Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects

Trusiak, Maciej; Styk, Adam; Patorski, Krzysztof

doi:10.1016/j.optlaseng.2018.05.021

Cited by 19 publications

(5 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1) has to be a slowly varying function and generally low-pass banded with respect to the carrier cosine term. It is known as so-called Bedrosian theorem 67 and is fulfilled for relatively low carrier spatial frequencies (slightly-off axis regime) for all pure phase objects and, e.g., in the time-averaged interference microscopy for MEMS vibration testing where amplitude modulation of the interferogram is described by the Bessel function and encodes the information on spatial distribution of the vibration amplitude 68,69 . However, the Bedrosian requirement is clearly not satisfied, e.g., in a very common imaging case of the well-established USAF target with sharp bars and numbers in it.…”

Section: Proposed Numerical Scheme Descriptionmentioning

confidence: 99%

Variational Hilbert Quantitative Phase Imaging

Trusiak

Cywińska

Micó

et al. 2020

Sci Rep

Self Cite

View full text Add to dashboard Cite

Utilizing the refractive index as the endogenous contrast agent to noninvasively study transparent cells is a working principle of emerging quantitative phase imaging (QPI). In this contribution, we propose the Variational Hilbert Quantitative Phase Imaging (VHQPI)-end-to-end purely computational add-on module able to improve performance of a QPI-unit without hardware modifications. The VHQPI, deploying unique merger of tailored variational image decomposition and enhanced Hilbert spiral transform, adaptively provides high quality map of sample-induced phase delay, accepting particularly wide range of input single-shot interferograms (from off-axis to quasi on-axis configurations). It especially promotes high space-bandwidth-product QPI configurations alleviating the spectral overlapping problem. The VHQPI is tailored to deal with cumbersome interference patterns related to detailed locally varying biological objects with possibly high dynamic range of phase and relatively low carrier. In post-processing, the slowly varying phase-term associated with the instrumental optical aberrations is eliminated upon variational analysis to further boost the phase-imaging capabilities. The VHQPI is thoroughly studied employing numerical simulations and successfully validated using static and dynamic cells phase-analysis. It compares favorably with other single-shot phase reconstruction techniques based on the Fourier and Hilbert-Huang transforms, both in terms of visual inspection and quantitative evaluation, potentially opening up new possibilities in QPI. Optical imaging is a central aspect of biological research, biomedical examination, and medical diagnosis. Optical microscope is indispensable in biological and medical research facilitating a "seeing is believing" paradigm 1. Despite its rich history and well-established position, significant efforts are contemporarily put on developing new imaging modalities enabling enhanced resolution, contrast, depth, speed and information content. Among a suite of modern microscopy techniques, quantitative phase imaging (QPI) 2-4 stands out as a vividly blossoming label-free approach. It provides unique means for imaging cells and tissues merging beneficial features identified with microscopy 1 , interferometry and holography 5 , and numerical computations. Using refractive index as the endogenous contrast agent 6,7 QPI numerically converts recorded interference pattern into a nanoscale-precise subcellular-specific map of optical delay introduced by examined transparent specimen 7-9. This non-phototoxic non-destructive imaging technique brings biology and metrology closer as it generates quantitative maps of analyzed live bio-structure (related to cell mass, volume, surface area, and their evolutions in time). Therefore, QPI enables upgrading phase-contrast based 6 visualization of the sample to stain-free non-invasive measurement of sample-induced optical phase delay (related to refractive index and/or thickness variations). Impressive details can be imaged, e.g., via super-resolut...

show abstract

Section: Proposed Numerical Scheme Descriptionmentioning

confidence: 99%

Variational Hilbert Quantitative Phase Imaging

Trusiak

Cywińska

Micó

et al. 2020

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…6, the dynamic microbead profile provided by the single-shot Hilbert-Huang phase microscopy (S2H2PM) is smoother and has a more cone-like structure than the one retrieved using the FT approach [160]. Therefore, as an empirical approach, the developed algorithms based on the HHT are suitable for a wide variety of interference fringes acquired in an environment with noise and inconstant contrast and background, ensuring their applicability to dynamic measurements [161,162].…”

Section: Noise Resistancementioning

confidence: 99%

Development of surface reconstruction algorithms for optical interferometric measurement

2020

Front. Mech. Eng.

View full text Add to dashboard Cite

Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing. A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications, but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy, speed, robustness, and dynamic range, especially in on-line or on-machine conditions. This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements. Principles, configurations, and applications of typical optical interferometers with different capabilities and limitations are presented. Theoretical background and recent advances of fringe analysis algorithms, including coherence peak sensing and phase-shifting algorithm, are summarized. The new developments in measurement accuracy and repeatability, noise resistance, self-calibration ability, and computational efficiency are discussed. This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement. To address these challenges, advanced techniques in image stitching, on-machine measurement, intelligent sampling, parallel computing, and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.

show abstract

“…However, the instruments and methodology reported so far require high stability and are also limited by the experimental set-up [3][4], this problem has been solved with the use of interferometers that provide the stability and measurement range that is not achieved with conventional refractometers and holographic techniques, among them the Jamin, Mach Zehnder and Michelson interferometers [4,[10][11]. Despite the reliability that interferometers provide to the measurement, the problem of a later demodulation of the fringe pattern obtained arises, this pattern shows the changes before and after the deformation to later obtain the optical phase, commonly, by means of techniques based on Fourier Transform [12], Wavelet [13][14][15][16][17][18] and Hilbert [19][20][21][22][23], the problem increases if the interferograms obtained have a circular configuration, their carrier frequency is very low, and they also present several reflections caused by the arrangement of the instruments and the analysed material, requiring more computational work and the implementation of new spectral and temporal analysis techniques [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Hilbert transform for modulation of interference fringes of liquid substances

López-Álvarez

2023

JMQM

View full text Add to dashboard Cite

The demodulation of interferometric signals presents a challenge in the study of object, especially when working in environments with disturbances, instability or noise. This document presents a procedure to demodulate a pair of highly noisy interferograms obtained with a fiber optic Mach Zehnder interferometer, the procedure is based on using the reconfiguration of the interference fringes as a result of Hilbert Transform. The method shown is fast, it does not present susceptibilities at high frequencies, it avoids demodulating interference patterns of closed fringes and with little carrier signal, in addition, it allows to verify the mathematical equivalence of the spectral analysis using Fourier Transform. As an application model, samples of liquid substances were used, where it was possible to know changes between substances according to their density

show abstract

Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects

Cited by 19 publications

References 45 publications

Variational Hilbert Quantitative Phase Imaging

Variational Hilbert Quantitative Phase Imaging

Development of surface reconstruction algorithms for optical interferometric measurement

Hilbert transform for modulation of interference fringes of liquid substances

Contact Info

Product

Resources

About