Measurement of Single Cell Refractive Index, Dry Mass, Volume, and Density Using a Transillumination Microscope

Phase contrast microscopy has become ubiquitous in the field of biology, particularly in qualitative investigations of cellular morphology. However, the use of quantitative phase retrieval methods and their connection to cellular refractive index and dry mass density remain under utilized. This is due in part to the restriction of phase and cellular mass determination to custom built instruments, involved mathematical analysis, and prohibitive sample perturbations. We introduce tomographic bright field imaging, an accessible optical imaging technique enabling the three dimensional measurement of cellular refractive index and dry mass density using a standard transillumination optical microscope. The validity of the technique is demonstrated on polystyrene spheres. The technique is then applied to the measurement of the refractive index, dry mass, volume, and density of red blood cells. This optical technique enables a simple and robust means to perform quantitative investigations of engineered and biological specimens in three dimensions using standard optical microscopes.

Figure 1

Three dimensional TBFI refractive index reconstructions of polystyrene spheres. (a) $Enface$ bright field image of $0.1\mu \mathrm{m}$ polystyrene sphere ($n=1.597$, imaging wavelength $\lambda =540\mathrm{nm}$), suspended in fluoromount G ($n=1.4$) (b) corresponding refractive index map. (c) Cross sectional image of $0.1\mu \mathrm{m}$ sphere, (d) corresponding refractive index map. (e) $Enface$ bright field image of $2.8\mu \mathrm{m}$ polystyrene sphere suspended in glycerol ($n=1.474$), (f) corresponding refractive index map, (g) cross sectional bright field image of $2.8\mu \mathrm{m}$ sphere, (h) cross sectional refractive index map.

Figure 2

TBFI refractive index reconstructions of the central focal plane in thicker specimens. (a) Bright field image of water in a $100\mu \mathrm{m}$ wide fused silica microfluidic channel, air-coupled $\mathrm{x}10$ lens with $\mathrm{NA}=0.25$ and (b) $4.8\mu \mathrm{m}$ diameter polystyrene sphere suspended in glycerol, oil-coupled lens with $\mathrm{NA}=1.4$. (c) Refractive index map of water, $n=1.333$, in glass microfluidic, $n=1.460$, (d) index map of polystyrene sphere, $n=1.597$ in glycerol $n=1.474$. (e) Average refractive index profile versus the $x$ direction of the channel, (f) refractive index along the diagonal of (d). Shaded bars in (e),(f) denote $\pm 1\%$.

Figure 3

TBFI reconstruction of refractive index and dry mass density of red blood cells. (a) Bright field intensity image of RBCs, (b) refractive index map of RBCs computed using TBFI, (c) mass density map of RBCs using the Hb calibration reported in [13]. (d) Bright field intensity images at 0 and $\pm 0.4\mu \mathrm{m}$ of the boxed RBC in (a) about the focus, (e) corresponding refractive index maps, and (f) corresponding mass density maps. $xz$ projection averages of (g) bright field intensity, (h) refractive index, (i) mass density.