Non-linear errors are accuracy error motions that do not follow a straight line as the stage moves through its travel range. An example of an accuracy plot for a linear stage is shown below:

After we perform metrology on a system, we apply error compensation in the motion controller to calibrate (or correct) the repeatable positioning error of the system.  If done well, the black line in the plot becomes a flat line at zero.

Finally, there are linear errors. These are errors that are most commonly caused by thermal expansion effects. As the stage structure and encoders expand and contract with temperature changes, the flat straight line in the plot above becomes a diagonal line. However, since the error is linear, it can easily be addressed by applying a scaling factor to either the motion controller or in a machine vision system. 

If this behavior is a concern for the respective application, a calibration routine can be built into the machine, where the stage is moved to a fixed point in space to look at a fiducial, then is moved to another 2 or 3 fiducials. The errors between the expected locations and measured locations are then calculated. The scale factor can then be adjusted based on these measurements. Such calibrations are usually done periodically, either at a fixed time interval (i.e. every 10 minutes) or in a process interval (i.e. before the start of each batch). Any changes in machine accuracy due to thermal effects are taken care of in this way.

It is not practical, except in very extreme (and costly) cases, to try and build a motion system that holds its accuracy over a wide temperature range without using a calibration routine such as described above.