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ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Application of wavelet analysis for data.

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Presentation on theme: "ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Application of wavelet analysis for data."— Presentation transcript:

1 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Application of wavelet analysis for data treatment of small-angle neutron 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.ru litvin@nf.jinr.ru

2 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

3 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Introduction 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.

4 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies 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).

5 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Small angle neutron scattering YuMO spectrometer 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

6 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies IBR-2 reactor core IBR-2 beams IBR-2: http://nfdfn.jinr.ru/flnph/ibr2.html http://nfdfn.jinr.ru/flnph/ibr2.html

7 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies 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

8 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies 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. http://www.jinr.ru/~tsap/Koi/jinrlib/Xw012.htm

9 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies 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 evaluation

10 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Some apoferitin measurement results

11 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

12 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Q-resolution evaluations

13 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

14 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

15 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Smoothing window, 'new' detector

16 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Smoothing window, 'old' detector

17 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Median, 'new' detector

18 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Median, 'old' detector

19 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies The changes after spectra processing by traditional 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.

20 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Continious wavelet transform

21 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies The illustration is taken from the paper V. Uzhinsky et al, JINR Comm E11-119-2001, Dubna, 2001

22 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

23 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies 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.

24 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

25 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies CWT, ⌠'new' detector CWT, ⌠'new' detector

26 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies CWT, ⌠'old' detector CWT, ⌠'old' detector

27 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies The 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:

28 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

29 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Discrete wavelet transform (DWT), lifting scheme (part 2)

30 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies DWT, lifting scheme (part 3)

31 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

32 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies

33 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies DWT, 'new' detector

34 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies DWT, 'old' detector

35 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies The 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:

36 ACAT'2002 E.I. Litvinenko Joint Institute for Nuclear Research Labs: Neutron Physics & Information Technologies Conclusion 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.

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