In order to introduce many more evaluation points during the Hartmann test, the scanning of the screen across the pupil is proposed; after each step of the scan a different image of the bright spots is obtained. Basic ideas about how to design radial and square screens for the scanning are presented. Radial screens are scanned by rotation, whereas for square screens a linear inclined scan is enough to introduce many more evaluation points along two independent directions. For square screens it is experimentally shown that the lateral resolution of the test is improved.