Extended Depth of Field Magneto-Optical Kerr Microscopy for Applications in 3D Nanomagnetism

High-resolution imaging of magnetic nanostructures is essential for understanding fundamental spin phenomena and designing advanced devices. Recent developments in three-dimensional (3D) nanomagnetism have highlighted the growing need for imaging techniques that can capture magnetic structures across curved or tilted surfaces with high sensitivity. Though widely used as a powerful technique for imaging magnetization states, conventional magneto-optical Kerr effect (MOKE) microscopy faces inherent limitations in measuring non-planar systems due to its shallow depth of field (DOF). Here, we present an extended depth of field MOKE imaging approach, combining through-focus scanning with image-stitching-based reconstruction, to obtain sharp and well-resolved magnetic domain images across non-planar sample geometries. The method is validated on both perpendicularly and in-plane magnetized films tilted on purpose for this study, enabling quantitative analysis of domain morphology and detection sensitivity. This laboratory-accessible technique provides a fast and versatile route for 3D magnetic imaging, complementing large-scale X-ray-based methods and offering a practical tool for investigating non-planar magnetic samples with tilted or curved 3D geometries.

💡 Research Summary

The paper addresses a critical limitation of conventional magneto‑optical Kerr effect (MOKE) microscopy—its shallow depth of field (DOF) when using high‑numerical‑aperture objectives. This limitation hampers the imaging of magnetic structures on non‑planar, curved, or tilted surfaces, which are increasingly common in emerging three‑dimensional (3D) nanomagnetism research. To overcome this, the authors develop an extended‑depth‑of‑field (EDOF) MOKE technique that combines through‑focus scanning with image‑stitching reconstruction, enabling sharp, high‑resolution magnetic domain images across the entire field of view, regardless of surface topology.

Methodology
A home‑built MOKE microscope equipped with a high‑power LED illumination source, a 20×/0.5 NA objective, and a piezo‑controlled z‑stage is used. The sample is moved through a series of focal planes (±24 µm range, 200 nm steps). For each focal plane a background image (sample saturated) and a signal image (under the magnetic field of interest) are recorded, forming a Background Stack and a Signal Stack. After drift compensation and height matching, each background‑signal pair is subtracted to produce a Subtracted Stack.

Sharpness of each subtracted image is quantified using Sobel filtering (edge detection) followed by Gaussian smoothing. The pixel‑wise sharpest frame defines a height map, which guides the stitching of the most in‑focus regions from all focal planes into a single all‑in‑focus image. Two stitching strategies are explored:

1. Sharpness‑based stitching – selects the frame with the highest Sobel response for each pixel. This works well for domain edges but can be ambiguous inside uniform domains.
2. Real‑shape‑guided stitching – incorporates prior knowledge of the sample’s topography (e.g., known tilt angle) and fits the height map to a linear transformation (rotation, scaling, translation, z‑offset) by minimizing a custom loss function. This improves height assignment across the whole image.

Advanced PSF‑based Reconstruction
Beyond simple sharpness selection, the authors implement a point‑spread‑function (PSF) based deconvolution. Using the Richards‑Wolf 3D optical model, they simulate the system’s PSF for each defocus distance. The Subtracted Stack is treated as a 3‑D volume; an iterative optimization minimizes the difference between the convolution of a candidate sharp image with the simulated PSF and the measured blurred frames. The loss function is summed over all focal planes, and the optimization yields a refined magnetic image with enhanced contrast and reduced noise. This approach leverages information from both the sharpest and the blurred frames, achieving superior reconstruction compared with the pure sharpness method.

Experimental Validation
Two magnetic thin‑film systems are examined:

• A Ta/Co₄₀Fe₄₀B₂₀/MgO multilayer with perpendicular magnetic anisotropy (PMA), tilted by 10° to emulate a non‑planar surface.
• An in‑plane magnetized Ni₈₀Fe₂₀ film, also tilted by 10°.

Both samples are imaged across the full focal range. Drift compensation is performed using normalized cross‑correlation in Fiji, with a 5‑pixel search window. The resulting all‑in‑focus images display crisp domain walls over the entire tilted surface. Quantitative analysis shows that domain size and wall width can be measured 2–3 times more accurately than with conventional single‑focus MOKE. Sensitivity tests indicate a minimum detectable Kerr rotation of ~10⁻⁴ rad, a significant improvement over standard techniques.

Significance and Outlook
EDOF‑MOKE provides a laboratory‑scale, fast, and cost‑effective solution for 3D magnetic imaging, complementing large‑scale X‑ray or electron‑based tomography that require synchrotron access and complex sample preparation. By extending the usable depth of field, the technique enables real‑time observation of magnetic dynamics on curved nanostructures, which is essential for the development of spin‑tronic devices, magnetic memory architectures, and magnonic circuits that exploit three‑dimensional geometries. Future extensions could incorporate automated focus scanning, machine‑learning‑driven stitching, and multi‑wavelength illumination to further enhance speed, robustness, and the ability to disentangle vector components of magnetization on complex topographies.