High space-time bandwidth product imaging in low coherence quantitative phase microscopy.

Current low coherence quantitative phase microscopy (LC-QPM) systems suffer from either reduced field of view (FoV) or reduced temporal resolution due to the short temporal coherence (TC) length of the light source. Here, we propose a hybrid, experimental and numerical approach to address this core problem associated with LC-QPM. We demonstrate high spatial resolution and high phase sensitivity in LC-QPM at high temporal resolution. High space-time bandwidth product is achieved by employing incoherent light source for sample illumination in QPM to increase the spatial resolution and single-shot Hilbert spiral transform (HST) based phase recovery algorithm to enhance the temporal resolution without sacrificing spatial resolution during the reconstruction steps. The high spatial phase sensitivity comes by default due to the use of incoherent light source in QPM which has low temporal coherence length and does not generate speckle noise and coherent noise. The spatial resolution achieved by the HST is slightly inferior to the temporal phase-shifting (TPS) method when tested on a specimen but surpasses that of the single-shot Fourier transform (FT) based phase recovery method. Contrary to HST method, FT method requires high density fringes for lossless phase recovery, which is difficult to achieve in LC-QPM over entire FoV. Consequently, integration of HST algorithm with LC-QPM system makes an attractive route. Here, we demonstrate scalable FoV and resolution in single-shot LC-QPM and experimentally corroborate it on a test object and on both live and fixed biological specimen such as MEF, U2OS and human red blood cells (RBCs). LC-QPM system with HST reconstruction offer high-speed single-shot QPM imaging at high phase sensitivity and high spatial resolution enabling us to study sub-cellular dynamic inside U2OS for extended duration (3 h) and observe high-speed (50 fps) dynamics of human RBCs. The experimental results validate the effectiveness of the present approach and will open new avenues in the domain of biomedical imaging in the future.

Physics-driven universal twin-image removal network for digital in-line holographic microscopy.

Digital in-line holographic microscopy (DIHM) enables efficient and cost-effective computational quantitative phase imaging with a large field of view, making it valuable for studying cell motility, migration, and bio-microfluidics. However, the quality of DIHM reconstructions is compromised by twin-image noise, posing a significant challenge. Conventional methods for mitigating this noise involve complex hardware setups or time-consuming algorithms with often limited effectiveness. In this work, we propose UTIRnet, a deep learning solution for fast, robust, and universally applicable twin-image suppression, trained exclusively on numerically generated datasets. The availability of open-source UTIRnet codes facilitates its implementation in various DIHM systems without the need for extensive experimental training data. Notably, our network ensures the consistency of reconstruction results with input holograms, imparting a physics-based foundation and enhancing reliability compared to conventional deep learning approaches. Experimental verification was conducted among others on live neural glial cell culture migration sensing, which is crucial for neurodegenerative disease research.

Single-shot wavelength-multiplexed phase microscopy under Gabor regime in a regular microscope embodiment.

Phase imaging microscopy under Gabor regime has been recently reported as an extremely simple, low cost and compact way to update a standard bright-field microscope with coherent sensing capabilities. By inserting coherent illumination in the microscope embodiment and producing a small defocus distance of the sample at the input plane, the digital sensor records an in-line Gabor hologram of the target sample, which is then numerically post-processed to finally achieve the sample's quantitative phase information. However, the retrieved phase distribution is affected by the two well-known drawbacks when dealing with Gabor's regime, that is, coherent noise and twin image disturbances. Here, we present a single-shot technique based on wavelength multiplexing for mitigating these two effects. A multi-illumination laser source (including 3 diode lasers) illuminates the sample and a color digital sensor (conventional RGB color camera) is used to record the wavelength-multiplexed Gabor hologram in a single exposure. The technique is completed by presenting a novel algorithm based on a modified Gerchberg-Saxton kernel to finally retrieve an enhanced quantitative phase image of the sample, enhanced in terms of coherent noise removal and twin image minimization. Experimental validations are performed in a regular Olympus BX-60 upright microscope using a 20X 0.46NA objective lens and considering static (resolution test targets) and dynamic (living spermatozoa) phase samples.

Experimental optimization of lensless digital holographic microscopy with rotating diffuser-based coherent noise reduction.

Laser-based lensless digital holographic microscopy (LDHM) is often spoiled by considerable coherent noise factor. We propose a novel LDHM method with significantly limited coherent artifacts, e.g., speckle noise and parasitic interference fringes. It is achieved by incorporating a rotating diffuser, which introduces partial spatial coherence and preserves high temporal coherence of laser light, crucial for credible in-line hologram reconstruction. We present the first implementation of the classical rotating diffuser concept in LDHM, significantly increasing the signal-to-noise ratio while preserving the straightforwardness and compactness of the LDHM imaging device. Prior to the introduction of the rotating diffusor, we performed LDHM experimental hardware optimization employing 4 light sources, 4 cameras, and 3 different optical magnifications (camera-sample distances). It was guided by the quantitative assessment of numerical amplitude/phase reconstruction of test targets, conducted upon standard deviation calculation (noise factor quantification), and resolution evaluation (information throughput quantification). Optimized rotating diffuser LDHM (RD-LDHM) method was successfully corroborated in technical test target imaging and examination of challenging biomedical sample (60 µm thick mouse brain tissue slice). Physical minimization of coherent noise (up to 50%) was positively verified, while preserving optimal spatial resolution of phase and amplitude imaging. Coherent noise removal, ensured by proposed RD-LDHM method, is especially important in biomedical inference, as speckles can falsely imitate valid biological features. Combining this favorable outcome with large field-of-view imaging can promote the use of reported RD-LDHM technique in high-throughput stain-free biomedical screening.

DeepOrientation: convolutional neural network for fringe pattern orientation map estimation.

Fringe pattern based measurement techniques are the state-of-the-art in full-field optical metrology. They are crucial both in macroscale, e.g., fringe projection profilometry, and microscale, e.g., label-free quantitative phase microscopy. Accurate estimation of the local fringe orientation map can significantly facilitate the measurement process in various ways, e.g., fringe filtering (denoising), fringe pattern boundary padding, fringe skeletoning (contouring/following/tracking), local fringe spatial frequency (fringe period) estimation, and fringe pattern phase demodulation. Considering all of that, the accurate, robust, and preferably automatic estimation of local fringe orientation map is of high importance. In this paper we propose a novel numerical solution for local fringe orientation map estimation based on convolutional neural network and deep learning called DeepOrientation. Numerical simulations and experimental results corroborate the effectiveness of the proposed DeepOrientation comparing it with a representative of the classical approach to orientation estimation called combined plane fitting/gradient method. The example proving the effectiveness of DeepOrientation in fringe pattern analysis, which we present in this paper, is the application of DeepOrientation for guiding the phase demodulation process in Hilbert spiral transform. In particular, living HeLa cells quantitative phase imaging outcomes verify the method as an important asset in label-free microscopy.

Numerical analysis of the effect of reduced temporal coherence in quantitative phase microscopy and tomography.

We present the numerical analysis of the effect of the temporarily partially coherent illumination on the phase measurement accuracy in digital holography microscopy (DHM) and optical diffraction tomography (ODT), as reconstruction algorithms tend to assume purely monochromatic conditions. In the regime of reduced temporal coherence, we simulate the hologram formation in two different optical setups, representing classical off-axis two-beam and grating common-path configurations. We consider two ODT variants: with sample rotation and angle-scanning of illumination. Besides the coherence degree of illumination, our simulation considers the influence of the sample normal dispersion, shape of the light spectrum, and optical parameters of the imaging setup. As reconstruction algorithms we employ Fourier hologram method and first-order Rytov approximation with direct inversion and nonnegativity constraints. Quantitative evaluation of the measurement results deviations introduced by the mentioned error sources is comprehensively analyzed, for the first time to the best of our knowledge. Obtained outcomes indicate low final DHM/ODT reconstruction errors for the grating-assisted common-path configuration. Nevertheless, dispersion and asymmetric spectrum introduce non-negligible overestimated refractive index values and noise, and should be thus carefully considered within experimental frameworks.

Accurate automatic object 4D tracking in digital in-line holographic microscopy based on computationally rendered dark fields.

Building on Gabor seminal principle, digital in-line holographic microscopy provides efficient means for space-time investigations of large volumes of interest. Thus, it has a pivotal impact on particle tracking that is crucial in advancing various branches of science and technology, e.g., microfluidics and biophysical processes examination (cell motility, migration, interplay etc.). Well-established algorithms often rely on heavily regularized inverse problem modelling and encounter limitations in terms of tracking accuracy, hologram signal-to-noise ratio, accessible object volume, particle concentration and computational burden. This work demonstrates the DarkTrack algorithm-a new approach to versatile, fast, precise, and robust 4D holographic tracking based on deterministic computationally rendered high-contrast dark fields. Its unique capabilities are quantitatively corroborated employing a novel numerical engine for simulating Gabor holographic recording of time-variant volumes filled with predefined dynamic particles. Our solution accounts for multiple scattering and thus it is poised to secure an important gap in holographic particle tracking technology and allow for ground-truth-driven benchmarking and quantitative assessment of tracking algorithms. Proof-of-concept experimental evaluation of DarkTrack is presented via analyzing live spermatozoa. Software supporting both novel numerical holographic engine and DarkTrack algorithm is made open access, which opens new possibilities and sets the stage for democratization of robust holographic 4D particle examination.

Hilbert phase microscopy based on pseudo thermal illumination in the Linnik configuration.

Quantitative phase microscopy (QPM) is often based on recording an object-reference interference pattern and its further phase demodulation. We propose pseudo Hilbert phase microscopy (PHPM) where we combine pseudo thermal light source illumination and Hilbert spiral transform (HST) phase demodulation to achieve hybrid hardware-software-driven noise robustness and an increase in resolution of single-shot coherent QPM. Those advantageous features stem from physically altering the laser spatial coherence and numerically restoring spectrally overlapped object spatial frequencies. The capabilities of PHPM are demonstrated by analyzing calibrated phase targets and live HeLa cells in comparison with laser illumination and phase demodulation via temporal phase shifting (TPS) and Fourier transform (FT) techniques. The performed studies verified the unique ability of PHPM to combine single-shot imaging, noise minimization, and preservation of phase details.

Low-intensity illumination for lensless digital holographic microscopy with minimized sample interaction.

Exposure to laser light alters cell culture examination via optical microscopic imaging techniques based on label-free coherent digital holography. To mitigate this detrimental feature, researchers tend to use a broader spectrum and lower intensity of illumination, which can decrease the quality of holographic imaging due to lower resolution and higher noise. We study the lensless digital holographic microscopy (LDHM) ability to operate in the low photon budget (LPB) regime to enable imaging of unimpaired live cells with minimized sample interaction. Low-cost off-the-shelf components are used, promoting the usability of such a straightforward approach. We show that recording data in the LPB regime (down to 7 µW of illumination power) does not limit the contrast or resolution of the hologram phase and amplitude reconstruction compared to regular illumination. The LPB generates hardware camera shot noise, however, to be effectively minimized via numerical denoising. The ability to obtain high-quality, high-resolution optical complex field reconstruction was confirmed using the USAF 1951 amplitude sample, phase resolution test target, and finally, live glial restricted progenitor cells (as a challenging strongly absorbing and scattering biomedical sample). The proposed approach based on severely limiting the photon budget in lensless holographic microscopy method can open new avenues in high-throughout (optimal resolution, large field-of-view, and high signal-to-noise-ratio single-hologram reconstruction) cell culture imaging with minimized sample interaction.

Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy.

We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by applying the golden selection search with parabolic interpolation, which is the gold standard for tackling single-variable optimization problems. The proposed approach is successfully applied to three diverse autofocusing cases, providing up to 136-fold speed-up.

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform.

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD - we have considerably increased algorithm's application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data.

Common-path intrinsically achromatic optical diffraction tomography.

In this work we propose an open-top like common-path intrinsically achromatic optical diffraction tomography system. It operates as a total-shear interferometer and employs Ronchi-type amplitude diffraction grating, positioned in between the camera and the tube lens without an additional 4f system, generating three-beam interferograms with achromatic second harmonic. Such configuration makes the proposed system low cost, compact and immune to vibrations. We present the results of the measurements of 3D-printed cell phantom using laser diode (coherent) and superluminescent diode (partially coherent) light sources. Broadband light sources can be naturally employed without the need for any cumbersome compensation because of the intrinsic achromaticity of the interferometric recording (holograms generated by -1st and +1st conjugated diffraction orders are not affected by the illumination wavelength). The results show that the decreased coherence offers much reduced coherent noise and higher fidelity tomographic reconstruction especially when applied nonnegativity constraint regularization procedure.

Fringe analysis: single-shot or two-frames? Quantitative phase imaging answers.

Conditions of the digital recording of the fringe pattern determine the phase reconstruction procedure, which in turn directly shapes the final accuracy and throughput of the full-field (non-scanning) optical measurement technique and defines the system capabilities. In this way, the fringe pattern analysis plays a crucial role in the ubiquitous optical measurements and thus is under constant development focused on high temporal/spatial resolution. It is especially valuable in the quantitative phase imaging technology, which emerged in the high-contrast label-free biomedical microscopy. In this paper, I apply recently blossomed two-frame phase-shifting techniques to the QPI and merge them with advanced adaptive interferogram pre-filtering algorithms. Next, I comprehensively test such frameworks against classical and adaptive single-shot methods applied for phase reconstruction in dynamic QPI enabling highest phase time-space-bandwidth product. The presented study systematically tackles important question: what is the gain, if any, in QPI realized by recording two phase-shifted interferograms? Counterintuitively, the results show that single-shot demodulation exhibited higher phase reconstruction accuracy than two-frame phase-shifting methods in low and medium interferogram signal-to-noise ratio regimes. Thus, the single-shot approach is promoted due to not only high temporal resolution but also larger phase-information throughput. Additionally, in the majority of scenarios, the best option is to shift the paradigm and employ two-frame pre-filtering rather than two-frame phase retrieval. Experimental fringe analysis in QPI of LSEC/RWPE cell lines successfully corroborated all novel numerical findings. Hence, the presented numerical-experimental research advances the important field of fringe analysis solutions for optical full-field measurement methods with widespread bio-engineering applications.

FPM app: an open-source MATLAB application for simple and intuitive Fourier ptychographic reconstruction.

SUMMARY: Fourier ptychographic microscopy (FPM) is a computational microscopy technique that enables large field of view and high-resolution microscopic imaging of biological samples. However, the FPM does not yet have an adequately capable open-source software. In order to fill this gap we are presenting novel, simple, universal, semi-automatic and highly intuitive graphical user interface (GUI) open-source application called the FPM app enabling wide-scale robust FPM reconstruction. Apart from implementing the FPM in accessible GUI app, we also made several improvements in the FPM image reconstruction process itself, making the FPM more automatic, noise-robust and faster. AVAILABILITY AND IMPLEMENTATION: FPM app was implemented in MATLAB and all MATLAB codes along with standalone executable version of the FPM app and the online documentation are freely accessible at https://github.com/MRogalski96/FPM-app. Our exemplary FPM datasets may be downloaded at https://bit.ly/2MxNpGb. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Author Correction: Variational Hilbert Quantitative Phase Imaging.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Variational Hilbert Quantitative Phase Imaging.

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.

Automatic fringe pattern enhancement using truly adaptive period-guided bidimensional empirical mode decomposition.

Fringe patterns encode the information about the result of a measurement performed via widely used optical full-field testing methods, e.g., interferometry, digital holographic microscopy, moiré techniques, structured illumination etc. Affected by the optical setup, changing environment and the sample itself fringe patterns are often corrupted with substantial noise, strong and uneven background illumination and exhibit low contrast. Fringe pattern enhancement, i.e., noise minimization and background term removal, at the pre-processing stage prior to the phase map calculation (for the measurement result decoding) is therefore essential to minimize the jeopardizing effect the mentioned error sources have on the optical measurement outcome. In this contribution we propose an automatic, robust and highly effective fringe pattern enhancement method based on the novel period-guided bidimensional empirical mode decomposition algorithm (PG-BEMD). The spatial distribution of the fringe period is estimated using the novel windowed approach and then serves as an indicator for the truly adaptive decomposition with the filter size locally adjusted to the fringe pattern density. In this way the fringe term is successfully extracted in a single (first) decomposition component alleviating the cumbersome mode mixing phenomenon and greatly simplifying the automatic signal reconstruction. Hence, the fringe term is dissected without the need for modes selection nor summation. The noise removal robustness is ensured employing the block matching 3D filtering of the fringe pattern prior to its decomposition. Performance validation against previously reported modified empirical mode decomposition techniques is provided using numerical simulations and experimental data verifying the versatility and effectiveness of the proposed approach.

Grating deployed total-shear 3-beam interference microscopy with reduced temporal coherence.

Interference microscopy is a powerful optical imaging technique providing quantitative phase distribution information to characterize various type technical and biomedical objects. Static and dynamic objects and processes can be investigated. In this paper we propose very compact, common-path and partially coherent diffraction grating-based interference microscopy system for studying small objects like single cells with low densities being sparsely distributed in the field of view. Simple binary amplitude diffraction grating is the only additional element to be introduced into a conventional microscope optical system. By placing it at a proper distance in front of the microscope image plane the total-shear operation mode is deployed resulting in interferograms of the object-reference beam type. Depending on the grating to image plane separation distance two or three-beam interferograms are generated. The latter ones are advantageous since they contain achromatic second harmonics in the interferogram intensity distributions. This feature enables to use reduced temporal coherence light sources for the microscope to reduce coherent noise and parasitic interference patterns. For this purpose we employ the laser diode with driving current below the threshold one. Results of conducted experiments including automatic computer processing of interferograms fully corroborate analytical description of the proposed method and illustrate its capabilities for studying static and dynamic phase objects.

Full-field vibration profilometry using time-averaged interference microscopy aided by variational analysis.

Full-field vibration testing is indispensable in characterization of micro-electro-mechanical components. Time-averaged interference (TAI) microscopy is a very capable and accurate vibration profilometry technique. It employs natural all-optical multiplexing of required information, i.e., recorded interferogram is amplitude-modulated by the Bessel pattern, which in turn encodes spatial distribution of vibration amplitude in its underlying phase function. We propose a complete end-to-end numerical scheme for efficient and robust vibration amplitude map demodulation based on the variational data-analysis paradigm. First, interferogram is variationally pre-filtered and complex analytic-interferogram is generated, exploiting the Hilbert spiral transform. The amplitude term of analytic-interferogram is accessed for Besselogram, i.e., TAI amplitude modulation distribution. Next, the Besselogram is variationally pre-filtered and complex analytic-Besselogram is calculated applying the Hilbert spiral transform. Finally, the phase term of the analytic-Besselogram is determined, unwrapped and post-filtered to achieve spatial distribution of vibration amplitude. Proposed approach is verified using simulated interferograms and corroborated upon experimental vibration testing. Reported method compares favorably with the reference Hilbert-Huang transform-based method. The improvement was gained by adding two new steps to the calculation path: (1) additional removal of the interferogram's residual background and noise and (2) variational based vibration amplitude map error correction method.

Numerically Enhanced Stimulated Emission Depletion Microscopy with Adaptive Optics for Deep-Tissue Super-Resolved Imaging.

In stimulated emission depletion (STED) nanoscopy, the major origin of decreased signal-to-noise ratio within images can be attributed to sample photobleaching and strong optical aberrations. This is due to STED utilizing a high-power depletion laser (increasing the risk of photodamage), while the depletion beam is very sensitive to sample-induced aberrations. Here, we demonstrate a custom-built STED microscope with automated aberration correction that is capable of 3D super-resolution imaging through thick, highly aberrating tissue. We introduce and investigate a state of the art image denoising method by block-matching and collaborative 3D filtering (BM3D) to numerically enhance fine object details otherwise mixed with noise and further enhance the image quality. Numerical denoising provides an increase in the final effective resolution of the STED imaging of 31% using the well established Fourier ring correlation metric. Results achieved through the combination of aberration correction and tailored image processing are experimentally validated through super-resolved 3D imaging of axons in differentiated induced pluripotent stem cells growing under an 80 µm thick layer of tissue with lateral and axial resolution of 204 and 310 nm, respectively.