Imaging through scattering media using differential intensity transmission matrices with different Hadamard orderings

A transmission matrix (TM) is a powerful tool for light focusing and imaging through scattering media. For measuring it, the normal way requires establishing a multiple-step phase-shifting interferometer, which makes the TM measurement not only complex and sensitive but also time-consuming. Imaging through scattering media using an intensity TM method can make the setup for TM measurement without the phase-shifting interferometer, thus it is much simple, more stable, and several times faster. Here, based upon a differential intensity TM method, we demonstrated it to do imaging through scattering media using different Hadamard orderings. To accelerate the TM measuring speed while degrading as little as possible of the imaging quality, a relatively reasonable strategy to plan Hadamard orderings for the TM measurement is designed since it can suggest us to preferentially measure the components in TM that are more important to the imaging quality. Thanks to the different Hadamard orderings, their influences on the imaging quality at different measuring ratios are investigated, thus an optimal measuring ordering for accelerating the TM measurement can be obtained, while only sacrificing as little as possible of the image fidelity. Simulations and experiments verify the effectiveness of the proposed method.