Iterative phase retrieval for digital holography: tutorial

Non-contact lensless holographic reconstruction of diffractive intraocular lenses profiles

A lensless compact arrangement based on digital in-line holography under Gabor's regime is proposed as a novel contactless method to assess the profile of multifocal intraocular lenses (MIOLs) which are conformed by several diffractive rings. Diffractive MIOLs are a widely adopted ophthalmologic option for the correction of presbyopia in patients undergoing cataract surgery. The MIOL optical design might introduce non-negligible optical performance differences between lenses as well as the introduction of undesirable photic phenomena (such as halos and glare) affecting the vision of users. Therefore, the customized topographic control of each manufactured MIOL model, along with the advancement of optical simulation routines, is increasingly necessary to provide users with optimized performance of these implanted optics, as well as predictable and realistic expectations of their future vision with these solutions. In this manuscript, experimental results of the reconstruction of different smooth and highly edged diffractive profiles from a pair of commercially available MIOLs are presented. Besides, a study evaluating the convergence and robustness of the proposed iterative phase-retrieval routine based on a modified classical Gerchberg-Saxton algorithm is performed. These results provide experimental validation of the proposed technique for accurately measuring the optical profiles of MIOLs.

Interframe-tunable ultrafast differential-displacement holography

We describe the details of a digital holographic microscopy diagnostic capable of quantifying both the topography and velocity of a km/s object with adjustable temporal sensitivity. This technique involves spatially multiplexing a double pulse reflected from a target with reference beams of precisely known temporal separation.

Roadmap on computational methods in optical imaging and holography [invited]

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

Quantitative phase imaging based on holography: trends and new perspectives

In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.

Digital in-line holographic microscopy for label-free identification and tracking of biological cells

Digital in-line holographic microscopy (DIHM) is a non-invasive, real-time, label-free technique that captures three-dimensional (3D) positional, orientational, and morphological information from digital holographic images of living biological cells. Unlike conventional microscopies, the DIHM technique enables precise measurements of dynamic behaviors exhibited by living cells within a 3D volume. This review outlines the fundamental principles and comprehensive digital image processing procedures employed in DIHM-based cell tracking methods. In addition, recent applications of DIHM technique for label-free identification and digital tracking of various motile biological cells, including human blood cells, spermatozoa, diseased cells, and unicellular microorganisms, are thoroughly examined. Leveraging artificial intelligence has significantly enhanced both the speed and accuracy of digital image processing for cell tracking and identification. The quantitative data on cell morphology and dynamics captured by DIHM can effectively elucidate the underlying mechanisms governing various microbial behaviors and contribute to the accumulation of diagnostic databases and the development of clinical treatments.

Improving Equity in Deep Learning Medical Applications with the Gerchberg-Saxton Algorithm

Deep learning (DL) has gained prominence in healthcare for its ability to facilitate early diagnosis, treatment identification with associated prognosis, and varying patient outcome predictions. However, because of highly variable medical practices and unsystematic data collection approaches, DL can unfortunately exacerbate biases and distort estimates. For example, the presence of sampling bias poses a significant challenge to the efficacy and generalizability of any statistical model. Even with DL approaches, selection bias can lead to inconsistent, suboptimal, or inaccurate model results, especially for underrepresented populations. Therefore, without addressing bias, wider implementation of DL approaches can potentially cause unintended harm. In this paper, we studied a novel method for bias reduction that leverages the frequency domain transformation via the Gerchberg-Saxton and corresponding impact on the outcome from a racio-ethnic bias perspective.

Double-slit holography-a single-shot lensless imaging technique

In this study, we propose a new method for single-shot, high-resolution lensless imaging called double-slit holography. This technique combines the properties of in-line and off-axis holography in one single-shot measurement using the simplest double-slit device: a plate with two apertures. In double-slit holography, a plane wave illuminates the two apertures giving rise to two spherical waves. While diffraction of one spherical wave from a sample positioned behind the first aperture (the object aperture) provides the object wave, the other spherical wave diffracted from the second (reference) aperture provides the reference wave. The resulting interference pattern in the far-field (hologram) combines the properties of an in-line (or Gabor-type) hologram and an off-axis hologram due to the added reference wave from the second aperture. Both the object and reference waves have the same intensity, which ensures high contrast of the hologram. Due to the off-axis scheme, the amplitude and phase distributions of the sample can be directly reconstructed from the hologram, and the twin image can be easily separated. Due to the object wave being the same as in-line holography with a spherical wave, imaging at different magnifications is similarly done by simply adjusting the aperture-to-sample distance. The resolution of the reconstructed object is given by the numerical aperture of the optical setup and the diameter of the reference aperture. It is shown both by theory and simulations that the resolution of the reconstructed object depends on the diameter of the reference wave aperture but does not depend on the diameter of the object aperture. Light optical proof-of-concept experiments are provided. The proposed method can be particularly practical for X-rays, where optical elements such as beam splitters are not available and conventional off-axis holography schemes cannot be realised.

Three-dimensional computer-generated holography based on the hybrid iterative angular spectrum algorithm

This paper proposes a novel three-dimensional hologram calculation method based on the angular spectrum approach, with the aim of reducing the noise generated during the hologram reconstruction process. The proposed algorithm divides the spatial domain into multiple layers and employs the angular spectrum method to propagate the image between these layers, thus avoiding the paraxial approximation. To enhance the quality of the hologram, an error iteration algorithm is utilized to alleviate the occurrence of aliasing errors when directly superimposing holograms. Moreover, constraint factors are introduced between different layers within the same region to effectively utilize spatial resources for multi-image reconstruction, thereby mitigating the noise caused by inter-layer crosstalk. The feasibility of the proposed method is demonstrated through numerical simulations and optical experiments, highlighting its potential applicability to a wide range of three-dimensional reconstruction algorithms.

Coherent imaging with low-energy electrons, quantitative analysis

Low-energy electrons (20-300eV) hold the promise for low-dose, non-destructive, high-resolution imaging, but at the price of challenging data analysis. This study provides theoretical considerations and models for the quantitative analysis of experimental data observed in low-energy electron transmission microscopy and in-line holography. The scattering of low-energy electrons and the imaging parameters, such as the inelastic mean free path, point spread function, depth of focus, and resolution, are quantitatively described. It is shown that unlike high-energy electrons (20-300 keV), low-energy electrons (20-300eV) introduce a large phase shift into the probing electron waves. Using the projected potentials formalism, the maximal phase shift acquired by a 120eV electron wave scattered by a carbon atom is theoretically estimated to be 5.03 radian and experimentally measured to be between 3 and 7.5 radian. The point spread function evaluated for low-energy electrons shows that they diffract much stronger than high-energy electrons, and that only very thin objects of up to 3Å in thickness can be imaged in focus. Thus, when imaging an object of finite thickness, such as a macromolecule, the obtained image will always be blurred due to the out-of-focus signal. This can provide an explanation for a long-standing problem of limited resolution in low-energy electron holography of macromolecules. As for imaging of a macromolecule's structure, it is shown that the amplitude of the wavefront reconstructed from the sample's hologram provides the best match to the projected potential distribution of the macromolecule. To evaluate the absorption properties, the inelastic mean free path (IMFP) is considered. The IMFP values calculated from theoretical models agree with the measured values. The IMFP of about 5Å was measured by transmission through graphene of 50-200eV electrons. This result implies that the internal structure of only very thin samples can be imaged in transmission mode. A simple method to quantitatively evaluate the absorption of a specimen from its in-line hologram without the need to reconstruct the hologram is presented.

Randomness assisted in-line holography with deep learning

We propose and demonstrate a holographic imaging scheme exploiting random illuminations for recording hologram and then applying numerical reconstruction and twin image removal. We use an in-line holographic geometry to record the hologram in terms of the second-order correlation and apply the numerical approach to reconstruct the recorded hologram. This strategy helps to reconstruct high-quality quantitative images in comparison to the conventional holography where the hologram is recorded in the intensity rather than the second-order intensity correlation. The twin image issue of the in-line holographic scheme is resolved by an unsupervised deep learning based method using an auto-encoder scheme. Proposed learning technique leverages the main characteristic of autoencoders to perform blind single-shot hologram reconstruction, and this does not require a dataset of samples with available ground truth for training and can reconstruct the hologram solely from the captured sample. Experimental results are presented for two objects, and a comparison of the reconstruction quality is given between the conventional inline holography and the one obtained with the proposed technique.

Adaptive constraints by morphological operations for single-shot digital holography

Digital holography provides access to quantitative measurement of the entire complex field, which is indispensable for the investigation of wave-matter interactions. The emerging iterative phase retrieval approach enables to solve the inverse imaging problem only from the given intensity measurements and physical constraints. However, enforcing imprecise constraints limits the reconstruction accuracy and convergence speed. Here, we propose an advanced iterative phase retrieval framework for single-shot in-line digital holography that incorporates adaptive constraints, which achieves optimized convergence behavior, high-fidelity and twin-image-free reconstruction. In conjunction with morphological operations which can extract the object structure while eliminating the irrelevant part such as artifacts and noise, adaptive constraints allow the support region to be accurately estimated and automatically updated at each iteration. Numerical reconstruction of complex-valued objects and the capability of noise immunity are investigated. The improved reconstruction performance of this approach is experimentally validated. Such flexible and versatile framework has promising applications in biomedicine, X-ray coherent diffractive imaging and wavefront sensing.

Adapting a Blu-ray optical pickup unit as a point source for digital lensless holographic microscopy

The adaptation of an off-the-shelf Blu-ray optical pickup unit (OPU) into a highly versatile point source for digital lensless holographic microscopy (DLHM) is presented. DLHM performance is mostly determined by the optical properties of the point source of spherical waves used for free-space magnification of the sample's diffraction pattern; in particular, its wavelength and numerical aperture define the achievable resolution, and its distance to the recording medium sets the magnification. Through a set of straightforward modifications, a commercial Blu-ray OPU can be transformed into a DLHM point source with three selectable wavelengths, a numerical aperture of up to 0.85, and integrated micro-displacements in both axial and transversal directions. The functionality of the OPU-based point source is then experimentally validated in the observation of micrometer-sized calibrated samples and biological specimens of common interest, showing the feasibility of obtaining sub-micrometer resolution and offering a versatile option for the development of new cost-effective and portable microscopy devices.

DH-GAN: a physics-driven untrained generative adversarial network for holographic imaging

Digital holography is a 3D imaging technique by emitting a laser beam with a plane wavefront to an object and measuring the intensity of the diffracted waveform, called holograms. The object's 3D shape can be obtained by numerical analysis of the captured holograms and recovering the incurred phase. Recently, deep learning (DL) methods have been used for more accurate holographic processing. However, most supervised methods require large datasets to train the model, which is rarely available in most DH applications due to the scarcity of samples or privacy concerns. A few one-shot DL-based recovery methods exist with no reliance on large datasets of paired images. Still, most of these methods often neglect the underlying physics law that governs wave propagation. These methods offer a black-box operation, which is not explainable, generalizable, and transferrable to other samples and applications. In this work, we propose a new DL architecture based on generative adversarial networks that uses a discriminative network for realizing a semantic measure for reconstruction quality while using a generative network as a function approximator to model the inverse of hologram formation. We impose smoothness on the background part of the recovered image using a progressive masking module powered by simulated annealing to enhance the reconstruction quality. The proposed method exhibits high transferability to similar samples, which facilitates its fast deployment in time-sensitive applications without the need for retraining the network from scratch. The results show a considerable improvement to competitor methods in reconstruction quality (about 5 dB PSNR gain) and robustness to noise (about 50% reduction in PSNR vs noise increase rate).

Spectroscopic atomic sample plane localization for precise digital holography

In digital holography, the coherent scattered light fields can be reconstructed volumetrically. By refocusing the fields to the sample planes, absorption and phase-shift profiles of sparsely distributed samples can be simultaneously inferred in 3D. This holographic advantage is highly useful for spectroscopic imaging of cold atomic samples. However, unlike e.g. biological samples or solid particles, the quasi-thermal atomic gases under laser-cooling are typically featureless without sharp boundaries, invalidating a class of standard numerical refocusing methods. Here, we extend the refocusing protocol based on the Gouy phase anomaly for small phase objects to free atomic samples. With a prior knowledge on a coherent spectral phase angle relation for cold atoms that is robust against probe condition variations, an "out-of-phase" response of the atomic sample can be reliably identified, which flips the sign during the numeric back-propagation across the sample plane to serve as the refocus criterion. Experimentally, we determine the sample plane of a laser-cooled ³⁹K gas released from a microscopic dipole trap, with a δz ≈ 1 µm ≪ 2λ_p/NA² axial resolution, with a NA=0.3 holographic microscope at λ_p = 770 nm probe wavelength.

Three-dimensional spline-based computer-generated holography

Electro-holography is a promising 3D display technology, as it can, in principle, account for all visual cues. Computing the interference patterns to drive them is highly calculation-intensive, requiring the design and development of efficient computer-generated holography (CGH) algorithms to facilitate real-time display. In this work, we propose a new algorithm for computing the CGH for arbitrary 3D curves using splines, as opposed to previous solutions, which could only draw planar curves. The solutions are analytically expressed; we conceived an efficiently computable approximation suitable for GPU implementations. We report over 55-fold speedups over the reference point-wise algorithm, resulting in real-time 4K holographic video generation of complex 3D curved objects. The proposed algorithm is validated numerically and optically on a holographic display setup.

Inverse diffraction in phase space

Inverse diffraction refers to recovering the input field in the plane z=0 from the knowledge of the field in some plane z>0 of the free half-space to which the input field propagates. With the rapid development of computational optics, inverse diffraction is increasingly used in optimization and imaging simulations involving round-trip wave propagation. This increasing usage makes it necessary and valuable to revisit this old, important problem and clarify some existing ambiguities. In this study, an exhaustive inverse diffraction analysis is presented from the perspective of phase space. With the help of the Wigner distribution function, it is shown that the forward and inverse diffraction processes in phase space are geometrically equivalent to the deformation and recovery of the phase space diagram (PSD). The symmetries of PSD transformations corresponding to different inverse diffraction forms are revealed. The ambiguities between the conjugation of diffraction kernels and the negative diffraction distance are clarified. The physical pictures of inverse diffraction are further given. This phase space analysis provides an intuitive view on problems involving inverse diffraction and a more concise approach for understanding propagation behaviors of three-dimensional wave fields, including the phase conjugation in holography.

Effect of hologram plane position on particle tracking using digital holographic microscopy

This paper discusses the effect of hologram plane position on the tracking of particle motions in a 3D suspension using digital holography microscopy. We compare two optical configurations where the hologram plane is located either just outside the particle suspension or in the middle of the suspension. In both cases, we record two axially separated holograms using two cameras and subsequently adopt an iterative phase retrieval approach to solve the virtual image problem. We measure the settling motions of 2 µm spheres in a 2 mm thick sample containing 300 to 1500p a r t i c l e s/m m ³. We show that the optical setup where the hologram plane is located in the middle of the sample provides superior tracking results compared to the other, including higher accuracy in the measurement of particle displacement and longer particle trajectories. The accuracy of particle displacement increases by a maximum of 18%, and the trajectory length increases by a maximum of 16%. This superior outcome is due to the less overlapping of the diffraction patterns on the holograms when the separation distance between particles and the hologram plane is minimized.

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.

Quantitative Phase Imaging: Recent Advances and Expanding Potential in Biomedicine

Quantitative phase imaging (QPI) is a label-free, wide-field microscopy approach with significant opportunities for biomedical applications. QPI uses the natural phase shift of light as it passes through a transparent object, such as a mammalian cell, to quantify biomass distribution and spatial and temporal changes in biomass. Reported in cell studies more than 60 years ago, ongoing advances in QPI hardware and software are leading to numerous applications in biology, with a dramatic expansion in utility over the past two decades. Today, investigations of cell size, morphology, behavior, cellular viscoelasticity, drug efficacy, biomass accumulation and turnover, and transport mechanics are supporting studies of development, physiology, neural activity, cancer, and additional physiological processes and diseases. Here, we review the field of QPI in biology starting with underlying principles, followed by a discussion of technical approaches currently available or being developed, and end with an examination of the breadth of applications in use or under development. We comment on strengths and shortcomings for the deployment of QPI in key biomedical contexts and conclude with emerging challenges and opportunities based on combining QPI with other methodologies that expand the scope and utility of QPI even further.

Advances in Digital Holographic Interferometry

Holographic interferometry is a well-established field of science and optical engineering. It has a half-century history of successful implementation as the solution to numerous technical tasks and problems. However, fast progress in digital and computer holography has promoted it to a new level of possibilities and has opened brand new fields of its application. In this review paper, we consider some such new techniques and applications.

Enhanced Single-Beam Multiple-Intensity Phase Retrieval Using Holographic Illumination

Single-beam multiple-intensity iterative phase retrieval is a high-precision and lens-free computational imaging method, which reconstructs the complex-valued distribution of the object from a volume of axially captured diffraction intensities using the post-processing algorithm. However, for the object with slowly-varying waves, the method may encounter the problem of convergence stagnation since the lack of diversity between the captured intensity patterns. In this paper, a novel technique to enhance phase retrieval using holographic illumination is proposed. One special computer-generated hologram is designed, which can generate multiple significantly different images at the required distances. The incident plane wave is firstly modulated by the hologram, and then the exit wave is used to illuminate the object. Benefitting from this holographic illumination, remarkable intensity changes in the given detector planes can be produced, which is conducive to fast and high-accuracy reconstruction. Simulation and optical experiments are performed to verify the feasibility of the proposed method.

Speeding up reconstruction of 3D tomograms in holographic flow cytometry via deep learning

Tomographic flow cytometry by digital holography is an emerging imaging modality capable of collecting multiple views of moving and rotating cells with the aim of recovering their refractive index distribution in 3D. Although this modality allows us to access high-resolution imaging with high-throughput, the huge amount of time-lapse holographic images to be processed (hundreds of digital holograms per cell) constitutes the actual bottleneck. This prevents the system from being suitable for lab-on-a-chip platforms in real-world applications, where fast analysis of measured data is mandatory. Here we demonstrate a significant speeding-up reconstruction of phase-contrast tomograms by introducing in the processing pipeline a multi-scale fully-convolutional context aggregation network. Although it was originally developed in the context of semantic image analysis, we demonstrate for the first time that it can be successfully adapted to a holographic lab-on-chip platform for achieving 3D tomograms through a faster computational process. We trained the network with input-output image pairs to reproduce the end-to-end holographic reconstruction process, i.e. recovering quantitative phase maps (QPMs) of single cells from their digital holograms. Then, the sequence of QPMs of the same rotating cell is used to perform the tomographic reconstruction. The proposed approach significantly reduces the computational time for retrieving tomograms, thus making them available in a few seconds instead of tens of minutes, while essentially preserving the high-content information of tomographic data. Moreover, we have accomplished a compact deep convolutional neural network parameterization that can fit into on-chip SRAM and a small memory footprint, thus demonstrating its possible exploitation to provide onboard computations for lab-on-chip devices with low processing hardware resources.

Lensless phase imaging microscopy using multiple intensity diffraction patterns obtained under coherent and partially coherent illumination

In this paper, we show how high-resolution phase imaging is obtained from multiple intensity diffraction patterns. The results of the experiments carried out with different microscopic phase and amplitude samples illuminated with coherent and partially coherent light are presented. A comparison with experimental results obtained by digital holographic microscopy is given, and advantages/disadvantages of the techniques are discussed.

Ptychographic sensor for large-scale lensless microbial monitoring with high spatiotemporal resolution

Traditional microbial detection methods often rely on the overall property of microbial cultures and cannot resolve individual growth event at high spatiotemporal resolution. As a result, they require bacteria to grow to confluence and then interpret the results. Here, we demonstrate the application of an integrated ptychographic sensor for lensless cytometric analysis of microbial cultures over a large scale and with high spatiotemporal resolution. The reported device can be placed within a regular incubator or used as a standalone incubating unit for long-term microbial monitoring. For longitudinal study where massive data are acquired at sequential time points, we report a new temporal-similarity constraint to increase the temporal resolution of ptychographic reconstruction by 7-fold. With this strategy, the reported device achieves a centimeter-scale field of view, a half-pitch spatial resolution of 488 nm, and a temporal resolution of 15-s intervals. For the first time, we report the direct observation of bacterial growth in a 15-s interval by tracking the phase wraps of the recovered images, with high phase sensitivity like that in interferometric measurements. We also characterize cell growth via longitudinal dry mass measurement and perform rapid bacterial detection at low concentrations. For drug-screening application, we demonstrate proof-of-concept antibiotic susceptibility testing and perform single-cell analysis of antibiotic-induced filamentation. The combination of high phase sensitivity, high spatiotemporal resolution, and large field of view is unique among existing microscopy techniques. As a quantitative and miniaturized platform, it can improve studies with microorganisms and other biospecimens at resource-limited settings.

Design, Calibration, and Application of a Robust, Cost-Effective, and High-Resolution Lensless Holographic Microscope

Lensless holographic microscope (LHM) is an emerging very promising technology that provides high-quality imaging and analysis of biological samples without utilizing any lens for imaging. Due to its small size and reduced price, LHM can be a very useful tool for the point-of-care diagnosis of diseases, sperm assessment, or microfluidics, among others, not only employed in advanced laboratories but also in poor and/or remote areas. Recently, several LHMs have been reported in the literature. However, complete characterization of their optical parameters remains not much presented yet. Hence, we present a complete analysis of the performance of a compact, reduced cost, and high-resolution LHM. In particular, optical parameters such as lateral and axial resolutions, lateral magnification, and field of view are discussed into detail, comparing the experimental results with the expected theoretical values for different layout configurations. We use high-resolution amplitude and phase test targets and several microbeads to characterize the proposed microscope. This characterization is used to define a balanced and matched setup showing a good compromise between the involved parameters. Finally, such a microscope is utilized for visualization of static, as well as dynamic biosamples.

Muscope: a miniature on-chip lensless microscope

We report the Muscope, a miniature lensless holographic microscope suitable for on-chip integration. The prototype of the Muscope measured approximately only 7 mm × 4 mm × 4 mm, and was capable of offering a sub-micron half-pitch resolution. We have used, for the first time, a microLED display as the light source in a microscope. The individual pixels of a microLED display chip are used as programmable, microscopic and intense LEDs which can be spatially moved in a two-dimensional plane with a 5 μm pitch. This unique feature set of the display was used to implement computational super-resolution and wide-field imaging without any extra hardware, unlike many other lensless microscopes. We also report a new method to evaluate the magnification in our setting. The Muscope surpasses the existing lensless microscopes in compactness, scalability for production, automated operation and system integration. It provides exciting opportunities for a new class of devices with in-built optical imaging and monitoring and/or sensing capabilities.

ADMM approach for efficient iterative tomographic deconvolution reconstruction of 3D quantitative phase images

Tomographic deconvolution phase microscopy (TDPM) is a promising approach for 3D quantitative imaging of phase objects such as biological cells and optical fibers. In the present work, the alternating direction method of multipliers (ADMM) is applied to TDPM to shorten its image acquisition and processing times while simultaneously improving its accuracy. ADMM-TDPM is used to optimize the image fidelity by minimizing Gaussian noise and by using total variation regularization with the constraints of nonnegativity and known zeros. ADMM-TDPM can reconstruct phase objects that are shift variant in three spatial dimensions. ADMM-TDPM achieves speedups of 5x in image acquisition time and greater than 10x in image processing time with accompanying higher accuracy compared to TDPM.

Improving axial localization of weak phase particles in digital in-line holography

One shortcoming of digital in-line holography (DIH) is the low axial position accuracy due to the elongated particle traces in the reconstruction field. Here, we propose a method that improves the axial localization of DIH when applying it to track the motion of weak phase particles in dense suspensions. The proposed method detects particle positions based on local intensities in the reconstruction field consisting of scattering and incident waves. We perform both numerical and experimental tests and demonstrate that the proposed method has a higher axial position accuracy than the previous method based on the local intensities in the reconstructed scattered field. We show that the proposed method has an axial position error below 1.5 particle diameters for holograms with a particle concentration of 4700particles/mm³. The proposed method is further validated by tracking the Brownian motion of 1µmparticles in dense suspensions.

Three-Dimensional Structure from Single Two-Dimensional Diffraction Intensity Measurement

Conventional three-dimensional (3D) imaging methods require multiple measurements of the sample in different orientation or scanning. When the sample is probed with coherent waves, a single two-dimensional (2D) intensity measurement is sufficient as it contains all the information of the 3D sample distribution. We show a method that allows reconstruction of 3D sample distribution from a single 2D intensity measurement, at the z resolution exceeding the classical limit. The method can be practical for radiation-sensitive materials, or where the experimental setup allows only one intensity measurement.

Separating twin images in digital holographic microscopy using weak scatterers

When using inline digital holographic microscopy (DHM) and placing the hologram plane within a particle suspension, both real and virtual images come into focus during reconstruction, limiting our ability to resolve three-dimensional (3D) particle distribution. Here, we propose a new method to distinguish between real and virtual images in the 3D reconstruction field. This new method is based on the use of weak scatterers, and the fact that the real and virtual images of weak scatterers display distinct intensity distributions along the optical axis. We experimentally demonstrate this method by localizing and tracking 1 µm particles in a 3D volume with a particle concentration ranging from 200 to 6000particles/mm³. Unlike previous approaches to address the virtual image problem, this method does not require the recording of multiple holograms or the insertion of additional optical components. The proposed method allows the hologram plane to be placed within the sample volume, and extends the capability of DHM to measure the 3D movements of particles in deep samples far away from the optical window.

Random object optical field diagnostics by using carbon nanoparticles

We propose a new approach of using carbon nanoparticles for correlation optical diagnostics of а complex scalar optical field created by scattering and diffraction of radiation off a rough surface. This surface is simulated and we generate a diffraction pattern of the amplitude and phase distribution in the far field. Carbon nanoparticles of a certain size and concentration are obtained by the bottom-up methods of hydrothermal synthesis of citric acid and urea followed by centrifugation. The optical properties of carbon nanoparticles, such as luminescence and absorption in the visible spectrum that essentially differs for different wavelengths, as well as particle size of about dozen nanometers, are the determining criteria for using these particles as probes for the optical speckle field. Luminescence made it possible to register the coordinate position of carbon nanoparticles in real time. The algorithm for reconstruction of the scalar optical field intensity distribution through the analysis of the nanoparticle positions is here displayed. The skeleton of the optical speckle field is analyzed by Hilbert transform to restore the phase. Special attention is paid to the restoration of the speckle field's phase singularities.

Measurement of Cell Volume Using In-Line Digital Holography

The measurement of the volume of blood cells is important for clinical diagnosis and patient management. While digital holography microscopy (DHM) has been used to obtain such information, previous off-axis setups usually involve a separated reference beam and are thus not very easy to implement. Here, we use the simple in-line Gabor setup without separation of a reference beam to measure the shape and volume of cells mounted on glass slides. Inherent to the in-line holograms, the reconstructed phase of the object is affected by the virtual image noise, producing errors in the cell volume measurement. We optimized our approach to use a single hologram without phase retrieval, increasing distance between cell and hologram plane to reduce the measurement error of cell volume to less than 6% in some instances. Therefore, the in-line Gabor setup can be a useful and simple tool to obtain volumetric and morphologic cellular information.

Holography and Coherent Diffraction Imaging with Low-(30-250 eV) and High-(80-300 keV) Energy Electrons: History, Principles, and Recent Trends

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Three-dimensional measurement of a particle field using phase retrieval digital holography

Digital inline holography (DIH) has long been used to measure the three-dimensional (3D) distribution of micrometer particles in suspensions. However, DIH experiences a virtual image problem that limits the particle density and the placement of the hologram plane relative to the sample volume. Here, we apply virtual-image-free phase retrieval digital holography (PRDH) to detect opaque particles in 3D volumes that exceed $ 2000\;{\rm particles}/{{\rm mm}^3} $2000particles/mm³. PRDH is based on recording two holograms whose planes are displaced along the optical axis, and then reconstructing the complete optical waves estimated by the iterative phase retrieval algorithm. Both numerical and experimental tests are performed, and results show that PRDH recovers the original 3D particle distributions even when the hologram planes are within the particle suspensions. Moreover, compared to single-hologram-based DIH, PRDH is proved to have better particle detection qualities. The uncertainty in the localization of particle centers is reduced to less than one particle diameter.

Iterative phase retrieval for digital holography: tutorial: publisher's note

This publisher's note corrects the paper type and title of J. Opt. Soc. Am. A36, D31 (2019)JOAOD60740-323210.1364/JOSAA.36.000D31.