Retrieving the spectrum of physical radiation from experimental measurements typically involves using a mathematical algorithm to deconvolve the instrument response function from the measured signal. However, in the field of signal processing known as “Source Separation” (SS), which refers to the process of computationally retrieving the separate source components that generate an overlapping signal on the detector, the deconvolution process can become an ill-posed problem and crosstalk complicates the separation of the individual sources. To overcome this problem, we have designed a magnetic spectrometer for inline electron energy spectrum diagnosis and developed an analysis algorithm using techniques applicable to the problem of SS. An unknown polychromatic electron spectrum is calculated by sparse coding using a Gaussian basis function and an L1 regularization algorithm with a sparsity constraint. This technique is verified by using a specially designed magnetic field electron spectrometer. We use Monte Carlo simulations of the detector response to Maxwellian input energy distributions with electron temperatures of 5.0 MeV, 10.0 MeV, and 15.0 MeV to show that the calculated sparse spectrum can reproduce the input spectrum with an optimum energy bin width automatically selected by the L1 regularization. The spectra are reproduced with a high accuracy of less than 4.0% error, without an initial value. The technique is then applied to experimental measurements of intense laser accelerated electron beams from solid targets. Our analysis concept of spectral retrieval and automatic optimization of energy bin width by sparse coding could form the basis of a novel diagnostic method for spectroscopy.
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July 2020
Research Article|
July 24 2020
New algorithm using L1 regularization for measuring electron energy spectra
Hironao Sakaki
;
Hironao Sakaki
a)
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
2
Kyushu University IGSES
, Kasuga, Fukuoka 816-8580, Japan
a)Author to whom correspondence should be addressed: [email protected]
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Tomohiro Yamashita
;
Tomohiro Yamashita
3
Hyogo Ion Beam Medical Center
, Tatsuno, Hyogo 679-5165, Japan
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Takashi Akagi;
Takashi Akagi
3
Hyogo Ion Beam Medical Center
, Tatsuno, Hyogo 679-5165, Japan
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Mamiko Nishiuchi
;
Mamiko Nishiuchi
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
4
PRESTO, Japan Science and Technology Agency
, Kawaguchi, Saitama 332-0012, Japan
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Nicholas P. Dover
;
Nicholas P. Dover
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
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Hazel F. Lowe
;
Hazel F. Lowe
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
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Kotaro Kondo;
Kotaro Kondo
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
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Akira Kon;
Akira Kon
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
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Masaki Kando
;
Masaki Kando
1
QST KPSI
, Kizugawa, Kyoto 6190-215, Japan
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Yasuhiko Tachibana
;
Yasuhiko Tachibana
5
QST NIRS
, Inage, Chiba 263-0024, Japan
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Takayuki Obata
;
Takayuki Obata
5
QST NIRS
, Inage, Chiba 263-0024, Japan
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Keiichiro Shiokawa;
Keiichiro Shiokawa
2
Kyushu University IGSES
, Kasuga, Fukuoka 816-8580, Japan
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Tatsuhiko Miyatake;
Tatsuhiko Miyatake
2
Kyushu University IGSES
, Kasuga, Fukuoka 816-8580, Japan
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Yukinobu Watanabe
Yukinobu Watanabe
2
Kyushu University IGSES
, Kasuga, Fukuoka 816-8580, Japan
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a)Author to whom correspondence should be addressed: [email protected]
Rev. Sci. Instrum. 91, 075116 (2020)
Article history
Received:
January 12 2020
Accepted:
June 28 2020
Citation
Hironao Sakaki, Tomohiro Yamashita, Takashi Akagi, Mamiko Nishiuchi, Nicholas P. Dover, Hazel F. Lowe, Kotaro Kondo, Akira Kon, Masaki Kando, Yasuhiko Tachibana, Takayuki Obata, Keiichiro Shiokawa, Tatsuhiko Miyatake, Yukinobu Watanabe; New algorithm using L1 regularization for measuring electron energy spectra. Rev. Sci. Instrum. 1 July 2020; 91 (7): 075116. https://doi.org/10.1063/1.5144897
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