No. 33 (00121)

Family name : Varlamov
Given name : Vladimir
Affiliation : Skobeltsyn Institute of Nuclear Physics, Moscow State
              University, Moscow, Russian Federation
Abbreviation : MSU SINP, Moscow, RF
E-mail address : Varlamov@depni.sinp.msu.ru
Title : EXPERIMENTAL DATA ACCURACY AND RELIABILITY INCREASING USING THE 
        MATHEMATICAL METHOD OF REDUCTION
Authors : D.S.Rudenko, M.E.Stepanov, V.V.Varlamov
Abstract : 
     Any measurement can be characterized as system of device, medium,
and measured object.  If device has parameters not close to ideal,
object parameters measured (its image) could be significantly different
from those of initial.  Therefore main task of researcher is to carry
out measurement in conditions for which distortion of initial object
image could be estimated as negligible.  But there are many tasks for
which these condition could not be realized.  Because measurement leads
to noticeable initial object image distortion, this image must be
restored.  Several mathematical methods have been developed for this -
method of maximal entropy, method of least squares, various versions of
method of regularization, etc.  The main lack of such methods is that
solution of task discussed is not concerned directly to the measurement
result uncertainty interpretation.  Method of reduction /1/ free of such
lack was developed on the base of theory of Measuring-Computer-Aided
Systems (MCAS) the scheme of which is the following "measured object -
medium - device - computer".  Main idea of MCAS differs significantly
from that used in traditional measurements: vise versa to classical
principle of minimal distortion, MCAS permits that but on the stadium of
measurements only.  But on the final stadium parameters of object
restored must be maximally close to those of object under investigation.
If this is realized the MCAS output signal S' could be interpreted as
maximally accurate version of output signal of ideal device U.  By other
words MCAS solves the task of reduction of real measurement result Y =
A*S obtained using device with apparatus function A (object parameters
in system "object") to result S' = U(S) obtained by ideal device (object
parameters in system "object-medium").  

     Method of reduction has been successfully used for solving many
tasks in various scientific fields such as optical spectroscopy
(determination of the amplitude of radiation line using radiation
spectrum), optical image restoration (concerned with the fact that real
image of luminous spot is always fuzzy), definition of spectral
distribution of radiation emitted by some substance, problem of
increasing resolution of scopes, such as electronic microscope, problem
of studying electromagnetic radiation of atmosphere leaving the Earth.
One of the most impressive application of the method of reduction is its
using for obtaining of photonuclear reaction cross sections.  The main
problem of such kind research is absence of really monoenergetic photons
sources.  Because all sources used have continuous photon spectra of
very complicated shape only yield of reaction - not cross section
directly but only its folding (integral of production) with real photon
spectrum (experimental apparatus function) - could be measured.
Therefore the task of reaction cross section obtaining presents itself
the task of solving integral equation - inverse ill-posed task.  Method
of reduction gives to one possibility for transformation of data
obtained for concrete experiment apparatus function A to the form they
have being measured by means of another ("near ideal") apparatus
function U.  Many accurate, reliable and free of systematical
disagreements due to differences in apparatus functions data have been
obtained /2/ from real experiments data carried out with various photon
beams.  New data for Giant Dipole Resonance structure were obtained with
high-energy resolution.

     Research was carried out at the Centre for Photonuclear Experiments
Data (MSU SINP Department of Electromagnetic Processes and Atomic Nuclei
Interaction) and supported in part by the President of Russia Federation
grant N SS-1619.2003.2 and the RBFR grant N 03-07-90431.

1.  Yu.P.Pyt'ev. Methods of Mathematical Modeling of
Measuring-Computer-Aided Systems. Fizmatlit, Russia, 2002.

2.  V.V.Varlamov, B.S.Ishkhanov, D.S.Rudenko, M.E.Stepanov. Giant Dipole
Resonance Structure in Experiments with Beams of Quasimonoenergetic
Photons. MSU SINP Preprint-2002-19/703, Moscow, 2002.