Spatial frequency filter

The classical treatment of diffuse SAXS (analysis and elimination) is restricted to isotropic scattering. Separation of its components is frequently impossible or resting on additional assumptions. Anyway, curves have to be manipulated one-by-one in a cumbersome procedure. Discussion of diffuse background can sometimes be avoided if investigations are resorting to time-resolved measurements and subsequent discussion of observed variations of SAXS pattern features. A background elimination procedure that does not require user intervention is based on spatial frequency filtering (cf. p. 140). 

Figure 8.19. Extraction of the scattering of an ideal two-phase structure from the raw scattering data of an isotropic UHMWPE material by means of spatial frequency filtering... 

By means of this procedure our problem is not only reduced from three to two dimensions, but also is the statistical noise in the scattering data considerably reduced. Multiplication by —4ns2 is equivalent to the 2D Laplacian89 in physical space. It is applied for the purpose of edge enhancement. Thereafter the 2D background is eliminated by spatial frequency filtering, and an interference function G(s 2,s ) is finally received. The process is demonstrated in Fig. 8.27. 2D Fourier transform of the interference function... 

The term NAcct> is multiplied by M to account for the difference between the NA on the object side of the microscope objective and the NA on the image side of the microscope objective. The sixth factor which influences the effective numerical aperture is the numerical aperture of microscope objective (NA cro)- These multiple NA terms can be interpreted as multiple low-pass spatial frequency filtering operations of the transverse light amplitude field. The effective spatial frequency is roughly limited by the lowest spatial cutoff frequency or the smallest NA term. Hence, the effective NA (AMeff) of the whole... 

At the low-aperture configuration, both codes show similar density (gray-scale) values. Because of the higher spatial frequency filter, the Feidkamp code better defines the edges of the blades than does the Radon code. 

Stribeck N (2002) Utilising spatial frequency filtering to extract nanoscale layer structure information from isotropic small-angle X-ray scattering data. Colloid Polym Sci 280 254-259. 

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