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...
In many full-field optical metrology techniques, i.e. interferometry, moiré, and structured light, the information about the measurand, e.g. displacement, strain, or 3D shape, is stored in the phase distribution of a recorded two-dimensional intensity pattern—the fringe pattern. Its analysis (phase demodulation) therefore plays a crucial role in the measurement procedure, significantly affecting the total accuracy of the optical system. Phase demodulation methods based on just a single fringe pattern are especially interesting, due to their robustness to environmental disturbances and ability to examine dynamic events. However, the calculated phase map is easily spoiled by errors, which appear mainly because of fringe pattern imperfections, i.e. random noise, parasitic interferences, a nonsinusoidal fringe pattern profile or a non-uniform image background. In this contribution, an advanced variational image decomposition scheme is proposed to reduce these phase demodulation errors. The reported purely phase domain method can be easily adopted to aid virtually any fringe analysis method, including single-frame and multi-frame phase-shifting, possibly enhancing retrieved phase distribution without the need for hardware manipulation. We employed it to improve single-frame Hilbert–Huang transform-based fringe analysis. The remarkable efficiency and versatility of the developed algorithm are verified by processing synthetic and experimental fringe patterns and phase maps. The demonstrated approach compares favorably with the very capable 2D empirical mode decomposition reference method.
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