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ACAT'2002 E.I. Litvinenko
Application of wavelet Application of wavelet analysis for data treatment analysis for data treatment
of small-angle neutron of small-angle neutron scattering scattering
A.Islamov(1), A.Kuklin(1), E.Litvinenko(1), A.Soloviev (2),
G.Ososkov(2)
(1) FLNP of JINR(2) LIT of JINR
Dubna, Russia
[email protected]@nf.jinr.ru
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
IntroductionIntroduction
Small-angle neutron scattering (SANS) is a very popular method used by physicists, material scientists, chemists and biologists.
The time-of-flight information needs to be preprocessed (calibration, normalization, smoothing, converting to proper scale).
The problem of spectra processing belongs to inverse problems (i.e. ill-posed problems).
It is important to obtain more smooth and valid spectra during the acquisition time.
ACAT'2002 E.I. Litvinenko
Problem formulation Problem formulation
Main problems with treatment of data measured on neutron instruments using TOF techniques:
very noisy data;
data summation (merging) from different parts of neutron detector (different rings in our case);
taking spectrometer resolution into account;
smoothing motivation (when it should be performed, what a method sould be used).
ACAT'2002 E.I. Litvinenko
Small angle neutron scattering YuMO spectrometerSmall angle neutron scattering YuMO spectrometer1 -- reflectors, 2 -- active zone with moderator, 3 -- breaker (shutter), 4 -- changeable collimator with different beam-holes, 5 -- vacuum tube, 6 -- adjustable collimator determining the size and position of the direct beam, 7 -- thermostats, 8 -- sample container, 9 -- sample table, 10 -- standart vanadium scatterer, 11, 12 -- ``old'' and ``new'' detectors, 13 -- direct beam detector
ACAT'2002 E.I. Litvinenko
IBR-2 reactor coreIBR-2 reactor core IBR-2 beams IBR-2 beams
IBR-2: IBR-2: http://nfdfn.jinr.ru/flnph/ibr2.html
ACAT'2002 E.I. Litvinenko
8-ring neutron detectors of YuMO 8-ring neutron detectors of YuMO 1 -- reflectors, 2 -- active zone with moderator, 3 -- breaker (shutter), 4 -- changeable collimator with different beam-holes, 5 -- vacuum tube, 6 -- adjustable collimator determining the size and position of the direct beam, 7 -- thermostats, 8 -- sample container, 9 -- sample table, 10 -- standart vanadium scatterer, 11, 12 -- ``old'' and ``new'' detectors, 13 -- direct beam detector
ACAT'2002 E.I. Litvinenko
Data summation (merging)Data summation (merging)
The existing data treatment program SAS (1992)(http://www.jinr.ru/~tsap/Koi/jinrlib/Xw012.htm) and new data treatment program OpenG2 (under development, http://nfdfn.jinr.ru/~litvin/openg2) allow user to perform a procedure, which is similar to re-binning, but it takes a statistical errors into account. This procedure requires user to give a valid Q-range by hand, and it affords smoother spectra with rarefied Q-grid after that.
ACAT'2002 E.I. Litvinenko
Experimental spectra for apoferritin protein are presented. The choice is stipulated by the following reasons: the sample is monodispersive; the apoferritin spectra is very distinctive,
has maxima and minima; the apoferritin solvent is always used for
tuning and testing of spectrometer elements.
Samples used for method evaluationSamples used for method evaluation
ACAT'2002 E.I. Litvinenko
Some apoferitin measurement results Some apoferitin measurement results
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
Q-resolution evaluationsQ-resolution evaluations
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
Smoothing window, 'new' detectorSmoothing window, 'new' detector
ACAT'2002 E.I. Litvinenko
Smoothing window, 'old' detectorSmoothing window, 'old' detector
ACAT'2002 E.I. Litvinenko
Median, 'new' detectorMedian, 'new' detector
ACAT'2002 E.I. Litvinenko
Median, 'old' detectorMedian, 'old' detector
ACAT'2002 E.I. Litvinenko
The changes after spectra processing by The changes after spectra processing by traditional smoothing techniquestraditional smoothing techniques
Determination of invariants for small-angle scattering curves allows one to analyze the structure of a particle under study. Upon the first step of this analysis the particle form is approximated by simple geometrical bodies - spheres, ellipsoids, cylinders, prisms [1]
The spectra above were fitted by spherical shell model. While the model parameters are preserved, the chi-square value is improved after processings:
[1] Feigin, L.A., Svergun, D.I. (1987) Structure analysis by small-angle X-ray and neutron scattering. New York: Plenum Press, 335 pp.
ACAT'2002 E.I. Litvinenko
Continious wavelet transformContinious wavelet transform
ACAT'2002 E.I. Litvinenko
The illustration is taken from the paper
V. Uzhinsky et al, JINR Comm E11-119-2001, Dubna, 2001
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
What is new ?What is new ?
We take Gaussian instead of a true basic wavelet ь (no inverse transform is performed).
We choose a dilation factor (RMS of Gaussian) depending on a point, according to a given Q-resolution of YuMO spectrometer at this point.
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
CWT, ⌠'new' detectorCWT, ⌠'new' detector
ACAT'2002 E.I. Litvinenko
CWT, ⌠'old' detectorCWT, ⌠'old' detector
ACAT'2002 E.I. Litvinenko
The changes after spectra processing by CWTThe changes after spectra processing by CWT
The spectra above were fitted by spherical shell model. While the model parameters are preserved, the chi-square value is improved after processings:
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
Discrete wavelet transform (DWT), Discrete wavelet transform (DWT), lifting scheme (part 2)lifting scheme (part 2)
ACAT'2002 E.I. Litvinenko
DWT, lifting scheme (part 3)DWT, lifting scheme (part 3)
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
ACAT'2002 E.I. Litvinenko
DWT, 'new' detectorDWT, 'new' detector
ACAT'2002 E.I. Litvinenko
DWT, 'old' detectorDWT, 'old' detector
ACAT'2002 E.I. Litvinenko
The changes after spectra processing by DWTThe changes after spectra processing by DWT
The spectra above were fitted by spherical shell model. While the model parameters are preserved, the chi-square value is improved after processings:
ACAT'2002 E.I. Litvinenko
ConclusionConclusion
Continuous wavelet transform of discretized signals (i.e. histograms) is similar to kernel estimates. It is modified to be more sutable tool for SANS spectra smoothing. The usage the spectrometer resolution leads to the improvement of the resulting scattering spectra quality. Chi-square is greatly improved without information loss.
The lifting scheme has some advantages in comparison with the classical discrete wavelets. This transform works for signals of an arbitrary size with correct treatment of the boundaries. Also, all computations can be done in-place. Moreover, the lifting scheme makes them optimal, sometimes increasing the speed of calculations by factor 2. An important quality of such an approach is the simultaneous access to all frequencies in the signal.
The usage of wavelet approach allows one to increase a valid range of transfered impulse. The usage of two-detector system confirms the validity of this result.