  Recently, digital holographic imaging techniques (including methods with
heterodyne detection) have found increased attention in the terahertz (THz)
frequency range. However, holographic techniques rely on the use of a reference
beam in order to obtain phase information. This letter investigates the
potential of reference-free THz holographic imaging and proposes novel
supervised and unsupervised deep learning (DL) methods for amplitude and phase
recovery. The calculations incorporate Fresnel diffraction as prior knowledge.
We first show that our unsupervised dual network can predict amplitude and
phase simultaneously, thus overcoming the limitation of previous studies which
could only predict phase objects. This is demonstrated with synthetic 2D image
data as well as with measured 2D THz diffraction images. The advantage of
unsupervised DL is that it can be used directly without labeling by human
experts. We then address supervised DL -- a concept of general applicability.
We introduce training with a database set of 2D images taken in the visible
spectra range and modified by us numerically to emulate THz images. With this
approach, we avoid the prohibitively time-consuming collection of a large
number of THz-frequency images. The results obtained with both approaches
represent the first steps towards fast holographic THz imaging with
reference-beam-free low-cost power detection.
