1 Introduction

Narrow-band tunable filtergraphs play an important role in solar physics, because only the simultaneous observation of both spatial dimensions permit studying the dynamics of small scale structure with sufficient temporal resolution. Efficient tunable filtergraphs can be constructed with Fabry-Pérot interferometers (FPIs) in combination with prefilters which select a suitable passband within the channeled spectrum. Several filtergraphs using FPIs have been recently constructed for solar observations (Bonaccini et al. 1989; Bendlin et al. 1992; Cavallini 1998; Kentischer et al. 1998). The spectral passband of an FPI varies with the angle of incidence of a plane wave which transverses the interferometer. In all designs except the one by Bendlin et al. (1992), the FPIs are operated in a telecentric configuration - i.e., with a collimated pupil - in order to maintain the passband in the same position at all field points. The consequence is a slight reduction in spectral resolution because the central wavelength of the passband varies across the pupil. This reduction is accounted for in the specification of the FPI to meet the design goal of the filtergraph.

Beckers (1998a, 1998b) has investigated the effects of the passband variation across the pupil on high spatial resolution spectrometry. In monochromatic light, the variation causes an apodisation within the pupil which modifies the point spread function (PSF) in the image plane compared to the PSF of a uniformly illuminated pupil. We refer to this modification as pupil apodisation in the following. As Beckers points out, spectral variations of the PSF in combination with the intensity variations of a Fraunhofer line may lead to spurious signals in Dopplergrams and may render a telecentric design unsuitable for high resolution work. Beckers limited his investigations to the variation of the magnitude of the electromagnetic field within the pupil, the corresponding effects on the field phase were not treated. The effects could therefore be even worse than descibed by Beckers.

The Telecentric Etalon SOlar Spectrometer (TESOS) is a Fabry-Pérot etalon based filtergraph which operates at the Vacuum Tower Telescope of the Observatorio del Teide on Tenerife since a few years (Kentischer et al. 1998). TESOS originally used two FPIs in a telecentric configuration; it was recently upgraded with a third FPI which is also in the telecentric beam (Kentischer et al. 2000). Since high spatial resolution - although not at the diffraction limit - is a prime science goal of TESOS, we were concerned by Beckers' findings. In this paper, we repeat his analyses specifically for TESOS, extend the treatment to the full complex field, and investigate the combined effects of three FPIs.