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.
The multi-frequency temporal phase unwrapping (MF-TPU) method, as a classical phase unwrapping algorithm for fringe projection techniques, has the ability to eliminate the phase ambiguities even while measuring spatially isolated scenes or the objects with discontinuous surfaces. For the simplest and most efficient case in MF-TPU, two groups of phase-shifting fringe patterns with different frequencies are used: the high-frequency one is applied for 3D reconstruction of the tested object and the unit-frequency one is used to assist phase unwrapping for the wrapped phase with high frequency. The final measurement precision or sensitivity is determined by the number of fringes used within the high-frequency pattern, under the precondition that its absolute phase can be successfully recovered without any fringe order errors. However, due to the non-negligible noises and other error sources in actual measurement, the frequency of the high-frequency fringes is generally restricted to about 16, resulting in limited measurement accuracy. On the other hand, using additional intermediate sets of fringe patterns can unwrap the phase with higher frequency, but at the expense of a prolonged pattern sequence. With recent developments and advancements of machine learning for computer vision and computational imaging, it can be demonstrated in this work that deep learning techniques can automatically realize TPU through supervised learning, as called deep learning-based temporal phase unwrapping (DL-TPU), which can substantially improve the unwrapping reliability compared with MF-TPU even under different types of error sources, e.g., intensity noise, low fringe modulation, projector nonlinearity, and motion artifacts. Furthermore, as far as we know, our method was demonstrated experimentally that the high-frequency phase with 64 periods can be directly and reliably unwrapped from one unit-frequency phase using DL-TPU. These results highlight that challenging issues in optical metrology can be potentially overcome through machine learning, opening new avenues to design powerful and extremely accurate high-speed 3D imaging systems ubiquitous in nowadays science, industry, and multimedia.
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.
Off-axis holographic multiplexing involves capturing several complex wavefronts, each encoded into off-axis holograms with different interference fringe orientations, simultaneously, with a single camera acquisition. Thus, the multiplexed off-axis hologram can capture several wavefronts at once, where each one encodes different information from the sample, using the same number of pixels typically required for acquiring a single conventional off-axis hologram encoding only one sample wavefront. This gives rise to many possible applications, with focus on acquisition of dynamic samples, with hundreds of scientific papers already published in the last decade. These include field-of-view multiplexing, depth-of-field multiplexing, angular perspective multiplexing for tomographic phase microscopy for 3-D refractive index imaging, multiple wavelength multiplexing for multiwavelength phase unwrapping or for spectroscopy, performing super-resolution holographic imaging with synthetic aperture with simultaneous acquisition, holographic imaging of ultrafast events by encoding different temporal events into the parallel channels using laser pulses, measuring the Jones matrix and the birefringence of the sample from a single multiplexed hologram, and measuring several fluorescent microscopy channels and quantitative phase profiles together, among others. Each of the multiplexing techniques opens new perspectives for applying holography to efficiently measure challenging biological and metrological samples. Furthermore, even if the multiplexing is done digitally, off-axis holographic multiplexing is useful for rapid processing of the wavefront, for holographic compression, and for visualization purposes. Although each of these applications typically requires a different optical system or processing, they all share the same theoretical background. We therefore review the theory, various optical systems, applications, and perspectives of the field of off-axis holographic multiplexing, with the goal of stimulating its further development.
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