Tomographic Diffractive Microscopy Research Articles

Jones tomographic diffractive microscopy with a polarized array sensor.

Tomographic diffractive microscopy (TDM) based on scalar light-field approximation is widely implemented. Samples exhibiting anisotropic structures, however, necessitate accounting for the vectorial nature of light, leading to 3-D quantitative polarimetric imaging. In this work, we have developed a high-numerical aperture (at both illumination and detection) Jones TDM system, with detection multiplexing via a polarized array sensor (PAS), for imaging optically birefringent samples at high resolution. The method is first studied through image simulations. To validate our setup, an experiment using a sample containing both birefringent and non-birefringent objects is performed. Araneus diadematus spider silk fiber and Pinna nobilis oyster shell crystals are finally studied, allowing us to assess both birefringence and fast-axis orientation maps.

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.

From digital holographic microscopy to optical coherence tomography – separate past and a common goal

In this paper we briefly present the history and outlook on the development of two seemingly distant techniques which may be brought close together with a unified theoretical model described as common k-space theory. This theory also known as the Fourier diffraction theorem is much less common in optical coherence tomography than its traditional mathematical model, but it has been extensively studied in digital holography and, more importantly, optical diffraction tomography. As demonstrated with several examples, this link is one of the important factors for future development of both techniques. Full Text: PDF ReferencesN. Leith, J. Upatnieks, "Reconstructed Wavefronts and Communication Theory", J. Opt. Soc. Am. 52(10), 1123 (1962). CrossRef Y. Park, C. Depeursinge, G. Popescu, "Quantitative phase imaging in biomedicine", Nat. Photonics 12, 578 (2018). CrossRef D. Huang et al., "Optical Coherence Tomography", Science 254(5035), 1178 (1991). CrossRef D. P. Popescu, C. Flueraru, S. 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Kak, "Reflection Mode Diffraction Tomography", Ultrason. Imag. 7, 300 (1985). CrossRef M. Sarmis et al., "High resolution reflection tomographic diffractive microscopy", J. Mod. Opt. 57(9), 740 (2010). CrossRef L. Foucault et al., "Versatile transmission/reflection tomographic diffractive microscopy approach", J. Opt. Soc. Am. A 36(11), C18 (2019). CrossRef W. Krauze, P. Ossowski, M. Nowakowski, M. Szkulmowski, M. Kujawińska, "Enhanced QPI functionality by combining OCT and ODT methods", Proc. SPIE 11653, 116530B (2021). CrossRef E. Mudry, P.C. Chaumet, K. Belkebir, G. Maire, A. Sentenac, "Mirror-assisted tomographic diffractive microscopy with isotropic resolution", Opt. Lett. 35(11), 1857 (2010). CrossRef P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, P. So, "Scanning color optical tomography (SCOT)", Opt. Expr. 23(15), 19752 (2015). CrossRef J. Jung, K. Kim, J. Yoon, Y. Park, "Hyperspectral optical diffraction tomography", Opt. Expr. 24(3), 1881 (2016). CrossRef T. 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Optimizing sample illumination scanning for reflection and 4Pi tomographic diffractive microscopy

Tomographic diffractive microscopy (TDM) is increasingly gaining attention, owing to its high-resolution, label-free imaging capability. Fast acquisitions necessitate limiting the number of holograms to be recorded. Reconstructions then rely on optimal Fourier space filling to retain image quality and resolution, that is, they rely on optimal scanning of the tomographic illuminations. In this work, we theoretically study reflection TDM, and then the 4Pi TDM, a combination of transmission and reflection systems. Image simulations are conducted to determine optimal angular sweeping. We found that three-dimensional uniform scanning fills Fourier space the best for both reflection and 4Pi configurations, providing a better refractive index estimation for the observed sample.

Reconstruction enhancement via projection screening in holographic tomography

This paper presents an algorithm for automatic detection of erroneous amplitude and phase components of a sample’s optical field, acquired by a holographic tomograph with a limited angle of projection. By applying image processing methods and statistical analysis to find and remove unfit projections, the quality of tomographic reconstruction of a 3D refractive index distribution of an object is greatly improved. The proposed methods can find their application in preprocessing of data in holographic tomography. Full Text: PDF ReferencesA. Kuś, W. Krauze, P. L. Makowski, and M. Kujawińska, "Holographic tomography: hardware and software solutions for 3D quantitative biomedical imaging (Invited paper)", ETRI Journal, 41, 1 (2019). CrossRef V. Balasubramani et al., "Phase unwrapping in ICF target interferometric measurement via deep learning", Appl. Opt., 60, 10 (2021). CrossRef Y. Park, C. Depeursinge, and G. Popescu, "Quantitative phase imaging in biomedicine", Nature Photonics, 12, 10 (2018). CrossRef W. Krauze, P. Makowski, M. Kujawińska, and A. Kuś, "Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography", Opt. Express, 24, 5 (2016). CrossRef D. Ryu et al., "A non-calorimetric approach for investigating the moisture-induced ageing of a pyrotechnic delay material using spectroscopies", Sci Rep, 9, 1 (2019). CrossRef B. S. Lipkin, Picture Processing and Psychopictorics. (Saint Louis, Elsevier Science 2014). DirectLink A. M. Taddese, N. Verrier, M. Debailleul, J.-B. Courbot, and O. Haeberlé, "Optimizing sample illumination scanning in transmission tomographic diffractive microscopy", Appl. Opt., 60, 6 (2021). CrossRef

Optimizing sample illumination scanning in transmission tomographic diffractive microscopy.

Due to the sequential nature of data acquisition, it is preferable to limit the number of illuminations to be used in tomographic diffractive microscopy experiments, especially if fast imaging is foreseen. On the other hand, for high-quality, high-resolution imaging, the Fourier space has to be optimally filled. Up to now, the problem of optimal Fourier space filling has not been investigated in itself. In this paper, we perform a comparative study to analyze the effect of sample scanning patterns on Fourier space filling for a transmission setup. Optical transfer functions for several illumination patterns are studied. Simulation as well as experiments are conducted to compare associated image reconstructions. We found that 3D uniform angular sweeping best fills the Fourier space, leading to better quality images.

A fast homotopy algorithm for gridless sparse recovery* *Submitted to the editors on december 1, 2020.

In this paper, we study the solving of the gridless sparse optimization problem and its application to 3D image deconvolution. Based on the recent works of [] introducing the sliding Frank–Wolfe algorithm to solve the Beurling LASSO problem, we introduce an accelerated algorithm, denoted BSFW, that preserves its convergence properties, while removing most of the costly local descents. Besides, as the solving of BLASSO still relies on a regularization parameter, we introduce a homotopy algorithm to solve the constrained BLASSO that allows to use a more practical parameter based on the image residual, e.g. its standard deviation. Both algorithms benefit from a finite termination property, i.e. they are guaranteed to find the solution in a finite number of step under mild conditions. These methods are then applied on the problem of 3D tomographic diffractive microscopy images, with the purpose of explaining the image by a small number of atoms in convolved observations. Numerical results on synthetic and real images illustrates the improvement provided by the BSFW method, the homotopy method and their combination.

Versatile transmission/reflection tomographic diffractive microscopy approach.

Tomographic diffractive microscopy (TDM) has gained interest in recent years due to its ability to deliver high-resolution, three-dimensional images of unlabeled samples. It has been applied to transparent samples in transmission mode, as well as to surface studies in reflection mode. Mudry et al. [Opt. Lett.35, 1857 (2010)OPLEDP0146-959210.1364/OL.35.001857] introduced the concept of mirror-assisted TDM (MA-TDM), an elegant approach for achieving quasi-isotropic-resolution microscopic imaging, but which is still to be experimentally applied. In this work, we show that a simplified version of MA-TDM allows for transforming a reflective TDM setup into a more versatile instrument, also capable of observing transparent samples in transmission mode if using specific sample holders made out of a mirror and coated with a low-thickness transparent spacer.

Tomographic Diffractive Microscopy: A Review of Methods and Recent Developments

Tomographic diffractive microscopy (TDM) is a label-free, far-field, super-resolution microscope. The significant difference between TDM and wide-field microscopy is that in TDM the sample is illuminated from various directions with a coherent collimated beam and the complex diffracted field is collected from many scattered angles. By utilizing inversion procedures, the permittivity/refractive index of investigated samples can be retrieved from the measured diffracted field to reconstruct the geometrical parameters of a sample. TDM opens up new opportunities to study biological samples and nano-structures and devices, which require resolution beyond the Rayleigh limit. In this review, we describe the principles and recent advancements of TDM and also give the perspectives of this fantastic microscopy technique.

Simplified tomographic diffractive microscopy for axisymmetric samples

Tomographic diffractive microscopy exhibits intrinsic features making it a method of choice for 3D high-resolution label-free imaging. However, these results are achieved at the cost of a heavy data acquisition/reconstruction process. This drawback can be circumvented for certain classes of samples. For example, axisymmetric samples, like optical or textile fibers, present geometrical properties that can be advantageously used to speed-up the acquisition process. We propose to take benefit of these properties to allow for full reconstruction of axisymmetric samples’ complex refractive index distribution, using four approaches, adapted to 3D samples. We applied the proposed reconstruction scheme, based on a numerical rotation of data, to both simulated and experimental data sets.

Morphometric analysis of erythrocytes from patients with thalassemia using tomographic diffractive microscopy.

Complete blood count is the most common test to detect anemia, but it is unable to obtain the abnormal shape of erythrocytes, which highly correlates with the hematologic function. Tomographic diffractive microscopy (TDM) is an emerging technique capable of quantifying three-dimensional (3-D) refractive index (RI) distributions of erythrocytes without labeling. TDM was used to characterize optical and morphological properties of 172 erythrocytes from healthy volunteers and 419 erythrocytes from thalassemic patients. To efficiently extract and analyze the properties of erythrocytes, we developed an adaptive region-growing method for automatically delineating erythrocytes from 3-D RI maps. The thalassemic erythrocytes not only contained lower hemoglobin content but also showed doughnut shape and significantly lower volume, surface area, effective radius, and average thickness. A multi-indices prediction model achieved perfect accuracy of diagnosing thalassemia using four features, including the optical volume, surface-area-to-volume ratio, sphericity index, and surface area. The results demonstrate the ability of TDM to provide quantitative, hematologic measurements and to assess morphological features of erythrocytes to distinguish healthy and thalassemic erythrocytes.

Tomographic diffractive microscopy: Towards high-resolution 3-D real-time data acquisition, image reconstruction and display of unlabeled samples

Tomographic diffractive microscopy allows for imaging unlabeled specimens, with a better resolution than conventional microscopes, giving access to the index of refraction distribution within the specimen, and possibly at high speed. Principles of image formation and reconstruction are presented, and progresses towards real-time, three-dimensional acquisition, image reconstruction and final display, are discussed.

Tomographic diffractive microscopy with isotropic resolution

Microscopy techniques allowing observation of unlabeled samples have recently experienced a regain of interest. In particular, approaches based on recording of the optical field diffracted by the specimen, in amplitude and phase, have proven their capacities for biological investigations. When combined with variations of specimen illumination, tomographic acquisitions are possible. One limitation of previously developed approaches is the anisotropic resolution, characteristic of all transmission microscopes. In this context, an instrument, characterized by isotropic high-resolution 3D imaging capabilities, is still awaited. For the first time, to the best of our knowledge, we have developed tomographic diffractive microscopy combining specimen rotation and illumination rotation, which delivers images with (almost) isotropic resolution below 200 nm. The method is illustrated by observations of nanoscopic fiber tips, microcrystals and pollens, and should be helpful for characterizing freestanding natural (diatoms, spores, red or white blood cells, etc.) or artificial samples.

Improved longitudinal resolution in tomographic diffractive microscopy with an ellipsoidal mirror.

Tomographic diffractive microscopy is a technique, which is able to image transparent unstained samples with high resolution. The three-dimensional distribution of the complex refractive index can be reconstructed quantitatively from the measured scattered fields under various illumination and detection angles, according to the diffraction tomography theorem. We propose a tomographic diffractive microscopy setup with an ellipsoidal mirror as the light collector. We demonstrate analytically and with numerical simulation that this approach permits to obtain images with drastically improved resolution.

Tomographic diffractive microscopy with agile illuminations for imaging targets in a noisy background.

Tomographic diffractive microscopy is a marker-free optical digital imaging technique in which three-dimensional samples are reconstructed from a set of holograms recorded under different angles of incidence. We show experimentally that, by processing the holograms with singular value decomposition, it is possible to image objects in a noisy background that are invisible with classical wide-field microscopy and conventional tomographic reconstruction procedure. The targets can be further characterized with a selective quantitative inversion.

Superresolution with full-polarized tomographic diffractive microscopy.

Tomographic diffractive microscopy is a three-dimensional imaging technique that reconstructs the permittivity map of the probed sample from its scattered field, measured both in phase and in amplitude. Here, we detail how polarization-resolved measurements permit us to significantly improve the accuracy and the resolution of the reconstructions, compared to the conventional scalar treatments used so far. An isotropic transverse resolution of about 100nm at a wavelength of 475nm is demonstrated using this approach.

Tomographic diffractive microscopy of living cells based on a common-path configuration

We demonstrate a common-path tomographic diffractive microscopy technique for three-dimensional (3D) refractive-index (RI) imaging of unstained living cells. A diffraction grating is utilized to generate a reference beam that traverses a blank region of the sample in a common-path off-axis interferometry setup. Single-shot phase images captured at multiple illumination angles are used for 3D RI reconstruction based on optical diffraction tomography. The common-path configuration shows lower temporal phase fluctuations and better RI resolution than a Mach-Zehnder configuration. 3D subcellular RI distributions of live HeLa cells are quantified.

Tomographic diffractive microscopy and multiview profilometry with flexible aberration correction

We have developed a tomographic diffractive microscope in reflection, which permits observation of sample surfaces with an improved lateral resolution, compared to a conventional holographic microscope. From the same set of data, high-precision measurements can be performed on the shape of the reflective surface by reconstructing the phase of the diffracted field. Doing so allows for several advantages compared to classical holographic interferometric measurements: improvement in lateral resolution, easier phase unwrapping, reduction of the coherent noise, combined with the high-longitudinal precision provided by interferometric phase measurements. We demonstrate these capabilities by imaging various test samples.

Limited-angle tomography applied to biological objects

Optical limited-angle tomography is strongly required in biological applications, as often there is an access to projections gathered from a small angle range. Choosing a reconstruction algorithm among many available is always a tradeoff between speed of calculation and quality of reconstruction. In this paper we present the studies how the a priori information about object’s geometry influences efficiency of the Data Replenishment Algorithm. The analysis is based on tomographic reconstruction of real biological cell of human malignant lymphoma. Full Text: PDF References S. Kou, C. Sheppard, "Image formation in holographic tomography", Opt. Lett. 33, 2362 (2008). CrossRef J. Hsieh, Computed Tomography Principles, Design, Artifacts, and Recent Advances (Wiley 2009). S. Isikman et al., "Lens-free optical tomographic microscope with a large imaging volume on a chip", P. Natl. Acad. Sci. USA 108, 7296 (2011). CrossRef S. Vertu, E. Maeda, J. Flügge, J. Delaunay, O. Haeberlé, "Comparison of resolution in tomographic diffractive microscopy using combinations of sample rotation and illumination rotation", Proc. SPIE 7904 (2011). CrossRef A. Likhachov, "Projection data replenishment algorithm for limited angle tomography", Optoelectron. Instrum. Data Process. 45, 55 (2009). DirectLink R. Gordon, "A tutorial on art (algebraic reconstruction techniques)", IEEE T. Nucl. Sci. 21, 78 (1974). CrossRef A. Andersen, A. Kak, "Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the Art Algorithm", Ultrasonic Imaging 6, 81 (1984). CrossRef D. Verhoeven, "Limited-data computed tomography algorithms for the physical sciences", Appl. Optics 32, 3736 (1993). CrossRef J. Fessler, B. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation", IEEE T. Signal Proces. 51, 560 (2003). CrossRef Z. Wang, A. Bovik, "A universal image quality index", IEEE Signal Proc. Let. 9, 81 (2002). CrossRef M. Kujawińska et al., "Problems and Solutions in Tomographic Analysis of Phase Biological Objects", Fringe 2013, 671 (2013) CrossRef

High-resolution tomographic diffractive microscopy in reflection configuration

Tomographic diffractive microscopy (TDM) is a label-free imaging technique that reconstructs the 3D refractive index map of the probed object with an improved resolution compared to confocal microscopy. In this work, we consider a TDM implementation in which the sample is deposited on a reflective substrate. We show that this configuration requires calibration and inversion procedures that account for the presence of the substrate for getting highly resolved quantitative reconstructions.