  The numerical wavefront backpropagation principle of digital holography
confers unique extended focus capabilities, without mechanical displacements
along z-axis. However, the determination of the correct focusing distance is a
non-trivial and time consuming issue. A deep learning (DL) solution is proposed
to cast the autofocusing as a regression problem and tested over both
experimental and simulated holograms. Single wavelength digital holograms were
recorded by a Digital Holographic Microscope (DHM) with a 10$\mathrm{x}$
microscope objective from a patterned target moving in 3D over an axial range
of 92 $\mu$m. Tiny DL models are proposed and compared such as a tiny Vision
Transformer (TViT), tiny VGG16 (TVGG) and a tiny Swin-Transfomer (TSwinT). The
proposed tiny networks are compared with their original versions (ViT/B16,
VGG16 and Swin-Transformer Tiny) and the main neural networks used in digital
holography such as LeNet and AlexNet. The experiments show that the predicted
focusing distance $Z_R^{\mathrm{Pred}}$ is accurately inferred with an accuracy
of 1.2 $\mu$m in average in comparison with the DHM depth of field of 15
$\mu$m. Numerical simulations show that all tiny models give the
$Z_R^{\mathrm{Pred}}$ with an error below 0.3 $\mu$m. Such a prospect would
significantly improve the current capabilities of computer vision position
sensing in applications such as 3D microscopy for life sciences or
micro-robotics. Moreover, all models reach an inference time on CPU, inferior
to 25 ms per inference. In terms of occlusions, TViT based on its Transformer
architecture is the most robust.
