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On axis means central to field of view - assuming everthing is collimated - so its the focus at the centre of your eyepiece / camera view, effectively.

Off axis in this context means at the edges of your filed of view - typically where optical errors show up, ie coma and astigmatism.

A poor optical set up will show a decent image on axis but will show up distortions nearer the edge of the field of view

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Off axis guiders allow you to image through the main axis of the scope with an additional camera on the side where you can put a guide cam. This receives an image from the edge of the field of view produced by a small diagonal mirror poked into the edge of the light train. Sometimes the diagonal is rotatable around all or part of the image edges. Here you can pick a star to guide by through the same optical setup and reduce drastically any flexure :)

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