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:
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).
Experimental assembly
Multiwavelength Abbe
refractometer
ATAGO DR-M2 / 1550
1. Abbe refractometer ATAGO DRM2 / 1550.
2. halogen illuminator with
changeable interference filters
3. controller of refractometer
Results
а)
b)
c)
The image of the field of view of the refractometer, the fixed of the
camcorder.
a)
b)
c)
- distilled water, measurement wavelength of 690 nm, the position of the crosshair - 1.3310;
- 40% fructose solution, measurement wavelength 690 nm, the position of the crosshairs 1.4004;
- pork muscle tissue, measurement wavelength 930 nm, the position of the crosshair 1.3675.
Data Processing
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 = 1.6889, λ=930nm)
Data Processing
Experimental data (●) and approximation (—), using a equation (8) for
muscle tissue and a 40% fructose solution.
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%
Data Processing
The experimental results(•) and approximation(-) for the muscle
tissue with glucose 40%
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%
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.