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High‐fidelity spectroscopy presents challenges for both observations and in designing instruments. High‐resolution and high‐accuracy spectra are required for verifying hydrodynamic stellar atmospheres and for resolving intergalactic absorption‐line structures in quasars. Even with great photon fluxes from large telescopes with matching spectrometers, precise measurements of line profiles and wavelength positions encounter various physical, observational, and instrumental limits. The analysis may be limited by astrophysical and telluric blends, lack of suitable lines, imprecise laboratory wavelengths, or instrumental imperfections. To some extent, such limits can be pushed by forming averages over many similar spectral lines, thus averaging away small random blends and wavelength errors. In situations where theoretical predictions of lineshapes and shifts can be accurately made (e.g., hydrodynamic models of solar‐type stars), the consistency between noisy observations and theoretical predictions may be verified; however this is not feasible for, e.g., the complex of intergalactic metal lines in spectra of distant quasars, where the primary data must come from observations. To more fully resolve lineshapes and interpret wavelength shifts in stars and quasars alike, spectral resolutions on order  R  = 300 000 or more are required; a level that is becoming (but is not yet) available. A grand challenge remains to design efficient spectrometers with resolutions approaching  R  = 1 000 000 for the forthcoming generation of extremely large telescopes (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

High‐fidelity spectroscopy at the highest resolutions