Handbook of Dimensional Measurement, Fourth Edition

Autocollimators are sensitive and inherently very accurate optical instruments for the measurement of small angular deviations of a light-reflecting flat surface. The autocollimator resembles the telescope, although its operation is not restricted to the observation of an extraneous target point. The autocollimator has its own target that is projected by collimated light beams on a remotely placed surface and the reflected target image is observed in the ocular of the instrument.
Figure 11-31 illustrates the optical principle of autocollimation. The illuminated hairline target is projected through a collimating objective in the form of a parallel rays onto a flat surface that acts like a mirror. The reflected image, passing through the objective of the autocollimator, appears on a graticule and is observed through the magnifying ocular of the instrument. The position of the reflected image, in relation to the graticule's reference mark, indicates whether the reflector surface is exactly normal to the projected light beams, or tilted relative to that reference direction.
When the reflector surface is tilted, the direction of the returning light beams are deflected from the projected ones by twice the angle of tilt a; the resulting deflection is the sum of the incident and of the reflected angles. This angular deflection causes the reflected image, which appears in the focal plane of the objective lens, to be shifted by the linear distance y, which...