The High-resolution Mid-infrared Spectrometer (HIRMES) will be in-flight aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA) in late 2019, which will allow for observations of the structure and evolution of protoplanetary disks. SOFIA has a different coordinate system from the system being used to build HIRMES and needs to be defined and applied to HIRMES. This is necessary because the first mirror, which is aiming the incoming light onto the slit wheel by allowing for tip and tilt adjustments, cannot rotate. Thus, the SOFIA coordinate system allows for this additional degree of freedom and allows for the slit wheel to be in line with the telescope. Using a laser radar, multiple measurements around the instrument were taken of tooling balls, which quantified an uncertainty with the measurements. Also, a laser radar was used to scan the entirety of the instrument. The center of the front flange was determined using the measurements and scans of the instrument, which was used to determine the origin of the SOFIA coordinate system and its uncertainty. By knowing the center of the front flange, an off-center, rotated coordinate system was created, matching the mechanics' schematics for the system. Going forward, this coordinate system will allow for continued alignment of the instrument in preparation for flight and for accurate measurements when aboard SOFIA.