A miniaturized Holographic Fourier transform imaging spectrometer HFTIS, made from simple all-reflective components and with no moving parts, is provided. This HFTIS includes an all-reflective two beam interferometer, which provides two interfering beams; a two-dimensional detector array to detect the interference pattern created by the beams; a computing machine for correcting the distortions in the pattern and calculating the spectrum from the corrected interferogram. The same principle can be used to build spot spectrometers, line-scan imaging spectrometers (also called array spectrometers or line-scan hyperspectral cameras) as well as two-dimensional instantaneous imaging spectrometers (also called staring hyperspectral cameras). In all variants of HFTIS that can be built using this invention, the wave-signal collecting element can also be built of all-reflective components. Digital correction can be utilized to straighten the interference fringes and to compensate for the impact of used lenses and other refractive components, to produce correct spectra after Fourier Transformation.