# porod

Porod function

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
0.001 |

The returned value is scaled to units of cm^{-1} sr^{-1}, absolute scale.

This model fits the Porod function

\[I(q) = C/q^4\]

to the data directly without any need for linearisation (cf. Log I(q) vs Log q).

Here \(C = 2\pi (\Delta\rho)^2 S_v\) is the scale factor where \(S_v\) is the specific surface area (ie, surface area / volume) of the sample, and \(\Delta\rho\) is the contrast factor.

For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as

\[q = \sqrt{q_x^2+q_y^2}\]

**References**

G Porod. *Kolloid Zeit*. 124 (1951) 83.

L A Feigin, D I Svergun, G W Taylor. *Structure Analysis by Small-Angle
X-ray and Neutron Scattering*. Springer. (1987)