GNOM

Introduction

GNOM is an indirect transform program for small-angle scattering data processing. It reads one-dimensional scattering curves (possibly smeared with instrumental distortions) and evaluates a distance distribution function p(r) for monodisperse systems or a size distribution function D(R) for polydisperse systems. The main equations relating the scattering intensity to the distribution functions and describing the smearing effects can be found in the text-books (e.g. [1-3]). The idea of the indirect transform method was first proposed by Glatter [2] and also implemented in other packages e.g. [3,4]. The algorithms used in GNOM are described elsewhere [5-8]. They are based on Tikhonov's regularisation technique [9] ; several subroutines published in [10] are modified and employed in GNOM.

Main features of the program are summarized below.

1. GNOM can treat experimental data for the following types of systems:
   • monodisperse systems of globular particles;
   • monodisperse systems of elongated particles;
   • monodisperse systems of flattened particles;
   • polydisperse systems of spherical particles;
   • polydisperse systems of particles with an arbitrary form factor.
2. Like other indirect transform packages, GNOM produces a smooth and stable solution using the regularisation technique. Unlike these packages, where the user must adjust the regularisation parameters, GNOM finds the solution automatically. A built-in Expert estimate [8] of the solution based on perceptual criteria is used to this end. Apart from finding the solution, GNOM gives an estimate of its quality that allows to verify the validity of the assumptions made about the system.
3. GNOM is made as user-friendly as possible. The user has to specify only the expected range of definition of the distribution function. Default answers to all other questions are normally sufficient to obtain the solution.
4. Different types of experimental conditions are supported (point collimation, slit geometry, 1D and averaged 2D detector data). It is possible to automatically merge two data sets recorded for the same sample in different angular ranges with different smearing conditions.
5. The knowledge of the errors in the input data is desirable but not compulsory. A build-in procedure estimates the input statistical errors if they are not known. Error propagation is computed using a Monte-Carlo technique [11].

References

1. Feigin L.A. & Svergun D.I. (1987) Structure Analysis by Small-Angle X-Ray and Neutron Scattering. NY: Plenum Press.
2. Glatter O. (1977). J.Appl.Cryst., 10, 415-421
3. Moore P.B. (1980). J.Appl.Cryst., 13, 168-175
4. Provencher S.W. (1982). Computer Phys.Commun., 27, 213-227, 229-242
5. Svergun D.I. & Semenyuk A.V. (1987). Doklady AN SSSR, 297,1373-1377 (in Russian)
6. Svergun D.I., Semenyuk A.V. & Feigin L.A. (1988). Acta Cryst., A44, 244-250
7. Svergun D.I. (1991). J.Appl.Cryst., 24, 485-492
8. Svergun D.I. (1992). J. Appl. Cryst., 495-503
9. Tikhonov A.N. & Arsenin V.Ya. (1977) Solution of Ill-Posed Problems. NY: Wiley
10. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. (1983) Regularizing Algorithms and a priori Information. Moscow: Nauka, (in Russian)
11. Svergun, D.I. & Pedersen, J.Skov (1994). J. Appl. Cryst., 27, 241-248.
12. GNOM manual