In optics, it is usually straightforward to calculate the intensity distribution that is scattered from a source field. However, the inverse problem, which is to calculate the source field from the scattered intensity distribution, is significantly more difficult because there is no information about the phase distribution. In case there is some prior knowledge about the source (e.g. boundaries – compact support), it is possible to use iterative algorithms to reconstruct the source. Unfortunately, such algorithms are time consuming, even with advanced computational resources, and they do not always converge to the right solution.

We developed a novel method to rapidly solve the optical inverse problem using a digital degenerate cavity laser. It involves a computer controlled hologram and a mask inside the degenerate cavity, which correspond to the scattered intensity distribution and the compact support of the source respectively. The lasing process mimics the iterative algorithm, used to obtain a solution to the inverse problem, to yield a consistent and rapid solution that satisfies both the scattered intensity distribution and the compact support. Since the laser can support many degenerate lasing modes (about 1 million), i.e. a million degrees of freedom, the potential spatial resolution that can be obtained with our method is very high. The laser arrangement, simulations and experimental results that clearly demonstrate the validity and speed of our method will be presented.