of second and third harmonics in the fringes). Each type of noise can be considered separately or all of them - cumulatively. The effectiveness of the Hilbert transform is compared to that of complex Gabor transform [1], which can be used for phase retrieval, too. Wavelet de-noising is compared to that of windowed Fourier filter [2] and others filters, as well (see below). In all simulations the phase unwrapping is done by the Itoh approach [3]. The smoothed final result is ‘cleared’ by an adaptive Wiener filter [1]. PHASE AND NOISE MODELS; FRINGES AND COMPUTATIONAL PROCEDURES The phase model (pm) in the simulations below is the function “peaks”, which is more or less accepted as a standard in surface profile analysis: © 2016 Bulgarian Academy of Sciences, Union of Chemists in Bulgaria * To whom all correspondence should be sent: E-mail: pete@iomt.bas.bg