A multiplexing spectrometer measures at least one parameter, such as temperature, pressure or stress. The system multiplexes the outputs of Bragg stack sensors deposited at the distant ends of optical fibers brought in contact or in close proximity to objects. The spectrometer detects the peaks of the optical signals returned from the Bragg stacks and converts them into corresponding values of the parameters of interest. The spectrometer includes an optical system that comprises an entrance slit, a diffraction grating as a light dispersing means. Multiplexing occurs on a two-dimensional solid state matrix photo detector detects and converts the light signals returned from the Bragg stack sensing elements into corresponding electrical signals, and a built-in look-up table to provides the values of the parameters of interest that correspond the spectral characteristics of the returned light signals.