Measurement of the object angular position and its change is one of the important tasks in measurement technique. Our method is based on determination of the angular position of a 2D periodical optical pattern (2D mark) at the object, captured by the sensor of a digital camera. System performance can be frustrated by errors in determination of the spot coordinates on the camera sensor; by the presence of lens aberrations; by deviations from the parallelism of the pattern planes and the camera sensor; and by differences between the actual spots positions and the ideal grid. In the paper we discuss the effect of these errors and the way to correct or eliminate them. We have developed the mathematical routine and the corresponding numerical codes for correction of the said errors. The code and the routine we checked in a real experiment. It has shown that the correction decreases the standard deviation in 15 times.