Inside SPHIRE, we define the spatial frequencies are handled in absolute units. This means that the spatial frequencies are expressed in term of pixels units, or absolute frequency $f_a$, instead of units of inverse distance. In this way $f_a=0$ corresponds to the zero Fourier term (zero frequency), while $f_a=0.5$ corresponds to Nyquist frequency $f_N$. The Nyquist frequency corresponds the maximum spatial frequency contained in an image. In absolute frequencies this always has a value of 0.5 while in inverse distance it will correspond to $f_N=\frac{1}{2p}$, where $p$ is the pixel size usually in Å.

A simple relation exists between spatial frequencies $f_s$ and absolute frequencies $f_a$:

For an image with pixel size $p$ [Å] by: $$ f_s=\frac{f_a}{p} \\ f_a=f_s \times p $$

For an n-pixels image sampled, the k'th Fourier pixel ($0\Leftarrowk\Leftarrown/2$) is related to frequency by:

$$ f_s=k/n/p`}}}
. f_a_k_n} $$ Resolution r [Å] (defined as inverse of spatial frequency) is:

. r_1_f_s_p_n_k}

For examples of code in which Fourier pixels are handled check sparx/filter.cpp.