Hilbert-Huang processing for single-exposure two-dimensional grating interferometry

Abstract

Single-shot crossed-type fringe pattern processing and analysis method called Hilbert-Huang grating interferometry (HHGI) is proposed. It consist of three main procedures: (1) crossed pattern is resolved into two fringe families using novel orthogonal empirical mode decomposition approach, (2) separated fringe sets are filtered using modified automatic selective reconstruction aided by enhanced fast empirical mode decomposition and mutual information detrending, and (3) Hilbert spiral transform is employed for fringe phase demodulation. Numerical and experimental studies corroborate the validity, versatility and robustness of the proposed HHGI technique. It can be successfully applied to multiplicative and additive type crossed patterns with sinusoidal and binary orthogonal component structures. Efficient adaptive filtering enables successful fast processing and analysis of complex and defected patterns.

Hilbert-Huang processing and analysis of complex fringe patterns

“…(4). Numerical studies presented in [60] corroborate the validity, robustness and versatility of the proposed HHP scheme. It can be successfully applied to crossed patterns obtained using both multiplicative and additive type superimpositions of binary and cosinusoidal unidirectional component structures.…”

“…To sensitize the decomposition to the direction of component structures (maintaining the ability to decouple various spatial frequency components), e.g., to obtain horizontal and vertical components in consecutive BIMFs, the OEMD algorithm (Orthogonal Empirical Mode Decomposition) was proposed in [60]. It employs similar filtering scheme as the EFEMD method but with rectangular (or disk/shaped) isotropic filter mask replaced by a single direction array.…”

“…Fringe families extraction, enhancement and phase demodulation in case of the crossed fringe pattern analysis can be very efficiently performed employing the Hilbert-Huang processing scheme [60]. 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.…”

“…HHP is fast, adaptive, automatic, local and enables successful analysis of complex low quality fringes due to very efficient filtering provided by the modified ASR-EFEMD technique. Although the HHP algorithm was originally applied for 0/90 degrees fringe set separation (horizontal and vertical families) [60] it can be readily adjusted to serve the 45/135 degrees fringe set extraction.…”

“…Simply one needs to design order-statistic and averaging filters for the OEMD sifting process [60] to work in diagonal directions. Employed Hilbert-Huang based processing path can be summarized in the following steps: 1. obtaining the orientation angle for both fringe sets (a priori knowledge is needed); 2. detecting the fringe pattern extrema, estimating the filter window width w using formula , MN w a n =…”