Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy.

We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by applying the golden selection search with parabolic interpolation, which is the gold standard for tackling single-variable optimization problems. The proposed approach is successfully applied to three diverse autofocusing cases, providing up to 136-fold speed-up.

Fast multiple-scattering holographic tomography based on the wave propagation method.

We develop a time-efficient computation scheme for a holographic tomography reconstruction technique that accounts for multiple scattering by applying the forward model based on the wave propagation method (WPM). The computational efficiency is achieved by employing adjoint equations for calculation of the gradient of the data fidelity term in the gradient descent optimization procedure. In the paper we provide a general computation scheme that is suitable for various forward models that can be represented in the form of an iterative equation. Next, we provide the complete solution for the time-efficient reconstruction utilizing WPM. In the considered reconstruction case, the proposed algorithm enables the 114-fold speed-up of computations with respect to the original tomographic method.