Comparative study of fully three-dimensional reconstruction algorithms for lens-free microscopy

Lens-free on-chip 3D microscopy based on wavelength-scanning Fourier ptychographic diffraction tomography

Lens-free on-chip microscopy is a powerful and promising high-throughput computational microscopy technique due to its unique advantage of creating high-resolution images across the full field-of-view (FOV) of the imaging sensor. Nevertheless, most current lens-free microscopy methods have been designed for imaging only two-dimensional thin samples. Lens-free on-chip tomography (LFOCT) with a uniform resolution across the entire FOV and at a subpixel level remains a critical challenge. In this paper, we demonstrated a new LFOCT technique and associated imaging platform based on wavelength scanning Fourier ptychographic diffraction tomography (wsFPDT). Instead of using angularly-variable illuminations, in wsFPDT, the sample is illuminated by on-axis wavelength-variable illuminations, ranging from 430 to 1200 nm. The corresponding under-sampled diffraction patterns are recorded, and then an iterative ptychographic reconstruction procedure is applied to fill the spectrum of the three-dimensional (3D) scattering potential to recover the sample's 3D refractive index (RI) distribution. The wavelength-scanning scheme not only eliminates the need for mechanical motion during image acquisition and precise registration of the raw images but secures a quasi-uniform, pixel-super-resolved imaging resolution across the entire imaging FOV. With wsFPDT, we demonstrate the high-throughput, billion-voxel 3D tomographic imaging results with a half-pitch lateral resolution of 775 nm and an axial resolution of 5.43 μm across a large FOV of 29.85 mm2 and an imaging depth of >200 μm. The effectiveness of the proposed method was demonstrated by imaging various types of samples, including micro-polystyrene beads, diatoms, and mouse mononuclear macrophage cells. The unique capability to reveal quantitative morphological properties, such as area, volume, and sphericity index of single cell over large cell populations makes wsFPDT a powerful quantitative and label-free tool for high-throughput biological applications.

Lensless holographic microscope with a time and memory-saving algorithm for large-volume imaging of organoids

Organoids, the 3D culture systems derived from stem cells, are promising models for human organs. However, organoid study requires large-volume imaging with single cell resolution, which is beyond the spatial bandwidth limit of conventional optical microscopy. Herein, we propose a lensless holographic microscope empowered with a time and memory-saving algorithm. It solves the trade-off between the imaging field of view, resolution, and processing speed, and provides a practical tool for the study of organoids. We first build a compact microscopy system using a multi-angle LED illumination scheme and an on-chip structure. Then we develop a fast angular spectrum formula for fast reconstruction of oblique-illuminated coaxial holography under the under-sampling condition. Additionally, we derive a multi-angle illuminated filtered backpropagation algorithm to achieve high-precision and slice-wise recovery of 3D structures of objects. The reconstruction process demands only 1/50 of the memory required by a traditional optical diffraction tomography algorithm. Experimental results indicate that the proposed method can achieve 6.28 mm × 4.71 mm × 0.37 mm volume imaging within 104 s. Through the standardized polystyrene beads test, we demonstrate that the proposed microscope has micrometer-scale resolution in both lateral and axial directions. In addition, the 3D imaging results of salivary gland organoids show great application prospects of the proposed method in the field of living biological sampling imaging.

Multi-slice ptychographic imaging with multistage coarse-to-fine reconstruction

The ability to image 3D samples with optical sectioning is essential for the study of tomographic morphology in material and biological sciences. However, it is often hampered by limitations of acquisition speed and equipment complexity when performing 3D volumetric imaging. Here, we propose, to the best of our knowledge, a new method for 3D reconstruction from a minimum of four intensity-only measurements. The complementary structured patterns provided by the digital micromirror device (DMD) irradiate the outermost layer of the sample to generate the corresponding diffraction intensities for recording, which enables rapid scanning of loaded patterns for fast acquisition. Our multistage reconstruction algorithm first extracts the overall coarse-grained information, and then iteratively optimizes the information of different layers to obtain fine features, thereby achieving high-resolution 3D tomography. The high-fidelity reconstruction in experiments on two-slice resolution targets, unstained Polyrhachis vicina Roger and freely moving C. elegans proves the robustness of the method. Compared with traditional 3D reconstruction methods such as interferometry-based methods or Fourier ptychographic tomography (FPT), our method increases the reconstruction speed by at least 10 times and is suitable for label-free dynamic imaging in multiple-scattering samples. Such 3D reconstruction suggests potential applications in a wide range of fields.

The Incubascope: a simple, compact and large field of view microscope for long-term imaging inside an incubator

Optical imaging has rapidly evolved in the last decades. Sophisticated microscopes allowing optical sectioning for three-dimensional imaging or sub-diffraction resolution are available. Due to price and maintenance issues, these microscopes are often shared between users in facilities. Consequently, long-term access is often prohibited and does not allow to monitor slowly evolving biological systems or to validate new models like organoids. Preliminary coarse long-term data that do not require acquisition of terabytes of high-resolution images are important as a first step. By contrast with expensive all-in-one commercialized stations, standard microscopes equipped with incubator stages offer a more cost-effective solution despite imperfect long-run atmosphere and temperature control. Here, we present the Incubascope, a custom-made compact microscope that fits into a table-top incubator. It is cheap and simple to implement, user-friendly and yet provides high imaging performances. The system has a field of view of 5.5 × 8 mm², a 3 μm resolution, a 10 frames per second acquisition rate, and is controlled with a Python-based graphical interface. We exemplify the capabilities of the Incubascope on biological applications such as the hatching of Artemia salina eggs, the growth of the slime mould Physarum polycephalum and of encapsulated spheroids of mammalian cells.

GSURE criterion for unsupervised regularized reconstruction in tomographic diffractive microscopy

We propose an unsupervised regularized inversion method for reconstruction of the 3D refractive index map of a sample in tomographic diffractive microscopy. It is based on the minimization of the generalized Stein's unbiased risk estimator (GSURE) to automatically estimate optimal values for the hyperparameters of one or several regularization terms (sparsity, edge-preserving smoothness, total variation). We evaluate the performance of our approach on simulated and experimental limited-view data. Our results show that GSURE is an efficient criterion to find suitable regularization weights, which is a critical task, particularly in the context of reducing the amount of required data to allow faster yet efficient acquisitions and reconstructions.

Tomography of irregular rough particles using the error-reduction algorithm with multi-views interferometric particle imaging

This work reports the 3D reconstruction of a particle from a set of three simulated interferometric images of this particle (from three perpendicular angles of view). The reconstruction of each view from its corresponding interferometric pattern uses the error-reduction (ER) algorithm. The 3D reconstruction enables an estimation of the volume of the particle. The method is tested on a dendrite-like particle. An experimental demonstration of the technique is done using a digital micromirror device (DMD) that generates the interferometric images of "programmable" rough particles.

Fast compressive lens-free tomography for 3D biological cell culture imaging

We present a compressive lens-free technique that performs tomographic imaging across a cubic millimeter-scale volume from highly sparse data. Compared with existing lens-free 3D microscopy systems, our method requires an order of magnitude fewer multi-angle illuminations for tomographic reconstruction, leading to a compact, cost-effective and scanning-free setup with a reduced data acquisition time to enable high-throughput 3D imaging of dynamic biological processes. We apply a fast proximal gradient algorithm with composite regularization to address the ill-posed tomographic inverse problem. Using simulated data, we show that the proposed method can achieve a reconstruction speed ∼10× faster than the state-of-the-art inverse problem approach in 3D lens-free microscopy. We experimentally validate the effectiveness of our method by imaging a resolution test chart and polystyrene beads, demonstrating its capability to resolve micron-size features in both lateral and axial directions. Furthermore, tomographic reconstruction results of neuronspheres and intestinal organoids reveal the potential of this 3D imaging technique for high-resolution and high-throughput biological applications.

From Fienup's phase retrieval techniques to regularized inversion for in-line holography: tutorial

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

Reconstruction of in-line holograms: combining model-based and regularized inversion

In-line digital holography is a simple yet powerful tool to image absorbing and/or phase objects. Nevertheless, the loss of the phase of the complex wavefront on the sensor can be critical in the reconstruction process. The simplicity of the setup must thus be counterbalanced by dedicated reconstruction algorithms, such as inverse approaches, in order to retrieve the object from its hologram. In the case of simple objects for which the diffraction pattern produced in the hologram plane can be modeled using few parameters, a model fitting algorithm is very effective. However, such an approach fails to reconstruct objects with more complex shapes, and an image reconstruction technique is then needed. The improved flexibility of these methods comes at the cost of a possible loss of reconstruction accuracy. In this work, we combine the two approaches (model fitting and regularized reconstruction) to benefit from their respective advantages. The sample to be reconstructed is modeled as the sum of simple parameterized objects and a complex-valued pixelated transmittance plane. These two components jointly scatter the incident illumination, and the resulting interferences contribute to the intensity on the sensor. The proposed hologram reconstruction algorithm is based on alternating a model fitting step and a regularized inversion step. We apply this algorithm in the context of fluid mechanics, where holograms of evaporating droplets are analyzed. In these holograms, the high contrast fringes produced by each droplet tend to mask the diffraction pattern produced by the surrounding vapor wake. With our method, the droplet and the vapor wake can be jointly reconstructed.

Lens-free microscopy for 3D + time acquisitions of 3D cell culture

Thanks to a novel three-dimensional imaging platform based on lens-free microscopy, it is possible to perform multi-angle acquisitions and holographic reconstructions of 3D cell cultures directly into the incubator. Being able of reconstructing volumes as large as ~5 mm3 over a period of time covering several days, allows us to observe a broad range of migration strategies only present in 3D environment, whether it is single cell migration, collective migrations of cells and dispersal of cells. In addition we are able to distinguish new interesting phenomena, e.g. large-scale cell-to-matrix interactions (>1 mm), fusion of cell clusters into large aggregate (~10,000 µm2) and conversely, total dissociation of cell clusters into clumps of migrating cells. This work on a novel 3D + time lens-free microscopy technique thus expands the repertoire of phenomena that can be studied within 3D cell cultures.

Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology

Reconstruction of phase objects is a central problem in digital holography, whose various applications include microscopy, biomedical imaging, and fluid mechanics. Starting from a single in-line hologram, there is no direct way to recover the phase of the diffracted wave in the hologram plane. The reconstruction of absorbing and phase objects therefore requires the inversion of the non-linear hologram formation model. We propose a regularized reconstruction method that includes several physically-grounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation on reconstructions of accurate simulations of in-line holograms based on the Mie theory. As our approach is adaptable to several in-line digital holography configurations, we present and discuss the promising results of reconstructions from experimental in-line holograms obtained in two different applications: the tracking of an evaporating droplet (size ∼ 100μm) and the microscopic imaging of bacteria (size ∼ 1μm).

Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy [Invited]

Quantitative label-free imaging is an important tool for the study of living microorganisms that, during the last decade, has attracted wide attention from the optical community. Optical diffraction tomography (ODT) is probably the most relevant technique for quantitative label-free 3D imaging applied in wide-field microscopy in the visible range. The ODT is usually performed using spatially coherent light illumination and specially designed holographic microscopes. Nevertheless, the ODT is also compatible with partially coherent illumination and can be realized in conventional wide-field microscopes by applying refocusing techniques, as it has been recently demonstrated. Here, we compare these two ODT modalities, underlining their pros and cons and discussing the optical setups for their implementation. In particular, we pay special attention to a system that is compatible with a conventional wide-field microscope that can be used for both ODT modalities. It consists of two easily attachable modules: the first for sample illumination engineering based on digital light processing technology; the other for focus scanning by using an electrically driven tunable lens. This hardware allows for a programmable selection of the wavelength and the illumination design, and provides fast data acquisition as well. Its performance is experimentally demonstrated in the case of ODT with partially coherent illumination providing speckle-free 3D quantitative imaging.