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## [gnuastro-commits] master e46d675 1/3: Book: added section on measuring

 From: Mohammad Akhlaghi Subject: [gnuastro-commits] master e46d675 1/3: Book: added section on measuring the magnitude limit of an image Date: Wed, 27 Oct 2021 19:17:51 -0400 (EDT)

branch: master
commit e46d67535a3447fb524c78502042dcfcc74bb488

Book: added section on measuring the magnitude limit of an image

Until now, the "Quantifying magnitude limits" section of the book didn't
include the magnitude limit of the dataset at a certain S/N. This is also
used by some studies to quantify "depth", and can be mentioned as
"magnitude limit" or "detection limit".

With this commit, a section describing this measure has been added to the
book and the caveat of it (how it depends on the morphology of the objects)
is also discussed.
---
doc/gnuastro.texi | 35 +++++++++++++++++++++++++++--------
1 file changed, 27 insertions(+), 8 deletions(-)

diff --git a/doc/gnuastro.texi b/doc/gnuastro.texi
index f9182a5..4ba7d38 100644
--- a/doc/gnuastro.texi
+++ b/doc/gnuastro.texi
@@ -563,8 +563,9 @@ Quantifying measurement limits
* Surface brightness error of each detection::  Error in measuring the Surface
brightness.
* Completeness limit of each detection::  Possibility of detecting similar
objects?
* Upper limit magnitude of each detection::  How reliable is your magnitude?
-* Surface brightness limit of image::  How deep is your data?
-* Upper limit magnitude of image::  How deep is your data for certain
footprint?
+* Magnitude limit of image::    Measured magnitude of objects at certain S/N.
+* Surface brightness limit of image::  Extrapolate per-pixel noise-level to
standard units.
+* Upper limit magnitude of image::  Measure the noise-level for a certain
aperture.

Invoking MakeCatalog

@@ -18455,8 +18456,9 @@ Therefore the measurements discussed here are commonly
used in units of magnitud
* Surface brightness error of each detection::  Error in measuring the Surface
brightness.
* Completeness limit of each detection::  Possibility of detecting similar
objects?
* Upper limit magnitude of each detection::  How reliable is your magnitude?
-* Surface brightness limit of image::  How deep is your data?
-* Upper limit magnitude of image::  How deep is your data for certain
footprint?
+* Magnitude limit of image::    Measured magnitude of objects at certain S/N.
+* Surface brightness limit of image::  Extrapolate per-pixel noise-level to
standard units.
+* Upper limit magnitude of image::  Measure the noise-level for a certain
aperture.

@node Magnitude measurement error of each detection, Surface brightness error
of each detection, Quantifying measurement limits, Quantifying measurement
limits
@@ -18521,7 +18523,7 @@ However in such a study we must be really careful to
choose model profiles as si

-@node Upper limit magnitude of each detection, Surface brightness limit of
image, Completeness limit of each detection, Quantifying measurement limits
+@node Upper limit magnitude of each detection, Magnitude limit of image,
Completeness limit of each detection, Quantifying measurement limits
@subsubsection Upper limit magnitude of each detection
Due to the noisy nature of data, it is possible to get arbitrarily low values
for a faint object's brightness (or arbitrarily high @emph{magnitudes}).
Given the scatter caused by the dataset's noise, values fainter than a certain
level are meaningless: another similar depth observation will give a radically
different value.
@@ -18562,7 +18564,23 @@ You can get the full list of upper-limit related
columns of MakeCatalog with thi
\$ astmkcatalog --help | grep -- --upperlimit
@end example

-@node Surface brightness limit of image, Upper limit magnitude of image, Upper
limit magnitude of each detection, Quantifying measurement limits
+@node Magnitude limit of image, Surface brightness limit of image, Upper limit
magnitude of each detection, Quantifying measurement limits
+@subsubsection Magnitude limit of image
+
+@cindex Magnitude limit
+Suppose we have taken two images of the same field of view with the same CCD,
once with a smaller telescope, and once with a larger one.
+Because we used the same CCD, the noise will be very similar.
+However, the larger telescope has gathered more light, therefore the same star
or galaxy will have a higher signal-to-noise ratio (S/N) in the image taken
with the larger one.
+The same applies for a stacked image of the field compared to a
single-exposure image of the same telescope.
+
+This concept is used by some researchers to define the magnitude limit'' or
detection limit'' at a certain S/N (sometimes 10, 5 or 3 for example, also
written as @mymath{10\sigma}, @mymath{5\sigma} or @mymath{3\sigma}).
+To do this, they measure the magnitude and signal-to-noise ratio of all the
objects within an image and measure the mean (or median) magnitude of objects
at the desired S/N.
+
+However, this method should be used with extreme care!
+This is because the shape of the object becomes important in this method: a
sharper object will have a higher @emph{measured} S/N compared to a more
diffuse object at the same original magnitude.
+Besides the inherent shape/sharpness of the object, issues like the PSF also
become important in this method (because the finally observed shapes of objects
are important here): two surveys with the same surface brightness limit (see
@ref{Surface brightness limit of image}) will have different magnitude limits
if one is taken from space and the other from the ground.
+
+@node Surface brightness limit of image, Upper limit magnitude of image,
Magnitude limit of image, Quantifying measurement limits
@subsubsection Surface brightness limit of image
@cindex Surface brightness
As we make more observations on one region of the sky and add/combine the
observations into one dataset, both the signal and the noise increase.
@@ -18638,8 +18656,9 @@ A more accurate measure which will provide a realistic
value for every labeled r

@node Upper limit magnitude of image,  , Surface brightness limit of image,
Quantifying measurement limits
@subsubsection Upper limit magnitude of image
-As mentioned above, the upper-limit magnitude will depend on the shape of each
object's footprint.
-Therefore we can measure the dataset's upper-limit magnitude using standard
shapes.
+As mentioned in @ref{Upper limit magnitude of each detection}, the upper-limit
magnitude will depend on the shape of each object's footprint.
+Therefore we can measure a dataset's upper-limit magnitude using standard
shapes.
+
Traditionally a circular aperture of a fixed size (in arcseconds) has been
used.
For a full example of implementing this, see the respective section in the
tutorial (@ref{Image surface brightness limit}).