An air stabilization system employing two substantially parallel, codirectional Coanda nozzles, that are positioned adjacent a flexible moving web, with each nozzle exhausting gas at the same downstream machine direction, subjects the moving web to shear forces effective to stabilize the web. Each nozzle includes an elongated slot that is substantially perpendicular to the path of the moving web and a backstep located downstream of the direction of airflow extending from the Coanda slot. The two Coanda nozzles serve as separate points along the machine direction for controlling the height of the moving web. By modulating the velocities or other parameters of gases exiting the Coanda nozzles, the shape of the moving web between the nozzles can be manipulated to present a planar contour for measurements. The air stabilization system can be incorporated into a scanner head to measure the caliper of paper, plastic, and other flexible web products.