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The method to use differs depending on whether the alignment is taking place in daylight or in night. Furthermore, the method differs if the alignment is done in the Northern Hemisphere or Southern Hemisphere. The purpose of the alignment also must be considered. For example, the demand for accuracy is much more significant in astrophotography than in occasional stargazing.
Aiming at the pole stars
In the Northern hemisphere, sighting Polaris the North Star is the usual procedure for aligning a telescope mount's polar axis parallel to the Earth's axis. Polaris is approximately three quarters of a degree from the North Celestial Pole and is easily seen by the naked eye.
σ Octantis, sometimes known as the South Star, can be sighted in the Southern hemisphere to perform polar alignment. At magnitude +5.6, it is difficult for inexperienced observers to locate in the sky. Its declination of -88° 57′ 23″ places it within 1° 2′ 37" of the South Celestial Pole. An even closer star BQ Octantis of magnitude +6.9 lies 10' from the South Pole as of 2016. Although not visible to the naked eye, it is easily visible in most polar scopes. It will be closest (9') to the South Pole in the year 2027.
Rough alignment method
In the Northern hemisphere, rough alignment can be done by visually aligning the axis of the telescope mount with Polaris. In the Southern hemisphere or places where Polaris is not visible, a rough alignment is performed by ensuring the mount is level, adjusting the latitude adjustment pointer to match the observer's latitude, and aligning the axis of the mount with true south or north by means of a magnetic compass (after taking the local magnetic declination into account). This method can sometimes be adequate for general observing through the eyepiece or for very wide angle astro-imaging with a tripod-mounted camera. This method is often used by newcomers to amateur astronomy equipped with an equatorially-mounted telescope.
There are ways to improve the accuracy of this method. For example, instead of reading the latitude scale directly, a calibrated precision inclinometer can be used to measure the altitude of the polar axis of the mount. If the setting circles of the mount is then used to find a bright object of known coordinates, the object should only mismatch in azimuth, so centering the object by adjusting the azimuth of the mount should complete the polar alignment process. Typically, this provides enough accuracy to allow tracked (i.e. motorized) telephoto images of the sky.
For astro-imaging through a lens or telescope of significant magnification, a subsequent drift alignment is necessary to refine the rough alignment.
Drift alignment method
Drift alignment is a method to refine the polar alignment after a rough alignment is done. The method is based on attempting to track stars in the sky using the clock drive; any error in the polar alignment will show up as the drift of the stars in the eyepiece/sensor. Adjustments are then made to reduce the drift, and the process is repeated until the tracking is satisfactory. For the polar axis altitude adjustment, one can attempt to track a star low in the east or west. For the azimuth adjustment, one typically attempts to track a star close to the meridian, with declination about 20° from the equator, in the hemisphere opposite of the observing location.
Equipment used in polar alignment
A crosshair eyepiece is an ordinary ocular with the only difference that it has a crosshair for aiming and measurement of the angular distance. This is useful in any type of polar alignment, but especially in drift.
Auto guiding systems
Dedicated polar scope
A small telescope usually with an etched reticle that is inserted into the rotational axis of the mount.