An energy spectrum smoothing algorithm based on TCC-DEE

  • Bo Lu
  • Yong Chen
  • Yue Zhu
  • Yan-Ji Yang
  • Wei-Wei Cui
  • Yu-Mei Zhou


A smoothing algorithm for energy spectrum based on differential nonlinearity (DNL) error elimination with total counts conservation for high-energy particle detector systems is presented. It is physics based and is only determined by the DNL error of analog-to-digital converter device itself. From the experimental results, this algorithm slightly improves both noise performance and energy resolution, while greatly reduces the testing errors by almost a half compared to their original values. In addition, the reduced-\(\chi ^2\) statistic for evaluating the Gaussian fitting goodness is significantly reduced by almost two orders after smoothing. As a typical verification example, this algorithm is successfully applied in the ground calibration of the Low Energy X-ray Instrument onboard the Hard X-ray Modulation Telescope (HXMT-LE) satellite, lending it a powerful, nondestructive and low-cost tool for both calibration and data processing for high-energy particle detector systems.


Smoothing algorithm Energy spectrum TCC-DEE DNL error Low-cost 


  1. 1.
    M. Prokesch, S.A. Soldner, A.G. Sundaram et al., CdZnTe detectors operating at X-ray fluxes of 100 million photons/(mm2 sec). IEEE Trans. Nucl. Sci. 63, 1854–1859 (2016). doi: 10.1109/TNS.2016.2556318 CrossRefGoogle Scholar
  2. 2.
    P. Xu, S. Wang, X.H. Cai et al., The extraction and smoothing algorithms for gamma-ray spectrum of a CdZnTe detector system. Nucl. Sci. Tech. 25, 50402–050402 (2014). doi: 10.13538/j.1001-8042/nst.25.050402 Google Scholar
  3. 3.
    G.F. Hartner, D.E. Blodgett, S.B. Bracker et al., A recoil proton detector using cylindrical proportional chambers and scintillator counters. Nucl. Instrum. Methods 216, 113–119 (1983). doi: 10.1016/0167-5087(83)90337-X CrossRefGoogle Scholar
  4. 4.
    G.D. Alkhazov, A.A. Vorobyov, A.V. Dobrovolsky et al., Investigation of the structure of light exotic nuclei by proton elastic scattering in inverse kinematics. Phys. Atom. Nuclei 78, 381–386 (2015). doi: 10.1134/S1063778815020076 CrossRefGoogle Scholar
  5. 5.
    T.L. Collums, M.R. Islam, E.R. Benton et al., Comparison of plastics used in proportional counters for proton and heavy ion measurements. Nucl. Instrum. Methods B 333, 69–72 (2014). doi: 10.1016/j.nimb.2014.04.016 CrossRefGoogle Scholar
  6. 6.
    Z. Fu, Y. Heng, S. Gu et al., Efficiency-determined method for thermal neutron detection with inorganic scintillator. Nucl. Sci. Tech. 24, 40205–040205 (2013). doi: 10.13538/j.1001-8042/nst.2013.04.010 Google Scholar
  7. 7.
    B. Lu, W.W. Cui, Y.S. Wang et al., Design and optimization of the readout system for X-ray CCDs. Chin. Phys. C 36, 846–855 (2012). doi: 10.1088/1674-1137/36/9/009 CrossRefGoogle Scholar
  8. 8.
    B. Lu, Y.S. Wang, Y. Chen et al., Hard X-ray imaging techniques based on CCD and CsI Scintillator. Optic. Precis. Eng. (2012) (in press) Google Scholar
  9. 9.
    Y.C. Wang, X.F. Cao, Q. Yu et al., A fully integrated 0.055% INL X-ray CCD readout ASIC with incremental \(\Delta \Sigma \)ADC. IEEE Tran. Nucl. Sci 63, 1733–1739 (2016). doi: 10.1109/TNS.2016.2543261 CrossRefGoogle Scholar
  10. 10.
    P. Bury, N. Ennode, J.M. Petit et al., Wavelet analysis of X-ray spectroscopic data part I. The method. Nucl. A 383, 572–588 (1996). doi: 10.1016/S0168-9002(96)00721-8 Google Scholar
  11. 11.
    G. Xiao, L. Deng, B. Zhang et al., A nonlinear wavelet method for data smoothing of low-level gamma-ray spectra. J. Nucl. Sci. Technol. 41, 73–76 (2004). doi: 10.1080/18811248.2004.9715460 CrossRefGoogle Scholar
  12. 12.
    M. Gu, L.Q. Ge, Smoothing technology of gamma-ray spectrometry data based on matched filtering. Nucl. Electron. Detect. Technol. 29, 978–980 (2009). doi: 10.3969/j.issn.0258-0934.2009.05.012 Google Scholar
  13. 13.
    P.A. Gorry, General least-squares smoothing and differentiation by the convolution (Savitzky–Golay) method. Anal. Chem. 62, 570–573 (1990). doi: 10.1021/ac00205a007 CrossRefGoogle Scholar
  14. 14.
    H. Lu, X. Li, T. Hsia et al., Analytical noise treatment for low-dose CT projection data by penalized weighted least-square smoothing in the KL domain. Proc. SPIE 4682, 146–152 (2002). doi: 10.1117/12.465552 CrossRefGoogle Scholar
  15. 15.
    D. Alberto, E. Falletti, L. Ferrero et al., FPGA implementation of digital filters for nuclear detectors. Nucl. Instrum. Methods A 611, 99–104 (2009). doi: 10.1016/j.nima.2009.09.049 CrossRefGoogle Scholar
  16. 16.
    F.J. Lu, The current status of the hard X-ray modulation telescope. Proc. SPIE 5900, 266–275 (2005). doi: 10.1117/12.925620 CrossRefGoogle Scholar
  17. 17.
    Y.S. Wang, Y. Chen, Y.P. Xu et al., Low temperature testing and neutron irradiation of a swept charge device on board the HXMT satellite. Chin. Phys. C 36, 991–995 (2012). doi: 10.1088/1674-1137/36/10/013 CrossRefGoogle Scholar
  18. 18.
    IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters, IEEE Standard 1241–2010, 2011, 46–64. doi: 10.1109/IEEESTD.2011.5692956
  19. 19.
    W. Kester, The Data Conversion Handbook (Newnes, Burlington, 2005), pp. 303–316CrossRefGoogle Scholar
  20. 20.
    DS360-Ultra-low distortion function generator, Datasheet. Stanford Research Systems.
  21. 21.
    A. DasGupta, Asymptotic Theory of Statistics and Probability (Springer, New York, 2008), pp. 441–450CrossRefGoogle Scholar
  22. 22.
    Y.S. Zhu, Probability and Statistics in Experimental Physics (Science Press, Beijing, 2006), pp. 410–425Google Scholar

Copyright information

© Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Chinese Nuclear Society, Science Press China and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Bo Lu
    • 1
    • 2
    • 3
  • Yong Chen
    • 1
    • 3
  • Yue Zhu
    • 1
    • 3
  • Yan-Ji Yang
    • 1
  • Wei-Wei Cui
    • 1
  • Yu-Mei Zhou
    • 2
    • 3
  1. 1.Institute of High Energy PhysicsChinese Academy of SciencesBeijingChina
  2. 2.Institute of MicroelectronicsChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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