Spectral resolution and sampling present a design trade-off when building spectropolarimetric instruments to observe the Sun with very high spatial resolution. On the one hand, for spectropolarimetric inversions, high spectral resolution translates into a high depth resolution along the line of sight. On the other hand, fine spectral sampling results in increased noise per wavelength bin, smaller spectral ranges, and higher data rates. In this talk, we will explore how a finite spectral resolution changes the information content in stellar spectra. We do that by synthesizing spectra of the two magnetically sensitive photospheric lines of iron around 630 nm and applying various spectral degradations and rebinning. We analyze how the dimensionality of the spectra changes and the performance of the spectropolarimetric inversions applied to these different synthetic datasets. We are especially interested in the effects of noise on the inferred parameters. We conclude that the fine spectral resolution (and high spectral fidelity) result in excellent inversions, even at nominally high noise levels. We support these conclusions with a few examples from TRIPPEL-SP and MiHI instruments at the Swedish Solar Telescope.
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