Field-based Tomographic Phase Microscopy

1. Background

High resolution light microscopy is limited not only by the diffraction properties of light, but also by the optical heterogeneities of the sample. Adaptive optics and deconvolution techniques can be used to correct sample-induced aberrations if the aberrations due to the refractive index variations are adequately measured. To be most effective, however, both correction strategies require quantitative knowledge of the 3-D position-dependent refractive index of the sample.

The refractive index reveals a unique aspect of cellular structure, and is important in studies of cell and tissue light scattering, laser trapping of single cells, flow cytometry, total internal reflection microscopy, and other areas involving the interaction of light with cells and tissues.

2. Experimental set up

We developed a technique for quantitative, high-resolution 3-D refractive index measurements of suspended or substrate-attached cells and multicellular organisms with no sample perturbation of any kind or immersion in special media [1]. The set up (Fig. 1) is based on a Mach-Zehnder heterodyne interferometer. A helium-neon laser beam (l = 633 nm) is divided into sample and reference arm paths by a beamsplitter.  A galvanometer-mounted tilting mirror is used to vary the angle of illumination of the sample, which is positioned between the oil-immersion condenser and objective lenses.  In the reference arm, the laser beam passes through two acousto-optic modulators (AOMs), which shift the frequency of the laser beam by 1250 Hz. A beam-splitter recombines the sample and reference laser beams, forming an interference pattern at the image plane. For each angle of illumination a CMOS camera (Photron 1024PCI) records 4 images at 5000 frames per second, such that the sample-reference phase shift between consecutive frames is p/2.  Phase images are then calculated by applying phase shifting interferometry. From four consecutive images I1, I2, I3, and I4, the sample phase fS(x,y, t) = arg zS(x,y, t) can be obtained from complex representation of the sample field, zS(x,y, t) = (I4 − I2) + i (I3 − I1). 

Figure 1. Tomographic phase microscope.  GM: galvanometer scanning mirror; L1: f=250mm lens; BF: back focal plane of condenser lens; The frequency-shifted reference laser beam is shown in blue. To the right of the camera is a typical fringe pattern for a tilted beam illuminating a single HeLa cell.

3. Reconstruction method and calibration

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. To reconstruct a 3-D refractive index tomogram from the projection phase images, we applied a procedure based on the filtered back-projection method (Kak 1999).  A discrete inverse Radon transform was applied to every X-q slice in the beam rotation direction, with X the coordinate in the tilt direction and q the relative angle between the incident beam and optic axis. To compensate for the angle between imaging and illumination directions, we first divide the X-values by cosq.  Illumination angles are limited to -60 < q  < 60 degrees by the numerical aperture of condenser and objective lenses.  To reduce the effects of the missing projections, we applied an iterative constraint method.

Figure 2. Refractive index tomogram of a HeLa cell. (a) 3-D rendered image. The outermost layer of the upper hemisphere of the cell is omitted to visualize the inner structure. Nucleoli are colored green and parts of cytoplasm with refractive index higher than 1.36 are colored red. The dotted box is a cube of side 20 mm. (b) Top view of (a). (c)-(h) Slices of the tomogram at heights indicated in (a).  Scale bar, 10 mm. The color bar indicates the refractive index at l = 633 nm. (i) and (j) Bright field images for objective focus corresponding to (e) and (f), respectively.

To validate our instrument’s measurements, we first measured refractive index tomograms of 10 mm polystyrene beads (Polysciences #17136, n=1.588 at l=633 nm) immersed in oil with a slightly smaller refractive index (Cargille #18095, n=1.559 at l=633 nm). Tomograms showed a constant refractive index inside each bead, and the refractive index difference between the bead and its surroundings was Dn = 0.0285±0.0005, in agreement with the manufacturers’ specifications for beads and oil (Dn = 0.029). Similar tests with a range of oil refractive indices from n=1.55 to n=1.59 also gave good agreement. By measuring the width (FWHM) of the derivative of line profiles of refractive index normal to the boundary of the sphere, we estimated the spatial resolution of our tomographic technique to be approximately 0.5 mm in the transverse (x-y) directions and 0.75 mm in the axial (z) direction.

B.2.2.4. Imaging live cells and multicellular organisms. We imaged single HeLa cells in culture medium.  Cells were dissociated from culture dishes and allowed to partially attach to the cover-slip substrate.  A 3-D index tomogram for a single cell (Fig. 2 a,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. 2 c-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 2 e-f are shown in Figure 2 i-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.

Figure 3. Effects of acetic acid on a HeLa cell. (a) X-Y slice of tomogram from a HeLa cell in normal culture medium, (b) after 3 minutes in a medium containing 0.38% acetic acid, (c) 3 minutes after replacing the original medium. Scale bar, 10 mm. (d) Mosaic of X-Y slices of index tomograms through the nematode C. elegans.  Anterior is to the right. Scale bar, 50 mm. The color bar indicates the refractive index at l = 633 nm.

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.

Tomograms can be obtained in less than 10 seconds, allowing measurements of relatively rapid changes in cell structure due to external perturbations.  As a demonstration of this capability, we investigated the effect of low concentrations of acetic acid on the structure of a cell. Whitening of areas of the cervix due to topically applied acetic acid is widely used to identify suspicious sites of precancerous lesions. It has been suggested that coagulation of nucleus protein may increase the refractive index contrast between nucleus and cytoplasm(Ronne 1989). Our tomographic microscope may be able to elucidate the mechanisms of acetic whitening by directly imaging acetic acid-induced changes of cell refractive index structure. 

We recorded index tomograms of HeLa cells after changing the cell environment from normal culture medium (Fig. 3 a) to a culture medium containing 0.38% acetic acid (Fig. 3 b). The refractive index of the nucleolus increased from 1.36 to 1.39 and the inhomogeneity of the rest of the nucleus increased dramatically. This suggests that the increased scattering associated with acetal whitening results from both increased refractive index contrast between nucleoli and the rest of the cell and increased inhomogeneity of refractive index throughout the cell.  Three minutes after replacing the acetic acid medium with normal culture medium, the spatial variation and refractive index of the nucleolus decreased somewhat but remained larger than the baseline value (Fig. 3 c).

To demonstrate tomographic imaging of a multicellular organism, we imaged the nematode C. elegans.  Worms were paralyzed with 10 mM sodium azide in NGM buffer and imaged in the same solution.  Overlapping tomograms were created and the resulting data assembled into a mosaic (Fig. 3 d). Several internal structures are visible, including a prominent pharynx and digestive tract.

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This material is based upon work supported in part by the National Science Foundation under Grant No. 0754339. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.