Spectral-domain interferometry for simultaneous measuring the refractive index and thickness

Abstract

A new method for real-time and simultaneous measuring the refractive index and thickness of thin films is proposed. The method is based on spectral dependence of phase-shifting on reflection at one of film's surface. The measurement consists in localizing t-phase shift observed in a channel spectrum.Various methods evaluating the phase data, measured by different interferometric methods, have been developed: phase-step interferometry, FFT, Kalman filtering, and interference order determination. Often, the knowledge of unwrapped phase function is not enough -information about the physical quantity represented by the phase in observed interferogram is an object of interest. For usual interferometry the distance (thickness) measurement can equally be regarded as a measurement of refractive index and a priori knowledge of one of the parameters is required in order to determine the other. Various experimental techniques propose a determination of thickness and refractive index in a single measurement. A common idea of [1,2] is to involve a local change of the fringes periodicity corresponding to preliminary known phase.In our method we have used the same idea providing t-phase shift observed in a channel spectrum. The channel spectrum is produced as a result of thin-film interference when the film is illuminated with a white light. The method is applied for measuring the refractive index, birefringence, and thickness of thin polymer anisotropic films. The principleThe method is based on spectral dependence of a change of phase on reflection of light at one of film's surface. The spectral dependence is provided when the film's surface is in contact with a substrate which is optically denser for one spectral range, and optically less dense for the others, comparing with the film. Fig. la shows the dispersion characteristics of the thin film and the dielectric substrate. At the crossing wavelength Xc, the thin film and the substrate have equal refractive indices. Figs. lb and Ic show the spectral dependence of the change of phase at the surface film-substrate.Assuming a normal dispersion, for k<kc there is not t phase jump, while for )&4c there is. Thus, the phase difference between the first two reflected beams at normal incidence is t (for k<)c) or 2r (for k>)c). The observed quasi-periodical channeled spectrum is affected at the crossing wavelength. Thus, the crossing point can be experimentally found. If the refractive index dispersion n,(Qc) of the substrate is known in advance, the refractive index of the thin film can be determined too. At observed crossing point there is equality of group refractive indices: n|_dn__ _=_nsA, dn_, _=2n,_(_ 2dnPhase refractive indices are equal if a change of phase *D change of phase d|nf dn, -an assumption not fulfilled in a general case, but can be equal to 7 equal to 7t dA dA°N o change of accepted with high accuracy for the materials have been measured.phase