definitions:absolute_frequency_units

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definitions:absolute_frequency_units [2016/12/14 10:37]
fmerino
definitions:absolute_frequency_units [2018/06/20 13:12] (current)
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 +~~NOTOC~~
 +
 ===== Absolute frequency ===== ===== Absolute frequency =====
  
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 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. 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 $f_a$:+A simple relation exists between spatial frequencies $f_s$ (e.g. ${Å}^{-1}$) and absolute frequencies $f_a$:
  
-For an image with pixel size $p$ by:+For an image with pixel size $p$:
 $$ $$
 f_s=\frac{f_a}{p} f_s=\frac{f_a}{p}
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 $$ $$
  
-For an n-pixels image sampled, the k'th Fourier pixel ($0<=k<=n/2$) is related to frequency by:+For an n-pixels image, the k'th Fourier pixel (with $0 \leq \leq 0.5n$) is related to frequency by:
  
 $$ $$
-f_s=k/n/p`}}}+f_s=\frac{k}{\times ​p}
 \\ \\
- ​. ​     {{{`f_a=k/n`}}}+f_a=\frac{k}{n}
 $$ $$
-Resolution r [Å] (defined as inverse of spatial frequency) is: 
  
- ​. ​     {{{`r=1/​f_s=p**n/​k`}}}+The resolution $r$ is defined as the inverse of the spatial frequency:
  
 +$$
 +r=\frac{1}{f_s}=p\frac{n}{k}
 +$$
  
 ==== Within the code ==== ==== Within the code ====
  • definitions/absolute_frequency_units.txt
  • Last modified: 2018/06/20 13:12
  • (external edit)