Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging

Iterative outlier detection and refinement rule of compensation for phase aberrations in digital holographic microscopy

We propose a robust and accurate compensation method for phase aberrations based on the iterative outlier detection and refinement (ODR) rule. This method does not require additional steps to select the known flat region manually or by image segmentation. Based on the proposed method, the phase aberration in regions of a specimen can be detected and refined iteratively. Then, the least squares fitting can be carried out to estimate the coefficients of Zernike polynomials and obtain the accurate phase aberration finally. Computer simulations and real experiments validate the feasibility and effectiveness, and the results show that the proposed method is robust to noise and has superior accuracy even when the specimen occupies half of the field of view.

Off-axis digital lensless holographic microscopy based on spatially multiplexed interferometry

Significance

Digital holographic microscopy (DHM) is a label-free microscopy technique that provides time-resolved quantitative phase imaging (QPI) by measuring the optical path delay of light induced by transparent biological samples. DHM has been utilized for various biomedical applications, such as cancer research and sperm cell assessment, as well as for in vitro drug or toxicity testing. Its lensless version, digital lensless holographic microscopy (DLHM), is an emerging technology that offers size-reduced, lightweight, and cost-effective imaging systems. These features make DLHM applicable, for example, in limited resource laboratories, remote areas, and point-of-care applications.

Aim

In addition to the abovementioned advantages, in-line arrangements for DLHM also include the limitation of the twin-image presence, which can restrict accurate QPI. We therefore propose a compact lensless common-path interferometric off-axis approach that is capable of quantitative imaging of fast-moving biological specimens, such as living cells in flow.

Approach

We suggest lensless spatially multiplexed interferometric microscopy (LESSMIM) as a lens-free variant of the previously reported spatially multiplexed interferometric microscopy (SMIM) concept. LESSMIM comprises a common-path interferometric architecture that is based on a single diffraction grating to achieve digital off-axis holography. From a series of single-shot off-axis holograms, twin-image free and time-resolved QPI is achieved by commonly used methods for Fourier filtering-based reconstruction, aberration compensation, and numerical propagation.

Results

Initially, the LESSMIM concept is experimentally demonstrated by results from a resolution test chart and investigations on temporal stability. Then, the accuracy of QPI and capabilities for imaging of living adherent cell cultures is characterized. Finally, utilizing a microfluidic channel, the cytometry of suspended cells in flow is evaluated.

Conclusions

LESSMIM overcomes several limitations of in-line DLHM and provides fast time-resolved QPI in a compact optical arrangement. In summary, LESSMIM represents a promising technique with potential biomedical applications for fast imaging such as in imaging flow cytometry or sperm cell analysis.

Improvement of digital Gabor holographic microscopy using a lens in plankton studies

This work utilizes a Gabor Holographic Optical Scheme integrated with a microscope objective and a thin convex plane lens. This bi-telecentric lens system corrects spherical aberration from the objective, maintains consistent magnification across various reconstruction distances, and ensures a plane incidence on CMOS. Depending on the focal lengths of the objective and lens, the final image can be enlarged or reduced compared to the classic Gabor system, resulting in high-quality reconstructed phase images without spherical aberration. This setup was employed to capture phase distribution and intensity images of planktonic objects, such as copepods, achieving superior image quality.

Snapshot dual-wavelength digital holography with LED and laser hybrid illumination

To address the problem of the time-sharing recording of dual-wavelength low-coherence holograms while avoiding the use of customized achromatic optical elements, a snapshot dual-wavelength digital holography with LED and laser hybrid illumination is proposed. In this method, the parallel phase-shifting method is firstly employed to suppress zero-order and twin-image noise, and to record a LED hologram with low speckle noise and full field of view. Secondly, another laser hologram with a different center wavelength affected by speckle noise is recorded simultaneously using the spatial multiplexing technique. Finally, dual-wavelength wrapped phase images are reconstructed from a spatial multiplexing hologram, and then are combined to achieve low-noise phase unwrapping utilizing the iterative algorithm. Simulation and optical experiments on a reflective step with a depth of 1.38µm demonstrate that the proposed method can achieve single-shot and large-range height measurements while maintaining low-noise and full-field imaging.

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource ( https://github.com/kqwang/phase-recovery ) for readers to learn more about PR.

Automatic aberration compensation for digital holographic microscopy based on bicubic downsampling and improved minimization of global phase gradients

In digital holographic microscopy, aberrations caused by imperfect optical system settings can greatly affect the quantitative measurement of the target phase, so the compensation of aberrations in the distorted phase has become a key point of research in digital holographic microscopy. Here, we propose a fully automatic numerical phase aberration compensation method with fast computational speed and high robustness. The method uses bicubic downsampling to smooth the sample phase for reducing its disturbance to the background aberration fit, while reducing the computational effort of aberration compensation. Polynomial coefficients of the aberration fitting are iteratively optimized in the process of minimizing the global phase gradient by improving the phase gradient operator and constructing the loss function to achieve accurate fitting of the phase aberration. Simulation and experimental results show that the proposed method can achieve high aberration compensation accuracy without prior knowledge of the hologram recording settings or manual selection of the background area free of samples, and it is suitable for samples with moderate and relatively flat background area, which can be widely used in the quantitative analysis of biological tissues and micro and nano structures.

Comprehensive tool for a phase compensation reconstruction method in digital holographic microscopy operating in non-telecentric regime

Quantitative phase imaging (QPI) via Digital Holographic microscopy (DHM) has been widely applied in material and biological applications. The performance of DHM technologies relies heavily on computational reconstruction methods to provide accurate phase measurements. Among the optical configuration of the imaging system in DHM, imaging systems operating in a non-telecentric regime are the most common ones. Nonetheless, the spherical wavefront introduced by the non-telecentric DHM system must be compensated to provide undistorted phase measurements. The proposed reconstruction approach is based on previous work from Kemper's group. Here, we have reformulated the problem, reducing the number of required parameters needed for reconstructing phase images to the sensor pixel size and source wavelength. The developed computational algorithm can be divided into six main steps. In the first step, the selection of the +1-diffraction order in the hologram spectrum. The interference angle is obtained from the selected +1 order. Secondly, the curvature of the spherical wavefront distorting the sample's phase map is estimated by analyzing the size of the selected +1 order in the hologram's spectrum. The third and fourth steps are the spatial filtering of the +1 order and the compensation of the interference angle. The next step involves the estimation of the center of the spherical wavefront. An optional final optimization step has been included to fine-tune the estimated parameters and provide fully compensated phase images. Because the proper implementation of a framework is critical to achieve successful results, we have explicitly described the steps, including functions and toolboxes, required for reconstructing phase images without distortions. As a result, we have provided open-access codes and a user interface tool with minimum user input to reconstruct holograms recorded in a non-telecentric DHM system.

Phase compensation algorithm based on image segmentation in dual-wavelength holographic microscopy

In order to solve the problem of phase compensation errors in the traditional 2π phase compensation method caused by a rough surface and complex structure of objects in dual-wavelength digital holographic microscopy, a phase compensation algorithm based on image segmentation was proposed. First, the phase less than zero in the phase obtained by an equivalent wavelength is compensated for by adding 2π initially. Then the phase after the initial compensation is binarized, and the small connected areas in the binarized graph are removed, so as to obtain a new binarized graph. Finally, according to the two binarized graphs, the phase of the object after the initial 2π phase compensation is recompensated for in different regions, so as to obtain the continuous phase distribution of the object. Based on the dual-wavelength digital holographic microscopy experimental system with an adjustable equivalent wavelength, the proposed algorithm is used to perform three-dimensional imaging of the channel of the microfluidic chip. The experimental results show that the proposed method can effectively obtain the continuous real phase of the object when the structure of the object is known, so as to obtain a more accurate and reliable three-dimensional topography of the object. The above results provide a new idea for the high-quality three-dimensional imaging of the microfluidic system.

Phase aberration adaptive compensation in digital holography based on phase imitation and metric optimization

We proposed a numerical and accurate quadratic phase aberration compensation method in digital holography. A phase imitation method based on Gaussian 1σ-criterion is used to obtain the morphological features of the object phase using partial differential, filtering and integration successively. We also propose an adaptive compensation method based on a maximum-minimum-average- α-standard deviation (MMAαSD) evaluation metric to obtain optimal compensated coefficients by minimizing the above metric of the compensation function. The effectiveness and robustness of our method are demonstrated by simulation and experiments.

Automatic elimination of phase aberrations in digital holography based on Gaussian 1σ- criterion and histogram segmentation

We propose a numerical and automatic quadratic phase aberration elimination method in digital holography for phase-contrast imaging. A histogram segmentation method based on Gaussian 1σ-criterion is used to obtain the accurate coefficients of quadratic aberrations using the weighted least-squares algorithm. This method needs no manual intervention for specimen-free zone or prior parameters of optical components. We also propose a maximum-minimum-average-standard deviation (MMASD) metric to quantitatively evaluate the effectiveness of quadratic aberration elimination. Simulation and experimental results are demonstrated to verify the efficacy of our proposed method over the traditional least-squares algorithm.

Phase aberration separation for holographic microscopy by alternating direction sparse optimization

The morphology and dynamics of label-free tissues can be exploited by sample-induced changes in the optical field from quantitative phase imaging. Its sensitivity to subtle changes in the optical field makes the reconstructed phase susceptible to phase aberrations. We import variable sparse splitting framework on quantitative phase aberration extraction based on alternating direction aberration free method. The optimization and regularization in the reconstructed phase are decomposed into object terms and aberration terms. By formulating the aberration extraction as a convex quadratic problem, the background phase aberration can be fast and directly decomposed with the specific complete basis functions such as Zernike or standard polynomials. Faithful phase reconstruction can be obtained by eliminating global background phase aberration. The aberration-free two-dimensional and three-dimensional imaging experiments are demonstrated, showing the relaxation of the strict alignment requirements for the holographic microscopes.

Expanded field of view frequency-selective incoherent holography by using a triple-beam setup

We propose a new, to the best of our knowledge, method of incoherent optical frequency selection called three-pack frequency-selective incoherent holography. Compressed holography is reconstructed using phase shift intercepts and spatial transfer function convolution in the form of separation without loss of magnification or resolution. The frequency-selective reconstruction process removes the conjugate and DC terms along with the interception of the object wave. This work attempts three-dimensional reconstruction and selected-frequency phase extraction of axial slices in submicron steps, and the experimental results show the potential of the proposed method in areas such as compressed holography, extended field of view, and slice tomography.

pyDHM: A Python library for applications in digital holographic microscopy

pyDHM is an open-source Python library aimed at Digital Holographic Microscopy (DHM) applications. The pyDHM is a user-friendly library written in the robust programming language of Python that provides a set of numerical processing algorithms for reconstructing amplitude and phase images for a broad range of optical DHM configurations. The pyDHM implements phase-shifting approaches for in-line and slightly off-axis systems and enables phase compensation for telecentric and non-telecentric systems. In addition, pyDHM includes three propagation algorithms for numerical focusing complex amplitude distributions in DHM and digital holography (DH) setups. We have validated the library using numerical and experimental holograms.

Accurate unsupervised estimation of aberrations in digital holographic microscopy for improved quantitative reconstruction

In the context of digital in-line holographic microscopy, we describe an unsupervised methodology to estimate the aberrations of an optical microscopy system from a single hologram. The method is based on the Inverse Problems Approach reconstructions of holograms of spherical objects. The forward model is based on a Lorenz-Mie model distorted by optical aberrations described by Zernike polynomials. This methodology is thus able to characterize most varying aberrations in the field of view in order to take them into account to improve the reconstruction of any sample. We show that this approach increases the repeatability and quantitativity of the reconstructions in both simulations and experimental data. We use the Cramér-Rao lower bounds to study the accuracy of the reconstructions. Finally, we demonstrate the efficiency of this aberration calibration with image reconstructions using a phase retrieval algorithm as well as a regularized inverse problems algorithm.

COVID-19 screening with digital holographic microscopy using intra-patient probability functions of spatio-temporal bio-optical attributes

We present an automated method for COVID-19 screening using the intra-patient population distributions of bio-optical attributes extracted from digital holographic microscopy reconstructed red blood cells. Whereas previous approaches have aimed to identify infection by classifying individual cells, here, we propose an approach to incorporate the attribute distribution information from the population of a given human subjects' cells into our classification scheme and directly classify subjects at the patient level. To capture the intra-patient distribution information in a generalized way, we propose an approach based on the Bag-of-Features (BoF) methodology to transform histograms of bio-optical attribute distributions into feature vectors for classification via a linear support vector machine. We compare our approach with simpler classifiers directly using summary statistics such as mean, standard deviation, skewness, and kurtosis of the distributions. We also compare to a k-nearest neighbor classifier using the Kolmogorov-Smirnov distance as a distance metric between the attribute distributions of each subject. We lastly compare our approach to previously published methods for classification of individual red blood cells. In each case, the methodology proposed in this paper provides the highest patient classification performance, correctly classifying 22 out of 24 individuals and achieving 91.67% classification accuracy with 90.00% sensitivity and 92.86% specificity. The incorporation of distribution information for classification additionally led to the identification of a singular temporal-based bio-optical attribute capable of highly accurate patient classification. To the best of our knowledge, this is the first report of a machine learning approach using the intra-patient probability distribution information of bio-optical attributes obtained from digital holographic microscopy for disease screening.

Addressing phase-curvature in Fourier ptychography

In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave illumination from various directions is commonly used, to stitch together the captured information into a high synthetic aperture. The underlying far-field (Fraunhofer) diffraction assumption connects the source, sample, and pupil planes by Fourier transforms. While computationally simple, this assumption neglects phase-curvature due to non-planar illumination from point sources as well as phase-curvature from finite-conjugate microscopes (e.g., using a single-lens for image-formation). We describe a simple, efficient, and accurate extension of Fourier ptychography by embedding the effect of phase-curvature into the underlying forward model. With the improved forward model proposed here, quantitative phase reconstruction is possible even for wide fields-of-views and without the need of image segmentation. Lastly, the proposed method is computationally efficient, requiring only two multiplications: prior and following the reconstruction.

Deep learning in optical metrology: a review

With the advances in scientific foundations and technological implementations, optical metrology has become versatile problem-solving backbones in manufacturing, fundamental research, and engineering applications, such as quality control, nondestructive testing, experimental mechanics, and biomedicine. In recent years, deep learning, a subfield of machine learning, is emerging as a powerful tool to address problems by learning from data, largely driven by the availability of massive datasets, enhanced computational power, fast data storage, and novel training algorithms for the deep neural network. It is currently promoting increased interests and gaining extensive attention for its utilization in the field of optical metrology. Unlike the traditional "physics-based" approach, deep-learning-enabled optical metrology is a kind of "data-driven" approach, which has already provided numerous alternative solutions to many challenging problems in this field with better performances. In this review, we present an overview of the current status and the latest progress of deep-learning technologies in the field of optical metrology. We first briefly introduce both traditional image-processing algorithms in optical metrology and the basic concepts of deep learning, followed by a comprehensive review of its applications in various optical metrology tasks, such as fringe denoising, phase retrieval, phase unwrapping, subset correlation, and error compensation. The open challenges faced by the current deep-learning approach in optical metrology are then discussed. Finally, the directions for future research are outlined.

Preprocessing methods for quantitative phase image stitching

Quantitative phase imaging of cell cultures and histopathological slides often requires measurements in large fields of view which is realized through the stitching of multiple high resolution phase maps. Due to the characteristic properties of phase images, careful preprocessing is crucial for maintaining the metrological value of the stitched phase image. In this work, we present various methods that address those properties. Our efforts are focused on increasing robustness to minimize error propagation in consecutive preprocessing steps.

Fast-iterative automatic reconstruction method for quantitative phase image with reduced phase perturbations in off-axis digital holographic microscopy

This works presents a reconstruction algorithm to recover the complex object information for an off-axis digital holographic microscope (DHM) operating in the telecentric regimen. We introduce an automatic and fast method to minimize a cost function that finds the best numerical conjugated reference beam to compensate the filtered object information, eliminating any undesired phase perturbation due to the tilt between the reference and object waves. The novelties of the proposed approach, to the best of our knowledge, are a precise estimation of the interference angle between the object and reference waves, reconstructed phase images without phase perturbations, and reduced processing time. The method has been validated using a manufactured phase target and biological samples.

Roadmap on digital holography [Invited]

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

Analysis of potential distortions corresponding to the hologram printed by a holographic wave-front printer

In this paper, potential distortions corresponding to the hologram printed by a holographic wave-front printer are analyzed. Potential distortions are classified as the magnification(demagnification) distortion, barrel distortion, pincushion distortion, SLM mounting distortion, and translation distortion, respectively. These distortions are grouped as the optics distortion, SLM mounting distortion and the translation distortion depending on the process of recording the hologram in the holographic wave-front printer. In order to evaluate each distortion, a distortion analysis method based on a local spatial frequency is proposed. Through the proposed method, a diffracted wavefield reconstructed from a quantitatively distorted hologram is theoretically analyzed, and the validity of this analysis is verified by applying the numerical reconstruction method. In the numerical reconstruction, a propagation of a distorted wavefield reconstructed from the quantitatively distorted hologram is confirmed and contributed to generate the distorted reconstruction plane, such as a focal cloud plane and a convergence plane, depending on the types of distortion.

Real-time holographic quantitative measurement of vapor density distribution of suspended droplets

We applied digital holography (DH) technology in a quantitative measurement of the density distribution of a low refractive index transparent substance (e.g., the vapor of suspended droplets). An optical setup was built based on the Mach-Zehnder interferometer. A measurement performance test showed the mean relative error of the measurement error was about 2.0%; that of the environment disturbance error was about 0.47%. By a quantitative method to assess the precision limit, the temperature measurement precision could achieve 0.01°C, and the vapor density measurement precision could achieve 0.0001kg/m³. We believe that all the benefits above make the setup a good choice for application in the Chinese space station.

Pupil-aberration calibration with controlled illumination for quantitative phase imaging

Quantitative phase imaging (QPI) exploits sample-induced changes in the optical field to analyze biological specimens in a label-free manner. However, the quantitative nature of QPI makes it susceptible to optical aberrations. We propose a method for calibrating pupil aberrations by imaging a sample of interest. The proposed method recovers pupil information by utilizing the cross-spectral density between optical fields at different incident angles and allows both thin and weakly scattering three-dimensional samples for calibration. We experimentally validate the proposed method by imaging various samples, including a resolution target, breast tissue, and a polystyrene bead, and demonstrate aberration-free two- and three-dimensional QPI.

Improving holographic particle characterization by modeling spherical aberration

Holographic microscopy combined with forward modeling and inference allows colloidal particles to be characterized and tracked in three dimensions with high precision. However, current models ignore the effects of optical aberrations on hologram formation. We investigate the effects of spherical aberration on the structure of single-particle holograms and on the accuracy of particle characterization. We find that in a typical experimental setup, spherical aberration can result in systematic shifts of about 2% in the inferred refractive index and radius. We show that fitting with a model that accounts for spherical aberration decreases this aberration-dependent error by a factor of two or more, even when the level of spherical aberration in the optical train is unknown. With the new generative model, the inferred parameters are consistent across different levels of aberration, making particle characterization more robust.

Real-time quantitative phase imaging by single-shot dual-wavelength off-axis digital holographic microscopy

A single-shot dual-wavelength digital holographic microscopy with an adjustable off-axis configuration is presented, which helps realize real-time quantitative phase imaging for living cells. With this configuration, two sets of interference fringes corresponding to their wavelengths can be flexibly recorded onto one hologram in one shot. The universal expression on the dual-wavelength hologram recorded under any wave vector orientation angles of reference beams is given. To avoid as much as possible the effect of zero-order spectrum, we can flexibly select their carry frequencies for the two wavelengths using this adjustable off-axis configuration, according to the distribution feature of object's spatial-frequency spectrum. This merit is verified by a quantitative phase imaging experiment for the microchannel of a microfluidic chip. The reconstructed phase maps of living onion epidermal cells exhibit cellular internal life activities, for the first time to the best of our knowledge, vividly displaying the progress of the nucleus, cell wall, cytoskeleton, and the substance transport in microtubules inside living cells. These imaging results demonstrate the availability and reliability of the presented method for real-time quantitative phase imaging.

Sensing morphogenesis of bone cells under microfluidic shear stress by holographic microscopy and automatic aberration compensation with deep learning

We present sensing time-lapse morphogenesis of living bone cells under micro-fluidic shear stress (FSS) by digital holographic (DH) microscopy. To remove the effect of aberrations on quantitative measurements, we propose a numerical and automatic method to compensate for aberrations based on a convolutional neural network (CNN). For the first time, the aberration compensation issue is considered as a regression task where optimal coefficients for constructing the phase aberration map act as responses corresponding to the input aberrated phase image. We adopted tens of thousands of living cells' phase images reconstructed from digital holograms for training the CNN. The experiments demonstrate that, based on the trained network, phase aberrations can be totally removed in real-time without any hypothesis of object and aberration phase, knowledge of the setup's physical parameters, and the operation of selecting background regions; hence, the morphogenesis of the bone cells under FSS is accurately detected and quantitatively analyzed. The results show that the proposed method could provide a highly efficient and versatile way to investigate the effects of micro-FSS on living biological cells in microfluidic lab-on-chip platforms thanks to the combination of phase-contrast label-free microcopy with artificial intelligence.

High-speed imaging of the sound field by parallel phase-shifting digital holography

Sound field imaging techniques have been found very useful for acoustic designs. Building on this idea, innovative techniques are needed and presented in this paper, where we report on developed imaging of the sound field radiated from speakers by parallel phase-shifting digital holography. We adopted an ultrasonic wave radiated from a speaker for an object. The phase distribution of the light wave was modulated by the sound field radiated from the speaker. The modulated phase distribution was recorded in the form of multiplexed phase-shifted holograms at the frame rate of 100,000 fps. A 40,000 Hz sound field radiated from a speaker is used as an observation target. Our proposed method can implement the imaging of the sound field successfully. Also, in order to demonstrate the digital refocusing capability of digital holography, we set two speakers, whose difference in depth positions was 6.6 cm, as a long-depth object. We demonstrated the digital refocusing on the two speakers along with the capability of measuring the positions of the objects. Furthermore, we succeeded in imaging of 40,000 Hz and 41,000 Hz sound fields radiated from the two speakers. The presented experimental results showed that parallel phase-shifting digital holography is very useful and suitable for sound field imaging.

EUV and Hard X-ray Hartmann Wavefront Sensing for Optical Metrology, Alignment and Phase Imaging

For more than 15 years, Imagine Optic have developed Extreme Ultra Violet (EUV) and X-ray Hartmann wavefront sensors for metrology and imaging applications. These sensors are compatible with a wide range of X-ray sources: from synchrotrons, Free Electron Lasers, laser-driven betatron and plasma-based EUV lasers to High Harmonic Generation. In this paper, we first describe the principle of a Hartmann sensor and give some key parameters to design a high-performance sensor. We also present different applications from metrology (for manual or automatic alignment of optics), to soft X-ray source optimization and X-ray imaging.

Calibration-free quantitative phase imaging using data-driven aberration modeling

We present a data-driven approach to compensate for optical aberrations in calibration-free quantitative phase imaging (QPI). Unlike existing methods that require additional measurements or a background region to correct aberrations, we exploit deep learning techniques to model the physics of aberration in an imaging system. We demonstrate the generation of a single-shot aberration-corrected field image by using a U-net-based deep neural network that learns a translation between an optical field with aberrations and an aberration-corrected field. The high fidelity and stability of our method is demonstrated on 2D and 3D QPI measurements of various confluent eukaryotic cells and microbeads, benchmarking against the conventional method using background subtractions.

Polychromatic digital holographic microscopy: a quasicoherent-noise-free imaging technique to explore the connectivity of living neuronal networks

Significance: Over the past decade, laser-based digital holographic microscopy (DHM), an important approach in the field of quantitative-phase imaging techniques, has become a significant label-free modality for live-cell imaging and used particularly in cellular neuroscience. However, coherent noise remains a major drawback for DHM, significantly limiting the possibility to visualize neuronal processes and precluding important studies on neuronal connectivity. Aim: The goal is to develop a DHM technique able to sharply visualize thin neuronal processes. Approach: By combining a wavelength-tunable light source with the advantages of hologram numerical reconstruction of DHM, an approach called polychromatic DHM (P-DHM), providing OPD images with drastically decreased coherent noise, was developed. Results: When applied to cultured neuronal networks with an air microscope objective ( 20 × , 0.8 NA), P-DHM shows a coherent noise level typically corresponding to 1 nm at the single-pixel scale, in agreement with the 1 / N -law, allowing to readily visualize the 1 - μ m -wide thin neuronal processes with a signal-to-noise ratio of ∼ 5 . Conclusions: Therefore, P-DHM represents a very promising label-free technique to study neuronal connectivity and its development, including neurite outgrowth, elongation, and branching.

Deep learning-based cell identification and disease diagnosis using spatio-temporal cellular dynamics in compact digital holographic microscopy

We demonstrate a successful deep learning strategy for cell identification and disease diagnosis using spatio-temporal cell information recorded by a digital holographic microscopy system. Shearing digital holographic microscopy is employed using a low-cost, compact, field-portable and 3D-printed microscopy system to record video-rate data of live biological cells with nanometer sensitivity in terms of axial membrane fluctuations, then features are extracted from the reconstructed phase profiles of segmented cells at each time instance for classification. The time-varying data of each extracted feature is input into a recurrent bi-directional long short-term memory (Bi-LSTM) network which learns to classify cells based on their time-varying behavior. Our approach is presented for cell identification between the morphologically similar cases of cow and horse red blood cells. Furthermore, the proposed deep learning strategy is demonstrated as having improved performance over conventional machine learning approaches on a clinically relevant dataset of human red blood cells from healthy individuals and those with sickle cell disease. The results are presented at both the cell and patient levels. To the best of our knowledge, this is the first report of deep learning for spatio-temporal-based cell identification and disease detection using a digital holographic microscopy system.

Sampling moiré method: a tool for sensing quadratic phase distortion and its correction for accurate quantitative phase microscopy

The advantages of quantitative phase microscopy (QPM) such as label-free imaging with high spatial sensitivity, live cell compatibility and high-speed imaging makes it viable for various biological applications. The measurement accuracy of QPM strongly relies on the shape of the recorded interferograms, whether straight or curved fringes are recorded during the data acquisition. Moreover, for a single shot phase recovery high fringe density is required. The wavefront curvature for the high-density fringes over the entire field of view is difficult to be discerned with the naked eye. As a consequence, there is a quadratic phase aberration in the recovered phase images due to curvature mismatch. In the present work, we have implemented sampling moiré method for real-time sensing of the wavefront curvature mismatch between the object and the reference wavefronts and further for its correction. By zooming out the interferogram, moiré fringes are generated which helps to easily identify the curvature of the fringes. The wavefront curvature mismatch correction accuracy of the method is tested with the help of low temporal coherent light source such as a white light (temporal coherence ∼ 1.6 µm). The proposed scheme is successfully demonstrated to remove the quadratic phase aberration caused due to wavefront mismatch from an USAF resolution target and the biological tissue samples. The phase recovery accuracy of the current scheme is further compared with and found to better than the standard method called principle component analysis. The proposed method enables recording of the corrected wavefront interferogram without needing any additional optical components or modification and also does not need any post-processing correction algorithms. The proposed method of curvature compensation paves the path for a high-throughput and accurate quantitative phase imaging.

Comparative phase imaging of live cells by digital holographic microscopy and transport of intensity equation methods

We describe a microscopic setup implementing phase imaging by digital holographic microscopy (DHM) and transport of intensity equation (TIE) methods, which allows the results of both measurements to be quantitatively compared for either live cell or static samples. Digital holographic microscopy is a well-established method that provides robust phase reconstructions, but requires a sophisticated interferometric imaging system. TIE, on the other hand, is directly compatible with bright-field microscopy, but is more susceptible to noise artifacts. We present results comparing DHM and TIE on a custom-built microscope system that allows both techniques to be used on the same cells in rapid succession, thus permitting the comparison of the accuracy of both methods.

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.

Monitoring of photochemically induced changes in phase-modulating samples with digital holographic microscopy

This paper analyzes the performance of single-shot digital holographic microscopy for rapid characterization of static step-index structures in transparent polymer materials and for online monitoring of the photoinduced polymerization dynamics. The experiments are performed with a modified Mach-Zehnder transmission digital holographic microscope of high stability (phase accuracy of 0.69°) and of high magnification (of ≈90×). Use of near-infrared illumination allows both nondestructive examination of the manufactured samples and monitoring of optically induced processes in a photosensitive material concurrently with its excitation. The accuracy of the method for a precise sample's topography evaluation is studied on an example of microchannel sets fabricated via two-photon polymerization and is supported by reference measurements with an atomic force microscope. The applicability of the approach for dynamic measurements is proved via online monitoring of the refractive index evolution in a photoresin layer illuminated with a focused laser beam at 405 nm. High correlation between the experimental results and a kinetics model for the photopolymerization process is achieved.

Phase curvature compensation in digital holographic microscopy based on phase gradient fitting and optimization

We propose a numerical method for phase curvature compensation in digital holographic microscopy, in which the phase curvature is compensated for by subtracting a numerical phase mask from the distorted phase. The parameters of the phase mask are obtained based on phase gradient fitting and optimization, in which the initial mask parameters are obtained by fitting the phase gradient, and then more accurate mask parameters are determined using a spectrum energy search. The compensation can be executed in a hologram without extra devices or any prior knowledge of the setup and specimen. A computer simulation and experimental results demonstrated the feasibility of the proposed method.

Quantitative phase imaging in common-path cross-referenced holographic microscopy using double-exposure method

This paper proposes an optimized implementation of the double-exposure method with emphasis on the uniformity and minimization of the residual phase imperfections in cross-referenced holographic microscopy (CRHM). The quantitative phase images are restored from single-shot cross-referenced holograms, which are separated in the Fourier space and processed to eliminate effects caused by imperfections of the optical path and sample background. CRHM is implemented in a microscope configuration supplemented by a Sagnac interference module providing splitting and shearing of the sample and reference waves. Utilization of the averaging process, which enhances precision of quantitative phase image (QPI) reconstruction, applicable in the methods with a replicated field of view is also presented. The high temporal stability of CRHM is verified in calibration measurements and its application potential demonstrated by a quantitative restoration of the phase resolution target and imaging of biological samples including cheek and sperm cells.

Quantitative phase imaging based on simple Michelson-type lateral shearing interferometry with rotational right-angle prisms

By using a kind of simple Michelson-type lateral shearing interferometry, in this paper, the precise quantitative phase measurement of transparent microscopic objects is realized successfully. For this interferometry, on the basis of the fundamental structure of the traditional Michelson interferometer, the two plane mirrors are replaced with two ordinary right-angle prisms. In the beginning, the ridges of the two right-angle prisms are set to align with the optical axis and be in the vertical direction. Subsequently, to achieve the lateral shear, one of these two right-angle prisms is rotated around its ridge. Furthermore, the goal to obtain more lateral shear can be achieved by introducing a bigger rotating angle or rotating another prism simultaneously. In addition, owing to the simple structure of the Michelson interferometer and the inexpensive optical components used, the system is compact, portable, easy to operate, and low cost. The experimental results show the practicability of this system.

Structured illumination in compact and field-portable 3D-printed shearing digital holographic microscopy for resolution enhancement

A compact and field-portable three-dimensional (3D)-printed structured illumination (SI) digital holographic microscope based on shearing geometry is presented. By illuminating the sample using a SI pattern, the lateral resolution in both reconstructed phase and amplitude images can be improved up to twice the resolution provided by conventional illumination. The use of a 3D-printed system and shearing geometry reduces the complexity of the system, while providing high temporal stability. The experimental results for the USAF resolution target show a resolution improvement of a factor of two which corroborates the theoretical prediction. Resolution enhancement in phase imaging is also demonstrated by imaging a biological sample. To the best of our knowledge, this is the first report of a compact and field-portable SI digital holographic system based on shearing geometry.

Low-coherent optical diffraction tomography by angle-scanning illumination

Temporally low-coherent optical diffraction tomography (ODT) is proposed and demonstrated based on angle-scanning Mach-Zehnder interferometry. Using a digital micromirror device based on diffractive tilting, the full-field interference of incoherent light is successfully maintained during every angle-scanning sequences. Further, current ODT reconstruction principles for temporally incoherent illuminations are thoroughly reviewed and developed. Several limitations of incoherent illumination are also discussed, such as the nondispersive assumption, optical sectioning capacity and illumination angle limitation. Using the proposed setup and reconstruction algorithms, low-coherent ODT imaging of plastic microspheres, human red blood cells and rat pheochromocytoma cells is experimentally demonstrated.

Alignment-tolerant single-shot digital holographic microscopy based on computer-controlled telecentricity

An alignment-tolerant telecentric digital holographic microscopy (AT-T-DHM) system based on computer-controlled telecentricity is proposed. It consists of a three-step process-optical recording, computational compensation, and retrieving processes. With a tube-lens-based two-beam interferometer, phase information of the object is recorded on the hologram, where another optical quadratic phase error (O-QPE) due to the misalignment of the tube lens happens to be added. In the computational compensation process, this phase error can be estimated, by which the O-QPE is balanced out from the recorded hologram. Then, only the phase information of the object can be retrieved from the O-QPE-compensated hologram. This computational compensation process makes the proposed system virtually operate in a telecentric imaging mode, which enables implementing a practical AT-T-DHM. Wave-optical analysis and experiments with a test object confirm the feasibility of the proposed system.

Multi-step phase aberration compensation method based on optimal principal component analysis and subsampling for digital holographic microscopy

Digital holographic microscopy (DHM) is a well-known powerful technique allowing measurement of the spatial distributions of both the amplitude and phase produced by a transparent sample. Nevertheless, in order to improve the transverse resolution of the DHM system, a microscope objective has to be introduced in the object beam path, which inevitably leads to phase aberration in the object wavefront. In recent decades, a multitude of techniques have been proposed to compensate for this phase aberration, and the principal component analysis (PCA) technique has proven to be one of the most promising approaches due to its high compensation accuracy, low computational complexity, and simplicity to implement. However, when it comes to high-order phase aberration, which is common for a mal-aligned DHM system, the PCA technique usually performs poorly since it is unable to fit the cross-terms of the standard Zernike polynomials. To address this problem, here we propose a multi-step phase-aberration-compensation method based on optimal PCA and sub-sampling where PCA is first applied to remove the non-cross-aberration terms, followed by sub-sampled fitting for the remaining cross-aberration correction. The key advantage of our approach is that it can handle both the conventional objective phase curvature and high-order aberrations such as astigmatism and anamorphism with very little computational overhead. Simulation and experimental results demonstrate that our method outperforms state-of-the-art approaches, and the compensation results are consistent with those obtained from the double-exposure method.

Digital holographic phase imaging with aberrations totally compensated

Digital holography is a well-accepted method for phase imaging. However, the phase of the object is always embedded in aberrations. Here, we present a digital holographic phase imaging with the aberrations fully compensated, including the high order aberrations. Instead of using pre-defined aberration models or 2D fitting, we used the simpler and more flexible 1D fitting. Although it is 1D fitting, data across the whole plane could be used. Theoretically, all types of aberrations can be compensated with this method. Experimental results show that the aberrations have been fully compensated and the pure object phase can be obtained for further studies.

Spatial multiplexing and autofocus in holographic contouring for inspection of micro-parts

We present a method for fast geometrical inspection of micro deep drawing parts. It is based on single-shot two-wavelength contouring digital holographic microscopy (DHM). Within the capturing process, spatial multiplexing is utilized in order to record the two required holograms in a single-shot. For fast evaluation, determining the locations where the object is in focus and stitching all focus object's areas together is achieved digitally without the need for any external intervention using an autofocus algorithm. Thus, the limited depth of focus of the microscope objective is improved. The autofocus algorithm is based on minimizing the total variation (TV) of phase difference residuals of the two-wavelength measurements. In contrast to standard DHM, an object side telecentric microscope objective is used for overcoming the image scaling distortions caused by a conventional microscope objective. The method is used to reconstruct the 3D geometrical shape of a cold drawing micro cup. Experimental results verify the improvement of DHM's depth of focus.

Phase-shifting-free resolution enhancement in digital holographic microscopy under structured illumination

In this paper, we present a phase-shifting-free method to improve the resolution of digital holographic microscopy (DHM) under the structured illumination (SI). The SI used in the system is different from the traditional SI for it is free of the visible structure due to two illumination lights with orthogonal polarization states. To separate the recorded information and also retrieve the object phase, two reference beams with different carrier frequencies and orthogonal polarization states are adopted. The principle component analysis (PCA) algorithm is introduced in the reconstruction process. It is found that the modulated frequency of SI besides the quadratic phases of the imaging system can be easily removed with help of PCA. Therefore, phase-shifting is not required both in recording and reconstruction process. The simulation is performed to validate our method, while the proposed method is applied to the resolution enhancement for amplitude-contrast and phase-contrast objects imaging in experiments. The resolution is doubled in the simulation, and it shows 78% resolution improvement in the experiments.

Label-free quantification of the effects of lithium niobate polarization on cell adhesion via holographic microscopy

The surface of a c- cut ferroelectric crystal at room temperature is characterized by the so-called screening surface charges, able to compensate the charge due to the spontaneous polarization. Recently, these charges inspired the investigation of the interaction affinity of live cells with lithium niobate and lithium tantalate crystals. However, different knowledge gaps still remain that prevent a reasonable application of these materials for biological applications. Here, a label-free holographic total internal reflection microscopy is shown; the technique is able to evaluate quantitatively the contact area of live fibroblast cells adhering onto the surface of a ferroelectric lithium niobate crystal. The results show values of contact area significantly different between cells adhering onto the positive or negative face of the crystal. This reinforces the reasons for using the polarization charge of these materials to study and/or control cellular processes and, thus, to develop an innovative platform based on polar dielectric functional substrates.

Through-focus or volumetric type of optical imaging methods: a review

In recent years, the use of through-focus (TF) or volumetric type of optical imaging has gained momentum in several areas such as biological imaging, microscopy, adaptive optics, material processing, optical data storage, and optical inspection. We provide a review of basic TF optical methods highlighting their design, major unique characteristics, and application space.

Precise calibration of spatial phase response nonuniformity arising in liquid crystal on silicon

In order to calibrate the spatial phase response nonuniformity of liquid crystal on silicon (LCoS), we propose to use a Twyman-Green interferometer to characterize the wavefront distortion, due to the inherent curvature of the device. During the characterization, both the residual carrier frequency introduced by the Fourier transform evaluation method and the lens aberration are error sources. For the tilted phase error introduced by residual carrier frequency, the least mean square fitting method is used to obtain the tilted phase error. Meanwhile, we use Zernike polynomials fitting based on plane mirror calibration to mitigate the lens aberration. For a typical LCoS with 1×12,288 pixels after calibration, the peak-to-valley value of the inherent wavefront distortion is approximately 0.25λ at 1550 nm, leading to a half-suppression of wavefront distortion. All efforts can suppress the root mean squares value of the inherent wavefront distortion to approximately λ/34.

Automatic phase aberration compensation for digital holographic microscopy based on phase variation minimization

We propose a numerical and totally automatic phase aberration compensation method in digital holographic microscopy. The phase aberrations are extracted in a nonlinear optimization procedure in which the phase variation of the reconstructed object wave is minimized. Not only phase curvature but also high-order aberrations could be corrected without extra devices. The correction is directly carried out with the wrapped phase map, which is not affected by phase unwrapping or fitting errors. Numerical simulation proves that the proposed method is more accurate than the conventional surface fitting method without selecting a cell-free background. Experimental results demonstrate the availability of the proposed method in real-time analysis of living cells.