1. Measurement of refractive index of tissues using a multi-wavelength refractometer
Y.V. Tarakanchikova, L.E. Dolotov, A.P. Popov, A.V. Bykov, V.V. Tuchin

2. Material and method
Determination of the refractive index is based on the Fresnel equations for the reflection of light using the FTIR. Fresnel equation for reflection light polarized parallel (p) and the normal (s) to the plane of incidence of light when the angle of incidence θi have the form:
where
If the incident light is unpolarized, the reflectance of the sample is equal to:

3. Material and method
The refractive index of biological tissue is considered complex:
ntissue = nr + i·ni
where nr - the real part of the refractive index, ni - the imaginary part, which characterizes the absorbing and scattering properties of tissue.
- angular dependence of the imaginary part of the refractive index (7).

4. Experimental assembly
Multiwavelength Abbe
refractometer
ATAGO DR-M2 / 1550
Abbe refractometer ATAGO DR-M2 / 1550.
halogen illuminator with changeable interference filters
controller of refractometer

5. Results а) b) c)
The image of the field of view of the refractometer, the fixed of the camcorder.
- distilled water, measurement wavelength of 690 nm, the position of the crosshair ;
- 40% fructose solution, measurement wavelength 690 nm, the position of the crosshairs ;
- pork muscle tissue, measurement wavelength 930 nm, the position of the crosshair

6. Data Processing n = nsc + ( Npix — Ncr)·K θi = arcsin (n/ np)
transform number pixel index of refraction n, related with the scale of the refractometer :
n = nsc + ( Npix — Ncr)·K
where n-refractive index, corresponding of the pixel; nsc - refractive index fixed to set up scale; Npix –pixel number of image; Ncr - number pixel of the image corresponding to position crosshair; K - calibration factor (for a wavelength of 930 nm, it equals 1.15 × 10-4).
θi = arcsin (n/ np)
where n- is refractive index, np - is refractive index of measurement prism (np = , λ=930nm)

7. Data Processing
Experimental data (●) and approximation (—), using a equation (8) for muscle tissue and a 40% fructose solution.

8. Data Processing
The approximation parameters — real nr(a) and imaginary ni(b) parts of refractive index, area of partial contact A(c) muscle tissue with fructose 40%

9. Data Processing
The experimental results(•) and approximation(-) for the muscle tissue with glucose 40%

10. Data Processing
The approximation parameters — real nr(a) and imaginary ni(b) parts of refractive index, area of partial contact A(c) muscle tissue with glucose 40%

11. Conclusion
Developed method gives a possibility to measure the refractive index of such turbid medias as biotissue and its mimicking phantoms at number of wavelengths.
Also this method allows to obtain time resolution of the diffuse processes under optical clearing of the biological tissues.
Suggested mathematical model allows to get the real and imaginary parts of the refractive index and, accordingly, the scattering coefficient μs` of tissues.