We describe the design and performance of the near-infrared (1.51-1.70μm), fiber-fed, multi-object (300 fibers), high resolution (R = λ/∆λ ̃22,500) spectrograph built for the Apache Point Observatory GalacticEvolution Experiment (APOGEE). APOGEE is a survey of ̃10⁵ redgiant stars that systematically sampled all Milky Way populations(bulge, disk, and halo) to study the Galaxy’s chemical and kinematicalhistory. It was part of the Sloan Digital Sky Survey III (SDSS-III) from2011 to 2014 using the 2.5 m Sloan Foundation Telescope at Apache PointObservatory, New Mexico. The APOGEE-2 survey is now using thespectrograph as part of SDSS-IV, as well as a second spectrograph, aclose copy of the first, operating at the 2.5 m du Pont Telescope at LasCampanas Observatory in Chile. Although several fiber-fed, multi-object,high resolution spectrographs have been built for visual wavelengthspectroscopy, the APOGEE spectrograph is one of the first suchinstruments built for observations in the near-infrared. Theinstrument’s successful development was enabled by several keyinnovations, including a “gang connector” to allow simultaneousconnections of 300 fibers; hermetically sealed feedthroughs to allowfibers to pass through the cryostat wall continuously; the firstcryogenically deployed mosaic volume phase holographic grating; and alarge refractive camera that includes mono-crystalline silicon and fusedsilica elements with diameters as large as ̃400 mm. This paper containsa comprehensive description of all aspects of the instrument includingthe fiber system, optics and opto-mechanics, detector arrays, mechanicsand cryogenics, instrument control, calibration system, opticalperformance and stability, lessons learned, and design changes for thesecond instrument.

We apply an iterative reconstruction method to galaxy mocks in redshiftspace obtained from N-body simulations. Comparing the two-pointcorrelation functions for the reconstructed density field, we find thatalthough the performance is limited by shot noise and galaxy biascompared to the matter field, the iterative method can still reconstructthe initial linear density field from the galaxy field better than thestandard method both in real and in redshift space. Furthermore, theiterative method is able to reconstruct both the monopole and quadrupolemore precisely, unlike the standard method. We see that as the numberdensity of galaxies gets smaller, the performance of reconstruction getsworse due to the sparseness. However, the precision in the determinationof bias ({̃ }20{{ per cent}}) hardly impacts on the reconstructionprocesses.