How the reduction works

In grating interferometry a grating is stepwise translated perpendicular to the grating lines. This produces a sinusoidal intensity oscillation for each pixel. The intensity variations can be described by $f(x,y,i)=B+A\sin\left(2\pi\frac{M}{N}i-\phi\right)+w(x,y,i)\quad{}i=0,1,\ldots,N$ where M is the number of periods. Sines

The nGI equations

The reduced images are computed using estimates of A, B, and $\phi$ from sample and reference images

Transmission images: $TI=\frac{B}{B_0}$
Differential phase images: $DPC=\phi-\phi_0$
Dark field images: $DFI=\frac{A/B}{A_0/B_0}=\frac{A\cdot{}B_0}{B\cdot{}A_0}$