  iLocater is a near-infrared, extremely precise radial velocity (EPRV)
spectrograph under construction for the dual 8.4 m diameter Large Binocular
Telescope (LBT). The instrument will undertake precision radial velocity
studies of Earth-like planets orbiting low-mass stars. Operating in the
diffraction-limited regime, iLocater uses adaptive optics to efficiently inject
starlight directly into single-mode fibers that illuminate a high spectral
resolution (R=190,500 median), cryogenic, diffraction-limited spectrograph. To
maximize performance, the spectrograph uses a new design strategy for EPRV
instruments, combining intrinsically stable materials for its optomechanical
fabrication with precision optical fabrication. This novel combination will
enable unique EPRV capabilities for exoplanet and astrophysics studies of the
solar neighborhood.
  We present the final optical and mechanical designs of the spectrograph
system. Ensuring the as-built spectrograph achieves its designed spectral
resolution and diffraction-limited performance has required careful control of
the end-to-end system wavefront error (WFE) budget. We discuss the efforts
undertaken to achieve this goal including minimizing residual WFE in the
optical design, assessing diffraction grating WFE performance, optimizing
material choices, and requiring precision optical design and fabrication. Our
goal is to deliver diffraction-limited performance across the full spectral
format, which, combined with intrinsic thermal stability requirements for EPRV
science, has driven the selection of silicon optics and Invar optomechanics.
The system performance is further optimized using precision (sub-mK) thermal
control. This set of design features will allow iLocater to achieve sub-m/s
radial velocity precision in the near-infrared, and to serve as the first
optimized diffraction-limited spectrograph for EPRV science.

Instrumentation and Methods for Astrophysics;Earth and Planetary Astrophysics