Freeform lens collimating spectrum-folded Hadamard transform near-infrared spectrometer

Abstract A novel Hadamard transform spectrometer collimated by a freeform lens has been designed, which doubles the working spectral range while the spectral resolution is maintained. The freeform lens is designed to redistribute the broadband spectra of the source from 800 nm to 2400 nm into two collimated beams with different wavelengths and different tilting angles, to achieve the folding of spectra on the digital micro-mirror devices (DMD). It is constructed by solving two partial differential equations. The grating diffraction efficiency of the two split beams are more uniform and higher compared with the traditional method. The simulation results show that the bandwidth of the spectrometer is doubled and the spectral resolution is better than 10 nm. The optical system becomes more compact, and the energy efficiency is improved by 11.98% by folding the spectra with one freeform lens and one grating.