# Optical Angle Measurement

### Collimator

The Collimator is an optical instrument consisting of a well corrected objective lens with an illuminated reticle at its focal plane.

The emerging beam is parallel (collimated beam), so that the image of the reticle is projected at infinity. The collimator is usually set up in this way known as infinity adjustment (setting).

When moving the reticle out of the focal plane of the objective lens, the shape of the emerging beam will change:

- Moving the reticle away from objective lens will result in a convergent beam. The image of the reticle is real and projected at a finite distance.
- Moving the reticle toward the objective lens will result in a divergent beam. If the beam diverges, a virtual image is produced at the aparent crossing point of the beam rays.This point is also located at a finite distance. This adjustment of the collimator is known as finite distance setting.

The collimator is often used as a test chart projector for the inspection of infinity corrected objective lenses, e.g. photography lenses. In combination with a telescope, the collimator can also be used for aligning machine elements along the line of sight.

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### Industrial telescope

The telescope is an optical tool that images an object at a far distance - usually preset to infinity - into the image plane of the objective lens. The image is then magnified and visually inspected by an eyepiece. For measurement purposes usually a graduated reticle is located in the image plane. The magnification of the telescope is given by the ratio of the objective focal length and the eyepiece focal length.

When the incoming beam is parallel, the image observed through the telescope is located at infinity i.e at a long distance. This set up in is known as infinity setting.

Similar to collimators, the telescopes can be focused at finite distances. Attaching a draw out tube to the reticle adapter to move the reticle out of the focal of the objective lens, the standard telescope becomes a focusing telescope. Depending on the location of the reticle relatively to the focal plane, it results a real or a virtual image at a finite distance.

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### Autocollimator

The autocollimator combines both optical tools, the collimator and the telescope into one instrument using a single objective lens. Both beam paths are seperated by using a beam splitter.

The autocollimator is a very sensitive angle measuring device and is thus used for the precise angular adjustment of optical or machine components. Due to the collimated beam (infinity adjustment) the measurement results are independent from the distance to the object under test. The operating principle is explained in the following.

Like in the collimator the image of the illuminated object reticle is projected by the objective lens to infinity. In some distance, the collimated beam is reflected back from a mirrored surface. If the mirror surface is tilted by an angle α with respect to the optical axis, the reflected beam will enter the objective lens with an angle 2α. This leads to a shift d of the image in the image plane which can be calculated with the objective focal length f giving d = 2α x f or α = d/( 2f ). Thus, the sample angle is directly proportional to the measured shift in the image plane (small angles assumed). The resolution of an autocollimator increases proportionally and the angular field of view reciprocally with the focal length of the objective lens.

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### Electronic Autocollimator

In an electronic autocollimator the eyepiece is replaced by an electronic camera with discrete sensor pixels (e.g. CCD or CMOS sensor type). It can be of a 2D frame type allowing angular measurements in two directions, or a 1D line scan sensor for single axis measurements. The digital camera is usually connected to a PC which calculates the measured angle from the image by using image analysis software. The PC assisted measurement guarantees much higher resolution, accuracy and repeatability of the results compared to the visual inspection, since it does not depend on the operators experience and attention.

The high resolution of electronic autocollimators is due to the evaluation of gray scale levels in the image which allows for sub pixel interpolation of the image position. Depending on the focal length of the objective lens and the stability of the setup, angular resolutions of 1/100 up to 1/1000 arcsecs can be achieved.