Piezoelectric scanning of Fabry-Perot spectrometers: nonlinearities

Abstract

Piezoelectric materials used in mechanical scanning of Fabry-Perot spectrometers are found to have measurable nonlinearities. Dynamic scanning has been used in the present investigation in order to decrease the effects of some of the variables, such as creep, of the piezoelectric material in static operation. The results show mainly a decrease in the distance between corresponding maxima, or apparent free spectral range, as the driving voltage increases to higher values. A relationship between this voltage and displacement (in terms of orders) has been derived, and it is given by v(i) = In {1 - (x(i) - x(0))/[a/(1 - b) - x(0)]}/In b, where v(i) is the displacement in orders from an arbitrary starting point, x(i) is a quantity directly proportional to the voltage, while x(0) is also a quantity proportional to the voltage at the arbitrary reference point, a is the distance between the arbitrary reference point and the next order, and b is the nonlinearity constant for a given piezoelectric material. Examples are given for emission and absorption measurements where the usually large effects of the piezoelectric material nonlinearities are derived, as well as schemes to minimize or altogether remove the effects by suitable handling of the data or by changing the experiment such that the scanning is forced to be linear.