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--- definitions:absolute_frequency_units [2016/12/14 10:37]
fmerino
+++ definitions:absolute_frequency_units [2018/06/20 13:12]
@@ Line 1: / Line 1: @@
-===== Absolute frequency =====
-==== Definitions ====
-Inside SPHIRE, spatial frequencies are handled in absolute units. This means that the spatial frequencies are expressed in term of pixels, or absolute frequency $f_a$, instead of units of inverse distance. The Nyquist frequency, the maximum spatial frequency contained in an image, corresponds to $f_a=0.5$. In inverse distance units, 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 $f_s$ (e.g. $\frac{1}{\text{\AA}}$) and absolute frequencies $f_a$:
-For an image with pixel size $p$ by:
-$$
-f_s=\frac{f_a}{p}
-\\
-f_a=f_s \times p
-$$
-For an n-pixels image sampled, the k'th Fourier pixel ($0<=k<=n/2$) 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.