sCWatter: Open source coupled wave scattering simulation for spectroscopy and microscopy

TL;DR

This work tackles the challenge of accurately modeling 3D light scattering in microscopy at high numerical aperture by using coupled wave theory (CWT) with a Fourier-based representation of both the field and the sample. It introduces novel layer-to-layer connection equations that reduce the CW linear system dimensionality by a factor of $L$, enabling efficient, parallelizable simulations on consumer hardware and accelerated computation with Intel MKL and CUDA. The authors demonstrate the approach on various scenarios, including scattering through a cylinder, absorbance spectroscopy, and periodic 3D tissue-like samples, and provide analyses of accuracy versus Fourier cutoff $M$ and performance-tuning guidance. The combination of fast, accurate field computation and real-time visualization has practical impact for designing optical systems, validating scattering in microscopy, and enabling accessible, open-source tools for spectroscopy and imaging research.

Abstract

Several emerging microscopy imaging methods rely on complex interactions between the incident light and the sample. These include interferometry, spectroscopy, and nonlinear optics. Reconstructing a sample from the measured scattered field relies on fast and accurate optical models. Fast approaches like ray tracing and the Born approximation have limitations that are limited when working with high numerical apertures. This paper presents sCWatter, an open-source tool that utilizes coupled wave theory (CWT) to simulate and visualize the 3D electric field scattered by complex samples. The sample refractive index is specified on a volumetric grid, while the incident field is provided as a 2D image orthogonal to the optical path. We introduce connection equations between layers that significantly reduce the dimensionality of the CW linear system, enabling efficient parallel processing on consumer hardware. Further optimizations using Intel MKL and CUDA significantly accelerate both field simulation and visualization.

Figures (7)

• Figure 1: The figure shows how a downward incident wave $\bar{\mathbf{P}}$ illuminates on a heterogeneous sample. The reflective waves on the upper boundary are $\hat{\mathbf{P}}$ and the transmitted waves on the lower boundary are $\check {\mathbf{P}}$. The refractive indices of the upper field and lower field are $\hat{n}$ and $\check n$. The sample is saved as the reciprocal of the sample refractive index $\frac{1}{n^2(\mathbf x_i)}$ at $\mathbf x_i$. The sample contains $L$ layers, and the boundary positions along $z$ direction are represented by $z_{\ell}$ for the $\ell_th$ layer
• Figure 2: The electric field vector $\mathbf P$ at the boundaries is calculated by solving the linear system. For the $6M$ linearly independent conditions, $2M$ linearly independent conditions are provided by Gauss' Equations (Equations \ref{['eqn:gauss_law']}), and $4M$ by the connection equations mentioned in the next subsection, in which $\mathbf{C}, \mathbf{C}^{\prime} \in \mathbb {C}^{4M\times 3M}$ and $\mathbf{K}, \hat{\mathbf{G}} \in \mathbb {C}^{4M\times4M}$.
• Figure 3: The continuity at the boundaries has three cases. Case $1$ represents the boundary conditions between the upper homogeneous field and the first sample layer; Case $2$ shows the continuity between two internal adjacent sample layers; Case $3$ represents the boundary conditions between the last sample layer and the lower homogeneous layer.
• Figure 4: The electric field collected from the bottom of the samples for different numbers of Fourier coefficients.
• Figure 5: (a) shows a $x-z$ cross-section of a cylinder. (b)-(f) are the electric field for the cross-section showing how the scattering happens around a cylinder under the incidence of different wavelengths.