Monocular augmented reality devices are used in aviation to help civilian or military pilots in their flying task. In those devices, a virtual image is projected in front of one eye on a see-through glass allowing them to see environment with both eyes. This glass is mounted on a helmet allowing users to maintain the virtual information, usually find in the primary flight display, in front of the eye. Given that the image is presented in front of only one eye, the two eyes are not stimulated in the same way and it can creates a phenomenon known as binocular rivalry. When it appeared, brain is not able to merge the two visuals information and an alternation between them can occur. This alternation appears according to visual condition and the question arises as is it relevant to choose the eye to display the image to limit binocular rivalry and guarantee a good performance in the tasks of recognition and control. The control task consists in matching a monocular item with a binocular item and the detection task consists in giving the right opening orientation of Landolt rings that can be monocular or binocular. Our study aims to compare the performances as a function of the position of the virtual image. These results are then compared to the results of several dominant eye tests to determine if one test can objectively determine on which eye the monocular information should be displayed when using a monocular see-through device.