Guillaume J. Laurent

Stéphane Cuenat, Louis Andréoli, Antoine N. André et al.

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 $μ$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 $μ$m in average in comparison with the DHM depth of field of 15 $μ$m. Numerical simulations show that all tiny models give the $Z_R^{\mathrm{Pred}}$ with an error below 0.3 $μ$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.

Guillaume J. Laurent, Patrick Sandoz

This paper presents a method for carrying fair comparisons of the accuracy of pose estimation using fiducial markers. These comparisons rely on large sets of high-fidelity synthetic images enabling deep exploration of the 6 degrees of freedom. A low-discrepancy sampling of the space allows to check the correlations between each degree of freedom and the pose errors by plotting the 36 pairs of combinations. The images are rendered using a physically based ray tracing code that has been specifically developed to use the standard calibration coefficients of any camera directly. The software reproduces image distortions, defocus and diffraction blur. Furthermore, sub-pixel sampling is applied to sharp edges to enhance the fidelity of the rendered image. After introducing the rendering algorithm and its experimental validation, the paper proposes a method for evaluating the pose accuracy. This method is applied to well-known markers, revealing their strengths and weaknesses for pose estimation. The code is open source and available on GitHub.

Patrick Sandoz, Antoine N. André, Guillaume J. Laurent

Pose estimation is still a challenge at the small scales. Few solutions exist to capture the 6 degrees of freedom of an object with nanometric and microradians resolutions over relatively large ranges. Over the years, we have proposed several fiducial marker and pattern designs to achieve reliable performance for various microscopy applications. Centimeter ranges are possible using pattern encoding methods, while nanometer resolutions can be achieved using phase processing of the periodic frames. This paper presents VERNIER, an open source phase processing software designed to provide fast and reliable pose measurement based on pseudo-periodic patterns. Thanks to a phase-based local thresholding algorithm, the software has proven to be particularly robust to noise, defocus and occlusion. The successive steps of the phase processing are presented, as well as the different types of patterns that address different application needs. The implementation procedure is illustrated with synthetic and experimental images. Finally, guidelines are given for selecting the appropriate pattern design and microscope magnification lenses as a function of the desired performance.