Hyperspectral imaging through scattering layers with incoherent light

Overcoming the light scattering for imaging under natural light conditions is a tough question to solve. One major issue is the absence of an efficient model to characterize the spectral features of incoherent light scattering. Here, we put forward the incoherent light transmission matrix (TM) approach in thin scattering layers. The proposed model is a unique form of TM that characterizes the spectral transmission feature of a system with multiple spatial transmission modes. With this method, we recover hyperspectral information from a single-shot monochromatic light spot without any additional dispersion or imaging elements. The proposed TM method can also be extended to recover other information from the light field, such as the polarization information without the use of a traditional polarizer. Our method also outperforms traditional optimization algorithms in terms of time and memory cost. The results demonstrate the feasibility of our method for retrieving the abundant information from natural light scattering with the help of simple optical setups.