Can quantum wave filters outperform image processing?

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As electron microscopists, we are often limited by both low contrast, and high‐noise levels for beam‐sensitive materials. The contrast is a function of the imaging technique, and the sample under study. The noise level of the image is a fundamental property of the finite electron dose, which must remain limited, to avoid damaging the sample. As a result of these, one route to improving microscopy images lies in developments of novel imaging techniques. Image post processing techniques are commonly used for example, to remove noise in images or increase the contrast of specific features of interest. These methods perform well in specific cases, but one can wonder whether this post processing approach is the most optimal in terms of electron dose efficiency. The primary source of noise in electron micrographs is Poisson noise due to the electron counting process occurring at the point of detection. However, if we can manipulate the coherent electron wave prior to its detection, implementing a specific operator acting on the wave, noise will occur on the detected processed image rather than prior to the processing. Such a setup can be obtained by using phase plates in the diffraction plane. Ideally, these phase plates affect the phase of the passing electron wave without invoking a detection process, effectively acting as a quantum filter. We discuss and compare three primary examples of such quantum wave filtering, and the results they have on the noise behaviour of the resulting images: vortex filtering as an edge enhancement filter [1], wave background removal [2], and tuneable wave background reduction. We find each method improves the image signal‐to‐noise ratio compared to image post processing implementing a similar filter. We show that each quantum wave filter has different advantages which may be used to enhance certain image features of interest. Removal of the background in the wave decreases noise specifically in image regions of low intensity, reducing the variance of the noise in the image, allowing more precise measurements. Reduction rather than removal of the background however, enables a noise decrease, while avoiding contrast reversals due to sign changes in the wave, improving direct interpretability. The vortex‐ filtering method provides robust directional, or isotropic edge detection, with high contrast possible. We demonstrate each of these options on a selection of different model samples, and discuss their noise properties, required dose levels and their possible implementation.