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Mathematical methods of data analysis: Deconvolution of measurement data in neutron spectrometry

Deconvolution methods are of basic importance in spectrometry and are needed for the data analysis of various types of spectrometers; e. g., Bonner sphere spectrometer, 3He proportional counters, recoil proton proportional counters and scintillation spectrometer.

Deconvolution is a mathematical method for the analysis of measurement data. A measurement carried out with a spectrometer provides in general an indirect rather than a direct measurement of the particle spectrum because the data results from a convolution of the response function with the spectrum. Deconvolution is the process “inverting” this procedure to determine the spectrum from the measurements, the response functions, and any relevant information available about the experiment.

Software for unfolding: The UMG package

UMG (Unfolding with MAXED and GRAVEL) is a software package written for the analysis of data measured with spectrometers that require the use of unfolding techniques. It is currently being distributed by RSICC and the NEA Data Bank. More information is available at:

Further information

  • Investigations on the energy resolution of spectrometers
    By means of deconvolution procedures it is possible to resolve structures in a spectrum which are finer than the instrument resolution of the spectrometer. A new procedure now allows this property (which is called "super-resolution") to be determined quantitatively for the first time for a scintillation spectrometer which is used for plasma diagnosis. This procedure is also of significance for other applications.

  • Bayesian analysis of spectrometric measurements in high-energy neutron fields
    The uncertainty of measurements made with an extended-range Bonner sphere spectrometer in high-energy neutron fields has been analysed by means of Bayesian methods. It was shown that the spectrum below approx. 1 MeV is well determined whereas the information from the measurements is not sufficient to determine the high-energy end of the spectrum with low uncertainty.

  • Data analysis for spectrometry on fusion plasmas
    Neutron spectrometry in plasma diagnosis requires complex data analysis procedures. A method which combines the procedures of the Bayes’s statistics and the maximum entropy allows parameters to be investigated which describe the plasma in fusion experiments.


  • M. Reginatto, F. Gagnon-Moisan, J. Guerrero Araque, R. Nolte, M. Zboril and A. Zimbal:
    A Bayesian method to estimate the neutron response matrix of a single crystal CVD diamond detector
    Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), September 21 – 26, 2014, Clos Lucé, Amboise, France
    AIP Conference Proceedings Vol. 1641, 321 (2015)

  • M. Reginatto, A. Kasper, H. Schuhmacher, B. Wiegel, A. Zimbal:
    Neutron fluence rate measurements at an underground laboratory: A Bayesian approach
    AIP Conf. Proc. 1553, 77, 2013
    doi: 10.1063/1.4819986

  • M. Reginatto and A. Zimbal:
    Superresolution of compact neutron spectrometers, with applications to fusion diagnostics
    AIP Conf. Proc. 1305, 227-234, 2011
    doi: 10.1063/1.3573621

  • M. Reginatto:
    Overview of spectral unfolding techniques and uncertainty estimation
    Radiation Measurements 45, 1323-1329, 2010
    doi: 10.1016/j.radmeas.2010.06.016

  • M. Reginatto:
    What can we Learn about the Spectrum of High-Energy Stray Neutron Fields from Bonner Sphere Measurements?
    Radiation Measurements 44, 692-699, 2009
    doi: 10.1016/j.radmeas.2009.04.005

  • M. Reginatto and A. Zimbal:
    Bayesian and maximum entropy methods for fusion diagnostic measurements with compact neutron spectrometers
    Rev. Sci. Instrum. 79, 023505, 2008
    doi: 10.1063/1.2841695

  • M. Reginatto, F. d'Errico and M. Luszik-Bhadra:
    An Unfolding Method for Directional Spectrometers
    Radiat. Prot. Dosim. 110, 539,-543, 2004
    doi: 10.1093/rpd/nch277

  • M. Reginatto, P. Goldhagen and S. Neumann:
    Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy deconvolution code MAXED
    Nucl. Instr. and Meth. A 476, 242-246, 2002
    doi: 10.1016/S0168-9002(01)01439-5