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Autocollimation is an optical return-path method: a source pattern is projected through a collimator, reflected back from an external surface, and examined through the same optical system. It is the process used by an autocollimator, rather than the instrument itself. A plane mirror normal to the outgoing collimated light returns the light along the reference direction.^[ref]

A typical apparatus uses an illuminated reticle near a focal plane, an objective and a beam splitter that separates the illumination and viewing paths. The outward projection and the return image are compared, making small changes in reflector orientation observable.^[ref]

For a small mirror tilt $\theta$, reflection changes the return direction by $2\theta$. In the ideal paraxial model, return-image displacement is $x\approx 2f\theta$, where $f$ is the effective focal length. An original example with $f=150\mathrm{mm}$ and $\theta =20\mu \mathrm{rad}$ gives $x\approx 6\mu \mathrm{m}$. This is displacement in the image plane, not a direct measurement of mirror translation.

The angular interpretation explains why simply moving an ideal plane mirror farther away does not multiply the focal-plane displacement by that distance. In practice, finite aperture, beam walk, alignment and diffraction limit the usable return. Measurement calibration and a stable reference remain necessary to distinguish a genuine angular change from movement of the optical system.

An 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.^[ref][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 iswith the angle in radians. For the independently chosen values $f=200\mathrm{mm}$ and $x=4\mu \mathrm{m}$, the mirror tilt is $10\mu \mathrm{rad}$, 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.^[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.

Collimated light is light whose propagation directions occupy a narrow angular range. In geometrical optics, ideal collimation is represented by parallel light rays. A collimator approximates this by placing a small source at the focal position of a lens. A reticle projected by an autocollimator provides a practical example: the outgoing pattern travels as an approximately collimated beam before reflection from a test mirror.^[ref]

A finite beam still undergoes diffraction. For an ideal Gaussian beam in free space, let $w_0$ be its beam waist radius, measured where the intensity has fallen to $1/e^2$ of its axial value, and let $\lambda$ be its wavelength. Its far-field beam divergence half-angle and Rayleigh range areThe radius at distance $z$ from the beam waist is $w(z)=w_0\sqrt{1+(z/z_R{)}^2}$. Thus small beam divergence can make a beam nearly constant in width over a useful distance without making it perfectly parallel everywhere.^[ref]

For an original example, choose $\lambda =500\mathrm{nm}$ and $w_0=1\mathrm{mm}$. Then $\theta \simeq 0.159\mathrm{mrad}$ and $z_R\simeq 6.28\mathrm{m}$. At $z=z_R$ the radius is $\sqrt{2}\mathrm{mm}$, so even this small-divergence beam eventually widens. Collimation describes propagation directions; optical coherence describes phase correlations and is a separate property.