1. Indirect Fourier Transformation (IFT)
(see Glatter, J. Appl. Cryst. (1980) 13, Determination of particle-size distribution functions from small-angle scattering data by means of the indirect transformation method)
Particles of identical shape, different sizes
(hR) = normalized scattered intensity from single particle, size R
Dn(R) = particle size distribution fcn
m(R) = integral of xs scattering length density particle
of size R
Infinite dilution, random orientation

2. Indirect Fourier Transformation (IFT)
(see Glatter, J. Appl. Cryst. (1980) 13, Determination of particle-size distribution functions from small-angle scattering data by means of the indirect transformation method)
Particles of identical shape, different sizes
(hR) = normalized scattered intensity from single particle, size R
Dn(R) = particle size distribution fcn
m(R) = integral of xs scattering length density particle
of size R
To get Dn(R) directly, must have known particle shape and
shape factor (hR)

3. Indirect Fourier Transformation (IFT)
Particles of identical shape, different sizes
(hR) = normalized scattered intensity from single particle, size R
Dn(R) = particle size distribution fcn
m(R) = integral of xs scattering length density particle
of size R
Alternatively, use IFT method

4. Indirect Fourier Transformation (IFT)
Particles of identical shape, different sizes
(hR) = normalized scattered intensity from single particle, size R
Dn(R) = particle size distribution fcn
m(R) = integral of xs scattering length density particle
of size R
Alternatively, use IFT method

5. Indirect Fourier Transformation (IFT)
Particles of identical shape, different sizes
(hR) = normalized scattered intensity from single particle, size R
Dn(R) = particle size distribution fcn
m(R) = integral of xs scattering length density particle
of size R
Alternatively, use IFT method
(solve for by c s by least squares)

6. Indirect Fourier Transformation (IFT)
Example - spheres w/ polynomial size distrib
starting
distrib fcn
x distrib fcn
calc'd from
scatt data

7. Indirect Fourier Transformation (IFT)
Example - spheres w/ polynomial size distrib
starting
distrib fcn
x distrib fcn
calc'd from
scatt data
smeared
scatt data

8. Indirect Fourier Transformation (IFT)
Example - spheres w/ double Gaussian size distrib
starting
distrib fcn
calc'd from
scatt data
smeared
scatt data

9. Indirect Fourier Transformation (IFT)
Previous examples used known particle shape factor
If wrong shape factor used (say, for prolate ellipsoids
w/ axes R and 3R):
distrib fcn
forspheres
for ellipsoids