Spectropolarimetric and imaging properties of Fabry-Pérot etalons. Applications to solar instrumentation

Laburpena

The use of Fabry-P\érot etalons as tunable narrow-band filters has consolidated over the last decades in solar instrumentation. However, its performance has been evaluated in most studies only to some extent ---e.g., assuming purely monochromatic effects, isotropy, or ideal illumination---. In this work we address the spectral, polarimetric, and imaging features of Fabry-Pérot etalons and their influence in solar spectropolarimeters in both collimated and telecentric configurations with especial considerations on (i) the quasi-monochromatic nature of the observations, (ii) possible birefringent effects appearing in solid etalons, (iii) imperfections on the illumination and (iv) the impact of etalon defects. This thesis is based on a series of four papers on Fabry-P\'erot etalon-based instruments published in The Astrophysical Journal Supplement Series. In the first paper we start with a general outlook of the basic characteristics of etalons. We revisit the historical approach followed to evaluate the impact of irregularities and inhomogeneities of etalons on the transmission profile and we generalize the commonly employed expressions for the finesse of the profile to any arbitrary magnitude of the defects in both air-gapped and crystalline etalons. We examine the spectral and imaging response of each setup, collimated or telecentric, including the polychromatic effects caused by the finite bandpass of the filter and possible deviations from ideal illumination. In particular, we pay special attention to pupil apodization effects occurring in telecentric mounts and we focus on the consequences of the asymmetries, shifts and widenings induced on the transmission profile and point-spread functions when the etalon is tilted with respect to the optical axis of the instrument, when considering errors in the alignment of the optical components, or by departures from the ideal paraxial propagation of light through the instrument. In the second paper, we tackle the polarimetric response of anisotropic etalons filled with a solid material (e.g., lithium niobate). We find that the analytical form for the Mueller matrix of etalons that exhibit an arbitrary birefringence depends only on four spectral coefficients that vary rapidly along the bandpass and show that the polarimetric response can be arranged as the combined Mueller matrices of a retarder and a mirror, properly modulated across the transmission profile. We derive a compact expression for the Mueller matrix of collimated etalons and we present explicit formulae to numerically evaluate the coefficients of the Mueller matrix for the telecentric configuration. We take care of the different orientations of the principal plane of the crystal in the two configurations and we present the explicit dependence of the birefringence induced in uniaxial crystals with the direction of the incident light beam and with the orientation of the optical axis, necessary to evaluate the Mueller matrix. Then, we assess the response of a Z-cut etalon for the telecentric and collimated cases and study the dependence of their PSFs with the polarization of incident light. In the third paper, we evaluate the spurious plasma velocities and magnetic field signals induced by the effects studied in the previous papers: pupil apodization arising in telecentric setups, asymmetries on the pupil apodization in imperfect telecentric mounts, and the birefringent effects that appear in the two mounts when a uniaxial etalon is employed. For this purpose, we simulate a spectropolarimeter in configurations similar to the ones of PHI and IMaX and we compare the line-of-sight plasma velocities and magnetic signals with the ones obtained when assuming an ideal behavior. We take care of the etalon location within the optical train and we distinguish between two important cases: when the etalon is placed after the polarimeter (occuring in dual-beam instruments) and when it is located before the analyzer. We also evaluate the possible contamination between orthogonal channels in dual-beam instruments. We show that birefringence has a minimal impact on the measured Stokes vector compared to the typical artificial signals expected by pupil apodization. In the fourth paper, we find an analytical formula that describes the transmitted electric field in telecentric mounts, in excellent agreement with the numerical solution of the electric field equation. We use such an expression to infer both the transmission profile and the transmitted wavefront and we derive expressions for the analytical derivatives of the electric field in order to carry out sensitivity analyses of these parameters. In particular, we obtain explicit expressions for the wavefront degradation produced by errors across the footprint of the incident beam and we discuss their maximum allowed magnitude to achieve diffraction-limited performance. We focus on the dependence of the wavefront error with the f-number, with the reflectivity and with the spectral resolution, taking care of the integrated response of the instrument across the transmission profile. We discuss the intrinsic errors on the optical phase introduced by the finite f-number of the incident beam and we compare qualitatively the performance of telecentric mounts with the one expected in collimated setups attending to considerations related to the size, quality, and cost of the etalon and of the instrument itself. Finally, we propose a method to analytically evaluate the Mueller matrix of telecentric etalons adapting the formulation derived for the isotropic case.