Modeling Microsphere Effects on Interferometric Resolution

Though microspheres — microscale spherical particles that can be manufactured from natural and synthetic materials — are known to improve lateral resolution and enhance magnification in microscopic imaging, a generally accepted explanation for their positive effect on resolution has yet to be introduced. Microsphere-assisted measurements are used in a wide range of applications: These measurements support examination of the features of engineered surfaces with lateral dimensions beyond the resolution limit, and also apply to evaluation of biological and medical objects such as viruses and subcellular structures.

As a result, many theoretical studies have been conducted to better understand the role of microspheres in resolution enhancement.

In a recent study, researchers at the University of Kassel developed a simulation model that examined the complete imaging process of a microsphere-enhanced interference microscope working in reflection mode and equipped with objective lenses of high numerical aperture. The researchers used the finite element method (FEM) to calculate the near-field scattering process.

Unlike previous models, the model for microsphere-enhanced interferometry considered full 3D conical illumination with incident waves, as well as conical imaging of the scattered light field by the microsphere.

Based on the information provided by the model, the researchers ultimately determined that a local enhancement of the numerical aperture (NA) is most likely the cause of the resolution enhancement provided with microspheres.

This FEM-based, numerical model of microsphere-enhanced coherence scanning interferometry could be used to analyze the influence of parameters to find the most appropriate experimental setup, depending on the shape, size, and material of the microelement and surrounding material. This could contribute to a better understanding of microsphere-assisted measurement systems, and it could help researchers improve the imaging capabilities of these systems through parameter studies.

Further, the model could be extended to conventional microscopy, confocal microscopy, and other optical profilers.

In the work, the researchers developed a virtual, microsphere-assisted interference microscope that took into account the conical illumination of the microscope, the interaction of light with the microsphere and the object’s surface, and the imaging properties. Using the virtual microscope model, they reproduced measurement results reliably based on these considerations.

The researchers also quantified the resolution enhancement and analyzed the resolution limit; they showed that the resolution limit was independent of the numerical aperture of the objective lenses. They further found that the lateral magnification corresponding to the number of imaged periods depended on the NA of the objective lenses. For smaller numerical aperture values, the magnification increased, leading to a decrease in the field of view.

When the researchers used the model to compare results obtained with and without whispering gallery modes (WGMs), they found that resolution was enhanced in both cases. The team also provided a standard for achievable resolution.

The research helps to resolve a long-standing question. Although, as the researchers said, multiple effects — including the enhancement of the NA — as well as photonic nanojets, WGMs, and evanescent waves have been identified as possible causes of microspheres’ resolution enhancement — none of these effects had yet been demonstrated definitively to be the cause.

Detailed parameter studies will be performed in future work, the researchers said.

The research was published in Light: Advanced Manufacturing (www.light-am.com/article/doi/10.37188/lam.2022.049).