Differences

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

--- definitions:absolute_frequency_units [2016/12/14 10:46]
fmerino
+++ definitions:absolute_frequency_units [2018/06/20 13:12]
@@ Line 1: / Line 1: @@
-~~NOTOC~~
-===== 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. ${Å}^{-1}$) 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:
-$$
-f_s=\frac{k}{n \times p}
-\\
-f_a=\frac{k}{n}
-$$
-The resolution $r$ is defined as the inverse of the spatial frequency:
-$$
-r=\frac{1}{f_s}=p\frac{n}{k}
-$$
-==== Within the code ====
-For examples of code in which Fourier pixels are handled check sparx/filter.cpp.