Brillouin light-scattering arises from the interaction of incident light with propagating thermodynamic fluctuations, also known as acoustic phonons, in the sample material. The Brillouin-scattered light is characterized by a frequency shift, Ω, which is related to the longitudinal elastic modulus,
M′ (the real part of complex modulus), of the sample via
23 –25 where λ is the optical wavelength in air, ρ is the mass density, and
n is the refractive index. Although the structural and optical properties of the cornea are generally anisotropic, our measurements of Brillouin frequency shifts indicated negligible dependence on the optical polarization state, compared to their variation over depth in the cornea. Brillouin microscopy measures the frequency shift by employing an ultrahigh-resolution spectrometer. In the case of backscattering of visible light, the Brillouin frequency shift is approximately 5 to 15 GHz in soft tissues, and the corresponding longitudinal modulus ranges typically from 2 to 6 GPa.
The conversion from the Brillouin shift to the elastic modulus requires the knowledge of the index–density factor ρ/
n 2. Both refractive index and density are not uniform in the cornea, mainly because of the spatial variations of hydration
26,27 and water/protein content.
28,29 Treating the cornea as an aqueous solution of collagen fibers and extrafibrillar material with spatially varying concentrations,
30,31 we can write
n = 1.335 + 0.04/(0.22 + 0.24
H), where corneal hydration (weight%)
H ranges from 3 to 4 in normal corneas,
31 –33 and ρ = (ρ
T +
H)/(1 +
H) where ρ
T = 1.33 is the density of dry tissue.
34 From the formulas, we calculate:
n = 1.3689–1.3775, ρ = 1.066–1.083 g/cm
3, and ρ/
n 2 = 0.569–0.571 g/cm
3. In ρ/
n 2, the index and density changes cancel each other, and the resultant variation of ρ/
n 2 is ∼0.3% in the cornea. Ignoring this small variation, we used a constant value of 0.57 g/cm
3 for ρ/
n 2 in our analysis.