The assembly variables of a high performance optical system are dependent on the design of optical and mechanical structure, however, the reference coordinates used in the system assembly are mostly different from those used in optical design. To describe paraxial image motions due to adjustments precisely, the Gaussian optical homogeneous coordinate transformation model with assembly error variables was established under a reference coordinate. According to specified optical-mechanical design, the Gaussian image rotation and defocus as functions of assembly variables were described. Then, the paraxial image motion induced by small deformation of a three-mirror off-axis telescope was calculated, which shows a relative difference less than 4％ compared with that from the optical software optimized image location. By the variance combining method, a linear optimization model was solved to get the loosest error budget for 17 variables and the Monte-Carlo simulation was used to verify the error budget. It indicates that all fields meet the focus depth of ±10 μm within the focusing ability of ±300 μm. This method ignores subtle influences caused by aberration, and is favorable for optical systems consisting of plane optical components and near aberration-free components.