We present the design and performance of the multi-object fiber spectrographs for the Sloan Digital Sky Survey (SDSS) and their upgrade for the Baryon Oscillation Spectroscopic Survey (BOSS). Originally commissioned in Fall 1999 on the 2.5-m aperture Sloan Telescope at Apache Point Observatory, the spectrographs produced more than 1.5 million spectra for the SDSS and SDSS-II surveys, enabling a wide variety of Galactic and extra-galactic science including the first observation of baryon acoustic oscillations in 2005. The spectrographs were upgraded in 2009 and are currently in use for BOSS, the flagship survey of the third-generation SDSS-III project. BOSS will measure redshifts of 1.35 million massive galaxies to redshift 0.7 and Lyman-α absorption of 160,000 high redshift quasars over 10,000 square degrees of sky, making percent level measurements of the absolute cosmic distance scale of the Universe and placing tight constraints on the equation of state of dark energy.The twin multi-object fiber spectrographs utilize a simple optical layout with reflective collimators, gratings, all-refractive cameras, and state-of-the-art CCD detectors to produce hundreds of spectra simultaneously in two channels over a bandpass covering the near ultraviolet to the near infrared, with a resolving power R = λ/FWHM ∼ 2000. Building on proven heritage, the spectrographs were upgraded for BOSS with volume-phase holographic gratings and modern CCD detectors, improving the peak throughput by nearly a factor of two, extending the bandpass to cover 360 < λ < 1000 nm, and increasing the number of fibers from 640 to 1000 per exposure. In this paper we describe the original SDSS spectrograph design and the upgrades implemented for BOSS, and document the predicted and measured performances.The 2.5-m SDSS telescope is a modified distortion-free Richey-Chrétien design with a 3 • diameter field of view, and f/5 final focal ratio, which provides a good match to fibers for spectroscopy (180 µm diameter, 3 ) and to the imaging CCDs (pixel size 24 µm, 0.4 ). The optical design incorporates two aspheric corrector lenses, a Gascoigne-type design located near the vertex of the primary mirror, and two interchangeable secondary correctors, one used for imaging and the other for spectroscopy. The imaging corrector is a thick fused silica lens located close to the focal plane and is incorporated into the SDSS camera, where it serves a mechanical function in addition

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