The Compton scattering process between a relativistic electron bunch and a high power laser pulse is still today the most efficient technique to generate high brilliance gamma ray beams. However, the main drawback of this physical process is its small cross-section which has to be compensated the use of a laser power at the limit of the existing technology to provide a high flux of gamma rays. In this presentation, we describe the optical design of the interaction point of a Compton gamma ray machine which has been proposed for the ELI-NP project. We have developed an optical system capable of recirculating 32 times a high energy pulsed laser beam. We fully modeled this apparatus using the Code V simulation software in order to perform tolerance studies. We obtain a low loss and aberration free system which provides a constant laser - electron beams crossing angle.
