'on-axis' is formed from the English preposition 'on' (from Old English 'on', meaning 'in contact with' or 'upon') combined with the noun 'axis' (from Latin 'axis', meaning 'axle' or 'pivot').

'axis' comes from Latin 'axis' (axle, pivot), passed through Medieval/Old French and Middle English as 'axis', and in modern English it combines with 'on' to form the compound adjective 'on-axis'.

Originally it simply meant 'on the axis' in a literal spatial sense; over time it became a technical adjective/adverb used especially in optics and engineering to mean 'aligned with the optical or mechanical axis'.