Pupil plane optimization for single-mode multi-axial optical interferometry with a large number of telescopes

Future and planned optical long-baseline interferometers will allow rapid spectro-imaging at high angular resolution. A non-homothetic Fizeau instrument using optical fibres is one of the most promising concepts because it combines good sensitivity and high spectral resolution capabilities. However, when increasing the number of input telescopes, one critical issue is the design of the beam recombination scheme, at the heart of the instrument. Extending our previous analysis on the multi-axial 'all-in-one' recombination, where the beams are mixed all together, in this paper we tackle the possibility of reducing the number of pixels that are coding the fringes by compressing the pupil plane from a partially redundant output pupils configuration. Shrinking the number of pixels, which drastically increases with the number of recombined telescopes, is indeed a key issue that enables one to reach a higher limiting magnitude, but also allows one to lower the required spectral resolution and fasten the fringe reading process. By means of numerical simulations, we study the performances of existing estimators of the squared visibility with respect to the compression process. We show that not only does the model-based estimator lead to better signal-to-noise ratio (S/N) performances than the Fourier ones, but above all it is the only one that prevents the introduction of baseline mixing biases in the visibilities as the pupil plane compression rate increases. Furthermore, we show that moderate compression allows one to keep the S/N of the visibilities unaffected. In light of these conclusions, we propose an optimized pupil arrangement for six- and eight-beam recombiners.