tokens: developed in our group, is available online in our web page ( http://www.iem.csic.es/fismol/fmap/descarga.htm ). An iterative method is implemented in the MIR with an algorithm described in detail by Zanchet et al. ( 2013 ). Briefly, two multidimensional functions, defined as differences between experimental and calculated spectra, are minimized iteratively. To calculate the transmission spectra through a three-layer system like our experimental one, an analytical model based on Fresnel coefficients was employed. Several variables are fitted: k and n at each wavelength, ice thickness, visible refractive index, and the ratio of coherent/incoherent transmitted IR radiation. To carry out this fitting, several experimental spectra of different thickness are necessary, as well as accurate measurements of the film thickness and of the refractive index n 0 of the ice. After the iterative procedure, the final fitted thickness and visible refractive indices differ from the measured values by less than the experimental error. This condition is used as a measure of the consistency of the fitting. For the NIR region, this procedure cannot be used due to problems in the baseline simulation, which is affected by scattering and double IR reflections. These effects are of the same order of magnitude than the NIR absorptions. Hence, in this frequency range, after a proper subtraction of a baseline in the absorbance spectrum, Lamberts law is applied to obtain the imaginary part of the refractive index: where L is the ice thickness, the absorbance spectrum and the imaginary part of the refractive index. The real part of the refractive index is subsequently obtained using the KramersKronig relation. Optical constants of the mixtures are presented in Fig. 6 . The corresponding n 0 values are the ones given in Table 1 . Optical constants for the mixtures are presented in Fig. 7 . Figure 7. Optical constants in the more relevant NIR and MIR spectral regions of CH 4 :C 2 H 4 ices with proportions (3:1), (1:1) and (1:3) at 30K. Files with the optical constants determined in this work for pure species and mixtures are given in the supplementary material . We have calculated also the optical constants of pure ethylene ice at 30K. Fig. 8 shows a comparison of absorption coefficients, in the NIR and values in the MIR obtained from the present data with previous results. Although the absorption coefficients given by Quirico Schmitt ( 1997 ) and those of Hudson et al. ( 2014 ) do not correspond exactly to the same phase of ethylene ice, the agreement in the NIR region is quite good (Fig. 8 , top panel). The comparison of in the MIR region with the data of Hudson et al. ( 2014 ) manifests the different phases of the ices that were already commented on in Fig. 3 (Fig. 8 , bottom panel). Figure 8. Absorption coefficients (a) and imaginary part of the refractive index (b) of pure ethylene ice at 30K determined in this work compared with previous literature data. 3.4
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