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definitions:absolute_frequency_units [2016/12/12 16:51] fmerino |
definitions:absolute_frequency_units [2018/06/20 13:12] (current) |
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===== Absolute frequency ===== | ===== Absolute frequency ===== | ||
- | ==== Definition | + | ==== Definitions |
- | Inside SPHIRE, | + | 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. |
- | . ''''' | + | |
- | + | ||
- | + | ||
- | For the pixel size p [Å], spatial frequency {{{`f_s`}}} [1/Å] is related to absolute frequency {{{`f_a`}}} by: | + | |
- | + | ||
- | . | + | |
- | + | ||
- | | + | |
- | For an image size n pixels sampled at p Å, k'th Fourier pixel (0< | + | A simple relation exists between spatial frequencies $f_s$ (e.g. ${Å}^{-1}$) and absolute frequencies $f_a$: |
- | | + | For an image with pixel size $p$: |
+ | $$ | ||
+ | f_s=\frac{f_a}{p} | ||
+ | \\ | ||
+ | f_a=f_s \times p | ||
+ | $$ | ||
- | | + | For an n-pixels image, the k'th Fourier pixel (with $0 \leq k \leq 0.5n$) is related to frequency by: |
- | Resolution r [Å] (defined as inverse of spatial frequency) is: | + | $$ |
+ | f_s=\frac{k}{n \times p} | ||
+ | \\ | ||
+ | f_a=\frac{k}{n} | ||
+ | $$ | ||
- | | + | 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 ==== |