Differences

This shows you the differences between two versions of the page.

--- definitions:absolute_frequency_units [2016/12/12 14:30]
fmerino created
+++ definitions:absolute_frequency_units [2016/12/12 16:56]
fmerino
@@ Line 1: / Line 1: @@
 ===== Absolute frequency =====
- . {{{`f_a=0`}}} corresponds to the zero Fourier term (zero frequency), while {{{`f_a=0.5`}}}  corresponds to Nyquist frequency {{{`f_N`}}}.
+==== Definition ====
- . '''''Nyquist frequency''''' is the maximum spatial frequency in an image scanned with a pixel size p [Å] and in pixels {{{`f_N=1/2`}}}, while in Å {{{`f_N=1/(2p) [1/Å]`}}}.
+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.
@@ Line 20: / Line 20: @@
  .      {{{`r=1/f_s=p**n/k`}}}
+==== Within the code ====
 For examples of code in which Fourier pixels are handled check sparx/filter.cpp.