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A cross-dispersed echelle spectrograph uses an echelle grating for strong dispersion and a cross-disperser in the perpendicular direction to separate overlapping diffraction orders. It records many orders simultaneously in an echellogram.

Built by André Baranne, Michel Mayor, Didier Queloz and colleagues, the ELODIE fiber-fed spectrograph carried light from Haute-Provence's 1.93-metre telescope through optical fibers. Its echelle grating dispersed light in high diffraction orders; an optical prism and grism cross-disperser separated them perpendicularly on a charge-coupled device. This cross-dispersed echelle spectrograph achieved spectral resolving power $R=42000$. A simultaneous thorium reference tracked instrumental drift. Wavelength calibration mapped detector positions to wavelengths; spectral cross-correlation combined many spectral lines into a fitted profile. A barycentric velocity correction removed the observer's motion.^[ref]

Why can a spectrograph measure a Doppler shift much smaller than one spectral resolution element? Resolution concerns separating neighbouring features, whereas locating the centre of a known profile uses information across that profile and across many spectral lines. For a chosen example, at $\lambda =500\mathrm{nm}$ a recession velocity of $60\mathrm{m}{\mathrm{s}}^{-1}$ givesAt $R=42000$, one spectral resolution element corresponds to $c/R\simeq 7.14\mathrm{km}{\mathrm{s}}^{-1}$, about $119$ times larger. A well measured centre can move by a small fraction of that width. More photons and more useful spectral lines improve the estimate, but do not remove wavelength calibration errors or stellar activity.

A simple mathematical picture of spectral cross-correlation makes the readout concrete. Define $x=c\log (\lambda /{\lambda }_0)$, with fixed reference wavelength ${\lambda }_0$, and let $d(x)$ be continuum-normalized line absorption. For small velocities, a common Doppler shift approximately translates $d(x)$. A positive absorption mask $m(x)$ then givesIf $d(x)=m(x-v_r)$, the maximum occurs at $u=v_r$; a convention correlating the received observed radiative flux instead produces a dip. A fitted correlation centre is an effective collective line position, not a claim that each individual spectral line has been resolved into a narrower feature. The lamp tracks instrumental drift, while the barycentric velocity correction removes the observer's changing line-of-sight velocity; neither removes changes in the star itself.

The echellogram contains nearly parallel traces, one for each diffraction order. Choose the main echelle grating dispersion to increase wavelength toward the right and the cross-disperser to increase wavelength upward. At a fixed horizontal coordinate, order $m+1$ has a shorter wavelength than order $m$, so it lies below order $m$ in this convention.

For field of view, fiber-fed spectrographs commonly cover wider sky areas: fibers can pick targets across a broad focal plane while feeding a compact spectrograph with a fixed output slit. A multi-slit spectrograph must image its field through the spectrograph optics, and spectra must fit on the detector without overlap, which restricts both field and target layout.

For spectral resolution, fibers can feed an optimized, stable high-dispersion instrument, including an echelle grating. The fiber image acts as its entrance width. In a multi-slit spectrograph, slit width and dispersion similarly determine the spectral resolving power. Neither feed type alone imposes a universal resolution ranking: narrower fibers or slits improve resolution at the cost of losing source light, and both can be designed for high or low resolution.

For faintness limit, slit masks often have an advantage for individual faint objects because they avoid fiber coupling and transmission losses, permit a slit width matched to astronomical seeing, and sample local sky along the slit. Fibers can admit more sky through a fixed circular aperture and require sky subtraction from separate locations; focal-ratio degradation can also reduce throughput. The actual limit depends on throughput, aperture size, background stability, and detector noise through the signal-to-noise ratio in photon counting. Well-designed fiber instruments can nevertheless be very efficient for wide-field surveys, so the comparison is conditional on the optical design and observing conditions.