Systems and methods for measuring tension distribution in webs of roll-to-roll processes

A system for monitoring tension distribution across a width of a web in a roll-to-roll system, the roll-to-roll system comprising the web, at least first and second rollers between which the web travels in a longitudinal direction of the web, tension inducing means for inducing tension in the web in the longitudinal direction thereof, and fabricating means for fabricating printed devices on a surface of a flexible substrate of the web, the system comprising:

• a first device for inducing deflection in the web by exciting vibration in the web without contacting the web between the first and second rollers;
• a second device for sensing vibration in the web in a transverse direction that is normal to the surface of the flexible substrate without contacting the web;
• and
• one or more computer processors configured to:
• process vibrational responses induced by the first device and sensed by the second device at a plurality of different locations across a width of the web while the first device is located at a single location along the width of the web;
• and
• determine from the processed vibrational responses an average tension and linear variation of tension present in the flexible substrate resulting from a nonuniform tension distribution induced in the flexible substrate between the first and second rollers.