Differences

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

--- definitions:absolute_frequency_units [2016/12/12 16:56]
fmerino
+++ definitions:absolute_frequency_units [2018/06/20 13:12]
@@ Line 1: / Line 1: @@
-===== Absolute frequency =====
-==== Definition ====
-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.
-For the pixel size p [Å], spatial frequency {{{`f_s`}}} [1/Å] is related to absolute frequency {{{`f_a`}}} by:
- .      {{{`f_s=f_a/p`}}}
- .      {{{`f_a=f_s**p`}}}
-For an image size n pixels sampled at p Å, k'th Fourier pixel (0<=k<=n/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`}}}
-==== Within the code ====
-For examples of code in which Fourier pixels are handled check sparx/filter.cpp.