Simulation of digital holographic recording and reconstruction using a generalized matrix method

In recent years, research efforts in the field of digital holography have expanded significantly, due to the ability to obtain high-resolution intensity and phase images. The information contained in these images have become of great interest to the machine learning community, with applications spanning a wide portfolio of research areas, including bioengineering. In this work, we seek to demonstrate a high-fidelity simulation of holographic recording. By accurately and numerically simulating the propagation of a coherent light source through a series of optical elements and the object itself, we accurately predict the optical interference of the object and reference wave at the recording plane, including diffraction effects, aberrations, and speckle. We show that the optical transformation that predicts the complex field at the recording plane can be generalized for arbitrary holographic recording configurations using a matrix method. In addition, we provide a detailed description of digital phase reconstruction and aberration compensation for a variety of off-axis holographic configurations. Reconstruction errors are presented for the various holographic recording geometries and complex field objects. While the primary objective of this work is not to evaluate phase reconstruction approaches, the reconstruction of simulated holograms provides validation of the generalized simulation method. The long-term goal of this work is that the generalized holographic simulation motivates the use of phase reconstruction of the simulated holograms to populate databases for training machine-learning algorithms aimed at classifying relevant objects recorded through a variety of holographic setups.