Fast Autofocusing using Tiny Transformer Networks for Digital Holographic Microscopy

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 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 state of the art inference time on CPU, less than 25 ms per inference