Unfolding of Neutron and Photon Spectra
Principle of MAXIMUM ENTROPY and Theorem of BAYES,
The HEPROW and RESTRAW program packages
Manfred Matzke
D-38116 Braunschweig
UNFANA MIEKE
GRAVEL HEPRO
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Introduction
In neutron- and photon-spectrometry the spectral particle fluence
ΦE(E) is the interesting quantity, where E is the energy of the particles (neutronen or photons).

For the determination of ΦE(E) from integrating measurements the following system of integral equations has to be solved:

   zi = ∫dE Ri(EΦE(E)     (i = 1,...,M)
The M values zi denote the (measured) readings of the detector system.
The kernels Ri(E) are the response functions for the energy E of the M detector channels of the measuring system.

For the solution of the equation above computer codes based on Bayes theorem and the maximum entropy method have been developed in the PTB  and have been successfully applied in many metrological fields to determine the spectral neutron or photon fluence (look also at the unfolding page of PTB).
The HEPROW program system described here is an updated version of the PTB HEPRO system already described in an earlier report (see : M. Matzke, "Unfolding of Pulse Height Spectra: The HEPRO Program System", Report PTB-N-19, Physikalisch-Technische Bundesanstalt, Braunschweig, 1994). It contains a number of programs for data handling, plotting, folding and unfolding. The codes run in the DOS-Box of a PC and are tested under WINDOWS95 and WINDOWS98.
A CD containing the EXE versions and a demonstration of some examples may be obtained from the author. (is available here as download)
The following Fortran computer programs are described:
  • UMSPHW
    to transform a file containing a measured pulse-height spectrum to a file in HEPRO format. Energy calibration parameters assigning "energy" values to channel numbers are needed.
  • RSPGW
    GAUSSIAN broadening of a response matrix, rebinning of a matrix.
  • OPERAW
    Program for combination of HEPRO files and multiplication/division addition/subtraction by numbers.
  • FALTW
    Program to fold a fluence file with a response matrix and compare measured and calculated pulse-height spectra
  • GRAVELW
    Modified SAND-II code for unfolding. (Logarithm of pulse-height spec­trum used). Response matrix and a pulse-height spectrum file as input.
  • UNFANAW
    Maximum entropy code for unfolding. The program needs a file called UNFANA.ASC produced before by a GRAVELW run.
  • MIEKEW
    Maximum entropy code for unfolding The program needs a file called UNFANA.ASC produced before by a GRAVELW run. The propagation of uncertainties is performed with a so-called ambiguity term .
  • PLOFW
    to plot data files or parts of the response function library on the screen, or to create an HPGL file for subsequent plotting The plot program may be used for a variety of data formats of the files, including the ENDF format.
  • PLOTAW
    to plot control data curves from a plot file created while one of the other codes is running.


Der Autor dankt Prof. Dr. Klaus Weise für viele wichtige Diskussionen und Anregungen und für das UNFANA Programm, das bisher in vielen Gebieten der Metrologie erfolgreich angewendet wurde.

  Stand: 12.12.2005