Abstract

Holographic tomography (HT) is an advanced label-free optical microscopic imaging method used for biological studies. HT uses digital holographic microscopy to record the complex amplitudes of a biological sample as digital holograms and then numerically reconstruct the sample’s refractive index (RI) distribution in three dimensions. The RI values are a key parameter for label-free bio-examination, which correlate with metabolic activities and spatiotemporal distribution of biophysical parameters of cells and their internal organelles, tissues, and small-scale biological objects. This article provides insight on this rapidly growing HT field of research and its applications in biology. We present a review summary of the HT principle and highlight recent technical advancement in HT and its applications.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Holography is a quantitative imaging technique used to record and reconstruct the whole optical field. The term holography was named and pioneered by Dennis Gabor around in the 1940s [13] but the technique did not get significant interest until the 1960s when a coherent laser source became available [4]. At the same time, phase contrast microscopy has started to realize the phase nature of the light to replicate the sample’s nature for investigation [5,6]. Meanwhile, the holographic technique was implemented in microscopy using a visible light source for the hologram recording [7]. The analog carrier frequency technique was combined with holography and reframed as off-axis holography to overcome the zero-order and twin image problem [810]. The holographic technique created a significant impact after the invention of charge-coupled devices (CCDs), and by utilizing CCDs to digitally record the interference patterns as a hologram, and the computer for numerical reconstructions, the technique referred to as digital holography (DH) [1115]. The DH extended the range of applications in optical metrology [16] for measuring refractive index (RI) distribution [1719], particle tracking microscopy [20,21], phase-shifting analysis [22,23], and sample profile reconstruction [2426]. Later, the quantitative microscopic imaging method [2729]—referred to as digital holographic microscopy (DHM), interferometric phase microscopy, quantitative phase microscopy, or 2D quantitative phase imaging (2D QPI) [3034]—allowed the measurement of morphological structures such as dry mass density, cell volume ratio, sectional depth resolved [35,36], and three-dimensional RI information [37,38].

The DHM technique extended the methodological practice by adapting filtered back projection techniques similar to the image reconstruction principle used in the x-ray computed tomography (CT) method [39]. This digital holography-based tomographic method is promising for quantitative RI cell imaging and analysis [4046] and is referred in different terminology such as synthetic aperture microscopy, optical diffraction tomography (ODT), phase nanoscopy, tomographic phase microscopy, optical diffraction microscopy, 3D QPI, and holographic tomography (HT) [29,40,4653]. In this review we call this technique as holographic tomography. In general, HT includes three main modules as shown in Fig. 1: a digital holographic microscope, a module delivering variable illumination directions, and a numerical module which performs the tomographic reconstruction. This review paper is organized as follows: Section 2 discusses the HT measurement principles; Section 3 reviews the HT experimental architectures to demonstrate full projection angle and limited projection angle tomography realized by sample rotation, beam rotation, and integrated approaches; Section 4 describes software algorithms used in HT; and Section 5 provides an overview of HT applications in the biomedical field. Finally, Section 6 draws the summary and the outlook of HT techniques.

 figure: Fig. 1.

Fig. 1. Basic modules of holographic tomography: FAT, full-angle tomography; LAT, limited-angle tomography.

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2. HOLOGRAPHIC TOMOGRAPHY

Holographic tomography is a quantitative 3D imaging technique used to study thesubcellular structural nature of the cell and micrometer structures of thesamples. In general, a 3D volumetric sample with a spatially distributed RI is a collection of slices along the incident wave propagation direction [54], as shown in Fig. 2. The basic expression of transmitted wavefronts (${U_t}$) in a weakly scattering media with anincident wave ${U_o}(t)$ can be expressed as [38]

$${U_t}({r^\prime} ) = \int O(r ){U_o}({r} ) G({r^\prime - r} ){\rm d}r,$$
where ${G}({r})$ is Green’s function [55,56], and ${O}({r})$ is the object function with wave vector ${K}$, with RI values of sample ($n_s^2$) and surrounding medium ($n_m^2$) can be expressed as
$$O(r ) = {K^2}\left[{n_s^2(r) - n_m^2} \right].$$
The symbols $r$ and $r^{\prime}$ in Eq. (1) corresponding to the coordinates (${x},\;{y},\;{z}$) and (${{x}^{\prime}},\;{{y}^{\prime}},\;{{z}^{\prime}}$) are shown in Fig. 1. The integral function can be obtained by expandingEq. (1) as shown:
 figure: Fig. 2.

Fig. 2. Illustration of a three-dimensional volumetric sample arrangement with spatially distributed refractive values. Reprinted from [54].

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 figure: Fig. 3.

Fig. 3. Simplified illustration of holographic tomography image recording, spatial frequency mapping, and 3D image reconstruction of the object used. Reprinted from [54].

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$$\begin{split}&{{U}_{t}}\left({x^{\prime}},{y^{\prime}},{z^{\prime}}=l \right)=\iint \exp \!\left(j\!\left( u{x^{\prime}}+v{y^{\prime}} \right) \right){\rm d}u{\rm d}v\\&\qquad\times\iiint\left\{ {\left( O( x,y,z ){{U}_{o}}( x,y,z) \right)}/_{\sqrt{{{k}^{2}}-{{u}^{2}}-{{v}^{2}}}}\right\}\\&\qquad\times \exp \left[{- { j}({{ux} + {vy}} )}\right]\exp\! \left[ {j\sqrt {{k^2} - {u^2} - {v^2}} \left( {l - z}\right)} \right]{\rm d}x{\rm d}y{\rm d}z.\end{split}$$
The sample’s slice separation ($\Delta z$) is considered, and total summation of the output wave corresponds to the sample contribution $U_B^m({x^\prime ,y^\prime;z^\prime = l - m\Delta z})$ with each slice $o({x,y;m\Delta z})$ corresponding to each illumination wave ${U_o}({x,y;m \Delta z})$ and expressed as
$$\begin{split}{{U}_{o}}\!\left( x,y;m \Delta z\right)&={{U}_{o}}\!\left( x,y;\left( m-1 \right)\Delta z\right)\\&\quad \times xo\!\left( x,y;\left( m-1 \right)\Delta z\right)h( x,y;\Delta z ),\end{split}$$
where $h({x,y;\Delta z})$ is the free space impulse response [38,54] and $m$ is the integer which represents theslice. The transmitted object wave is allowed to interfere with the reference wave and the corresponding interference is recorded as a digital hologram for numerical reconstruction. The reconstructed wavefronts are then Fourier transformed, and the corresponding spatial frequencies are mapped in the frequency domain based on the Fourier diffraction theorem along the semi-circular arc, which covers the frequency up to $\sqrt 2 k$ as illustrated in Fig. 3. The radius of the $\rm arc (k)$ depends on the wavelength and can beexpressed as $k =\frac{{2\pi}}{\lambda}$. To estimate the Fourier transform of the object function for all frequencies centered at the origin, the simplified 2D frequency collection and mapping, and the 3D image reconstruction as shown in Fig. 3.

For classical microscopic imaging, the maximum spatial frequency collection is limited by the numerical aperture (NA) of the lens used. The maximum spatial cutoff frequency coverages for the microscopic imaging system in the lateral and axial directions are $k\rm NA$ and $k({1 - \sqrt {1 - {{\rm NA}^2}}})$, respectively, as illustrated in Fig. 4(a). For the 3D tomographic reconstruction, the transmitted object frequencies collected at different illumination angles are mapped to the Ewald’s sphere, and the 2D representation of the frequency coverage and its expansions are illustrated in Fig. 4(b).

 figure: Fig. 4.

Fig. 4. Spatial cutoff frequency coverages of (a) microscopic imaging (single illumination) and (b) tomographic imaging system (multiple illuminations). Reprinted from [54].

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As briefly mentioned in the introduction, HT can be achieved by different approaches such as by sample rotation (SR), beam rotation (BR), and integrated dual-mode tomography (IDT) approaches. Each approach has its own advantages and disadvantages. The 3D coherent transfer functions (CTFs) [31,52,57] corresponding to SR, BR, and IDT approaches are constructed and compared in Fig. 5. Here, (m, n, s) are the Fourier frequencies along the (${x},\;{y},\;{ z}$) directions.

 figure: Fig. 5.

Fig. 5. Comparison of coherent transfer functions (CTFs) in three-dimensional space. (a),(b) Single-direction SR approach in which the missing frequency coverage can be seen in the inset images, (c) full-angle SR CTF shows an isotropic frequency coverage. (d),(e) Single-axis ($x$ and $y$ axis) beam rotation CTF, (f) BRCTF of ${x} {-}{y}$ directions offers laterally extended frequency coverages, but there are still missing frequencies in the axial direction as shown in the inset images. (g) The integrated dual-mode approach offers UFO-like-shaped CTF with benefits of both beam and sample rotation approaches as the sectional images shown in (h) and (i).(j) Shows the extended isotropic frequency coverages in 2D as shown in (k), (l). Reprinted from [57,58].

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The 3D CTFs of single-direction SR along the ${x} {-} {z}$ and ${y} {-} {z}$ directions are shown in Figs. 5(a) and 5(b), in which the “missing apple core” (MAC) problem occurred along the $m$ and $n$ directions, as shown in the inset image. The MAC problem can be overcome by rotating the sample in full-angle directions and the CTF shows the isotropic spatial frequency coverage as shown in Fig. 5(c). The 3D CTFs of beam rotation along a single axis in the ${x}$ and ${y}$ directions can get the extended lateral spatial frequency coverage along the rotation direction, as shown in Figs. 5(d) and 5(e). When the illumination beam is rotated in full circle, it offers doughnut-like-shaped CTF with fully extended spatial frequency coverage in the lateral direction; however, it still has the “missing cone” along the optical axis and this leads to limited frequency coverage in the axial direction, as shown in Fig. 5(f). In the IDT approach, the full-angle sample rotation and circular beam rotation approaches are combined to obtain the benefits of both the approaches which offered an unidentified flying object (UFO)-like-shaped CTF, as shown in Fig. 5(g), and the center slice images showed an extended spatial frequency coverage in Figs. 5(h) and 5(i). In order to improve the spatial frequency coverage, simultaneous sample rotation with beam rotation approach extended isotropic frequency coverages, as shown in Fig. 5(j), and the center slice images shown in Figs. 5(k) and 5(l) visualize the full frequency extensions. The overall frequency coverages of the holographic microscopic system in the lateral and axial directions are given by [29]

$${F}_{{x},{y}}^{{\rm microscopy}} = \frac{{2{n \sin\theta}}}{{\lambda}}\,\,{\rm and}\,\,{F}_{z}^{{\rm microscopy}} = \frac{{{n}\!\left( {1 - {\cos\theta }} \right)}}{{\lambda}}.$$
HT with SR is given by
$${F}_{{x},{z}}^{{\rm SR}} = \frac{{4{n \sin}\!\left({{{\theta} / 2}} \right)}}{{\lambda}}\,\,{\rm and}\,\,{F}_{y}^{{\rm SR}} = \frac{{2{n \sin\theta }}}{{\lambda}}.$$
For HT with the BR approach,
$${F}_{{x},{y}}^{{\rm BR}} = \frac{{4{n \sin\theta}}}{{\lambda}}\,\,{\rm and}\,\,{F}_{z}^{{\rm BR}} = \frac{{2{ n}\!\left( {1 - {\cos\theta }} \right)}}{{\lambda}}.$$
For HT with the IDT approach,
$${F}_{{ x},{y}}^{{\rm IDT}} = \frac{{4{n \sin\theta}}}{{\lambda}}\,\,{\rm and}\,\,{F}_{z}^{{\rm IDT}} = \frac{{2{n \sin\theta }}}{{\lambda}}.$$

When HT with simultaneous sample and beam rotation approach,

$${F}_{{x},{y},{z}}^{{\rm isotropic}} = \frac{{4{n \sin\theta}}}{{\lambda}}.$$

3. HT: MEASUREMENT SYSTEMS

In HT, the sample’s projection measurements are conducted either by rotating theillumination beam or by rotating the sample [3741,45,59]. In the beam rotation approach, thesample and observation systems are kept static whereas the illuminationoptical beam is controlled to alter the angular views. The conventionalgalvanomirror-based experimental architecture was adapted to rotate theillumination beam, and later the liquidcrystal on silicon (LCoS) spatial light modulators (SLMs) [53,6064], digital micromirror devices (DMDs) were used as an alternative to the galvanomirror system which also led to the creation of structured light illumination [6569] and the other high-speed implementations [6974] in the HT system. The drawback of the BR approach is the limited anglemeasurements resulting in anisotropic resolution with missing spatial frequency coverages [31,45]. An alternative to the BR approach isthe SR method, in which under static illumination, the sample is rotatedand its projections are captured which offers isotropic spatial frequencycoverage resulting in high-quality tomographic reconstructions [75,76]. The SR technique usescapillary-supported approaches [37,76,77], the co-axial rotation method [78], and optical tweezers techniques [59,7982]. It is also possible to combine bothBR and SR HT approaches in a single system to capture the benefits fromboth the methods [5456,59]. In this section, wepresent an overview of the different available approaches used inachieving HT.

 figure: Fig. 6.

Fig. 6. Sample rotation HT with rotary holder. (a) Experimental schematic,(b) HT system photo. CL, condenser lens; PD, Petri dish; MO,microscope objective; RH, rotary holder. Reprinted from [77].

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A. HT: Sample Rotation Approach

The HT by SR approach is achieved by keeping the illumination beam stationary without any tilt angles; however, the angular scanning is attained by rotating the sample under observation [37,83, 75]. The SR approach has high potential to deliver an isotropic frequency coverage when the sample rotates in full-angle directions- as shown in Fig. 4(c), which results in high-quality tomographic image reconstruction. The key point lies in the method used to manipulate the biological sample for the rotation and there are several methods demonstrated to rotate the sample. In general, the sample is loaded into a micropipette [37,84,85] or cuvette with a motorized rotating stage [70,72]; for the sample rotation and for the hologram recording either common-path or off-axis interferometric configuration was used. In the SR approach, the angular phase maps acquisition may also support the phase unwrapping of the objects from the optically thick perspective [86].

The experimental schematic of the sample rotation tomography system withcapillary-supported sample manipulation with common-path DHMarchitecture is shown in Fig. 6. The alignment of the illumination condenser lens CL, Petridish arrangement, and the microscopic objective MO with an accuraterotary holder are illustrated in Figs. 6(a) and 6(b),respectively. These types of capillary-supported rotation approachessuffer from the aberrations due to the perturbations created bytumbling of whole sample medium during the rotation [77,87]. Additionally there is alsoa refractive index mismatch between the cell culture medium and thesurrounding medium, as shown in Fig. 6(a). It is highly difficult to match the refractive index of the cell culture medium and the capillary, which results in strongrefraction from the inner boundary of the surface as brieflyillustrated in Fig. 7. However,this problem has been addressed with a computational data processingalgorithm and a compensation approach was demonstrated and verifiedwith both numerical simulation and experimental data [87].

 figure: Fig. 7.

Fig. 7. Wave propagation nature of the capillary supported approach. W,plane wave; B1, first boundary of the capillary generatescylindrical wave; S, sample; B2, second boundary of thecapillary creates the aberration in the sample wave; B3, Petridish boundary creates the deformation of the wave field. Reprinted from [87].

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 figure: Fig. 8.

Fig. 8. Experimental schematic of the coaxial rotation HT. BS, beamsplitter; CMOS, image sensor. Reprinted from [78].

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To overcome the perturbation created by the whole sample medium, coaxial rotation was adapted in HT [78]. In this method, the sample is loaded into a microtube and kept stationary. The illumination and detection optics were simultaneously rotated as like the conventional CT approach [39]. This method of approach reduces the mechanical perturbations induced by the sample holder and limits the optical aberrations induced by the sample medium tumbling during the sample measurement. The experimental schematic of the coaxial rotation HT architecture is shown in Fig. 8. The coaxial rotation method also depends on mechanical components to handle the whole optical system’s rotation. Furthermore, all of the SR approaches mentioned above are limited in handling the sample due to the limitations imposed by the mechanical components used [88]. The limited single direction sample rotation (either in the ${x} {-} {z}$ or ${y} {-} {z}$ directions) observation results in missing spatial frequencies, as shown in Figs. 5(a) and 5(b).

Optical tweezers are one such potential approach to manipulate the free-floating biological sample in all directions [79,8992]. The optical tweezers were combined with a microfluidic channel [81], and flow cytometer [93] was also utilized for the sample rotation; however, the control of the microchannel’s confinement and the stable flow strength is required for the hologram recording process. Optical tweezers combined with phase imaging [80,9294] and realized ${180^\circ}$ sample rotation in HT by utilizing the advantage of holographic optical tweezers (HOT). This experimental setup also has the confocal fluorescent microscopy module to validate the label-free HT results [79]. The HOT uses a SLM to generate a controlled twin trap beam for the trapping and rotation with an angular scanning range of ${180^\circ}$ which allowed a noninvasive tomographic imaging of suspended live cells. Later the HOT-based HT system as shown in Fig. 9, extended the angular scanning range to ${360^\circ}$ to achieve a full-angle sample rotation to solve the MAC problem [82], resulting in the isotropic frequency coverage.

 figure: Fig. 9.

Fig. 9. Experimental schematic of sample rotation HT. Green representation shows the DHM for the hologram recording, red representation shows the HOT for the sample manipulation, and blue representation shows the fluorescent microscope. Reprinted from [82].

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This experimental architecture allows manipulation of the single live cell in a more convenient way in all directions without any mechanical components. For the arbitrary shaped sample manipulation, a HT-activated trapping was demonstrated to control the position and alignment of arbitrarily shaped samples with a stable manner in the (${x},{y},{z}$) axis [95].

B. HT: Beam Rotation Approach

The main advantage of BR HT is the lack of a direct interaction with the sample—it is simply illuminated with a set of plane waves incident at different angles. There is no mechanical contact—contrary to capillary-based rotation [87]—and the laser power at the sample plane is at low levels—contrary to optical-tweezers-based systems [84]. The technique may be regarded as synthetic aperture approach, since the illumination direction is altered and the detector is kept stationary. With each hologram different frequency content is recorded and as a result the resolution in the sample plane is increased. The systems may be grouped either based on interferometer type used or as it is in this case, key component used to produce the beam rotation.

1. Mechanical Beam Rotation

The very first generation of HT systems utilized a motorized mirror conjugated to the sample plane with a 4f optical system to alter the direction of the beam [29,95]. The beam rotation should provide as much spatial frequency coverage in the 3D Fourier space as possible in order to reduce the missing data range. This is realized by providing beam rotation along a specific trajectory within a cone with respect to the sample, preferably entirely filling the NA of the imaging objective or even exceeding it into the dark field region [96]. For this reason, 2D scanners are used, and to provide speed and accuracy, galvanometer mirrors are the most commonly used components, as shown in Fig. 10 [41,49,60,97101]. The actual scanning strategy within the NA of the objective does not influence the reconstruction result significantly [102], and for this reason the preferred beam rotation trajectory is the cone—or a circle in the front focal plane of the illuminating microscope objective. In other words, rotating the beam at a constant tilt angle along the $Z$ axis is enough to provide an efficient dataset. This can be realized with a prism [50], which could contribute to device cost reduction. Alternatively, BR could be realized with a set of light sources placed around the sample [103]. This idea, however, has been realized with in-line holography (without the reference beam) rather than off-axis DHM.

 figure: Fig. 10.

Fig. 10. Mach–Zehnder-based HT with a two-axis galvanometer mirror scanner (GM) and illumination optical system (L2-O1). Reprinted from [98].

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2. Optical Beam Rotation in HT

As the illumination optical systems used in the BR approach require high magnification to provide illumination angles as large as possible, there is a concern for the mechanical scanning stability and its impact on the reconstruction quality [104]. This is also important because the optical angle of the rotated beam is twice the mechanical angle of the scanning mirror. For this reason, a new group of solutions, avoiding mechanically moved components, was developed. The first ideas involved phase-only SLM [63,105]. An example of a HT with such a modulator instead of a galvanometer mirror is shown in Fig. 11(a). While the mechanical stability of the beam rotation was the initial motivation for such systems, an additional benefit of using an SLM is the possibility to correct the wavefront of the illuminating beam. This is done as a pre-calibration of the system, in which a series of look-up tables with wavefront profiles that cancel out the phase aberrations of the beam [53,57,62,63,105] are calculated based on a measurement without the sample in the field of view (FoV). The SLM-based tomographic systems, however, showed little prospect for time-efficient data acquisition due to framerate being generally limited to 30 Hz for a standard SLM. For this reason, the second group utilizing DMDs, as shown in Fig. 11(b), emerged [64,106]. While the framerate of the modulator is no longer an issue, in the case of DMDs, the beam rotation device is an amplitude modulator that strongly acts as a diffraction grating and requires additional methods to mitigate related detrimental effects [106], ultimately leading to structured illumination (SI) in HT [67]. SI in this case means that there are at least two and usually three illumination directions present in a single hologram and this technique is not limited to DMD-based HT. Using an SLM always leads to producing unwanted zero diffraction order by the modulator that requires correction, e.g., by placing a physical mask in an intermediate focus plane of a $4f$ system, as shown in Fig. 11. Interestingly, one can phase shift the pattern on the modulator to retrieve the information for each illumination direction in the hologram [67].

 figure: Fig. 11.

Fig. 11. (a) Beam rotation HT using LCoS SLM, reprinted from [63]. The unwanted zero order is blocked by a spatial filter ${F}$ placed in the Fourier plane of the T1-T2 ${4f}$ system and the moving ${+}{1}$ order is transmitted to illuminate the sample. (b) Beam rotation in HT using a DMD, reprinted from [64].

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C. Integrated Tomography Method

In order to obtain the highestpossible resolution in HT, the best approach is tocombine the SR and BR approaches. This covers the most information inFourier space, as shown in Fig. 5(j). In this approach, one should collect a BR dataset for anumber of consecutive objects’ angular positions [52,107]. One of the main challenges of these methods is thecombination of usually mechanical movement of the sample at high NAand magnification of the optical system [56,108]. Froman object-rotation point of view, lower magnification of the systemprovides more room for mechanical rotation imprecision. Resolution-wise, however, providing as high NA as possible isrequired. For this reason, the concept of integrating beam rotationand optically driven object rotation with HOT emerged [57] and provided a compromise betweennoninvasiveness and high quality of theresult.

D. Wavelength Scanning Tomography

The location of information recorded in a single hologram, which is mapped in the Fourier domain, depends on the illumination/object rotation angle, NA of the system and wavelength, as described in Section 2 and illustrated in Fig. 4. So far, the solutions provided in this review have focused on the first part, while maximizing the NA and using a short wavelength for resolution improvement. An interesting approach, however, is to fill in the Fourier space by varying the wavelength of the illumination [71]. Unfortunately, the wavelength change itself is insufficient to provide enough frequency coverage on its own and needs to be supported by one of the main approaches to HT, preferably illumination rotation [71]. In this case three fixed illumination directions were used. With this approach, there is a risk of RI dispersion affecting the result. Alternatively, instead of utilizing the wavelength scanning for filling the Fourier space, the dispersion of the sample can be characterized using a single wavelength at a time for multiple reconstructions throughout the visible spectrum [72].

E. Multiplexed Tomography

The topic of hologram multiplexing has recently gained increased attention [109]. In HT, one of the challenges for measurement systems is to shorten the data acquisition time, simultaneously providing a cost-effective device. The reason for this is, first of all, the stability of the system. When using high magnification optics to provide high NA and recording a series of holograms, the measured object should neither change nor move during the measurement in order to fully use the resolution provided by HT. The idea of shortening the measurement time and increasing the acquisition speed was first solved with a high-speed camera and galvanometer mirrors [41]. A more efficient solution would be to minimize the number of projections required for a high-quality reconstruction by using more sophisticated algorithms (discussed in Section 4). Second, more than one projection could be acquired in a single (multiplexed) hologram, which was already the case in some of the aforementioned systems [67,68,71,108]. Depending on the approach the data is either fully demultiplexed [67,68] or the effective NA of the system is reduced, because there are at least two [108] or three [71] projections placed in a single hologram and overlapped in its NA region. This approach was also extended to allow up to four projections in a single hologram [69] up to the point in which the full tomographic dataset is acquired within a single hologram [110,111]. In this case the beam scanning component is replaced with a microlens array, as shown in Fig. 12. Unfortunately, this is suitable for rather low-scattering objects, since the information from multiple illumination directions overlaps in the Fourier domain of the hologram. In fact, the bandwidth of a single hologram allows for lossless packing of up to six projections [112], although such an approach requires six independent reference beams.

 figure: Fig. 12.

Fig. 12. Single-shot HT with projection multiplexing for a full projection set using a microlens array (MLA) to generate illuminations. Reprinted from [110].

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F. System Validation

As shown in Sections 3.A3.E, there are multiple approaches to experimental systems in the area of HT. These differ significantly in terms of system NA, wavelength, number of projections acquired, configuration, frequency spectrum coverage, and aberration corrections employed in the preprocessing of holograms. This fact leads to a conclusion that the same object measured in each HT system would produce a different result. Usually, these systems would be numerically analyzed with synthetic test objects and then verified with either simple samples, such as microspheres, or already complex ones, such as cells, to test the effectiveness of the solution presented in each case. Since HT is a quantitative phase imaging technique it should focus on the first part as a quantitative character and provide full metrology of the result. There have been attempts to impose standard imaging tests for coherent imaging techniques such as a Siemens star [113]. However, such a test is not sufficient for 3D RI measurement. One of the solutions could be to use spatial bandwidth coverage [114]. Unfortunately, this approach does not fully compensate for measurement-related errors.

For this reason, more complex calibration objects (phantoms) with optical and structural properties and features typically found in mammalian cells were developed [115]. The phantoms were manufactured by 3D laser photolithography (direct laser writing) with the RI engineered during a single fabrication step. This method allows for sophisticated structures exhibiting step-like and gradient phase features as depicted in Fig. 13 to be manufactured.

 figure: Fig. 13.

Fig. 13. RI calibration object: (a) model, (b) horizontal and vertical cross sections of the RI measured with beam rotation tomography. Reprinted from [115].

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4. SOFTWARE DEVELOPMENTS

In this section, a description of state-of-the-art algorithms for the retrieval of 3D RI distribution of analyzed biological samples is given. In general, there are two objectives that are addressed by any tomographic reconstruction method: (1) high-resolution reconstruction and (2) isotropic resolution (obtained by filling in the missing frequency information as shown in Fig. 5). Some methods presented in this section have been created to solve only one of these problems while others attempted to address both.

A. First-Order Scattering Approximation

In HT, tomographic reconstruction algorithms that assume that only first-order scattering is taking place when the incident field propagates through the investigated sample are currently the most popular ones. These methods give satisfactory results when applied to measurements of weakly scattering specimens, such as individual biological cells on a Petri dish or thin tissue slices.

One group of such methods utilizes the Fourier diffraction theorem [45] which relates the complex scattering potential of an object with the complex amplitude of an object’s projections. This relation is linear through application of first-order Born or Rytov approximation. It has already been shown that the Rytov approximation is more suitable for biological samples as it does not limit the maximum optical path difference introduced by the specimen [116]. One example of such methods is the Gerchberg–Papoulis (GP) algorithm [117,118] which iteratively computes the Fourier transform of the reconstruction and inverse Fourier transform of the reconstruction’s spectrum. Simultaneously, constraints are applied in each domain: specifically, nonnegativity (in the reconstruction domain) and consistency with measured data (in the spatial domain). This method gives high-quality results in reconstruction planes that are perpendicular to the optical axis and are close to the focal plane; however, axial resolution is relatively low and elongation of the reconstruction is visible in this direction. The computation time of this method is usually around a few seconds per iteration. While the number of iterations is of the order of hundreds.

In the modified version of this method, one additional constraint is automatically generated and applied in the reconstruction domain, namely finite object support (the new method is then called Gerchberg-Papoulis with support constraint, GP-SC) [119]. It is generated through an auxiliary algorithm, which utilizes total variation minimization [120]. Without affecting the computation time, this method gives a superior quality of results, especially in the axial direction, as shown in Fig. 14. When compared to classical GP, the computation time is similar: it takes time to compute the object support; however, when it is taken into account, the number of GP iterations reduces to approximately 10–20.

 figure: Fig. 14.

Fig. 14. Comparison of reconstruction results obtained with (a), (b), (g), (h) direct inversion; (c), (d), (i), (j) Gerchberg–Papoulis algorithm with nonnegativity constraint, and (e), (f), (k), (l) Gerchberg–Papoulis algorithm with additional constraint in the form of automatically generated object support. The objects presented are (a)–(f) 3D-printed cell phantom and (g)–(l) keratinocyte cell. The red contour shows the extent of the object support generated with the auxiliary algorithm in the GP-SC method. Reprinted from [119].

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B. Propagation-based Solutions

Another group of methods are procedures that incorporate propagation of the complex field through the reconstruction volume. In contrast tothe algorithms that are based on the first-order approximation, thesemethods give higher-quality results when applied to measurements ofmultiple-scattering specimens. One example of such a technique is theextended-depth-of-focus filtered backpropagation algorithm which wasdeveloped for object rotation configuration (ORC-EDOF-FBPP) [121] and later for the illuminationscanning scenario (ISC-EDOF-FBPP) [98]. Here, each measured complex field is rigorouslybackpropagated through the immersion medium. The resultant field isthen transformed according to the Rytov approximation. When measuredfields for all angles undergo this procedure, they are summed to formthe tomographic reconstruction. Despite the fact that this algorithmutilizes the first-order Rytov approximation, it is in fact designedto offer accuracy which is constant for all ${z}$-planes (where “${z}$” stands for optical axis direction as shown in Fig. 2), since itperforms rigorous field propagation. Thus, it gives superior resultswhen compared to procedures based on the first-order approximation,however at a cost of high computational burden—calculation of areconstruction can take up to 1 min.

One disadvantage of EDOF-FBPP is that it does not address missing-coneartifacts in illumination scanning scenarios. Thus, a modified versionof this method has been proposed. In the new algorithm, callediterative ODT (iODT) [122,123], in eachiteration for every captured tomographic projection two fieldpropagations are computed: the plane wave is forward propagatedthrough the estimate of the reconstruction, and the complex fieldcaptured at the camera plane is backpropagated through the sameestimate. Then, based on the difference between these two propagatedfields, the error distribution is calculated and used to update theestimate of the reconstruction. This approach allows not only takingmultiple scattering into account but can also potentially minimize themissing-cone artifacts in illumination scanning scenarios due to theiterative nature of the procedure.

Another numerical reconstruction method that is designed to retrieve RIinformation from multiple-scattering samples is learning tomography(LT). It was designed first with the beam propagation method (LT-BPM)as the forward model [124] andlater BPM was changed to the split-step nonparaxial method (LT-SSNPM)[125]. In this technique, theplane wave for each illumination direction is propagated through theestimate of the reconstruction with the given forward model. Then, theresultant field is compared with the measured field. The differencebetween the fields is treated as a cost function, which is minimizedwith an optimization procedure. As a result, in each iteration thereconstruction is corrected. By applying constraints in eachiteration, such as nonnegativity or smoothness of the result, thisapproach allows minimization of the missing-cone artifacts.

In the above-mentioned methods, when the field is propagated throughthe reconstruction, the reconstruction is treated as a series ofslices with infinitesimally small thickness. Recently, a differentpropagation model has been proposed, called the multilayer Born (MLB)model [126]. In this method,the reconstruction is treated as a sequence of slices with finitethickness. Then, the field is propagated through the first slab withthe use of the Born approximation. The resultant field is treated asan incident field which is propagated through the second slab. Thisprocess is repeated until the propagation through the whole estimateof the reconstruction is performed. The advantage of MLB overpreviously described models is higher accuracy, especially when highvalues of illumination angles are used in illumination scanningscenarios. Also, this procedure enables retrieval of the backwardscattered field. The computational time of iODT, LT-SSNPM, and MLB iscomparable and equals around 1 h.

C. Machine Learning Algorithms

During the last decade, a significant shift has been visible within the research groups working in the field of optical tomography toward development of reconstruction procedures that are utilizing machine learning. A review of such methods can be found in [127].

In the last year, several new approaches have been proposed. One example includes a sparse dictionary learning algorithm which specifically addresses the missing-cone artifacts in illumination-scanning HT [128]. In this approach, first a total-variation (TV)-regularized reconstruction is calculated with traditional algorithms. From the obtained result, features from lateral planes are extracted to form a dictionary which is then used in the final reconstruction to correct features in the lateral and axial directions, thus minimizing the missing-cone artifacts. An obvious advantage of this procedure is that it does not require prior learning.

Another method, called deep prior diffraction tomography [129] follows a different philosophy. It uses a convolutional neural network (CNN), however without its prior training. Instead, the authors make use of the fact that CNNs inherently favor natural images and thus would disfavor tomographic reconstructions with missing-cone artifacts. Based on this property, a complete reconstruction approach has been designed and tested. It takes several hours to compute the result with this approach.

DeepRegularizer is a more traditional approach [130]. Here, the authors generated pairs of reconstructions: one with a quick low-resolution algorithm and another with a high-resolution procedure that utilizes TV regularization. These pairs were then used to train a deep neural network which later was applied to rapidly transform low-resolution reconstructions into high-quality ones.

5. APPLICATIONS

As mentioned throughout the previous sections, 3D quantitative phase imaging has emerged as one of the most powerful imaging tools for the study of cells and tissues in a noninvasive manner. Its popularity in the biomedical community is quickly increasing mainly due to the availability of the commercial holographic tomography systems offered by the companies Tomocube Inc. [131] and Nanolive [132]. On the other hand, the continuous development of innovative solutions by the research photonics community brings improved measurement accuracy to the systems, ease, and certainty of analysis, as well as access to new functionalities and multimodality [133135]. In this section we review representative examples of HT applications in cells and tissues investigations.

A. Quantitative Imaging of Single Cells and Their Internal Organelles

The quantitative 3D imaging capability of HT enables label-free and high-accuracy retrieval of various physiological parameters of cells and their internal organelles, including morphological (shape, volume, sphericity) and biophysical (RI distribution, dry mass, dry mass density) parameters.

The most widely studied cells are red blood cells (RBCs) and white blood cells. This is due to their important functions in living organisms: carrying oxygen from lungs to tissues and defending the body against infection, respectively. RBCs are lack of nucleus or subcellular organelles, and therefore the investigation of RBC focuses on measuring cell volume, surface area, sphericity, cytoplasmic Hb concentration [136], morphological and biophysical properties [137], and various blood storage duration and conditions [138]. HT was utilized for identification of metabolic disorder [139]. The RI distribution has been explored for visualizing the morphological alterations of RBCs caused by parasitized protozoa, such as Plasmodium (P.) falciparum [99] and Babesia microti [140].

Several works investigate white blood cell types with focus on basic parameters, mentioned above in relation to RBC [78] response to immune stimulus [78,141] and external mechanical stimuli [142]. In order to have sufficient statistical analysis of blood cells, studies are often connected with application of fluidic systems [93].

Numerous works are focused on the measurements of internal cells structures. For instance, lipid droplets (LDs) and their biochemical change under oleic acid. LDs as subcellular organelles with an important role of lipid storage and metabolism can be measured with a HT system, without using any markers [143]. Researchers found, with 4D tracking of the fast dynamic of LDs, that there is intracellular transport of LDs in living cells [144]. Kim et al. demonstrated changes in physicochemical properties of nucleoli in HeLa cells [145], Schürmann et al. observed inversion in the chromatin arrangement in the nuclei of mouse retina cells [146], and Umemura et al. presented the imaging and analysis of living diatom Cylindrotheca sp. in seawater without using any pretreatment such as fluorescence staining [147]. Also based on optical properties measured by means of HT systems, lots of comparative studies have been conducted. The changes in the RI values after the fixation process were detected in the reconstructed phase distributions [148]. According to Baczewska et al. studies the RI values inside cell compartments decrease after the PFA fixation process, and the observed RI changes were found to have the most significant loss in the nucleolus; however, the RI values are different for various cell lines, as shown in Fig. 15. These findings may have significant impact while using QPI data for diagnostics and for machine learning procedures design. Fang-yen et al. found rapid increases in RI values of cytoplasm upon exposure to the acetic acid solution, while there were no significant changes in nucleoli [60]. A good quantitative RI comparison between the tomographic methods was analyzed using a single living cell Candida rugosa (ATCC 200555) using the integrated tomography setup described in Section 3.D; the center sliced tomographic reconstruction comparison and its subcellular level tomographic reconstruction are shown in Fig. 16. Furthermore, 3D dynamics of RI distributions of lipid droplets in human hepatocytes (Huh-7) were described in order to investigate structural and biochemical changes of internal vesicles during chemical treatment [149]. It should be mentioned that in order to overcome the limited molecular specificity in QPI, the HT measurements are combined with fluorescence imaging [143,145,146].

 figure: Fig. 15.

Fig. 15. HT measurements and analysis of four cell lines: (a) 3D visualization of cell lines NRK-52E and RAW 264.7, (b) 2D RI cross section of the RI distribution in the best focal plane of live and fixed NRK-52E and RAW 264.7 cells, (c) differences in RI between nucleolus–nucleus and nucleolus–cytoplasm for four representative cell lines. Reprinted from [148].

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 figure: Fig. 16.

Fig. 16. HT reconstruction of Candida rugosa (ATCC 200555). (i): RI distribution comparison of center slice results between (a) full-angle sample rotation, (b) beam rotation, and (c) integrated tomography approaches. Scale bar: 3 µm, color bar: RI values. (ii): subcellular tomographic reconstruction. Reprinted from [57].

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 figure: Fig. 17.

Fig. 17. Four refractive index images of high and continuous regions of chromosome of DM cells during four stages of mitosis. Reprinted from [150].

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B. Monitoring of Cell Processes and Pathology

Applying dry mass and dry mass density determined by HT measurements as a biomarker enables measurement and monitoring of cell processes such as mitosis or cell death, either as apoptosis or necrosis. Serial RI tomography images of chromosomes in live cells during mitosis (Fig. 17) were compared with three-dimensional confocal micrographs to demonstrate that compaction and decompaction of chromosomes induced by osmotic change were characterized by linked changes in chromosome RI, volume, and the motilities of fluorescent proteins [150]. Variations in induced apoptosis have been presented, such as responses of normal muscle cells (C2C12) and rhabdomyosarcoma cells to calcium electroporation, which previously has been reported as an effective method of rhabdomyosarcoma cells reduction [151]. Another important field of application of HT and 3D-QPI systems can be applied is cancer biology. Recently, Simon et al. presented 3D RI tomograms of human alveolar epithelial A549 cells infected with H3N2 influenza [152]. In other works, 3D RI of healthy and cancerous epithelial cells (CA9-22 and BCC cell lines) were measured and analyzed [153], live HT29 cells were investigated to image a human colon adenocarcinoma cell line [42], the mass of chromosomes in intact living cells was quantified and two human colon cancer lines HT-29 and T84 cells were differentiated [49], and morphology of living specimen (testate amoeba, Protista) was measured [84]. Quantitative monitoring capabilities of HT were also used to identify and quantify differences in single live platelet in its morphology, cell volume, as well as changes in biophysical parameters [154,155]. Most recently, multimodal approaches combining HT and fluorescence microscopic techniques have been used in the correlative study of cell pathophysiology [156].

C. Investigations of Tissues and Small-Scale Biological Objects

The emerging, but not fully implemented, HT applications are connected with phase investigations of tissues including 3D histopathology, cancer tissues classification, and utilizing RI as a biomarker of diseases in tissue biopsies or investigations of small biological objects [157]. The most demanded application is label-free volumetric imaging of thick-tissue slides, exploiting refractive index distributions as intrinsic imaging contrast. It is considered as future support for the digital histopathology [158], which relies upon the staining and sectioning of biological tissues. This process is laborious and may cause artefacts and distort tissues. Importantly, the staining and visualization of thicker (${\gt} 5\,\,{\unicode{x00B5}\rm m}$) tissues is limited by strong light absorption and scattering. An important aspect and challenge in implementation of HT in histopathology is the use of thick samples measured in a large FoV with high resolution. This is connected with overcoming the main technical issues, namely image degradation due to multiple light scattering and small holographic retrieval FoV. For large-scale HT of biological tissues/samples, the RI variation must be small enough in order to minimize refraction, diffraction, and scattering effects, but the imaging method must be sensitive enough to still detect this RI variation in the wavefront and allow for sufficient contrast in the reconstructed image. The standard way to minimize the RI variations in a sample is to apply optical clearing [159,160]. Optical clearing aims to homogenize the RI in a sample in order to increase imaging depth and image quality [159]. However, optical clearing causes RI differences to be (very) small, necessitating high sensitivity and a low noise level in the reconstruction. van Rooij et al. had recently proposed the full experimental and processing path for imaging an optically cleared zebrafish larva in $13\,\,{\rm mm}^{3}$ volume with 4 mm resolution [160]. The authors also demonstrated a clinical application of the technique by imaging an entire adult cryoinjured zebrafish heart. The processing includes high-resolution imaging using a large image sensor and phase-shifting digital holography to make full use of the spatial frequency bandwidth of the system and high-sensitivity RI detection through off-axis sample placement combined with numerical focus tracking during rotation, and acquisition of a large number of projections, as shown in Fig. 18.

 figure: Fig. 18.

Fig. 18. (a) Coronal, (b) sagittal, and (c) axial cross sections of HT reconstructed refractive index contrast of an optically cleared 3 day old zebrafish larva. Reprinted from [160].

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 figure: Fig. 19.

Fig. 19. Sliced image comparison of a normal colon tissue (a) bright field and stained with H&E staining and (b) an unstained neighbor tissue imaged with HT. Reprinted from [161].

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However, the application of a clearing procedure in combination with the necessity of mechanical fixing of a biological sample for HT with object rotation has significant limitations, as described in Section 3.A. Hugenneta et al. have presented a different approach to multiscale label-free volumetric histopathology of thick-tissue slides. They addressed the scattering and limited FoV issues by constructing a long-working-distance HT optical setup and multiscale HT reconstruction and seamless stitching of multiple 3D tomograms algorithm, which considers optical aberration due to thick tissues [161]. The experimental setup enabled mesoscopic imaging of human pancreatic and small and large intestine tissues over a millimeter-scale FoV (${2}\;{\rm mm} \times {1.75}\;{\rm mm} \times {0.2}\;{\rm mm}$) with submicrometer spatial resolution (${170}\;{\rm nm} \times {170}\;{\rm nm} \times {1200}\;{\rm nm}$), as shown in Figs. 19(a) and 19(b). For validation purposes, adjacent tissues were prepared and imaged using the conventional H&E staining method, which exhibits good agreement with the presented method. Volumetric RI-based histopathology could potentially be used for rapid cancer diagnosis during intraoperative pathology consultations or small biopsy samples.

However, it still needs several enhancements and innovative solutions to overcome the issues connected with scattering and absorption by thick tissues, histological interpretation of RI-based biophysical parameters, data capture speed, and their tomographic analysis. Support should come from newly emerging machine-learning-based methods [124,162] for segmentation [163] and cell-type classifications [164166].

6. SUMMARY AND OUTLOOK

HT is a promising label-free quantitative three-dimensional imaging and analysis technique which demonstrated numerous applications in various fields, for example, to study the micrometer-sized 3D samples with small fraction of micrometer spatial resolution and ${{10}^{- 4}}$ RI sensitivity. This article provides fundamental principal insights of constructing CTFs for all the possible cases in implementing HT with its spatial cutoff frequency constraints imposed by the high NA of the objective lens used. Also, the power of resolution for all the possible cases is briefly described. In general, HT methodology acquires the sample’s information either by adapting the SR or by BR approaches. The SR approach demonstrated its potential ability to achieve isotropic resolution enhancements especially when implemented by noncontact optical techniques based on HOT. The SR experimental methodologies and their implementation challenges with the possible solutions were discussed in this paper. The BR method is another possible approach to achieve HT, in which the illumination beam control is the key factor to collect the sample information at different illuminations angles. The development of BR HT under different implementation techniques with their subsequent advantages and disadvantages were elaborated in this paper. In addition, the integrated tomography method which combines both SR and BR techniques to archive the full extended isotropic resolution was covered in this paper, including other extended HT approaches by wavelength scanning and multiplexed HT techniques. Once the experimental systems are developed, it is important to validate the system resolution and other key parameters with the standard target. In HT, numerical algorithms play a vital role in reconstructing the high-quality tomographic images, and its state of art with its recent trends including machine learning algorithm developments were also outlined. Finally, a wide range of applications in biological studies and quantitative analysis of different cells and tissues were presented with a selection of the results highlighted in the paper.

The advantages of the label-free measurement principle of the HT technique attracts researchers and scientists to study the biological specimens in the native culture environment with insightful nature at its subcellular level analysis. Over the past decade, we have clearly witnessed the sustained growth of HT and its popularity rapidly increased when companies such as Tomocube Inc. and Nanolive launched the commercialized HT products. However, the works focused on further increase of measurement volumetric accuracy in HT are continued through the implementation of novel, improved system architectures, development of enhanced reconstruction algorithms, and implementation of machine learning approaches. Additionally, HT has become an important technique in biological correlative microscopy, a technology that allows the acquisition of large amounts of data from a single tissue block or cells. HT is most often paired with fluorescence and polarization-based systems as well as traditional staining methods. Hopefully, multimodal HT systems will support the research and implementation into medical practice in 3D phase histopathology. However, to make the method fully applicable, more research is needed on the histological interpretation of RI information. Moreover, this generic approach could have far-reaching applications in histopathology and cytometry, possibly in conjunction with machine learning methods. At present, HT has just begun to achieve recognition for its capabilities and in the near future will undoubtedly hold an irreplaceable role in biological studies and analysis.

Funding

Ministry of Science and Technology, Taiwan (108-2221-E-003-019-MY3, 109-2811-E-003-500); Narodowe Centrum Badań i Rozwoju (PL-TW/V/5/2018); Fundacja na rzecz Nauki Polskiej (TEAM TECH/2016-1/4); European Regional Development Fund.

Disclosures

The authors declare no conflicts of interest.

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85. S. Vertu, M. Ochiai, M. Shuzo, I. Yamada, J. J. Delaunay, O. Haeberle, and Y. Okamoto, “Optical projection microtomography of transparent objects,” Proc. SPIE 6627, 66271A (2007). [CrossRef]  

86. G. Dardikman, S. Mirsky, M. Habaza, Y. Roichman, and N. T. Shaked, “Angular phase unwrapping of optically thick objects with a thin dimension,” Opt. Express 25, 3347–3357 (2017). [CrossRef]  

87. J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23, 7908–7923 (2015). [CrossRef]  

88. M. Kujawinska, W. Krauze, A. Kus, J. Kostencka, T. Kozacki, B. Kemper, and M. Dudek, “Problems and solutions in 3-D analysis of phase biological objects by optical diffraction tomography,” Int. J. Optomechatron. 8, 357–372 (2014). [CrossRef]  

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98. J. Kostencka, T. Kozacki, A. Kuś, B. Kemper, and M. Kujawińska, “Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy,” Biomed. Opt. Express 7, 4086–4101 (2016). [CrossRef]  

99. K. Kim, H. Yoon, M. D. Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).

100. J.-W. Su, W.-C. Hsu, C.-Y. Chou, C.-H. Chang, and K.-B. Sung, “Digital holographic microtomography for high-resolution refractive index mapping of live cells,” J. Biophotonics 6, 416–424 (2013). [CrossRef]  

101. K. Kim, Z. Yaqoob, K. Lee, J. W. Kang, Y. Choi, P. Hosseini, P. T. C. So, and Y. Park, “Diffraction optical tomography using a quantitative phase imaging unit,” Opt. Lett. 39, 6935–6938 (2014). [CrossRef]  

102. W. Krauze, P. Makowski, and M. Kujawińska, “Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise constant structures,” Proc. SPIE 9526, 95260Y (2015). [CrossRef]  

103. S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011). [CrossRef]  

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105. A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015). [CrossRef]  

106. D. Jin, R. Zhou, Z. Yaqoob, and P. T. C. So, “Dynamic spatial filtering using a digital micromirror device for high-speed optical diffraction tomography,” Opt. Express 26, 428–437 (2018). [CrossRef]  

107. B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberle, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4, 460–463 (2017). [CrossRef]  

108. J. Kostencka, T. Kozacki, and M. Józwik, “Holographic tomography with object rotation and two-directional off-axis illumination,” Opt. Express 25, 23920–23934 (2017). [CrossRef]  

109. N. T. Shaked, V. Micó, M. Trusiak, A. Kuś, and S. K. Mirsky, “Off-axis digital holographicmultiplexing for rapid wavefront acquisition andprocessing,” Adv. Opt. Photonics 12, 556–611 (2020). [CrossRef]  

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111. Y. Sung, “Snapshot holographic optical tomography,” Phys. Rev. Appl. 11, 014039 (2019). [CrossRef]  

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129. K. C. Zhou and R. Horstmeyer, “Diffraction tomography with a deep image prior,” Opt. Express 28, 12872–12896 (2020). [CrossRef]  

130. D. H. Ryu, D. Ryu, Y. S. Baek, H. Cho, G. Kim, Y. S. Kim, Y. Lee, Y. Kim, J. C. Ye, H. S. Min, and Y. K. Park, “DeepRegularizer: rapid resolution enhancement of tomographic imaging using deep learning,” arXiv preprint arXiv:2009.13777 (2020).

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135. K. Kim, J. Yoon, S. Shin, S. Y. Lee, S. A. Yang, and Y. K. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 020201 (2016). [CrossRef]  

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137. S. Y. Lee, H. J. Park, C. B. Popescu, S. Jang, and Y. K. Park, “The effects of ethanol on the morphological and biochemical properties of individual human red blood cells,” PloS One 10, 1–14 (2015). [CrossRef]  

138. H. Park, M. Ji, S. Y. Lee, K. Kim, Y. H. Sohn, S. Jang, and Y. K. Park, “Alterations in cell surface area and deformability of individual human red blood cells in stored blood,” arXiv:1506.05259 (2015).

139. S. Y. Lee, H. J. Park, K. Kim, Y. H. Sohn, S. Jang, and Y. K. Park, “Refractive index tomograms and dynamic membrane fluctuations of red blood cells from patients with diabetes mellitus,” Sci. Rep. 7, 1039 (2017). [CrossRef]  

140. H. Park, S. H. Hong, K. Kim, S. H. Cho, W. J. Lee, Y. Kim, S. E. Lee, and Y. Park, “Characterizations of individual mouse red blood cells parasitized by Babesia microti using 3-D holographic microscopy,” Sci. Rep. 5, 10827 (2015). [CrossRef]  

141. J. Yoon, K. Kim, H. Park, C. Choi, S. Jang, and Y. Park, “Label-free characterization of white blood cells by measuring 3D refractive index maps,” Biomed. Opt. Express 6, 3865–3875 (2015). [CrossRef]  

142. K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2, 343–346 (2015). [CrossRef]  

143. P. A. Sandoz, C. Tremblay, F. G. van der Goot, and M. Frechin, “Image-based analysis of living mammalian cells using label-free 3D refractive index maps reveals new organelle dynamics and dry mass flux,” PLoS Biol. 17, e3000553 (2019). [CrossRef]  

144. K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6, 36815 (2016). [CrossRef]  

145. T. K. Kim, B. W. Lee, F. Fujii, J. K. Kim, and C. G. Pack, “Physicochemical properties of nucleoli in live cells analyzed by label-free optical diffraction tomography,” Cells 8, 699 (2019). [CrossRef]  

146. M. Schürmann, G. Cojoc, S. Girardo, E. Ulbricht, J. Guck, and P. Muller, “Three-dimensional correlative single-cell imaging utilizing fluorescence and refractive index tomography,” J. Biophotonics 11, e201700145 (2017). [CrossRef]  

147. K. Umemura, Y. Matsukawa, Y. Ide, and S. Mayama, “Label-free imaging and analysis of subcellular parts of a living diatom cylindrotheca sp. using optical diffraction tomography,” MethodsX 7, 100889 (2020). [CrossRef]  

148. M. Baczewska, K. Eder, S. Ketelhut, B. Kemper, and M. Kujawińska, “Refractive index changes of cells and cellular compartments upon paraformaldehyde fixation acquired by tomographic phase microscopy,” Cytometry Part A 97, 1–11 (2020). [CrossRef]  

149. S. E. Lee, K. Kim, J. Yoon, J. H. Heo, H. Park, C. Choi, and Y. Park, “Label-free quantitative imaging of lipid droplets using quantitative phase imaging techniques,” in Asia Communications and Photonics Conference (Optical Society of America, 2014), paper ATh1I.3.

150. T. K. Kim, B. W. Lee, F. Fujii, K. H. Lee, S. Lee, Y. Park, J. K. Kim, S. W. Lee, and C. G. Pack, “Mitotic chromosomes in live cells characterized using high-speed and label-free optical diffraction tomography,” Cells 8, 1368 (2019). [CrossRef]  

151. A. Szewczyk, J. Saczko, and J. Kulbacka, “Apoptosis as the main type of cell death induced by calcium electroporation in rhabdomyosarcoma cells,” Bioelectrochemistry 136, 107592 (2020). [CrossRef]  

152. B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberle, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010). [CrossRef]  

153. W. C. Hsu, J. W. Su, C. C. Chang, and K. B. Sung, “Investigating the back scattering characteristics of individual normal and cancerous cells based on experimentally determined three-dimensional refractive index distributions,” Proc. SPIE 8553, 85531O (2012). [CrossRef]  

154. T. A. Stanly, R. Suman, G. F. Rani, P. J. Otoole, P. M. Kaye, and I. S. Hitchcock, “Quantitative optical diffraction tomography imaging of mouse platelets,” Front. Physiol. 11, 568087 (2020). [CrossRef]  

155. S. Y. Lee, S. Jang, and Y. K. Park, “Measuring three-dimensional dynamics of platelet activation using 3-D quantitative phase imaging,” bioRxiv (2019).

156. Y. S. Kim, S. Lee, J. Jung, S. Shin, H. G. Choi, G. H. Cha, W. Park, S. Lee, and Y. Park, “Combining three-dimensional quantitative phase imaging and fluorescence microscopy for the study of cell pathophysiology,” Yale J. Biol. Med. 91, 267–277 (2018).

157. Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16, 116017 (2011). [CrossRef]  

158. L. Barisoni, K. J. Lafata, S. M. Hewitt, A. Madabhushi, and A. G. J. Balis, “Digital pathology and computational image analysis in nephropathology,” Nat. Rev. Nephrol. 16, 669–685 (2020). [CrossRef]  

159. D. S. Richardson and J. W. Lichtman, “Clarifying tissueclearing,” Cell 162, 246–257 (2015). [CrossRef]  

160. J. V. Rooij and J. Kalkman, “Large-scale high-sensitivity optical diffraction tomography of zebrafish,” Biomed. Opt. Express 10, 1782–1793 (2019). [CrossRef]  

161. H. Hugonnet, Y. W. Kim, M. Lee, S. Shin, R. H. Hruban, S. M. Hong, and Y. Park, “Multiscale label-free volumetric holographic histopathology of thick-tissue slides with subcellular resolution,” bioRxiv (2020).

162. K. W. Dunn, C. Fu, D. J. Ho, S. Lee, S. Han, P. Salama, and E. J. Delp, “DeepSynth: three-dimensional nuclear segmentation of biological images using neural networks trained with synthetic data,” Sci. Rep. 9, 18295 (2019). [CrossRef]  

163. Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. S. Min, and Y. Park, “Quantitative phase imaging and artificial intelligence: a review,” arXiv: 1806.03982 (2018).

164. Y. Rivenson, T. Liu, Z. Wei, Y. Zhang, K. D. Haan, and A. Ozcan, “PhaseStain: the digital staining of label-free quantitative phase microscopy images using deep learning,” Light Sci. Appl. 8, 23 (2019). [CrossRef]  

165. J. Lim, A. B. Ayoub, and D. Psaltis, “Three-dimensional tomography of red blood cells using deep learning,” Adv. Photonics 2, 026001 (2020). [CrossRef]  

166. C.-J. Cheng, K.-C. C. Chien, and Y.-C. Lin, “Digital hologram for data augmentation in learning-based pattern classification,” Opt. Lett. 43, 5419–5422 (2018). [CrossRef]  

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  151. A. Szewczyk, J. Saczko, and J. Kulbacka, “Apoptosis as the main type of cell death induced by calcium electroporation in rhabdomyosarcoma cells,” Bioelectrochemistry 136, 107592 (2020).
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  152. B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberle, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
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  153. W. C. Hsu, J. W. Su, C. C. Chang, and K. B. Sung, “Investigating the back scattering characteristics of individual normal and cancerous cells based on experimentally determined three-dimensional refractive index distributions,” Proc. SPIE 8553, 85531O (2012).
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  154. T. A. Stanly, R. Suman, G. F. Rani, P. J. Otoole, P. M. Kaye, and I. S. Hitchcock, “Quantitative optical diffraction tomography imaging of mouse platelets,” Front. Physiol. 11, 568087 (2020).
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  155. S. Y. Lee, S. Jang, and Y. K. Park, “Measuring three-dimensional dynamics of platelet activation using 3-D quantitative phase imaging,” bioRxiv (2019).
  156. Y. S. Kim, S. Lee, J. Jung, S. Shin, H. G. Choi, G. H. Cha, W. Park, S. Lee, and Y. Park, “Combining three-dimensional quantitative phase imaging and fluorescence microscopy for the study of cell pathophysiology,” Yale J. Biol. Med. 91, 267–277 (2018).
  157. Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16, 116017 (2011).
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  158. L. Barisoni, K. J. Lafata, S. M. Hewitt, A. Madabhushi, and A. G. J. Balis, “Digital pathology and computational image analysis in nephropathology,” Nat. Rev. Nephrol. 16, 669–685 (2020).
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  159. D. S. Richardson and J. W. Lichtman, “Clarifying tissueclearing,” Cell 162, 246–257 (2015).
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  160. J. V. Rooij and J. Kalkman, “Large-scale high-sensitivity optical diffraction tomography of zebrafish,” Biomed. Opt. Express 10, 1782–1793 (2019).
    [Crossref]
  161. H. Hugonnet, Y. W. Kim, M. Lee, S. Shin, R. H. Hruban, S. M. Hong, and Y. Park, “Multiscale label-free volumetric holographic histopathology of thick-tissue slides with subcellular resolution,” bioRxiv (2020).
  162. K. W. Dunn, C. Fu, D. J. Ho, S. Lee, S. Han, P. Salama, and E. J. Delp, “DeepSynth: three-dimensional nuclear segmentation of biological images using neural networks trained with synthetic data,” Sci. Rep. 9, 18295 (2019).
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  163. Y. Jo, H. Cho, S. Y. Lee, G. Choi, G. Kim, H. S. Min, and Y. Park, “Quantitative phase imaging and artificial intelligence: a review,” arXiv: 1806.03982 (2018).
  164. Y. Rivenson, T. Liu, Z. Wei, Y. Zhang, K. D. Haan, and A. Ozcan, “PhaseStain: the digital staining of label-free quantitative phase microscopy images using deep learning,” Light Sci. Appl. 8, 23 (2019).
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  165. J. Lim, A. B. Ayoub, and D. Psaltis, “Three-dimensional tomography of red blood cells using deep learning,” Adv. Photonics 2, 026001 (2020).
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  166. C.-J. Cheng, K.-C. C. Chien, and Y.-C. Lin, “Digital hologram for data augmentation in learning-based pattern classification,” Opt. Lett. 43, 5419–5422 (2018).
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2020 (15)

Y. Deng, C. H. Huang, B. Vinoth, D. Chu, X. J. Lai, and C. J. Cheng, “A compact synthetic aperture digital holographic microscope with mechanical movement-free beam scanning and optimized active aberration compensation for isotropic resolution enhancement,” Opt. Laser Eng. 134, 106251 (2020).
[Crossref]

Y. He, Y. Wang, and R. Zhou, “Digital micromirror device based angle-multiplexed optical diffraction tomography for high throughput 3D imaging of cells,” Proc. SPIE 11294, 1129402 (2020).
[Crossref]

B. Vinoth, A. Vijayakumar, M. R. Rai, J. Rosen, C. J. Cheng, O. V. Minin, and I. V. Minin, “Binary square axicon with chiral focusing properties for optical trapping,” Opt. Eng. 59, 041204 (2020).
[Crossref]

T. Chang, S. Shin, M. Lee, and Y. Park, “Computational approach to dark-field optical diffraction tomography,” APL Photonics 5, 040804 (2020).
[Crossref]

N. T. Shaked, V. Micó, M. Trusiak, A. Kuś, and S. K. Mirsky, “Off-axis digital holographicmultiplexing for rapid wavefront acquisition andprocessing,” Adv. Opt. Photonics 12, 556–611 (2020).
[Crossref]

W. Krauze, “Optical diffraction tomographywith finite object support for the minimization of missing coneartifacts,” Biomed. Opt. Express 11, 1919–1926 (2020).
[Crossref]

S. Fan, S. Smith-Dryden, G. Li, and B. Saleh, “Reconstructing complex refractive-index of multiply-scattering media by use of iterative optical diffraction tomography,” Opt. Express 28, 6846–6858 (2020).
[Crossref]

M. Chen, D. Ren, H. Y. Liu, S. Chowdhury, and L. Waller, “Multi-layer Born multiple-scattering model for 3D phase microscopy,” Optica 7, 394–403 (2020).
[Crossref]

K. C. Zhou and R. Horstmeyer, “Diffraction tomography with a deep image prior,” Opt. Express 28, 12872–12896 (2020).
[Crossref]

K. Umemura, Y. Matsukawa, Y. Ide, and S. Mayama, “Label-free imaging and analysis of subcellular parts of a living diatom cylindrotheca sp. using optical diffraction tomography,” MethodsX 7, 100889 (2020).
[Crossref]

M. Baczewska, K. Eder, S. Ketelhut, B. Kemper, and M. Kujawińska, “Refractive index changes of cells and cellular compartments upon paraformaldehyde fixation acquired by tomographic phase microscopy,” Cytometry Part A 97, 1–11 (2020).
[Crossref]

A. Szewczyk, J. Saczko, and J. Kulbacka, “Apoptosis as the main type of cell death induced by calcium electroporation in rhabdomyosarcoma cells,” Bioelectrochemistry 136, 107592 (2020).
[Crossref]

T. A. Stanly, R. Suman, G. F. Rani, P. J. Otoole, P. M. Kaye, and I. S. Hitchcock, “Quantitative optical diffraction tomography imaging of mouse platelets,” Front. Physiol. 11, 568087 (2020).
[Crossref]

L. Barisoni, K. J. Lafata, S. M. Hewitt, A. Madabhushi, and A. G. J. Balis, “Digital pathology and computational image analysis in nephropathology,” Nat. Rev. Nephrol. 16, 669–685 (2020).
[Crossref]

J. Lim, A. B. Ayoub, and D. Psaltis, “Three-dimensional tomography of red blood cells using deep learning,” Adv. Photonics 2, 026001 (2020).
[Crossref]

2019 (11)

J. V. Rooij and J. Kalkman, “Large-scale high-sensitivity optical diffraction tomography of zebrafish,” Biomed. Opt. Express 10, 1782–1793 (2019).
[Crossref]

K. W. Dunn, C. Fu, D. J. Ho, S. Lee, S. Han, P. Salama, and E. J. Delp, “DeepSynth: three-dimensional nuclear segmentation of biological images using neural networks trained with synthetic data,” Sci. Rep. 9, 18295 (2019).
[Crossref]

Y. Rivenson, T. Liu, Z. Wei, Y. Zhang, K. D. Haan, and A. Ozcan, “PhaseStain: the digital staining of label-free quantitative phase microscopy images using deep learning,” Light Sci. Appl. 8, 23 (2019).
[Crossref]

T. K. Kim, B. W. Lee, F. Fujii, K. H. Lee, S. Lee, Y. Park, J. K. Kim, S. W. Lee, and C. G. Pack, “Mitotic chromosomes in live cells characterized using high-speed and label-free optical diffraction tomography,” Cells 8, 1368 (2019).
[Crossref]

T. K. Kim, B. W. Lee, F. Fujii, J. K. Kim, and C. G. Pack, “Physicochemical properties of nucleoli in live cells analyzed by label-free optical diffraction tomography,” Cells 8, 699 (2019).
[Crossref]

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light Sci. Appl. 8, 82 (2019).
[Crossref]

P. A. Sandoz, C. Tremblay, F. G. van der Goot, and M. Frechin, “Image-based analysis of living mammalian cells using label-free 3D refractive index maps reveals new organelle dynamics and dry mass flux,” PLoS Biol. 17, e3000553 (2019).
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M. Ziemczonok, A. Kuś, P. Wasylczyk, and M. Kujawińska, “3D-printed biological cell phantom for testing 3D quantitative phase imaging systems,” Sci. Rep. 9, 18872 (2019).
[Crossref]

Y. Sung, “Snapshot holographic optical tomography,” Phys. Rev. Appl. 11, 014039 (2019).
[Crossref]

S. K. Mirsky and N. T. Shaked, “First experimental realizationof six-pack holography and its application to dynamic syntheticaperture superresolution,” Opt. Express 27, 26708–26720 (2019).
[Crossref]

B. Vinoth, H. Y. Tu, X. J. Lai, and C. J. Cheng, “Adaptive wavefront correction structured illumination holographic tomography,” Sci. Rep. 9, 10489 (2019).
[Crossref]

2018 (9)

X. J. Lai, H. Y. Tu, Y. C. Lin, and C. J. Cheng, “Coded aperture structured illumination digital holographic microscopy for superresolution imaging,” Opt. Lett. 43, 1143–1146 (2018).
[Crossref]

B. Vinoth, X. J. Lai, Y. C. Lin, and C. J. Chrng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Sci. Rep. 8, 5943 (2018).
[Crossref]

S. Li, J. Ma, C. Chang, S. Nie, S. Feng, and C. Yuan, “Phase-shifting-free resolution enhancement in digital holographic microscopy under structured illumination,” Opt. Express 26, 23572–23584 (2018).
[Crossref]

D. Jin, R. Zhou, Z. Yaqoob, and P. T. C. So, “Dynamic spatial filtering using a digital micromirror device for high-speed optical diffraction tomography,” Opt. Express 26, 428–437 (2018).
[Crossref]

C. Park, S. Shin, and Y. Park, “Generalized quantification of three-dimensional resolution in optical diffraction tomography using the projection of maximal spatial bandwidths,” J. Opt. Soc. Am. A 35, 1891–1898 (2018).
[Crossref]

S. Fan, S. S. Dryden, J. Zhao, S. Gausmann, A. Schulzgen, G. Li, and B. E. A. Saleh, “Optical fiber refractive index profiling by iterative optical diffraction tomography,” J. Lightwave Technol. 36, 5754–5763 (2018).
[Crossref]

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12, 578–589 (2018).
[Crossref]

Y. S. Kim, S. Lee, J. Jung, S. Shin, H. G. Choi, G. H. Cha, W. Park, S. Lee, and Y. Park, “Combining three-dimensional quantitative phase imaging and fluorescence microscopy for the study of cell pathophysiology,” Yale J. Biol. Med. 91, 267–277 (2018).

C.-J. Cheng, K.-C. C. Chien, and Y.-C. Lin, “Digital hologram for data augmentation in learning-based pattern classification,” Opt. Lett. 43, 5419–5422 (2018).
[Crossref]

2017 (13)

M. Schürmann, G. Cojoc, S. Girardo, E. Ulbricht, J. Guck, and P. Muller, “Three-dimensional correlative single-cell imaging utilizing fluorescence and refractive index tomography,” J. Biophotonics 11, e201700145 (2017).
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S. Y. Lee, H. J. Park, K. Kim, Y. H. Sohn, S. Jang, and Y. K. Park, “Refractive index tomograms and dynamic membrane fluctuations of red blood cells from patients with diabetes mellitus,” Sci. Rep. 7, 1039 (2017).
[Crossref]

D. Jin, R. Zhou, Z. Yaqoob, and P. T. C. So, “Tomographic phase microscopy: principles and applications in bioimaging,” J. Opt. Soc. Am. B 34, B64–B77 (2017).
[Crossref]

M. T. Cann, K. H. Jin, and M. Unser, “Convolutional neural networks for inverse problems in imaging: a review,” IEEE Signal Process. Mag. 34(6), 85–95 (2017).
[Crossref]

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberle, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4, 460–463 (2017).
[Crossref]

J. Kostencka, T. Kozacki, and M. Józwik, “Holographic tomography with object rotation and two-directional off-axis illumination,” Opt. Express 25, 23920–23934 (2017).
[Crossref]

A. Kuś, “Illumination-related errors in limited-angle optical diffraction tomography,” Appl. Opt. 56, 9247–9256 (2017).
[Crossref]

F. Merola, P. Memmolo, L. Miccio, R. Savoia, M. Mugnano, A. Fontana, G. D. Ippolito, A. Sardo, A. Iolascon, A. Gambale, and P. Ferraro, “Tomographic flow cytometry by digital holography,” Light Sci. Appl. 6, e16241 (2017).
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A. Vijayakumar, B. Vinoth, I. V. Minin, J. Rosen, O. V. Minin, and C. J. Cheng, “Experimental demonstration of square Fresnel zone plate with chiral side lobes,” Appl. Opt. 56, F128–F133 (2017).
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Y.-C. Lin, H.-C. Chen, H.-Y. Tu, C.-Y. Liu, and C.-J. Cheng, “Optically driven full-angle sample rotation for tomographic imaging in digital holographic microscopy,” Opt. Lett. 42, 1321–1324 (2017).
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G. Dardikman, S. Mirsky, M. Habaza, Y. Roichman, and N. T. Shaked, “Angular phase unwrapping of optically thick objects with a thin dimension,” Opt. Express 25, 3347–3357 (2017).
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K. Lee, K. Kim, S. Shin, and Y. Park, “Time-multiplexed structured illumination using a DMD for optical diffraction tomography,” Opt. Lett. 42, 999–1002 (2017).
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S. Chowdhury, W. J. Eldridge, A. Wax, and J. Izatt, “Refractive index tomography with structured illumination,” Optica 4, 537–545 (2017).
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2016 (7)

G. Dardikman, M. Habaza, L. Waller, and N. T. Shaked, “Video-rate processing in tomographic phase microscopy of biological cells using CUDA,” Opt. Express 24, 11839–11854 (2016).
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J. Jung, K. Kim, J. Yoon, and Y. Park, “Hyperspectral optical diffraction tomography,” Opt. Express 24, 2006–2012 (2016).
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M. Habaza, M. Kirschbaum, C. G. Marschner, G. Dardikman, I. Barnea, R. Korenstein, C. Duschl, and N. T. Shaked, “Rapid 3D refractive-index imaging of live cells in suspension without labeling using dielectrophoretic cell rotation,” Adv. Sci. 4, 1600205 (2016).
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J. Kostencka, T. Kozacki, A. Kuś, B. Kemper, and M. Kujawińska, “Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy,” Biomed. Opt. Express 7, 4086–4101 (2016).
[Crossref]

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
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K. Kim, J. Yoon, S. Shin, S. Y. Lee, S. A. Yang, and Y. K. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 020201 (2016).
[Crossref]

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6, 36815 (2016).
[Crossref]

2015 (17)

S. Y. Lee, H. J. Park, C. B. Popescu, S. Jang, and Y. K. Park, “The effects of ethanol on the morphological and biochemical properties of individual human red blood cells,” PloS One 10, 1–14 (2015).
[Crossref]

H. Park, S. H. Hong, K. Kim, S. H. Cho, W. J. Lee, Y. Kim, S. E. Lee, and Y. Park, “Characterizations of individual mouse red blood cells parasitized by Babesia microti using 3-D holographic microscopy,” Sci. Rep. 5, 10827 (2015).
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J. Yoon, K. Kim, H. Park, C. Choi, S. Jang, and Y. Park, “Label-free characterization of white blood cells by measuring 3D refractive index maps,” Biomed. Opt. Express 6, 3865–3875 (2015).
[Crossref]

K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2, 343–346 (2015).
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U. S. Kamilov, L. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2, 517–522 (2015).
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J. Kostencka and T. Kozacki, “Computational and experimental study on accuracy of off-axis reconstructions in optical diffraction tomography,” Opt. Eng. 54, 024107 (2015).
[Crossref]

J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23, 16933–16948 (2015).
[Crossref]

P. Xiu, X. Zhou, C. Kuang, Y. Xu, and X. Liu, “Controllable tomography phase microscopy,” Opt. Lasers Eng. 66, 301–306 (2015).
[Crossref]

A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]

W. Krauze, P. Makowski, and M. Kujawińska, “Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise constant structures,” Proc. SPIE 9526, 95260Y (2015).
[Crossref]

W. Krauze, A. Kuś, and M. Kujawinska, “Limited-angle hybrid optical diffraction tomography system with total-variation-minimization-based reconstruction,” Opt. Eng. 54, 054104 (2015).
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M. Habaza, B. Gilboa, Y. Roichman, and N. T. Shaked, “Tomographic phase microscopy with 180° rotation of live cells in suspension by holographic optical tweezers,” Opt. Lett. 40, 1881–1884 (2015).
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J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23, 7908–7923 (2015).
[Crossref]

P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, and P. So, “Scanning color optical tomography (SCOT),” Opt. Express 23, 19752–19762 (2015).
[Crossref]

A. Kuś, W. Krauze, and M. Kujawińska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20, 111216 (2015).
[Crossref]

S. Shin, K. Kim, J. Yoon, and Y. Park, “Active illumination using a digital micromirror device for quantitative phase imaging,” Opt. Lett. 40, 5407–5410 (2015).
[Crossref]

D. S. Richardson and J. W. Lichtman, “Clarifying tissueclearing,” Cell 162, 246–257 (2015).
[Crossref]

2014 (10)

J. Kostencka, T. Kozacki, M. Dudek, and M. Kujawińska, “Noise suppressed optical diffraction tomography with autofocus correction,” Opt. Express 22, 5731–5745 (2014).
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A. Kuś, M. Dudek, B. Kemper, M. Kujawinska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19, 046009 (2014).

Y. C. Lin and C. J. Cheng, “Sectional imaging of spatially refractive index distribution using coaxial rotation digital holographic microtomography,” J. Opt. 16, 065401 (2014).
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Y.-C. Lin, C.-J. Cheng, and T. C. Poon, “A slice-integral method for calculating wave propagation through volumetric objects, and its application in digital holographic tomography,” J. Opt. 16, 065401 (2014).
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T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffractiontomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
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Y. Choi, P. Hosseini, W. Choi, R. D. Dasari, P. T. C. So, and Z. Yaqoob, “Dynamic speckle illumination wide-field reflection phase microscopy,” Opt. Lett. 39, 6062–6065 (2014).
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M. Kujawinska, W. Krauze, A. Kus, J. Kostencka, T. Kozacki, B. Kemper, and M. Dudek, “Problems and solutions in 3-D analysis of phase biological objects by optical diffraction tomography,” Int. J. Optomechatron. 8, 357–372 (2014).
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K. Kim, H. Yoon, M. D. Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).

K. Kim, Z. Yaqoob, K. Lee, J. W. Kang, Y. Choi, P. Hosseini, P. T. C. So, and Y. Park, “Diffraction optical tomography using a quantitative phase imaging unit,” Opt. Lett. 39, 6935–6938 (2014).
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Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. K. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
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2013 (4)

J.-W. Su, W.-C. Hsu, C.-Y. Chou, C.-H. Chang, and K.-B. Sung, “Digital holographic microtomography for high-resolution refractive index mapping of live cells,” J. Biophotonics 6, 416–424 (2013).
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N. Cardenas and S. K. Mohanty, “Optical tweezers assisted quantitative phase imaging led to thickness mapping of red blood cells,” Appl. Phys. Lett. 103, 013703 (2013).
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Y. Cotte, F. Toy, P. Jourdain, N. Pavillion, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
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K. L. Cooper, S. Oh, Y. Sung, R. R. Dasari, M. W. Kirschner, and C. J. Tabin, “Multiple phases of chondrocyte enlargement underlie differences in skeletal proportions,” Nature 495, 375–378 (2013).
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2012 (3)

Y. Sung, W. Choi, N. Lue, R. R. Dasari, and Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS One 7, e49502 (2012).
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T. Kozacki, K. Falaggis, and M. Kujawinska, “Computation of diffracted fields for the case of high numerical aperture using the angular spectrum method,” Appl. Opt. 51, 7080–7088 (2012).
[Crossref]

W. C. Hsu, J. W. Su, C. C. Chang, and K. B. Sung, “Investigating the back scattering characteristics of individual normal and cancerous cells based on experimentally determined three-dimensional refractive index distributions,” Proc. SPIE 8553, 85531O (2012).
[Crossref]

2011 (6)

C. M. F. Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).
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S. Vertu, J. Flügge, J.-J. Delaunay, and O. Haeberlé, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969 (2011).

L. Miccio, A. Finizio, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Dynamic DIC by digital holography microscopy for enhancing phase-contrast visualization,” Biomed. Opt. Express 2, 331–344 (2011).
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T. Yamauchi, H. Iwai, and Y. Yamashita, “Label-free imaging of intracellular motility by low-coherent quantitative phase microscopy,” Opt. Express 19, 5536–5550 (2011).
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S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16, 116017 (2011).
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2010 (2)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberle, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
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O. Haeberle, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
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2009 (5)

2008 (3)

Y. K. Park, M. D. Silva, G. Popesu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA 105, 13730 (2008).
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M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
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N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Opt. Express 16, 16240–16246 (2008).
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2007 (5)

C. F. Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, “Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy,” Opt. Lett. 32, 1572–1574 (2007).
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W. Choi, C. Y. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4,717–719 (2007).
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S. S. Kou and C. J. R. Sheppard, “Imaging in digital holographic microscopy,” Opt. Express 15, 13640–13648 (2007).
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S. Vertu, M. Ochiai, M. Shuzo, I. Yamada, J. J. Delaunay, O. Haeberle, and Y. Okamoto, “Optical projection microtomography of transparent objects,” Proc. SPIE 6627, 66271A (2007).
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W. Górski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. 32, 1977–1979 (2007).
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2006 (4)

2004 (1)

2003 (1)

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgetta, “Optically controlled three-dimensional rotation of microscopic objects,”Appl. Phys. Lett. 82, 829–831 (2003).
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Figures (19)

Fig. 1.
Fig. 1. Basic modules of holographic tomography: FAT, full-angle tomography; LAT, limited-angle tomography.
Fig. 2.
Fig. 2. Illustration of a three-dimensional volumetric sample arrangement with spatially distributed refractive values. Reprinted from [54].
Fig. 3.
Fig. 3. Simplified illustration of holographic tomography image recording, spatial frequency mapping, and 3D image reconstruction of the object used. Reprinted from [54].
Fig. 4.
Fig. 4. Spatial cutoff frequency coverages of (a) microscopic imaging (single illumination) and (b) tomographic imaging system (multiple illuminations). Reprinted from [54].
Fig. 5.
Fig. 5. Comparison of coherent transfer functions (CTFs) in three-dimensional space. (a),(b) Single-direction SR approach in which the missing frequency coverage can be seen in the inset images, (c) full-angle SR CTF shows an isotropic frequency coverage. (d),(e) Single-axis ( $x$ and $y$ axis) beam rotation CTF, (f) BRCTF of ${x} {-}{y}$ directions offers laterally extended frequency coverages, but there are still missing frequencies in the axial direction as shown in the inset images. (g) The integrated dual-mode approach offers UFO-like-shaped CTF with benefits of both beam and sample rotation approaches as the sectional images shown in (h) and (i).(j) Shows the extended isotropic frequency coverages in 2D as shown in (k), (l). Reprinted from [57,58].
Fig. 6.
Fig. 6. Sample rotation HT with rotary holder. (a) Experimental schematic,(b) HT system photo. CL, condenser lens; PD, Petri dish; MO,microscope objective; RH, rotary holder. Reprinted from [77].
Fig. 7.
Fig. 7. Wave propagation nature of the capillary supported approach. W,plane wave; B1, first boundary of the capillary generatescylindrical wave; S, sample; B2, second boundary of thecapillary creates the aberration in the sample wave; B3, Petridish boundary creates the deformation of the wave field. Reprinted from [87].
Fig. 8.
Fig. 8. Experimental schematic of the coaxial rotation HT. BS, beamsplitter; CMOS, image sensor. Reprinted from [78].
Fig. 9.
Fig. 9. Experimental schematic of sample rotation HT. Green representation shows the DHM for the hologram recording, red representation shows the HOT for the sample manipulation, and blue representation shows the fluorescent microscope. Reprinted from [82].
Fig. 10.
Fig. 10. Mach–Zehnder-based HT with a two-axis galvanometer mirror scanner (GM) and illumination optical system (L2-O1). Reprinted from [98].
Fig. 11.
Fig. 11. (a) Beam rotation HT using LCoS SLM, reprinted from [63]. The unwanted zero order is blocked by a spatial filter ${F}$ placed in the Fourier plane of the T1-T2 ${4f}$ system and the moving ${+}{1}$ order is transmitted to illuminate the sample. (b) Beam rotation in HT using a DMD, reprinted from [64].
Fig. 12.
Fig. 12. Single-shot HT with projection multiplexing for a full projection set using a microlens array (MLA) to generate illuminations. Reprinted from [110].
Fig. 13.
Fig. 13. RI calibration object: (a) model, (b) horizontal and vertical cross sections of the RI measured with beam rotation tomography. Reprinted from [115].
Fig. 14.
Fig. 14. Comparison of reconstruction results obtained with (a), (b), (g), (h) direct inversion; (c), (d), (i), (j) Gerchberg–Papoulis algorithm with nonnegativity constraint, and (e), (f), (k), (l) Gerchberg–Papoulis algorithm with additional constraint in the form of automatically generated object support. The objects presented are (a)–(f) 3D-printed cell phantom and (g)–(l) keratinocyte cell. The red contour shows the extent of the object support generated with the auxiliary algorithm in the GP-SC method. Reprinted from [119].
Fig. 15.
Fig. 15. HT measurements and analysis of four cell lines: (a) 3D visualization of cell lines NRK-52E and RAW 264.7, (b) 2D RI cross section of the RI distribution in the best focal plane of live and fixed NRK-52E and RAW 264.7 cells, (c) differences in RI between nucleolus–nucleus and nucleolus–cytoplasm for four representative cell lines. Reprinted from [148].
Fig. 16.
Fig. 16. HT reconstruction of Candida rugosa (ATCC 200555). (i): RI distribution comparison of center slice results between (a) full-angle sample rotation, (b) beam rotation, and (c) integrated tomography approaches. Scale bar: 3 µm, color bar: RI values. (ii): subcellular tomographic reconstruction. Reprinted from [57].
Fig. 17.
Fig. 17. Four refractive index images of high and continuous regions of chromosome of DM cells during four stages of mitosis. Reprinted from [150].
Fig. 18.
Fig. 18. (a) Coronal, (b) sagittal, and (c) axial cross sections of HT reconstructed refractive index contrast of an optically cleared 3 day old zebrafish larva. Reprinted from [160].
Fig. 19.
Fig. 19. Sliced image comparison of a normal colon tissue (a) bright field and stained with H&E staining and (b) an unstained neighbor tissue imaged with HT. Reprinted from [161].

Equations (9)

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U t ( r ) = O ( r ) U o ( r ) G ( r r ) d r ,
O ( r ) = K 2 [ n s 2 ( r ) n m 2 ] .
U t ( x , y , z = l ) = exp ( j ( u x + v y ) ) d u d v × { ( O ( x , y , z ) U o ( x , y , z ) ) / k 2 u 2 v 2 } × exp [ j ( u x + v y ) ] exp [ j k 2 u 2 v 2 ( l z ) ] d x d y d z .
U o ( x , y ; m Δ z ) = U o ( x , y ; ( m 1 ) Δ z ) × x o ( x , y ; ( m 1 ) Δ z ) h ( x , y ; Δ z ) ,
F x , y m i c r o s c o p y = 2 n sin θ λ a n d F z m i c r o s c o p y = n ( 1 cos θ ) λ .
F x , z S R = 4 n sin ( θ / 2 ) λ a n d F y S R = 2 n sin θ λ .
F x , y B R = 4 n sin θ λ a n d F z B R = 2 n ( 1 cos θ ) λ .
F x , y I D T = 4 n sin θ λ a n d F z I D T = 2 n sin θ λ .
F x , y , z i s o t r o p i c = 4 n sin θ λ .

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