Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba

: This paper presents an optical diffraction tomography technique based on digital holographic microscopy. Quantitative 2-dimensional phase images are acquired for regularly-spaced angular positions of the specimen covering a total angle of π , allowing to built 3-dimensional quantitative refractive index distributions by an inverse Radon transform. A 20x magnification allows a resolution better than 3 μ m in all three dimensions, with accuracy better than 0.01 for the refractive index measurements. This technique is for the first time to our knowledge applied to living specimen (testate amoeba, Protista). Morphometric measurements are extracted from the tomographic reconstructions, showing that the commonly used method for testate amoeba biovolume evaluation leads to systematic under evaluations by about 50%.


Introduction
Optical microscopy techniques nowadays offer non-contact, high-resolution and real-time cell imaging facilities. Though, the knowledge of the optical properties of the intracellular organelles is deemed to bring valuable information about cells morphology, cellular internal processes or organelles spatial distribution. A good review of the available techniques and refractive indices in the literature can be found in Ref.  4 However, these last two approaches allow to measure the 2D planar distribution of the RI integrated along the optical axis, making the visualization of individual intracellular organelles difficult.
A well-suited technique to address this particular problematic of measuring the 3dimentionnal (3D) refractive index distribution of a cell, is the so-called optical diffraction tomography (ODT), which theoretical bases have been developed by Wolf 5 and Dändliker 6 in the early seventies. ODT allows, by recording the complex wavefront diffracted by a transparent or semi-transparent object under varying illumination angles, to reconstruct its 3D scattering potential. Lauer used for example phase-shifting interferometry (PSI) to record the Fourier spectrum of the diffracted wavefront, varying the illumination direction by changing the direction of the beam itself. 7 Vishnyakov and Levin combined PSI with a Linnik interferometer also allowing multiple angles illumination. 8-9 Barty et al. developed a phaseretrieval algorithm, based on 3 intensity measurements performed on different focus planes, combined with a rotation of the specimen relatively to a fixed illumination beam. 8 There are really few successful applications of ODT techniques to living specimen imaging, mainly due to the difficulty of measuring accurately the complex diffracted wavefront: Lauer used his tomographic microscope to observe bacteria and yeasts, 7 Noda et al. investigated green mold (Aspergillus oryzae), 9 and Vishnyakov and Levin observed human red blood cells and lymphocites. [8][9] Note that quantitative RI data are found only in Refs. 8-9.
In a recent paper, 12 we have shown for the first time to our knowledge the quantitative 3D distribution of RI of a semi-transparent object, in our case a pollen grain, provided by backprojecting OPL values collected with digital holographic microscopy (DHM) on a series of projections of the preparation taken at various incidence angles. The accuracy of the RI determination was better than 0.01, and the 3D spatial resolution better than 1 μm in all 3D. Furthermore, DHM reconstructs the complex diffracted wavefront from a single hologram for each orientation of the specimen, while at least 3 images are required for PSI, reducing this way the acquisition time and the stability requirements for the system.
In the present paper, the system described in Ref. 12 has been further developed, to allow the first investigation of living biological specimens, thanks to a specifically designed observation chamber. The reconstructed 3D RI distributions, revealing intracellular structures, have permitted to accurately measure the volume of the specimen. The biological specimen observed, presented in Fig. 1, is a testate (or shelled) amoeba ("protozoa", more specifically a protist belonging to the Amoebozoa), Hyalosphenia papilio, with a shell approximately 130 μm long, 70 μm wide and 35 μm deep.
This species is commonly found in nutrient-poor peatlands, and the specimens presented in this work were collected in moss (Sphagnum) from Praz-Rodet Bog, Canton Vaud, Switzerland (46°33' N, 06°10' E). It is one of the few protozoa to house endosymbiotic algae, visible as small green spheres in Fig. 1(a), and hence its metabolism is referred to as mixotrophy, i.e. combing auto-and heterotrophy). Because of this interesting metabolism, its commonness in peatlands, and its characteristic morphology making it easily identifiable, it may represent a good candidate as a model organism for studies in population ecology or ecotoxicology. 13 Beyond the interest for a specific species, testate amoebae are increasingly used in community ecology with applications in the reconstruction of past climates (paleoecology), 14 the monitoring of pollution 15 or environmental changes. In many of these applications it is important to have precise estimates of cell volume. This allows the calculation of the biomass with the help of an appropriate conversion factor. 16 The biovolume is usually achieved using simple measurements and assuming geometrical shapes, but it is unclear if these correspond very well to the reality. 17-18 A much better approach would be to quantify exactly the volume and to determine how this compares to some easily measurable variable such as the length or width. If a clear correlation can be established in such as way for a number of specimens of each species, or morphological type for closely-related species, this data can then be used to derive allometric relationships that can be used in a standard way forever. Another interesting aspect is the presence of endosymbiotic algae. These may also respond to changes in the environment indirectly through the amoeba itself or directly if some contaminant enters the amoeba cell without affecting it directly. It would therefore be interesting to be able to quantify the number of algal cells and their individual volumes. This is clearly not possible using light microscopy, as in Fig. 1(a), but may be possible using holographic tomography.

Experimental setup
Transmission off-axis DHM (Fig. 2) used for the present study is described in details in Refs. 19 and 20. It is based on a Mach-Zehnder configuration. Half-wave plates and neutral filters are used in conjunction with a polarizing beam splitter to control the light intensity in the two arms of the interferometer. The light source is a polarized laser diode emitting at 635 nm. Results presented here have been obtained with an Olympus 20X 0.4 NA microscope objective (MO). A field lens is inserted in the reference arm in order to obtain a coarse compensation of the phase curvature induced by the MO into the object wave, while the fine tuning compensation is numerically achieved during the hologram reconstruction process, as extensively described in Ref. 14. The camera is a 512 x 512 pixels, 8 bit, black and white CCD, with square pixels of 6.7 μm, and a maximal frame rate up to 25Hz. The field of view is 200 μm x 200 μm. The transverse resolution (around 1.5 μm) as well as the transverse scale calibration have been determined with a USAF 1951 resolution test target. All measurements have been achieved without any particular vibrations-insulating system: since a single hologram is required to reconstruct the complex diffracted wavefront, this is performed in a short time (down to 20 μs with our CCD), leading to high measurement stability. With a Pentium 4 2.8Ghz, the phase reconstruction rate, described in the next paragraph, is 15 frames/second.
In the present work, the specimen is observed in a specifically designed chamber, principally composed by two microscope coverslips orthogonal to the optical axis. An aluminum frame maintains the two coverslips 4 mm distant, while fixations assure the watetightness of the chamber. One lateral side of the chamber is free to allow the introduction of a micropipette (MP) used to manipulate the specimen, or to change the perfusion medium during observation. 4 The manipulation method is similar to the so-called patch-clamp technique, in which thin MPs are used to maintain contact with a specific part of cells, for example the plasma membrane. These MPs are produced by the elongation of glass tubes during a controlled heating process. Their extremities, with a diameter around 1 micrometer, may then be polished to ensure a good contact with the cell membrane. Here, the specimen may be manipulated (translated or rotated) by one of these MPs, by using a little vacuum to maintain contact between the glass and the testate. To ensure good manipulation and rotation stability, the MP used during the final measurement had extremities about 10 μm, instead of the standard ones. The MP is fixed on a motorized rotating stage, and its position is adjusted with a micrometric xy-stage to place accurately its extremity on the rotation axis, minimizing therefore displacements of the specimen during rotation. A first micrometric xyz-stage allows moving the MP relatively to the chamber, to grab a specific specimen or to drag a selected specimen in a clean area of the preparation for observation, while a second xyz-stage allows moving simultaneously the MP and the chamber for a proper positioning in the field of view. Note that the chamber can be inclined relatively to the optical axis to allow picking up the desired specimen, in case it is laying on the bottom of the chamber due to gravity. In a previous work, 12 the specimen were embedded in a MP with an internal diameter of 100 μm to allow their rotation in the system. Compared to this first approach, the patch-clamp technique used in this study presents two decisive improvements. Firstly, the MP is now out of the light path going through the specimen: in the previous setup, the MP was acting like a cylindrical lens, introducing astigmatism in the imaging system. Therefore, an index matching liquid was used to minimize this astigmatism, and a numerical procedure was additionally applied to compensate for the residual phase aberrations (see Refs. 20 and 21). Note that the index matching liquid used to compensate partially for the astigmatism needed to be carefully chosen and adapted to the used MP, what requested an additional calibration procedure, and also that the requested numerical procedure consisted potentially in an additional noise source when not conducted carefully. This first modification reduces drastically the complexity of the setup and increases therefore its ease of use. Secondly, the previous embedding technique was not applicable on living animal cells, because the perfusion of the cells within the MP was not possible. Furthermore, the current system is more versatile, allowing for facilitated specimen selection and manipulation, compared to the non-displaceable specimen embedded randomly in the MP.
Glycerol (n=1.473) is used here as immersion liquid, to minimize the number of the socalled 2π-jumps in the phase signal by minimizing the refractive index difference between the specimen and its surrounding medium, suppressing ambiguity during the unwrapping procedure involved in the reconstruction. 12 Note that the chamber is waterproof enough to also work with less viscous immersion media such as water or physiological solution.

Holograms processing and tomographic reconstruction
Digital holographic microscopy (DHM) provides quantitative measurement of the OPL distribution that enable to describe semi-transparent samples, such as living cells with a diffraction-limited transverse resolution and a sub-wavelength axial accuracy. 22 The hologram processing, to reconstruct the complex diffracted wavefront, is described in details in Refs. 19 and 20. Briefly, it consists in multiplying the hologram by a digital reference wave simulating an illumination wave, then a propagation calculation within the Fresnel approximation allows to reconstruct a focused image of the specimen in a plane of coordinates, where a digital phase correction is applied to compensate for the wave front curvature induced by the objective lens and other aberrations of the optical imaging system.
In DHM, the reconstructed phase distribution depends on both specimen thickness and specimen RI distribution. 22 If in first approximation the case of a weekly diffracting object is assumed, the optical path length of the collimated illuminating photons across the specimen is parallel to the optical axis. This assumption was found to be in very good agreement with the DHM data in the case of cellular imaging. 23 The reconstructed phase distribution is therefore directly proportional to this optical path length: where z shows the optical axis direction, λ is the wavelength of the light source and Δn(x, y, z) is the difference between the 3D specimen RI spatial distribution and the RI of the surrounding medium. Consequently, ϕ(x,y) is only proportional to the projection of Δn(x, y, z) along the z-axis.
To achieve the tomographic reconstruction, the specimen is rotated step by step in the system, covering a total angle of π. 180 equally spaced holograms were acquired at a rate of 0.5 Hz and individually reconstructed. The representation of the reconstructed phase data as a function of the angle is known as a sinogram. The 3D signal Δn(x, y, z) can be reconstructed from the sinograms by a filtered backprojection algorithm (see for ex. Ref. 24). Instead of backpropagation 25 algorithm usually recommended in ODT, a backprojection is used consistently with the assumption of a phase proportional to the optical path length across the specimen. For this purpose, the standard inverse Radon transform was used and implemented slice-by-slice along the rotation axis. For further details about the validity of the employed tomographic technique, one should refer to Ref. 26, where it is shown that the so-called hybrid filtered backprojection equivalent to the reconstruction algorithm used in the present work, i.e. consisting in first a backpropagation in the Fresnel approximation of the measured wavefronts to the object plane followed by a backprojection algorithm, gives nearly equivalent results to the standard recommended backpropagation algorithm.

Results and discussion
Tomographic reconstructions were performed on 5 different Hyalosphenia papilio during this study. Central cuts in the reconstructed 3D refractive index volumes for 4 different amoebae are presented on Fig. 3 and Fig. 4. On these images, the cellular body of the amoebae themselves insides their testate can be easily discriminated thanks to the large difference (>0.2) between the cell RI and the RI inside the testate.
One can note on these images that the refractive index inside the testate is lower compared to the surrounding medium. This is due to the fact that glycerol (n=1.473) was used as immersion liquid: the mix of some remaining water inside the testate with the surrounding glycerol explains this decrease of the refractive index value. Note that if the measurement was performed immediately after the immersion of the amoeba in the glycerol, the refractive index inside the test corresponded directly to water (n=1.33), while in the presented measurements, higher values are obtained, indicating clearly the presence of glycerol inside the test. The presence of glycerol around the cellular body may slightly change its volume, but no dramatic changes were noticed during cells preparation and observation.  Morphometry measurements can be achieved on the tomographic reconstruction, to determine for example the biovolume of the amoebae. These volumes were evaluated by considering only the voxels with a refractive index value above an appropriate threshold. Note that the reconstructed volumes were first convoluted with a gaussian filter to minimize errors due to the reconstruction noise, and that the detected volumes distinct from the main cellular body were removed from counting.
The obtained results are presented in Table 1; the error ranges correspond to the optical resolution of the system. These volume measurements are compared in Table 1 with the estimation methods based on size measurements performed with light microscopy, 17-18 where such biovolumes estimations are calculated from the observed individuals using the formula for an ellipsoid: where w, l and d are respectively the width, the length and the depth of the amoeba, and 1/8 is a form factor.
The estimated errors on the volume estimation with Eq. (2) displayed in Table 1 correspond to an accuracy of 2 μm in the size measurements. DHM tomography clearly delivers the most precise estimations of the biovolumes, i.e. with the lowest standard error. This shows the advantage of taking into account the actual shape of the cellular body instead not an ellipsoid approximation, in which slightly errors in the dimension measurement lead to large variation in the volume estimation.  Fig. 3(a) 6.54·10 4 ± 0.05·10 4 2.8·10 4 ± 1.2·10 4 n°2: Fig. 3(b) 7.36·10 4 ± 0.04·10 4 3.7·10 4 ± 1.5·10 4 n°3: Fig. 4(a) 6.54·10 4 ± 0.04·10 4 4.9·10 4 ± 1.7·10 4 n°4: Fig. 4 The tomography also reveals that those volumes are under-estimated by nearly 50% with the actual standard method. This comparison illustrates the potential of DHM tomography for the precise and accurate estimation of biovolumes, which allows to determining biomasses. More generally, our results also show that in addition to the well-recognized problem of estimating the number of microorganisms in the environment, 27 more attention should be devoted to the estimation of the biovolume and biomass of individual species. A reliable estimate of biomass is crucial for understanding of the role of different microorganisms in the microbial food webs, 17,18,28 or the effect of environmental stress like organic pollutants or heavy metals on selected organisms in ecotoxicology.
At present, the whole reconstruction process involved in DHM tomography, including specimen manipulation, holograms acquisition/processing and tomographic reconstruction still requires too many operator interventions to calculate systematically the biovolumes of large amount of amoeba. However, as suggested above, this technique could help to derive allometric relationships that would greatly increase the precision of biovolumes and biomass estimates. The actual resolution in the tomographic reconstruction is mainly limited because of mechanical instabilities. Theoretically, the optical resolution in all three dimensions for the tomographic reconstructions is about 1.5 μm, but an inaccurate centering of the MP on its rotation axis leads to a precession movement of the specimen during rotation that tends to derogate from the final tomography resolution. Therefore, during the reconstruction, a recentering numerical procedure based on the MP edges detection in the phase images has been applied. Even if it is not currently possible to identify accurately all the symbiotic algae, with diameter around 3 μm, 29 and other organelles present in the amoeba cellular body, some of these organelles (principally the phagocytic vacuoles, but also some algal symbionts) are visible in the tomographic reconstructed volumes. Due to discrete color scale, it may be difficult to notice them in Fig. 3, but the continuous color scale make their spherical shape clearly visible, as shown in Fig. 4, especially in the linked movies presenting animations through the reconstructed volumes, in which they appear like spheres in the cellular body. This shows that potentially, the tomographic reconstructions could also be used to solve the problem of symbiotic algae counting and volume estimate inside the amoeba cellular body.

Conclusion
The present work illustrates that DHM tomography, with a resolution better than 3 μm, may successfully be applied to living specimen tomography. In comparison to a previous paper, 12 the presented technique, using a patch clamp micropipette to manipulate and rotate the specimen in a dedicated observation chamber, is much more flexible and opens wide perspectives in 3D cell imaging: the 3D quantitative refractive index distributions furnish invaluable data on the cell components optical properties, potentially leading to information about organelles intracellular distribution. Furthermore, it has been shown that morphometric measurements may be extracted from the tomographic data, by detecting for example the extension of the cellular body thanks to its specific refractive index contrast within the 3D reconstructions. The presented results shed new light on the biovolume estimation technique of testate amoeba, by stressing that the common biovolume measurement technique underestimates systematically the actual values by 50%.