In visualizing transparent biological cells and tissues, the phase contrast microscope and its related techniques have been a cornerstone of nearly every cell biology laboratory. However, phase contrast methods are inherently qualitative and lack in 3-D imaging capability. We introduce a novel tomographic microscopy for quantitative three-dimensional mapping of refractive index in live cells and tissues using a phase-shifting laser interferometric microscope with variable illumination angle.
Refractive Index as an Intrinsic Source of Contrast in Light Microscopy
Most biological cells and tissues exhibit negligible absorption under visible light illumination while there are still distinctive refractive index differences among organelles, which amount to several percents relative to the mean refractive index. For this reason, the refractive index has been served as a much better source of intrinsic contrast than absorption in biological studies.
Local variations of refractive index in the specimen induce different phase delays from point to point in the field of view. Phase microscopy techniques such as phase contrast microscopy, differential interference contrast (DIC) microscopy and quantitative phase microscopy are used to image such specimen-induced phase delay to visualize the biological structures [1 - 3]. These techniques are quite sensitive enough to easily resolve the phase delay induced by a single cell, which is typically around half a radian. However, the phase delay is proportional to the product of refractive index and path length or, more generally, the convolution of the refractive index with the point spread function of the optical system. Thus, phase microscopy techniques provide neither a 3-D image of the cell nor a 3-D map of the refractive index distribution.
One strategy for 3-D determination of refractive index is based on measurement of projections of refractive index in multiple directions, in analogy to computed x-ray tomography, in which the projection of absorption is measured. Projections of refractive index have been performed via a number of quantitative phase microscopy techniques and earlier studies used beam rotation  or sample rotation  to form tomographic images.
However, in one case quantitative index information was not provided , and the other required glycerol immersion of the sample and physical rotation of the sample in a micropipette .
CT Scan with Biological Cells and Multicelluar Organisms
In this article we present a technique for quantitative, high-resolution 3-D refractive index measurements of suspended or substrate-attached cells and multicellular organisms with no need for sample perturbation or immersion in special media .
For near-plane wave illumination of a thin sample with small index contrast, the phase of the transmitted field is to a good approximation equal to the line integral of the refractive index along the path of beam propagation. Therefore, the phase image can simply be interpreted as the projection of refractive index, analogous to the projection of absorption in x-ray tomography. If we take many angular projection phase images over wide range of angles, we can reconstruct a 3-D map of refractive index of the sample with similar algorithm used in x-ray tomography.
In obtaining a set of angular projection phase images, we change the direction of illumination beam rather than rotate the sample. This leaves the sample unperturbed during the measurement, which is critical for biological specimen, and enables a fast dynamic study as well. A novel heterodyne laser interferometric microscopy  is employed to quantitatively image the phase delay induced by the sample and a galvanometer scanning mirror is installed to change the direction of illumination. Illumination angles are limited to ϑ < 60 degrees by the numerical aperture of condenser and objective lenses. It takes about 10 sec to cover entire range of angles at every 1.2 degree.
To reconstruct a 3-D refractive index tomogram from the projection phase images, we applied a procedure based on the filtered back-projection method . A discrete inverse Radon transform was applied to every X-θ slice in the beam rotation direction, with X the coordinate in the tilt direction and θ the angle of illumination beam with respect to the optic axis of objective lens. An X-Z slice is reconstructed from an X-θ slice. By merging all the X-Z slices at every pixel in the Y-direction, we can get the 3-D map of refractive index. We validate that our instrument can determine the refractive index with an accuracy of 0.001 by imaging 10 µm polystyrene beads (Polysciences #17136, n=1.588 at θ =633 nm). The estimated the spatial resolution of our tomography technique to be approximately 0.5 µm in the transverse (x-y) directions and 0.75 µm in the longitudinal (z) direction.
We imaged single HeLa cells in culture medium. Cells were dissociated from culture dishes and allowed to partially attach to the coverslip substrate. A 3-D index tomogram for a single cell (Fig. 1a,b) and x-y tomographic slices of the same cell at heights of z = 12, 9.5, 8.5, 7.5, 6.5 and 5.5 microns above the substrate (Fig. 1c-h) show that the index of refraction is highly inhomogeneous, varying from 1.36 to 1.40. Bright field images for objective focus corresponding to Figure 1e-f are shown in Figure 1i-j, respectively. There is a clear correspondence between the tomographic and bright field images in terms of cell boundary, nuclear boundary, and size and shape of the nucleoli.
Note that the refractive index of the nucleus (n≈1.36), apart from the nucleolus, is smaller than some parts of the cytoplasm (n≈1.36-1.39) and that the refractive index of the nucleoli, n≈1.38, is larger than that of the rest of the nucleus. This is contrary to the widely cited claims that the refractive index of the nucleus as a whole is higher than that of the rest of the cell . Similar results were obtained for cultured HEK 293 cells, B35 neuroblastoma cells, and primary rat hippocampal neurons. All cells imaged contained many small cytoplasmic particles with high refractive index, which may be lipid droplets, lysosomes, vacuoles, or other organelles.
To demonstrate tomographic imaging of a multicellular organism, we imaged the nematode C. elegans. Worms were paralyzed with 10 mM sodium acide in NGM buffer and imaged in the same solution. Overlapping tomograms were created and the resulting data assembled into a mosaic (fig 2). Several internal structures are visible, including a prominent pharynx and digestive tract.
In summary, we have developed a technique for quantitative refractive index tomography of living cells and tissues. We note that the 3-D structure mapped by tomographic phase microscopy can complement the images revealed by techniques such as hematoxylin and eosin staining. Refractive index data can be used to study light scattering properties of cells and tissues and characterize sample-induced aberrations in microscopy. Characterization and correction of such aberrations may be particularly important for modern superresolution techniques such as STED and structured illumination microscopy.
This work was funded by the National Institutes of Health (P41-RR02594-18) and Hamamatsu Corporation.
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