The quality inspection of internal threads on tube coupling is an essential prerequisite for ensuring the safety of oil and gas transmission. Compared to the singular and inefficient manual contact measurement methods, existing mirrored structured light visual inspection methods and systems possess significant advantages in terms of accuracy, efficiency, and functionality. With the integration of unmanned aerial vehicle (UAV) technology, automatic positioning and inspection can be realized. However, the installation error of reflective prism, as a critical component of the system, is easy to cause misalignment of the structured light. For this reason, this paper proposes a prism installation error analysis method based on the existing mirror structured light visual inspection system. By constructing a three-dimensional installation error model and solving for the pose parameters of the structured light plane before and after reflection, the deviation relationship between the actual and ideal projected position of the structured light under six degrees of freedom adjustment errors is explored. Furthermore, the sensitivity influence law of the deviations in each dimension on measurement are analyzed in depth, which provides a theoretical basis for guiding the system adjustment and error compensation. This research plays a significant role in promoting the development of internal thread measurement technology.