# Digital Twins for 3D Confocal Microscopy: Near-Field, Far-Field, and Comparison with Experiments

## TL;DR

This paper introduces digital twins for confocal microscopy to improve accuracy by simulating light-surface interactions using advanced models.

## Contribution

The novel use of FMM for confocal microscopy and validation of three models against experimental data is presented.

## Key findings

- Three models (FEM, FMM, BEM) produce identical accurate results for rectangular gratings when validated experimentally.
- Digital twins reduce the need for repeated simulations during fine scanning in confocal microscopy.
- Simulations reveal insights into experimentally observed effects like instrument transfer functions and tilted gratings.

## Abstract

To push the boundaries of confocal microscopy beyond its current limitations by predicting sensor responses for complex surface geometries, we build digital twins using three rigorous models, the finite element method (FEM), Fourier modal method (FMM), and boundary element method (BEM) to model light–surface interactions. Fourier optics are then used to calculate the sensor signals at the back focal plane and at the detector. A 3D illumination model is applied to 2D periodic structures for FEM and FMM modelings and to 3D aperiodic structures for BEM modeling. The lateral and vertical scanning processes of the confocal microscope are achieved through focal-point shifts of the objective, using plane-wave illuminations with varying incident and azimuthal angles. This approach reduces the need for repeated, time-intensive rigorous simulations of the scattering process when a fine scanning is desired. Furthermore, we give an in-depth description of a novel confocal microscopy method using FMM. For rectangular grating surfaces, the three models yield identical, highly accurate results, as validated by measured results. Simulations of the instrument transfer function, tilted gratings, and gratings with edge rounding offer insights into some experimentally observed effects. This research therefore provides a promising approach for correcting systematic errors in confocal microscopy.