This invention addresses numerous shortcomings of conventional FT spectroscopic approaches that are less readily adaptable to devising a compact device, e.g. for use in smartphone spectroscopy. One problem with traditional spectrometers is that they contain dispersive elements, like gratings or prisms, which limit the spectral bandwidth of the device. The Inventors’ device does not require the filtering of wavelengths and can be tailored to work throughout the spectral bandwidth set by the detector that can typically be an order of magnitude. In traditional devices, these gratings are generally used off-axis in either transmission or reflection modes. In comparison, the Inventors offer a transmission setup offering the advantages of having all optical components on the optical axis. This results in low optical aberrations and thus compact systems with minimum number of optical elements. Additionally, their spectrometer system does not require a high degree of collimation, thus allowing for short focal length collimators that enable smaller, compact devices.