Removing grid structure in angle-resolved photoemission spectra via deep learning method Junde Liu1 2Dongchen Huang1 2Yi-feng Yang1 2 3and Tian Qian1 2 3y

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Removing grid structure in angle-resolved photoemission spectra via deep learning

method

Junde Liu,1, 2 Dongchen Huang,1, 2 Yi-feng Yang,1, 2, 3, ∗and Tian Qian1, 2, 3, †

1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics,

Chinese Academy of Sciences, Beijing 100190, China

2University of Chinese Academy of Sciences, Beijing 100049, China

3Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

(Dated: May 16, 2023)

Spectroscopic data may often contain unwanted extrinsic signals. For example, in the angle-

resolved photoemission spectroscopy (ARPES) experiment, a wire mesh is typically placed in front

of the CCD to block stray photo-electrons but could cause a grid-like structure in the spectra

during quick measurement mode. In the past, this structure was often removed using the mathe-

matical Fourier ﬁltering method by erasing the periodic structure. However, this method may lead

to information loss and vacancies in the spectra because the grid structure is not strictly linearly

superimposed. Here, we propose a deep learning method to overcome this problem eﬀectively. Our

method takes advantage of the self-correlation information within the spectra themselves and can

greatly optimize the quality of the spectra while removing the grid structure and noise simulta-

neously. It has the potential to be extended to all spectroscopic measurements to eliminate other

extrinsic signals and enhance the spectral quality based on the self-correlation of the spectra solely.

I. INTRODUCTION

In the past decades, ARPES has driven the research

of novel quantum materials with its incredible ability to

directly probe the electronic structures [1–7]. Owing to

the rapid development of experimental techniques, highly

rapid data acquisition modes (”ﬁxed” or ”dithered”

modes) are frequently required in many application sce-

narios. For example, the fast scanning mode is often used

in spatial-resolved ARPES experiments to map the en-

ergy band spectra of a wide area of the sample [8,9].

It is also preferred when the spot size of the laser beam

is tiny, in which case the measurement should be lim-

ited to a very short time to avoid sample damage [10]. In

addition, the fast scanning mode can save a lot of acquisi-

tion time for measuring higher-dimensional data, such as

band structures in two-dimensional momentum space or

dynamical electronic structures in time-resolved ARPES

[11–15].

However, because of the metal mesh in front of the

analyzer CCD, the spectra obtained using the fast scan-

ning mode typically have a grid-like structure as shown in

Fig. 1(a) [7,16], which hinders the direct observation of

energy band features. Although the grid structure may

be averaged out using the swept mode, measurements in

this mode often cover a large portion of unwanted energy

ranges, causing a signiﬁcant time waste in opposition to

the original purpose. Post-spectral processing techniques

and methods are hence needed to remove this grid struc-

ture.

A traditional method is to use Fourier ﬁltering by con-

verting the real space spectra to the Fourier domain [16].

∗Corresponding author:yifeng@iphy.ac.cn

†Corresponding author:tqian@iphy.ac.cn

But simply erasing the peaks in Fourier space may lose

intrinsic information because the grid structure is not

strictly periodic and linearly superimposed. For instance,

the peaks and energy bands in Fourier space may merge

together when their widths are comparable, which makes

it diﬃcult to remove the peaks without losing information

about the energy bands. It may become even more chal-

lenging when the data quality is noisy or not good enough

so that the peaks in Fourier space cannot be well identi-

ﬁed. Therefore, the traditional Fourier ﬁltering method

requires the peaks in Fourier space to be sharp and dis-

tinguishable from the intrinsic bands, which essentially

limits the range of its application scenarios.

Fortunately, machine learning methods have shown

strong capabilities in spectra processing [17–20]. Deep

learning-based methods can achieve better perfor-

mance than traditional mathematical Gaussian smooth-

ing methods in removing noise from spectra [20]. More

surprisingly, we have shown that a noisy spectra image

can be decomposed into an image of clean spectra and

an image corresponding to noise, provided that the noise

is sparse and not so coherent with the intrinsic energy

bands. This inspired us to view the grid structure as an

extrinsic signal, so that the spectra may be decomposed

into a clean part and a grid part.

Following the above line of thought, we propose a deep

learning-based method to remove the grid structure and

identify the intrinsic signal in the measured ARPES spec-

tra in this work. Our method utilizes the self-correlation

information of the spectra themselves and parameterizes

the observed ARPES data by two convolutional neural

networks (CNNs). One network is designed to extract

the clean spectra, and the other aims to extract the grid

texture. We show that this enables us to preserve the

signal of the energy bands in the spectra even if the grid

width and energy bandwidth are comparable or the spec-

tral quality is not so good. As a result, our method can

arXiv:2210.11200v2 [cond-mat.mtrl-sci] 15 May 2023

FIG. 1: (a) An illustration of the ARPES analyzer. (b) The raw spectra image is parameterized as a mixture of two textures

represented by two individual neural networks of the same structure. The ﬁrst texture aims to recover the spectra and the

other ﬁnds the grid structure somewhat attached to the energy bands. The residual is the general grid structure since the

neural network does not learn all the features in the input image.

nicely remove the grid structure and extend the appli-

cation of the fast scanning mode, which is essential for

ARPES experiments. Our idea can be applied to any ex-

trinsic structures from other multidimensional data, thus

improving the quality of the spectra obtained in more

general scenarios.

II. METHODS

We start by assuming that a complex image can be

represented by a mixture of two or more simple com-

ponents or textures, each of which can be viewed as an

image. At ﬁrst glance, this seems impossible and under-

determined because the unknown parameters are more

than the known ones. But this problem has been proved

solvable in the high-dimensional analysis if one compo-

nent is incoherent with another [21,22]. In other words,

pixels or patches are correlated within each texture but

independent of those within another texture. This in-

sight has led to successful algorithms showing good per-

formance in computer vision [23,24] and ARPES de-

noising [25] even without requiring a training set.

Motivated by these successes, we extend the above idea

and develop an algorithm for de-gridding the ARPES

data. As shown in Fig. 1(b), we attempt to decompose

a raw spectra image Iinto two textures Uand Vand

expect that Ugives the clean spectra and Vapproxi-

mates the grid structure. All the images I, U, V may be

viewed as matrices, and the entries in Uor Vshould be

correlated. We parameterize each texture via a U-shape

neural network [26], which has shown good performance

in modeling correlated data and real-world tasks in com-

puter vision [26]. Uand Vare then the outputs of two

individual neural networks of the same structure elabo-

rated in Appendix B.

The summation of both textures U, V should give the

raw spectra I, which we take as the loss function. This

yields

min

θ,φ kI−Uθ−Vφk2

F,(1)

where θ, φ are the parameter collections for each neural

network, and k.k2

Fdenotes the square of the Frobenius

norm, which is deﬁned as the summation of all entries of a

matrix. The parameters are then optimized by stochastic

gradient descent (SGD) with respect to the loss function

given in eq. (1). Our algorithm is implemented via Py-

torch [27] and the detailed training hyperparameters are

listed in Appendix B.

Noisy data. In practice, noise is unavoidable in the raw

data. To make the algorithm more practical, we combine

de-noising techniques into this framework. The noise s

is assumed to be sparse because an image of measured

spectra should not be corrupted everywhere. Following

similar techniques [28], we decompose the raw spectra

into three textures: the clean spectra U, the grid struc-

ture V, and the noise s. As discussed in [25], the noise can

be further parameterized as s=a◦a−b◦b, where a, b are

two vectors with learnable entries to be optimized, and

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Removinggridstructureinangle-resolvedphotoemissionspectraviadeeplearningmethodJundeLiu,1,2DongchenHuang,1,2Yi-fengYang,1,2,3,andTianQian1,2,3,y1BeijingNationalLaboratoryforCondensedMatterPhysicsandInstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China2UniversityofChineseAcademyofSciences,B...

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Removing grid structure in angle-resolved photoemission spectra via deep learning method Junde Liu1 2Dongchen Huang1 2Yi-feng Yang1 2 3and Tian Qian1 2 3y

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