Measuring the refractive index dispersion of (un)pigmented biological tissues by Jamin-Lebedeff interference microscopy

Jamin-Lebedeff interference microscopy is a powerful technique for measuring the refractive index of microscopically-sized solid objects. This method was classically used for transparent objects immersed in various refractive-index matching media by applying light of a certain predesigned wavelength. In previous studies, we demonstrated that the Jamin-Lebedeff microscopy approach can also be utilized to determine the refractive index of pigmented media for a wide range of wavelengths across the visible spectrum. The theoretical basis of the extended method was however only precise for a single wavelength, dependent on the characteristics of the microscope setup. Using Jones calculus, we here present a complete theory of Jamin-Lebedeff interference microscopy that incorporates the wavelength-dependent correction factors of the half- and quarter-wave plates. We show that the method can indeed be used universally in that it allows the assessment of the refractive index dispersion of both unpigmented and pigmented microscopic media. We illustrate this on the case of the red-pigmented wing of the damselfly Hetaerina americana and find that very similar refractive indices are obtained whether or not the wave-plate correction factors are accounted for.