A theodolite's accuracy depends on a set of fundamental-line relationships (vertical axis, horizontal axis/trunnion axis, line of sight, plate and altitude bubble-tube axes, and the graduated circles) that an ideal instrument must satisfy — e.g. the horizontal circle perpendicular to the vertical axis, the vertical circle perpendicular to the horizontal axis, and the vertical, horizontal, and sighting axes intersecting at a single instrument center. When these relationships are disturbed by wear, mishandling, or manufacturing defects, systematic instrumental errors (circle eccentricity, non-uniform graduation, bubble-tube misalignment, non-perpendicularity of the horizontal and vertical axes) are introduced into angle observations, and these can be either compensated for through an observation strategy — most notably the principle of reversal (averaging vernier pairs, face-left/face-right readings, or full-circle observations) — or corrected instrumentally through permanent adjustment procedures. This is a core topic in surveying/geomatics instrumentation theory, governing how horizontal and vertical angles are measured accurately with a theodolite or total station.
A theodolite's accuracy depends on a set of fundamental-line relationships (vertical axis, horizontal axis/trunnion axis, line of sight, plate and altitude bubble-tube axes, and the graduated circles…