Refractive indices of biomolecules play crucial roles in many optical imaging and microscopy techniques developed for cell biology. Phase contrast and differential interference contrast (DIC) microscopy have long been used to observe unstained live cells by generating contrast from refractive index variations of organelles within cells. This contrast provides fundamental biophysical information about the structure and organization of cells. In recent years, there has been growing interest in developing quantitative phase microscopy (QPM) techniques for cell characterization in both two dimensions and three dimensions [1
]. Compared to phase contrast and DIC microscopy, QPM enables one to obtain quantitative phase information proportional to the optical path length of transparent cells with sub-wavelength accuracy. This leads to the quantitative measurements of physical thickness and refractive index of cells, as well as qualitative study of cellular organization. A few examples of interesting applications include assessment of cellular morphology, measurement of cell dry mass and study of red blood cell dynamics [8
]. Most of these applications, however, are incapable of distinguishing different molecules present in the cell because measurements are performed in the visible wavelength range far from the resonance absorption wavelengths of most biomolecules. DNA molecules and most proteins have about the same specific refractive index increment α — the physical parameter which directly relates refractive index to molecular concentration C: n
+αC, where n0
are the index of the solvent and the solution, respectively. Typical value of α for proteins is around 0.18–0.19 mL/g[11
] whereas for DNA molecules, it is around 0.17–0.18 mL/g[12
]. Also, the refractive index dispersion of these molecules (the dependence of α on wavelength) is almost the same. As a result, it is very difficult to separately quantify them inside individual cells, which is an important issue in biology.
A straightforward solution is to make measurements in the ultraviolet (UV) region. As is well known, protein and DNA have distinct absorption spectra in the deep UV and they show substantially different refractive index dispersion near their absorption peaks. We note that absorption based microscopy technique has already demonstrated separate quantification of DNA and proteins [13
]. However, imaging at the absorption peak of protein and DNA, necessary to maximize the detection sensitivity, presents great challenges in controlling photodamage to the living cell. On the other hand, the refractive index dispersion is significant even tens of nanometers away from the absorption peak. Therefore, it is possible to separate them in the QPM while reducing the photodamage from strong absorption. However, very limited literature reports the refractive index measurement of biomolecules in the deep UV. Although the Kramers-Kronig relationship can be used to derive the refractive index dispersion from the measured absorption spectrum[14
], the difficulty in obtaining absorption spectrum below 200 nm prevents accurate calculation of the refractive index. While commercial refractometers based on total internal reflection can routinely achieve greater accuracy than 0.0001, none exists for measurement in the UV regime. Index of refraction can also be measured by the reflectance method [15
], but it is not accurate enough to measure dispersion shape near the absorption peak.
In this report, we propose a refractive index measurement method based on QPM. The light scattering distribution is obtained by taking the Fourier transform of the E-field image (both amplitude and phase images) taken by QPM [17
]. For a single microsphere immersed in a transparent medium, fitting the measured angular scattering spectrum with Mie scattering theory can determine the size of the microsphere and the refractive index ratio between the sphere and the immersion medium. We call this approach the field-based light scattering spectroscopy (FLSS) approach. This method has several advantages over the traditional reflectance or refraction based method. First, it uses the same setup as QPM, and therefore is readily adaptable to microscope based techniques. Second, it is not limited to solution measurement, but could in principle measure any spherical structures including spheroidal cells. We note that conventional light scattering spectroscopy also utilizes least square fitting of the scattering spectrum with Mie theory with large numbers of beads in the field of view[19
]. Our approach, however, presents enough sensitivity to detect scattering distribution from a single bead and thus exclude the effect of sample size distribution. With this FLSS method, we have measured the refractive index dispersion of SiO2
spheres and protein solutions in the deep UV region (λ
= 260 – 315 nm). Specific refractive index increment is obtained by linear regression of refractive indices on protein concentrations. The precision of refractive index determination is typically ≤0.001 for SiO2
spheres and ≤0.002 for protein solutions. Accuracy of refractive index determination is better than 0.003.