Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform

Abstract

Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.

Hilbert-Huang processing and analysis of complex fringe patterns

“…The approach for the fringe pattern enhancement, automatic bias term removal, noise suppression and normalization developed by our group employs the so-called selective reconstruction (SR) algorithm [79]. After decomposing the analyzed fringe pattern into a set of BIMFs only regions with high amplitude function values of each BIMF are assigned to the reconstruction process.…”

“…Proposed algorithm consists of three main computational routines: (1) Orthogonal Empirical Mode Decomposition employed for the orthogonal fringe set separation, (2) ASR-EFEMD [79,80] enriched by the Mutual Information Detrending procedure applied for further single-family pattern fast and adaptive filtering (bias term and noise removal) and (3) the Hilbert spiral transform for enhanced fringe phase demodulation. HS is used under the assumption of uniform fringe direction which is ensured in the crossed fringe pattern encountered in grating (moiré) interferometry or Talbot interferometry.…”

“…where M and N are image dimensions and a is a parameter controlling the orthogonal decomposition (influence of the parameter a was studied in [60] showing that too small value produces noisy fringe sets and too large value distorts fringe shape); 3. calculating the lower and upper envelopes using order-statistic and smoothing filters with previously designed masks (besides the mask dimension modification the decomposition is performed like in the FABEMD method [57,58,79,80]); 4. calculating the mean envelope as an arithmetic mean of the upper and lower envelopes; 5. subtracting the mean envelope from the initial cross interferogram to realize single fringe family extraction (only one iteration is required for single fringe family separation; the extracted fringe set orientation is perpendicular to the one dimensional filter array direction; in case of noisy interferograms additional Matlab's 'motion' filter is employed to directionally smooth the separated fringe set); 6. enhancing single family pattern applying the ASR-EFEMD technique [80] aided by the automatic detrending scheme based on the mutual information calculation [60]; 7. calculating phase distribution utilizing the analytic signal approach with the Hilbert spiral transform quadrature component generation [53,60,67,68,79,80]. Comprehensive studies performed for 0/90 degree fringe sets extraction presented in [60] are valid for 45/135 and therefore will not be repeated in this contribution.…”

Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem

“…In general, the inverse problem has no universal solution. The-state-of-the-art in this area of investigations is reflected in a series of original publications and reviews [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Denoising and extracting background from fringe patterns using midpoint-based bidimensional empirical mode decomposition

“…As the components are data driven (in contrary to the signal representation using arbitrary basis functions), they are referred to as the Intrinsic Mode Functions (IMFs). Comprehensive surveys of the development of EMD applications for fringe pattern processing can be found in [11,[13][14][15]. References [13,14] describe, in detail, powerful methods for the fringe pattern enhancement including background determination and removal (realized within the general processing frame of the fringe pattern normalization prior to its phase demodulation).…”