The Deep Space Network (DSN), located at the Jet Propulsion Laboratory (JPL), is developing an RF/Optical Hybrid Antenna. This antenna concept will support the reception of high-bandwidth optical deep-space communications with simultaneous support of conventional RF uplink and downlink. The optical system on the antenna consists of sixty-four hexagonal mirrors positioned to form a spherical aperture. To align the mirrors, a Position Opto-Electronic Metrology Sensor (POEMS) system is used to measure the position of each mirror relative to one another. The POEMS system consists of a sender called a collimator, which sends collimated light to the receiving component, called a quadrant diode. The purpose of this thesis is to gain insight into the required range of the POEMS system through a Monte Carlo stack-up tolerance analysis. Misalignments and tolerances may exceed current hardware capabilities of 0.3 mm. Furthermore, this thesis aims to understand the impacts of each tolerance through sensitivity analysis. The mathematical model of the mirror assembly, the Monte Carlo, and sensitivity analysis were modeled in MATLAB. The Monte Carlo analysis in this thesis takes a random value from a probability distribution of each tolerance. Then, the analysis calculates where the intersection of the representative collimator beam on its respective quadrant diode occurs. The analysis repeats this for the desired number of random stack-up of the tolerances. The maximum pointing error obtained from the Monte Carlo simulations is 6.003 mm. The tolerances which have the most considerable effect on pointing error are the decenter (which has the most significant impact), clocking, wedge, and mirror thickness. These are the tolerances to minimize if the hardware cannot be improved to meet the required range.