(1976). Nuclear Tracks in Solids (Principles and Applications) Nuclear Technology: Vol. 30, No. 1, pp. 91-92.

Nuclear Tracks in Solids (Principles and Applications)

MAXED was developed to apply the maximum entropy principle to the unfolding of neutron spectrometric measurements. The approach followed in MAXED has several features that make it attractive: it permits inclusion of a priori information in a well-defined and mathematically consistent way, the algorithm used to derive the solution spectrum is not ad hoc (it can be justified on the basis of arguments that originate in information theory), and the solution spectrum is a non-negative function that can be written in closed form. This last feature permits the use of standard methods for the sensitivity analysis and propagation of uncertainties of MAXED solution spectra. We illustrate its use with unfoldings of NE 213 scintillation detector measurements of photon calibration spectra, and of multisphere neutron spectrometer measurements of cosmic-ray induced neutrons at high altitude (∼20 km) in the atmosphere.

Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy deconvolution code MAXED

A reference facility for the calibration and inter-comparison of active and passive detectors in broad neutron fields has been available at CERN since 1992. A positively charged hadron beam (a mixture of protons and pions) with momentum of usually 120 GeV/c hits a copper target, 50 cm thick and 7 cm in diameter. The secondary particles produced in the interaction traverse a shield, at 90° with respect to the direction of the incoming beam, made of either 80 to 160 cm of concrete or 40 cm of iron. Behind the iron shield, the resulting neutron spectrum has a maximum at about 1 MeV, with an additional high-energy component. Behind the 80 cm concrete shield, the neutron spectrum has a second pronounced maximum at about 70 MeV and resembles the high-energy component of the radiation field created by cosmic rays at commercial flight altitudes. This paper describes the facility, reports on the latest neutron spectral measurements, gives an overview of the most important experiments performed by the various collaborating institutions over the past years, addresses the possible application of the facility to measurements related to the space programme and discusses the latest calculations performed in view of its development for such use.

/pdf/the-cern-eu-high-energy-reference-field-cerf-facility-for-1n3ya7fzog.pdf

The CERN-EU High-energy Reference Field (CERF) Facility for Dosimetry at Commercial Flight Altitudes and in Space

The basic characteristics of Bonner sphere spectrometry systems are first described, followed by a review of the different types of system which have been built, and of how their response functions have been determined. Spectrum unfolding and recent developments are covered briefly. The practical considerations for users are emphasised wherever possible, and the advantages, disadvantages, and problems of using this spectrometer are discussed.

Bonner sphere spectrometers—a critical review

The theory of measurement uncertainty outlined forms the mathematical foundation of the results of international discussions of many years. In contrast to the usual approaches in the literature, it is based entirely on Bayesian statistics and on the principle of maximum entropy. Individual and mutual uncertainties of measurement results are expressed and treated by a covariance matrix in conformity with international recommendations. The theory is universally applicable to most measurement data evaluation tasks including complex nonlinear adjustments and, in particular, in cases where the well-established least-squares or maximum-likelihood techniques fail, as in strongly underdetermined few-channel particle energy spectrum unfolding problems.

https://iopscience.iop.org/article/10.1088/0957-0233/4/1/001/pdf

A Bayesian theory of measurement uncertainty

A review of methods currently used to unfold particle spectra from measured pulse height distributions or other detector readings is given. It is pointed out that most of the measurements in particle spectrometry reveal ill-conditioned or ill-posed problems. The presentation which is given here for examples of such inverse problems is focussed on the algorithms used in the HEPRO unfolding program package of PTB. The question of uncertainty propagation is discussed for least-squares algorithms as well as for those based on maximum entropy. A first attempt has been made to quantify generally the “ambiguity” in ill-posed unfolding problems. The maximum entropy algorithm realized in the MIEKE code allows a clear distinction to be made between two parts of uncertainty, one part coming from ambiguity and one part coming from the usual uncertainty propagation. The resulting uncertainty matrix of the MIEKE code provides these two parts.

Propagation of uncertainties in unfolding procedures

A review of methods currently used to unfold particle spectra form measured pulse height distributions or other detector readings is given. Algorithms based on the least- squares principle and the principle of maximum entropy are reviewed. By the examples presented, it is shown that most of the detection systems reveal ill-conditioned problems.

Unfolding of particle spectra

Realistic fields similar to those occurring in practice can be approximately realised using the ISO-recommended radionuclide sources if the neutrons scattered by the concrete walls of a medium sized irradiation room are used. At the PTB, such fields were established at the irradiation facility with radionuclide reference neutron sources. In order to determine the spectral fluence rate at the point of test as the basis of calibrations, the different spectra were calculated using the MCNP code, and measured by means of a Bonner sphere spectrometer. The measured count rates were unfolded using different codes. The total fluence rate can be determined with a relative standard uncertainty of about 4%. The relative standard uncertainty of the ambient dose equivalent is found to be about 5%.

Scattered Neutron Reference Fields Produced by Radionuclide Sources

Monte Carlo spectrum unfolding requires an a priori probability distribution for drawing sample spectra from it at random. Such distributions are derived from the principle of maximum entropy, taking into account the information available in a variety of ways. The distribution which is most appropriate to the information in realistic situations - e.g. to measurement data together with their uncertainties, expressed by a covariance matrix - turns out to be a cut multivariate normal distribution with chi-square exponent and exhibiting a single essential Lagrange parameter only. This parameter can be calculated by the Monte Carlo method itself.

A priori distributions from the principle of maximum entropy for the Monte Carlo unfolding of particle energy spectra

A CR-39 track image analyser for neutron spectrometry

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