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definitions:absolute_frequency_units [2016/12/12 16:56] fmerino |
definitions:absolute_frequency_units [2016/12/14 10:37] fmerino |
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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. The Nyquist frequency, the maximum spatial frequency contained in an image, corresponds to $f_a=0.5$. In inverse distance |
+ | A simple relation exists between spatial frequencies $f_s$ (e.g. $\frac{1}{\text{\AA}}$) and absolute frequencies $f_a$: | ||
- | For the pixel size p [Å], spatial frequency {{{`f_s`}}} [1/Å] is related to absolute frequency {{{`f_a`}}} by: | + | For an image with pixel size $p$ by: |
+ | $$ | ||
+ | f_s=\frac{f_a}{p} | ||
+ | \\ | ||
+ | f_a=f_s \times p | ||
+ | $$ | ||
- | | + | For an n-pixels |
- | + | ||
- | | + | |
- | + | ||
- | For an image size n pixels sampled | + | |
- | + | ||
- | | + | |
+ | $$ | ||
+ | f_s=k/ | ||
+ | \\ | ||
| | ||
+ | $$ | ||
Resolution r [Å] (defined as inverse of spatial frequency) is: | Resolution r [Å] (defined as inverse of spatial frequency) is: | ||