Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram

Hough transform-based multi-object autofocusing compressive holography

Reconstruction of multiple objects from one hologram can be affected by the focus metric judgment of autofocusing. Various segmentation algorithms are applied to obtain a single object in the hologram. Each object is unambiguously reconstructed to acquire its focal position, which produces complicated calculations. Herein, Hough transform (HT)-based multi-object autofocusing compressive holography is presented. The sharpness of each reconstructed image is computed by using a focus metric such as entropy or variance. According to the characteristics of the object, the standard HT is further used for calibration to remove redundant extreme points. The compressive holographic imaging framework with a filter layer can eliminate the inherent noise in in-line reconstruction including cross talk noise of different depth layers, two-order noise, and twin image noise. The proposed method can effectively obtain 3D information on multiple objects and achieve noise elimination by only reconstructing from one hologram.

Deep learning for digital holography: a review

Recent years have witnessed the unprecedented progress of deep learning applications in digital holography (DH). Nevertheless, there remain huge potentials in how deep learning can further improve performance and enable new functionalities for DH. Here, we survey recent developments in various DH applications powered by deep learning algorithms. This article starts with a brief introduction to digital holographic imaging, then summarizes the most relevant deep learning techniques for DH, with discussions on their benefits and challenges. We then present case studies covering a wide range of problems and applications in order to highlight research achievements to date. We provide an outlook of several promising directions to widen the use of deep learning in various DH applications.

Underwater Light Manipulation by the Benthic Diatom Ctenophora pulchella: From PAR Efficient Collection to UVR Screening

Several species of diatoms, unicellular microalgae which constitute the main component of phytoplankton, are characterized by an impressive photosynthetic efficiency while presenting a noticeable tolerance versus exposure to detrimental UV radiation (UVR). In particular, the growth rate of the araphid diatom Ctenophora pulchella is not significantly affected by harsh treatments with UVR, even in absence of detectable, specific UV-absorbing pigments and even if it is not able to avoid high UV exposure by motility. In this work we applied a multi-disciplinary approach involving numerical computation, photonics, and biological parameters in order to investigate the possible role of the frustule, micro- and nano-patterned silica shell which encloses the cell, in the ability of C. pulchella to efficiently collect photosynthetic active radiation (PAR) and to simultaneously screen the protoplasm from UVR. The characterization of the photonic properties of the frustule has been accompanied by in vivo experiments conducted in water in order to investigate its function as optical coupler between light and plastids.

Autofocusing in digital holography using eigenvalues

A new autofocusing algorithm for digital holography is proposed based on the eigenvalues of the images reconstructed at different distances in the measurement volume. An image quality metric evaluated based on the distribution of its eigenvalues is compared in function of the reconstruction distance to identify the location of the focal plane. The proposed automatic focal plane detection algorithm is capable of working with amplitude objects, phase objects, and mixed type objects. A performance comparison of the proposed algorithm with some previously reported representative algorithms is provided. The simulation and experimental results demonstrate the practical applicability of the proposed algorithm.

A practical criterion for focusing of unstained cell samples using a digital holographic microscope

Digital holographic microscopy (DHM) is an important technique that may be used for quantitative phase imaging of unstained biological cell samples. Since the DHM technology is not commonly used in clinics or bioscience research labs, at present there is no well-accepted focusing criterion for unstained samples that users can follow while recording image plane digital holograms of cells. The usual sharpness metrics that are useful for auto-focusing of stained cells do not work well for unstained cells as there is no amplitude contrast. In this work, we report a practical method for estimating the best focus plane for unstained cells in the digital hologram domain. The method is based on an interesting observation that for the best focus plane the fringe pattern associated with individual unstained cells predominantly shows phase modulation effect in the form of bending of fringes and minimal amplitude modulation. This criterion when applied to unstained red blood cells shows that the central dip in the doughnut-like phase profile of cells is maximal in this plane. The proposed methodology is helpful for standardizing the usage of DHM technology across different users and application development efforts. LAY DESCRIPTION: Digital holographic microscopy (DHM) is slowly but steadily becoming an important microscopy modality and gaining acceptability for basic bio-science research as well as clinical usage. One of the important features of DHM is that it allows users to perform quantitative imaging of unstained transparent cells. Instead of using dyes or fluorescent labelling, DHM systems use quantitative phase as a contrast mechanism which depends on the natural refractive index variation within the cell samples. Since minimal wet lab processing is required in order to image cell samples with a DHM, cells can be imaged in their natural state. While DHM is gaining popularity among users, the imaging protocols across the labs or users need to be standardized in order to make sure that the same quantitative phase parameters are used for tasks such as quantitative phased based cell classification. One of the important operational tasks for any microscopy work is to focus the sample under study. While focusing comes naturally to users of brightfield microscopes based on image contrast, the focusing is not straightforward when samples are unstained so that they do not offer any amplitude contrast. When performing quantitative phase imaging, defocus can actually change the phase profile of the cell due to near-zone (Fresnel) diffraction effects. So unless a standardized focusing methodology is used, it will be difficult for multiple DHM users (potentially at different sites) to agree on quantitative results out of their phase images. DHM literature has prior works which perform numerical focusing of recovered complex wave-field in the hologram plane to find the best focus plane. However such methods are not user friendly and do not allow user the same focusing experience as in a brightfield microscope. The numerical focusing is therefore a reasonably good method for an optics researcher but not necessarily so for a microscopy technician looking at cell samples with a DHM system in a clinical setting. The present work provides a simple focusing criterion for unstained samples that works directly in the hologram domain. The technique is based on an interesting observation that the when an unstained cell sample is in the best-focus plane, its corresponding hologram (or fringe pattern) predominantly shows phase modulation manifested by bending of fringes at the location of the cell. This criterion can be converted into a simple numerical method as we have used to find the best-focus plane using a stack of through focus holograms. We believe that the technique can be used manually by visually observing the holograms or can be converted to an auto-focus algorithm for a motorized DHM system.

Robust autofocusing method for multi-wavelength lensless imaging

Lensless imaging based on multi-wavelength phase retrieval becomes a promising technology widely used as it has simple acquisition, miniaturized size and low-cost setup. However, measuring the sample-to-sensor distance with high accuracy, which is the key for high-resolution reconstruction, is still a challenge. In this work, we propose a multi-wavelength criterion to realize autofocusing modulation, i.e., achieving much higher accuracy in determining the sample-to-sensor distance, compared to the conventional methods. Three beams in different spectrums are adopted to illuminate the sample, and the resulting holograms are recorded by a CCD camera. The patterns calculated by performing back propagation of the recorded holograms, with exhaustively searched sample-to-sensor distance value, are adopted to access the criterion. Image sharpness can be accessed and the optimal sample-to-sensor distance can be finely determined by targeting the valley of the curve given by the criterion. Through our novel multi-wavelength based autofocusing strategy and executing further phase retrieval process, high-resolution images can be finally retrieved. The applicability and robustness of our method is validated both in simulations and experiments. Our technique provides a useful tool for multi-wavelength lensless imaging under limited experimental conditions.

Holographic tomography with object rotation and two-directional off-axis illumination

A hybrid system of holographic tomography, which utilizes rotation of a sample and two-directional, off-axis illumination is proposed. The applied type of illumination brings two major benefits. First, it offers theoretical potential for the resolution improvement with respect to conventional tomography. Second, it enables effective, numerical compensation of the defocus error, which is achieved with an accurate, noise-immune autofocusing. Hence, the main practical obstacle of hybrid tomography is removed and its high-resolution potential is put into practice. The utility of the proposed concept is experimentally demonstrated with the tomographic measurement of a photonic crystal fiber.

Opposite-view digital holographic microscopy with autofocusing capability

Digital holographic microscopy (DHM) has its intrinsic ability to refocusing a sample by numerically propagating an object wave from its hologram plane to its image plane. In this paper opposite-view digital holographic microscopy (OV-DHM) is demonstrated for autofocusing, namely, digitally determining the location of the image plane, and refocusing the object wave without human intervention. In OV-DHM, a specimen is illuminated from two sides in a 4π-alike configuration, and two holograms are generated and recorded by a CCD camera along two orthogonal polarization orientations. The image plane of the sample is determined by finding the minimal variation between the two object waves, and consequently refocusing is performed by propagating the waves to the image plane. Furthermore, the field of view (FOV) of OV-DHM can be extended by combining the two object waves which have an angle in-between. The proposed technique also has the potential to reduce speckle noise and out-of-focus background.

Fast autofocusing in digital holography using the magnitude differential

Typical methods of automatic estimation of focusing in digital holography calculate every single reconstructed frame to get a critical function and then ascertain the focal plane by finding the extreme value of that function. Here, we propose a digital holographic autofocusing method that computes the focused distance using the first longitudinal difference of the magnitude of the reconstructed image. We demonstrate the proposed method with both numerical simulations and optical experiments of amplitude-contrast and phase-contrast objects. The results suggest that the proposed method performs better than other existing methods, in terms of applicability and computation efficiency, with potential applications in industrial and biomedical inspections where automatic focus tracking is necessary.

Real-time computation of diffraction fields for pixelated spatial light modulators

Fast calculation of diffraction field from a three-dimensional object is an important problem in holographic three-dimensional television. As a result of this, several fast algorithms can be found in the literature, but most them omit pixelated structure of the display device used in the reconstruction process. We propose a fast algorithm for diffraction field calculation from a three-dimensional object for a pixelated display device. Real-time calculations can also be achieved when the proposed algorithm is run on a graphical processing unit. Performance assessment of the algorithm is obtained by the computation time of the diffraction field and the error on the reconstructed object. The proposed algorithm employs a precomputed look-up-table which is formed by one-dimensional kernels. Each kernel in the look-up-table denotes a diffraction field on the display device from a point light source at a specific depth along longitudinal axis. Allocated memory space by the precomputed look-up-table is optimized according to the sampling policy of the depth parameter. Look-up-table formed by uniformly sampled depth parameter provides the same error on the reconstructed object with less number of kernels. Also, optical experiments are conducted and successful results are obtained.

Label-free imaging and biochemical characterization of bovine sperm cells

A full label-free morphological and biochemical characterization is desirable to select spermatozoa during preparation for artificial insemination. In order to study these fundamental parameters, we take advantage of two attractive techniques: digital holography (DH) and Raman spectroscopy (RS). DH presents new opportunities for studying morphological aspect of cells and tissues non-invasively, quantitatively and without the need for staining or tagging, while RS is a very specific technique allowing the biochemical analysis of cellular components with a spatial resolution in the sub-micrometer range. In this paper, morphological and biochemical bovine sperm cell alterations were studied using these techniques. In addition, a complementary DH and RS study was performed to identify X- and Y-chromosome-bearing sperm cells. We demonstrate that the two techniques together are a powerful and highly efficient tool elucidating some important criterions for sperm morphological selection and sex-identification, overcoming many of the limitations associated with existing protocols.

Refocus criterion for both phase and amplitude objects in digital holographic microscopy

For digital holographic microscopy applications, we modify the focus criterion based on the integration of the amplitude modulus to make possible its use regardless of the phase or amplitude nature of the objects under test. When applied on holographic data, the original criterion gives, at the focus plane, a minimum or a maximum, for amplitude or phase objects. The criterion we propose here operates on high-pass filtered complex amplitudes. It is shown that the proposed criterion gives a minimum for both types of objects when the focus plane is reached. Experimental results on real samples and simulations are provided, illustrating the efficiency and the potential of the method.

Optical properties of diatom nanostructured biosilica in Arachnoidiscus sp: micro-optics from mother nature

Some natural structures show three-dimensional morphologies on the micro- and nano- scale, characterized by levels of symmetry and complexity well far beyond those fabricated by best technologies available. This is the case of diatoms, unicellular microalgae, whose protoplasm is enclosed in a nanoporous microshell, made of hydrogenated amorphous silica, called frustule. We have studied the optical properties of Arachnoidiscus sp. single valves both in visible and ultraviolet range. We found photonic effects due to diffraction by ordered pattern of pores and slits, accordingly to an elaborated theoretical model. For the first time, we experimentally revealed spatial separation of focused light in different spots, which could be the basis of a micro-bio-spectrometer. Characterization of such intricate structures can be of great inspiration for photonic devices of next generation.

Shedding light on diatom photonics by means of digital holography

Diatoms are among the dominant phytoplankters in the world's oceans, and their external silica investments, resembling artificial photonic crystals, are expected to play an active role in light manipulation. Digital holography allowed studying the interaction with light of Coscinodiscus wailesii cell wall reconstructing the light confinement inside the cell cytoplasm, condition that is hardly accessible via standard microscopy. The full characterization of the propagated beam, in terms of quantitative phase and intensity, removed a long-standing ambiguity about the origin of the light confinement. The data were discussed in the light of living cell behavior in response to their environment.

Refocusing based on amplitude analysis in color digital holographic microscopy

A refocusing criterion adapted to red-green-blue (RGB) digital holographic microscopy is established. It is applicable for both amplitude and phase objects. This color criterion is based on a monochromatic criterion, using the integrated modulus amplitude. Simulated RGB holograms show the value of having color information, even for colorless samples; in addition, the position of the focus plane along the optical axis is determined more accurately. Simulations take into account both the numerical apertures of lenses and noise during the holographic process. We also implement an algorithm exponentially reducing the computation time required for detecting the focus plane. The method is validated on experimental holograms.

4D tracking of clinical seminal samples for quantitative characterization of motility parameters

In this paper we investigate the use of a digital holographic microscope, with partial spatial coherent illumination, for the automated detection and tracking of spermatozoa. This in vitro technique for the analysis of quantitative parameters is useful for assessment of semen quality. In fact, thanks to the capabilities of digital holography, the developed algorithm allows us to resolve in-focus amplitude and phase maps of the cells under study, independently of focal plane of the sample image. We have characterized cell motility on clinical samples of seminal fluid. In particular, anomalous sperm cells were characterized and the quantitative motility parameters were compared to those of normal sperm.

Fast computation of Fresnel diffraction field of a three-dimensional object for a pixelated optical device

In this paper, a fast algorithm is proposed for accurate calculation of the scalar optical diffraction on a pixelated optical device used in the reconstruction process from a three-dimensional object that is formed by scattered sample points over the space. In computer-generated holography, fast and accurate calculation of the diffraction field is an important and a challenging problem. Therefore, several fast algorithms can be found in the literature. The accuracy of the calculations can be determined by the signal processing techniques and the numerical methods used in the calculation of diffraction fields. Furthermore, the quality of reconstructed objects can be affected by the properties of optical devices employed in the reconstruction process. For instance, the pixelated structure of those devices has a significant effect on the reconstruction process. Therefore, the pixelated structure of the display device has to be taken into account. Furthermore, fast calculation of the diffraction pattern can be a bottleneck in dynamic holographic content generation. As a solution to the problems, we propose a fast and accurate algorithm based on a precomputed one-dimensional kernel and scaling of that kernel for the computation of the diffraction pattern for a pixelated display.

Three-dimensional subpixel estimation in holographic position measurement of an optically trapped nanoparticle

We propose three-dimensional (3D) subpixel estimation in the position measurement of a nanoparticle held in optical tweezers in water by using an in-line, low-coherence digital holographic microscope. The 3D subpixel estimation was performed with the addition of axial subpixel estimation to the lateral subpixel estimation introduced in our previous work [Appl. Opt.50, H183 (2011)]. The axial subpixel estimation allowed the step length in the diffraction calculation of a hologram to be increased to ~20 nm while keeping the axial resolution of ~3 nm. This drastically decreased the computation time of the diffraction calculation to less than 10% of the two-dimensional subpixel estimation.

Autofocusing of digital holographic microscopy based on off-axis illuminations

An auto-focusing method for digital holographic microscopy has been proposed by employing two off-axis illumination beams. When specimens are illuminated by two plane waves in different directions, it is found that the farther the reconstruction plane is from the image plane, the wider the two reconstructed images are separated from each other. Thus, the image plane can be determinated by finding the minimum of the variation between the two reconstructed object waves on both the amplitude and phase distributions. The feasibility of the proposed method is demonstrated by the corresponding simulation and experiment.

Autofocusing based on wavelength dependence of diffraction in two-wavelength digital holographic microscopy

An autofocusing method for two-wavelength digital holographic microscopy (TWDHM) based on the wavelength dependence of the diffraction process is proposed. Red and green lights are employed for the illumination of the TWDHM, and the generated holograms are recorded simultaneously by a color CCD camera. Due to the wavelength dependency of the diffraction process, the farther the reconstruction plane is from the image plane, the larger the difference is between the red and green light distributions. Thus, the image plane can be determined by finding the minimum of the variation between the red and green lights on their amplitude distributions. The feasibility of the proposed method is demonstrated by simulation and experiment.

Digital holographic microscopy characterization of superdirective beam by metamaterial

Digital holographic microscopy (DHM) has been successfully applied for the first time to characterize the radiative out-of-plane emission properties of a superdirective device. Complementarily to near-field microscopy, DHM allows us to reconstruct the beam in the far-field region. The angular dispersion of the light beam radiated from a grating composed of air and anti-air metamaterial has been determined, and the proposed technique has highlighted a collimation degree higher than 0.04°, as already evaluated in a previous work. Further considerations on the retrieved phase map of the beam in the acquisition plane are presented.

Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy

We analyze the dependency and the accuracy of the refocusing criterion based on the integrated modulus amplitude in the case of amplitude object. Analytical dependencies on the defocus distance and the numerical aperture are found. This theoretical prediction for the refocusing criterion is well supported by simulation. We study also the robustness of the refocusing criterion by adding salt and pepper and speckle-type noises. We demonstrate that the refocusing criterion is robust up to an significant level of noise that can perturb the holograms.

High-performance holographic technologies for fluid-dynamics experiments

Modern technologies offer new opportunities for experimentalists in a variety of research areas of fluid dynamics. Improvements are now possible in the state-of-the-art in precision, dynamic range, reproducibility, motion-control accuracy, data-acquisition rate and information capacity. These improvements are required for understanding complex turbulent flows under realistic conditions, and for allowing unambiguous comparisons to be made with new theoretical approaches and large-scale numerical simulations. One of the new technologies is high-performance digital holography. State-of-the-art motion control, electronics and optical imaging allow for the realization of turbulent flows with very high Reynolds number (more than 10(7)) on a relatively small laboratory scale, and quantification of their properties with high space-time resolutions and bandwidth. In-line digital holographic technology can provide complete three-dimensional mapping of the flow velocity and density fields at high data rates (over 1000 frames per second) over a relatively large spatial area with high spatial (1-10 microm) and temporal (better than a few nanoseconds) resolution, and can give accurate quantitative description of the fluid flows, including those of multi-phase and unsteady conditions. This technology can be applied in a variety of problems to study fundamental properties of flow-particle interactions, rotating flows, non-canonical boundary layers and Rayleigh-Taylor mixing. Some of these examples are discussed briefly.

Experimental validation for the determination of particle positions by the correlation coefficient method in digital particle holography

The feasibility and the accuracy of the correlation coefficient (CC) method for the determination of particle positions along the optical axis in digital particle holography were verified by validation experiments. A translation system capable of high precision was used to move the particle objects by exact known distances between several different positions. The particle positions along the optical axis were calculated by the CC method and compared with their exact values to obtain the errors of the focus plane determination. The tested particles were two-dimensional (2D) dots in a calibration target along with different-sized glass beads and droplets that reflected and caused a three-dimensional (3D) effect. The results show that the CC method can work well for both the 2D dots and the 3D particles. The effect of other particles on the focus plane determination was also investigated. The CC method can locate the focus plane of particles with high precision, regardless of the existence of other particles.

Phase imaging of cells by simultaneous dual-wavelength reflection digital holography

We present a phase-imaging technique to quantitatively study the three-dimensional structure of cells. The method, based on the simultaneous dual-wavelength digital holography, allows for higher axial range at which the unambiguous phase imaging can be performed. The technique is capable of nanometer axial resolution. The noise level, which increases as a result of using two wavelengths, is then reduced to the level of a single wavelength. The method compares favorably to software unwrapping, as the technique does not produce non-existent phase steps. Curvature mismatch between the reference and object beams is numerically compensated. The 3D images of SKOV-3 ovarian cancer cells are presented.

Extended focused imaging of a microparticle field with digital holographic microscopy

We present a numerical technique for extended focused imaging and three-dimensional analysis of a microparticle field observed in a digital holographic microscope working in transmission. The three-dimensional localization of objects is performed using the local focus plane determination method based on the integrated amplitude modulus. We apply the refocusing criterion locally for each pixel, using small overlapping windows, to obtain the depth map and a synthetic image in which all objects are refocused independent from their refocusing distance. A successful application of this technique in the analysis of the microgravity particle flow experiment is presented.

Simultaneous depth determination of multiple objects by focus analysis in digital holography

Focus analysis techniques from computer vision are applied to digital holography to determine the depth (range) of multiple objects and their surfaces from a single hologram capture. With this method the depths of objects can be determined from a single hologram capture without the need for manual focusing and without prior information on object location. Variance and the Laplacian of Gaussian are analyzed as focus measures, and techniques are proposed for focus plane determination from the focus measure curves. The algorithm is described in detail and demonstrated through simulation and optical experiment.

Simultaneous dual-wavelength reflection digital holography applied to the study of the porous coal samples

We present a simultaneous dual-wavelength phase-imaging digital holographic technique demonstrated on porous coal samples. The use of two wavelengths enables us to increase the axial range at which the unambiguous phase imaging can be performed, but also increases the noise. We employ a noise reduction "fine map" algorithm, which uses the two-wavelength phase map as a guide to correct a single-wavelength phase image. Then, the resulting noise of a fine map is reduced to the level of single-wavelength noise. A comparison to software unwrapping is also presented. A simple way of correcting a curvature mismatch between the reference and the object beams is offered.

Application of the correlation coefficient method for determination of the focal plane to digital particle holography

The correlation coefficient (CC) method, which was proposed by our research group, is applied to digital particle holography to locate the focal plane of particles. It uses the fact that the CC is maximum at the focal plane. The factors influencing this method are discussed with a numerical simulation of holograms. For real holograms, the Wiener filter was proposed to process both recorded holograms and reconstructed images. The application results using the dot array target showed that the Wiener filter is a very effective tool for processing holography-related images. The effects of the dot size and the object distance on the errors in the determination of the focal plane by the CC method were investigated by using the calibration target.

Focus detection from digital in-line holograms based on spectral l1 norms

A rapid focus-detection technique based directly on the spectral content of digital holograms is developed. It differs from previous approaches in that it does not need a full reconstruction of the image. The technique uses l(1) norms of object spectral components associated with the real and imaginary parts of the reconstruction kernel. Further, the l(1) norms can be computed efficiently in the spatial frequency domain using a polar coordinate system, yielding a drastic speedup of approximately 2 orders of magnitude compared with image-based focus detection. Significant computational savings are achieved when subsequent image reconstructions are done selectively over the detected focus distances. Focus-detection results from holograms of plankton are demonstrated that show the technique is both accurate and robust.

Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method

A tomographic imaging system based on wavelength-scanning digital interference holography is developed by applying the angular spectrum method. Compared to the well-known Fresnel diffraction formula, which is subject to a minimum distance requirement in reconstruction, the angular spectrum method can reconstruct the wave field at any distance from the hologram plane. The new system allows three-dimensional tomographic images to be extracted with an improved signal-to-noise ratio, a more flexible scanning range, and an easier specimen size selection. Experiments are performed to demonstrate the effectiveness of the method.

Improvement in visibility of an in-focus reconstructed image in digital holography by reduction of the influence of out-of-focus objects

When a reconstruction is performed on a digital holographic image that contains small objects at different depths, diffraction that is due to out-of-focus objects disrupts the visibility of the nearby focused objects. We propose a method to substitute for focused object amplitudes other amplitudes that will reduce propagation diffraction effects when other depths are investigated. The replacement amplitudes are computed by use of an algorithm that reduces the highest spatial frequencies of the resultant image. The theoretical aspects of the method are presented, and results for simulated and experimental examples are shown.

Numerical reconstruction of digital holograms with variable viewing angles

Here we describe a new method for numerically reconstructing an object with variable viewing angles from its hologram(s) within the Fresnel domain. The proposed algorithm can render the real image of the original object not only with different focal lengths but also with changed viewing angles. Some representative simulation results and demonstrations are presented to verify the effectiveness of the algorithm.