Boresight

Right-handed facility frame with axes +X (boresight / reference), +Y, +Z. All four angles below are measured in the facility frame after calibration.

• Zenith — direct angle between the vector and +X, range 0–180 deg.
• Roll — CCW angle about +X, measured from +Z to the vector's projection in the YZ plane.
• Pitch — CCW angle about +Y, measured from +X to the vector's projection in the ZX plane.
• Yaw — CCW angle about +Z, measured from +Y to the vector's projection in the XY plane.

The results table shows calibrated elevation, roll, zenith, and facility direction cosines.

Subject theodolite is the instrument reading the target (a mirror cube face, an optical flat, etc.). Primary theodolite is the reference instrument that defines the azimuth origin for the session.

When subject = primary (one instrument, or two that share an azimuth reference), leave Subj az ref and Prim az ref blank. The pipeline uses the subject's azimuth as-is.

When subject ≠ primary, enter the azimuth each theodolite reads when pointed at the same tie-point. The pipeline runs sectoprim(subject_az, subj_ref, prim_ref) to rotate the subject's reading into the primary's frame before computing roll.

Az / El sec samples: type every arcsec reading you took (space or comma separated). The mean is used for the reduction; σ drives pass/fail vs. your tolerance.