= Autocollimator
{wiki}
An \b[autocollimator] is an <optical instrument> that measures small angular changes by sending <collimated light> toward a reflector and examining the returning image. The outgoing and returning paths share optical components: a <beam splitter> directs light from an illuminated <reticle> through a <collimator>, while the reflected light is imaged onto a detector or viewed through an eyepiece. The measurement uses <autocollimation>, the return of the instrument's own projected light.<Autocollimator Principles of Operation by Micro-Radian Instruments>[Principles of Operation; Digital vs Visual]{ref}<Measurements with autocollimators by TRIOPTICS>[Opening apparatus description: reticle, beam splitter and return camera plane]{ref}
A small tilt $\theta$ of a <plane mirror> changes the reflected beam direction by $2\theta$. In an ideal paraxial model with <focal length> $f$, the return-image displacement from its zero position is
$$
x\approx2f\theta,\qquad \theta\approx\frac{x}{2f},
$$
with the angle in <radians>. For the independently chosen values $f=200\,\mathrm{mm}$ and $x=4\,\mathrm{\mu m}$, the mirror tilt is $10\,\mathrm{\mu rad}$, about 2.063 <arcseconds>. The reflected beam turns through twice that angle: confusing mirror tilt with beam deflection introduces a factor-of-two error.
A mechanical application turns angular readings into height differences. A mirror carried on two supports separated by a base $b$ has height difference $h=b\tan\theta$ across that base. With an illustrative $b=100\,\mathrm{mm}$ and the tilt above, $h$ is about 1 micrometre. A series of such local slopes can constrain straightness, provided the support geometry and reference are accounted for.<Measurements with autocollimators by TRIOPTICS>[Checking straightness: support balls/pins, base length and height relation]{ref}
The instrument therefore senses orientation through image position. It is not directly a distance gauge: lateral translation of an ideal plane mirror without tilt does not encode that translation in the same angular reading. Zero setting, <measurement calibration> and optical alignment remain part of interpreting the observation.
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