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

solovjev@spp.jinr.rulitvin@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.