Additive Manufacturing (AM) to produce parts of optical systems is gaining popularity due to design flexibility and functional integration. However, one of the significant challenges in the field of AM for optical systems is the limited manufacturing accuracy compared to traditional manufacturing methods. This causes an increase in manufacturing and assembly errors, which affects the fit and function of the produced parts and therefore the performance of the optical system. This work aims to reduce the negative impact of manufacturing and assembly errors on optical performance, as exemplified in practice by additively manufacturing housings and lens mounts for a Raman spectroscopy system. For this, the simulated optical system of a Raman spectrometer is used to perform the optical tolerance analysis, such as identifying critical components and sensitivity analysis. The Manufacturability of additive manufacturing is then evaluated by measuring printed standard specimens. According to optical and mechanical tolerance analysis, design and manufacturing problems can be found. Then the structure is optimized using the design flexibility provided by additive manufacturing, and accumulated errors from assembly and manufacturing are reduced by minimizing the number of installed components. Measuring the intensity of the Raman signal revealed that the improved design reduced the accumulated errors in the mechanical structure. In addition, the signal-to-noise ratio is significantly enhanced by 265 % compared to the non-optimized design. Hence, this design optimization based on tolerance analysis is an effective methodology for enhancing the performance of additively manufactured optical systems from the perspective of AM technology development in optical domain.