Optimal scanning function of a galvanometer scanner for an increased duty cycle

We study different possible scanning functions of a galvanometer-based scanner (GS), considered with an optimal profile for the user, i.e., symmetrical, linear on their active portions, and with fast stop-and-turn parts. The scope is to obtain the function that provides the highest theoretical limit of the duty cycle of the device. From the equation of the oscillatory mirror, the active torque is obtained with regard to the scanning function. Several equations are studied for the stop-and-turn parts: polynomials of different orders and sinusoidal. We demonstrate that the choice has to be done between the two most advantageous scanning functions: linear plus parabolic and linear plus sinusoidal. The relationships between the characteristic parameters of the GS, i.e., stop-and-turn time interval, scan frequency and velocity, duty cycle, and maximum inertia torque are deduced and compared for these two functions. We demonstrate that, contrary to what is considered in the literature, the best function, i.e., the one that provides the highest duty cycle (and to obtain that, the lowest inertia torque, for minimum stop-and-turn time) is the linear plus parabolic function.