# Establishing a reference focal plane using convolutional neural networks and beads for brightfield imaging

## TL;DR

This paper introduces a method using beads and a neural network to define a reference focal plane for accurate and repeatable brightfield imaging.

## Contribution

A generalizable convolutional neural network approach for determining a reference focal plane using beads, improving accuracy and reducing instrument dependency.

## Key findings

- The REFP is refined using a cubic spline and shared information across experiments.
- A ResNet 18 model achieves high prediction accuracy with uncertainty within 7.5 µm of the desired focal plane.
- The method generalizes across two optical systems using only six beads per image.

## Abstract

Repeatability of measurements from image analytics is difficult, due to the heterogeneity and complexity of cell samples, exact microscope stage positioning, and slide thickness. We present a method to define and use a reference focal plane that provides repeatable measurements with very high accuracy, by relying on control beads as reference material and a convolutional neural network focused on the control bead images. Previously we defined a reference effective focal plane (REFP) based on the image gradient of bead edges and three specific bead image features. This paper both generalizes and improves on this previous work. First, we refine the definition of the REFP by fitting a cubic spline to describe the relationship between the distance from a bead’s center and pixel intensity and by sharing information across experiments, exposures, and fields of view. Second, we remove our reliance on image features that behave differently from one instrument to another. Instead, we apply a convolutional regression neural network (ResNet 18) trained on cropped bead images that is generalizable to multiple microscopes. Our ResNet 18 network predicts the location of the REFP with only a single inferenced image acquisition that can be taken across a wide range of focal planes and exposure times. We illustrate the different strategies and hyperparameter optimization of the ResNet 18 to achieve a high prediction accuracy with an uncertainty for every image tested coming within the microscope repeatability measure of 7.5 µm from the desired focal plane. We demonstrate the generalizability of this methodology by applying it to two different optical systems and show that this level of accuracy can be achieved using only 6 beads per image.