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This work presents the specifications, requirements, design, finite element analysis and results of the assembled subsystems: slit-mask, and the acquisition and guiding zone mechanisms of the ESOPO spectrograph. This spectrograph is a project of the Institute of Astronomy, National University of Mexico.

ESOPO will be a spectrograph of medium resolution for the 2.1 m telescope of the National Observatory at San Pedro Martir, Baja California, Mexico. It has been developed by the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (IA-UNAM). The main goal of this instrument is to modernize the capabilities of making science with that particular telescope. It is planned to achieve a spectral resolution between 500 and 5000. ESOPO is split into two arms; each one specialized in a specific wavelength range covering together all the visible light. A very important issue in spectrographs is to avoid inside thermal gradients. Different temperatures in the optical elements produce mechanical movements and image quality degradation during an exposition. The error budget analysis developed for ESOPO allows establishing the required limits for temperature gradients. In this paper is described the thermal analysis of the spectrograph, including specifications, finite element models, thermal equations and expected thermal gradients.

Working with big mirrors always is a great challenge, even more if the surfaces have great roughness. In this work we present a technique to verify the quality for surfaces around 3 meters in diameter and with roughness around 30 microns. In order to reach our goal we made an analysis of the grating pitch to avoid the roughness and we implement a common source light, which is independent of the angle of illumination of the surface under test. Also we implement the shadow moire and the phase shift method to obtain the wave front aberrations.