SM-4
Noise Reduction of Electron Holograms via Sparse Coding Free

Electron holography is one of the techniques of transmission electron microscopy (TEM) to visualize electromagnetic fields at the nanometer scale. Electron interference patterns (holograms) are formed by overlapping the object wave and the reference wave using an electron biprism. The phase in the object wave is modulated by the electromagnetic fields and is recorded as a bending of the interference fringes. To precisely visualize the electromagnetic fields, it is important to acquire the holograms with high signal to noise (S/N) ratio because random noises (shot noise, quantum noise etc.) in holograms limits the precision and accuracy of the phase detection. Long acquisition time reduces the noises, but it causes the spatial drifts of the sample and biprisms during the acquisition. This effect possibly degrades the spatial resolution and the fringe visibility of the interference patterns.

Here we propose an image processing technique with sparse coding to reduce the noises in the holograms taken by high speed acquisition [1]. Recently, it has been shown that the sparse coding algorithms improve the image quality of scanning electron microscopy (SEM) [2], electron tomography [3], and scanning transmission electron microscopy [4–6] by inpainting and denoising. In this study, we applied two step strategies of sparse coding to reduce the noises. In the first step, we extract hidden features from training holograms recorded with long acquisition time. Subsequently, using the extracted features, we sparsely represented the test holograms recorded with short acquisition times, resulting in the noise reduction.

We used GaAs p-n junction as a model sample. Figures 1(a)–(d) show the two sets of training holograms to extract hidden features of holograms and to determine the appropriate parameters of sparse coding algorithms. Figures 1(e)–(j) show original holograms and denoised holograms via sparse coding. The algorithms effectively reduce the noises and improve the quality of the holograms. In the presentation, quantitative comparison of reconstructed phases and precision of the phase detection will be discussed.

Fig. 1

Denoising of electron holograms by sparse cording. (a)–(d) Two sets of training holograms of GaAs p-n junction. (e)–(j) Original and denoised holograms with 40, 4, 1 sec acquisitions, respectively. Reprinted with permission from Ref. [1]. Copyright 2019 Elsevier V.B.

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1. S. Anada et al., Ultramicroscopy 206 (2019) 112818.

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