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International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 2.6, p. 106
Section 2.6.2.1.3. Correction of wavelength, slit, and detector-element effects
R. Mayb
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Resolution errors affect SANS data in the same way as X-ray scattering data, for which one may find a detailed treatment in an article by Glatter (1982b![[link]](/graphics/greenarr.gif)
); there is one exception to this; namely, gravity, which of course only concerns neutron scattering, and only in rare cases (Boothroyd, 1989). Since SANS cameras usually work with pin-hole geometry, the influences of the slit sizes, i.e. the effective source dimensions, on the scattering pattern are small; even less important is, in general, the pixel size of 2D detectors. The preponderant contribution to the resolution of the neutron-scattering pattern is the wavelength-distribution function after the monochromatizing device, especially at larger angles. The situation is more complicated for TOF SANS (Hjelm, 1988).
As has been shown in an analytical treatment of the resolution function by Pedersen, Posselt & Mortensen (1990), who also quote some relevant references, resolution effects have a small influence on the results of the data analysis for scattering patterns with a smooth intensity variation and without sharp features. Therefore, one may assume that a majority of SANS patterns are not subjected to desmearing procedures.
Resolution has to be considered for scattering patterns with distinct features, as from spherical latex particles (Wignall, Christen & Ramakrishnan, 1988) or from viruses (Cusack, 1984). Size-distribution and wavelength-smearing effects are similar; it is evident that wavelength effects have to be corrected for if the size distribution is to be obtained.
Since measured scattering curves contain errors and have to be smoothed before they can be desmeared, iterative indirect methods are, in general, superior: A guessed solution of the scattering curve is convoluted with known smearing parameters and iteratively fitted to the data by a least-squares procedure. The guessed solution can be a simply parameterized scattering curve, without knowledge of the sample (Schelten & Hossfeld, 1971), but it is of more interest to fit the smeared Fourier transform of the distance-distribution function (Glatter, 1979) or the radial density distribution (e.g. Cusack, Mellema, Krijgsman & Miller, 1981) of a real-space model to the data.
References
Boothroyd, A. T. (1989). The effect of gravity on the resolution of small-angle neutron scattering. J. Appl. Cryst. 22, 252–255.Google Scholar
Cusack, S. (1984). Neutron scattering studies of virus structure. Neutrons in biology; basic life sciences, Vol. 27, edited by B. P. Schoenborn, pp. 173–188. New York: Plenum.Google Scholar
Cusack, S., Mellema, J. E., Krijgsman, P. C. J. & Miller, A. (1981). An investigation of the structure of alfalfa mosaic virus by small-angle neutron scattering. J. Mol. Biol. 145, 525–543. Google Scholar
Glatter, O. (1979). The interpretation of real-space information from small-angle scattering experiments. J. Appl. Cryst. 12, 166–175.Google Scholar
Glatter, O. (1982b). In Small angle X-ray scattering, edited by O. Glatter & O. Kratky, Chap. 5. London: Academic Press.Google Scholar
Hjelm, R. P. (1988). The resolution of TOF low-Q diffractometers: instrumental, data acquisition and reduction factors. J. Appl. Cryst. 21, 618–628.Google Scholar
Pedersen, J. S., Posselt, D. & Mortensen, K. (1990). Analytical treatment of the resolution function for small-angle scattering. J. Appl. Cryst. 23, 321–333.Google Scholar
Schelten, J. & Hossfeld, F. (1971). Application of spline functions to the correction of resolution errors in small-angle scattering. J. Appl. Cryst. 4, 210–223.Google Scholar
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