Basic angles in microelectromechanical system scanning grating spectrometers

Modern miniaturized scanning grating spectrometers (SGSs) are often based on microelectromechanical system devices. In contrast to classical spectrometers, such systems exhibit additional design constraints, like a symmetrical motion of the grating with a limited deflection. A detailed mathematical analysis of typical SGS configurations based on the grating equation considering these constraints is presented. Equations that relate the basic angles on a scanning grating to the grating properties and the attainable wavelength range of a spectrometer are derived, and the solution set is examined. Furthermore, the analytical description can be used to optimize SGSs with symmetrically moving gratings. The attainable spectral range for a given deflection amplitude of the grating can be calculated. Alternatively, the required grating properties can be determined for a given spectral range.