The Inventors’ compact FT spectrometer is comprised of the following optical components: an entrance aperture, a collimating lens, a transmissive or reflective phase shifter array, a focusing lens and a zeroth diffraction order selecting exit aperture. The entrance aperture limits the incident radiation flux. The collimating lens, referred to as the micro-phase-shifter-array (MPSA), is focused on the entrance aperture, while a second lens focuses a parallel beam onto the exit aperture and simultaneously projects an image of the MPSA onto an array detector. The array detector records the pixelated interference pattern and sends is pixel information to a CPU computing the spectral composition of the input radiation via Fourier-transformation or matrix inversion. The device utilizes a specific optical configuration and shape of the MPSA, as well as a specific focal distance between the focusing lens and the exit aperature, that allows spatial filtering of higher diffraction orders.