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.
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