Absorption measurements are widely used in spectrophotometry for chemical analysis of molecules.1-3
The Beer–Lambert law enables one to extract the absorption coefficient, a quantity proportional to the molecular number density and absorption cross section.4
With known molecular specific absorption cross section, the molecular concentration can be determined. A similar approach can be developed using the refractive index instead of absorption coefficient. This complementarity between the refractive and absorption properties of materials stems from the fact that they represent the imaginary and real part of the material dielectric response function and, thus, are related via a Kramers–Kronig relationship. As is widely known, the refractive index is also linearly proportional to the concentration of molecules.5
Molecular concentrations thus can be determined from optical phase delay measurements with known physical path length. The absorption approach requires tuning the wavelength of light to the resonance to maximize the signal-to-noise ratio. In contrast, highly accurate phase detection provides enough detection sensitivity of refractive index even when the absorption is insignificant. Thus the refractive index approach is preferable where photodamage is of concern.
The spectrophotometry typically uses a cuvette to predetermine the thickness of a specimen through which light travels. In studying samples of arbitrary shapes with significant dynamics such as live biological cells, the thickness can vary continuously over time. This makes it difficult to detect absorption coefficient or refractive index in situ. Here we introduce a technique that can be used to determine the refractive index of an arbitrarily shaped specimen by means of optical microscopy. Our method will lead to the study the dynamics of protein concentrations in living biological cells.
The refractive index has been an important source of contrast in visualizing living cells because different cell organelles and compartments possess different refractive indices. Phase-sensitive microscopy techniques such as phase contrast microscopy and differential interference microscopy6,7
visualize minute spatial differences in indices and thus provide high-contrast cellular images. However, these traditional techniques provide only qualitative
information. Recently, advanced phase microscopy techniques have been used to quantify
the cellular refractive index.9-14
From this information, chemical content such as average hemoglobin concentration and average cell mass can be readily extracted.8,9
In previous studies it was demonstrated that refractive index can be used to determine biomolecular contents without such artifacts as photobleaching and interference on the normal physiological activities of living specimen typically present in chemical staining.
Several methods have been used to measure the refractive index of living cells. One of the most advanced methods is tomographic phase microscopy, which can determine 3D maps of refractive index.10
But the technique may not be readily available to general biology laboratories. Moreover, there can be many applications requiring only average refractive index, and not the detailed 3D maps.
Hilbert phase microscopy (HPM)11
is a quantitative phase imaging method that can be used to acquire the axially averaged refractive index of cells when the thickness is known.12
Since quantitative phase measurements provide only optical thickness, a phase shift induced by a specimen proportional to both the average index and the physical thickness, it is required to independently measure the physical thickness of the specimen to extract an average refractive index. To obtain the knowledge of cell thickness, we previously constrained the cells into a known dimensional microstructure.12
Another approach was to dissociate cells from a substrate to make the shape of cells approximately spherical.12
Further, it has been proposed to image the optical thickness of a given biological cell at two different media with different refractive indices, either by a perfusion of different media or by use of dye-induced dispersion.13,14
Confocal fluorescence microscopy was used to directly measure the physical thickness of the cells.15
However, all the techniques require either physical perturbation or chemical staining such as fluorescence dyes, which may introduce changes in actual refractive index.
We note that confocal reflectance microscopy can provide the physical contour of the cell without staining.16-18
The technique preserves the refractive indices of native cells and, at the same time, offers high resolution cell thickness maps due to its sectioning capability. Thus, this technique can be a good complement to quantitative phase microscopy. In this report, we combine the confocal reflectance microscopy with Hilbert phase microscopy to obtain the refractive index of cells without any assumptions, constraint and exogenous agents. We demonstrate full-field imaging of axially averaged refractive index map in live cells.