Skip to content
GitLab
Commit 040b827f authored by Emmanuel Bertin's avatar Emmanuel Bertin
Browse files

Doc: Added description on FLUX_PETRO in Photometry section. Re-wrote part of... 

Doc: Added description on FLUX_PETRO in Photometry section. Re-wrote part of the FLUX_AUTO subsection to better describe "reduced pseudo-radii".
parent f7f1176e
Hide whitespace changes
Inline Side-by-side
doc/src/Photom.rst
View file @ 040b827f
......@@ -30,7 +30,7 @@ Magnitude uncertainties (error estimates) are computed using
Isophotal flux: :param:`FLUX_ISO`
---------------------------------
:param:`FLUX_ISO` is computed simply by integrating pixels values :math:`p_i` within the detection footprint, with the additional constraint that the background-subtracted, filtered value of detection image pixels must exceed the threshold set with the ``ANALYSIS_THRESH`` configuration parameter:
:param:`FLUX_ISO` is computed simply by integrating the background-subracted pixels values :math:`p_i` from the measurement image within the detection footprint, with the additional constraint that the background-subtracted, filtered value of detection image pixels must exceed the threshold set with the ``ANALYSIS_THRESH`` configuration parameter:
.. math::
:label: fluxiso
......@@ -78,7 +78,7 @@ Clearly this cheap correction works best with stars; and although it gives reaso
Fixed-aperture flux: :param:`FLUX_APER`
---------------------------------------
:param:`FLUX_APER` estimates the flux above the background within a circular aperture.
:param:`FLUX_APER` estimates the flux from the measurement image above the background inside a circular aperture.
The diameter of the aperture in pixels is defined by the ``PHOTOM_APERTURES`` configuration parameter.
It does not have to be an integer: each "regular" pixel is subdivided in :math:`5\times 5` sub-pixels before measuring the flux within the aperture.
If :param:`FLUX_APER` is provided as a vector :param:`FLUX_APER[n]`, at least :math:`n` apertures must be specified with the ``PHOTOM_APERTURES`` configuration parameter.
......@@ -89,40 +89,49 @@ Automatic aperture flux: :param:`FLUX_AUTO`
-------------------------------------------
:param:`FLUX_AUTO` provides an estimate of the “total flux” by integrating pixel values within an adaptively scaled aperture.
|SExtractor|’s automatic aperture photometry routine is inspired by Kron’s “first moment” algorithm :cite:`1980ApJS_43_305K`.
|SExtractor|’s automatic aperture photometry routine derives from Kron’s “first moment” algorithm :cite:`1980ApJS_43_305K`:
#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution <shape_iso_def>`, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`.
The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis).
#. Within this elliptical aperture :math:`{\cal E}`, Kron's "first moment" is computed:
#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution <ellipse_iso_def>`, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`.
#. The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis).
#. Inside this elliptical aperture :math:`{\cal E}`, an analog of Kron's "first moment" is computed:
.. math::
:label: kron_r1
r_1 = \frac{\sum_{i\in\cal E} d_i\,p_i}{\sum_{i\in\cal E} p_i},
:label: kron_radius
where :math:`d_i` and :math:`p_i` are respectively the Euclidean distance to the (isophotal) centroid and the pixel value above the local background at image pixel :math:`i`.
:cite:`1980ApJS_43_305K` and :cite:`1987AA_183_177I` have shown that for stars and galaxy profiles convolved with Gaussian seeing, :math:`\ge 90\%` of the flux is expected to lie within a circular aperture of radius :math:`k r_1` if :math:`k = 2`, almost independently of the magnitude.
Experiments have shown :cite:`1996AAS_117_393B` that this conclusion remains unchanged if one replaces the circular aperture with a "Kron ellipse" :math:`{\cal K}`, which is simply the ellipse :math:`{\cal E}` above, scaled such that the principle axes become :math:`\sqrt{a/b}\,k r_1` and :math:`\sqrt{b/a}\,k r_1`.
r_{\rm Kron} = \frac{\sum_{i\in\cal E} r_i\,p^{(d)}_i}{\sum_{i\in\cal E} p^{(d)}_i},
:param:`FLUX_AUTO` is the flux above the background summed over the Kron ellipse:
where :math:`p^{(d)}_i` is the pixel value *in the detection image*. :math:`r_i` is what we shall call the "reduced pseudo-radius" at pixel :math:`i`
.. math::
:label: flux_auto
:label: reduced_radius
{\tt FLUX\_AUTO} = \sum_{i\in\cal K} p_i.
r_i \equiv \sqrt{{\tt CXX\_IMAGE} \times \Delta x_i^2 + {\tt CYY\_IMAGE} \times \Delta y_i^2 + {\tt CXY\_IMAGE} \times \Delta x_i \Delta y_i},
The quantity :math:`kr_1` is known as the *Kron radius*, and is provided in |SExtractor| by the :param:`KRON_RADIUS` catalog parameter in units of :param:`A_IMAGE` (or :param:`B_IMAGE`):
where :math:`\Delta x_i` and :math:`\Delta y_i` are the pixel coordinates relative to the detection centroid:
.. math::
:label: kron_radius
{\tt KRON\_RADIUS} = \frac{1}{\sqrt{{\tt A\_IMAGE}\times{\tt B\_IMAGE}}}\,k\,r_1.
\begin{aligned}
\Delta x_i & = x_i - {\tt X\_IMAGE}\\
\Delta y_i & = y_i - {\tt Y\_IMAGE}.
\end{aligned}
:cite:`1980ApJS_43_305K` and :cite:`1987AA_183_177I` have shown that for stars and galaxy profiles convolved with Gaussian seeing, :math:`\ge 90\%` of the flux is expected to lie inside a circular aperture of radius :math:`k r_{\rm Kron}` with :math:`k = 2`, almost independently of the magnitude.
Experiments have shown :cite:`1996AAS_117_393B` that this conclusion remains unchanged if one replaces the circular aperture with the "Kron elliptical aperture" :math:`{\cal K}` with reduced pseudo-radius :math:`k r_{\rm Kron}`.
:param:`FLUX_AUTO` is the sum of pixel values from the measurement image, subtracted from the local background, inside the Kron ellipse:
.. math::
:label: flux_auto
{\tt FLUX\_AUTO} = \sum_{i\in\cal K} p_i.
The quantity :math:`k r_{\rm Kron}`, known as the *Kron radius* (which in |SExtractor| is actually a "reduced pseudo-radius") is provided by the :param:`KRON_RADIUS`.
:math:`k = 2` defines a sort of balance between systematic and random errors.
By choosing a larger :math:`k = 2.5`, the mean fraction of flux lost drops from about 10% to 6%, at the expense of |SNR| in the measurement.
Very noisy objects may sometimes end up with a Kron radius being too small, even smaller that the isophotal footprint of the object itself. For this reason, |SExtractor| imposes a minimum size for the Kron radius, which must be larger than :math:`\sqrt{ab}\, r_{\rm min}`
The user has full control over the parameters :math:`k` and :math:`r_{\rm min}` through the ``PHOT_AUTOPARAMS`` configuration parameters. ``PHOT_AUTOPARAMS`` is set by default to ``2.5,3.5``.
Very noisy objects may sometimes end up with a Kron ellipse being too small, even smaller that the isophotal footprint of the object itself. For this reason, |SExtractor| imposes a minimum size for the Kron radius, which cannot be less than :math:`r_{\rm Kron,min}`.
The user has full control over the parameters :math:`k` and :math:`r_{\rm Kron,min}` through the ``PHOT_AUTOPARAMS`` configuration parameters. ``PHOT_AUTOPARAMS`` is set by default to ``2.5,3.5``.
..
.. figure:: ps/simlostflux.ps
......@@ -149,6 +158,43 @@ The user has full control over the parameters :math:`k` and :math:`r_{\rm min}`
Figure [figphot] shows the mean loss of flux measured with isophotal (threshold 24.4 magnitude.arsec\ :sup:`-2`), corrected isophotal and automatic aperture photometry for simulated galaxies on a typical Schmidt-survey B\ :sub:`J` plate image.
The automatic adaptive aperture photometry leads to the lowest loss of flux.
.. _flux_petro_def:
Petrosian aperture flux: :param:`FLUX_PETRO`
--------------------------------------------
Similar to :param:`FLUX_AUTO`, :param:`FLUX_PETRO` provides an estimate of the “total flux” by integrating pixel values within an adaptively scaled elliptical aperture. :param:`FLUX_PETRO`\ 's algorithm derives from Petrosian’s photometric estimator :cite:`1976ApJ_209L_1P,2001AJ_121_2358B,2001AJ_122_1104Y`:
#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution <ellipse_iso_def>`, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`.
#. The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis).
#. Within this elliptical aperture :math:`{\cal E}`, the *Petrosian ratio* :math:`R_{\rm P}(r)` is computed:
.. math::
:label: petrosian_ratio
R_{\rm P}(r) = \frac{\sum_{0.9r < r_i < 1.1r} p^{(d)}_i}{\sum_{r_i < r} p^{(d)}_i} \frac{N_{r_i < r}}{N_{0.9r < r_i < 1.1r}},
where :math:`p^{(d)}_i` is the pixel value *in the detection image*. :math:`r_i` is the "reduced pseudo-radius" at pixel :math:`i` as defined in :eq:`reduced_radius`.
The *Petrosian ellipse* :math:`{\cal P}` is the ellipse with reduced pseudo-radius :math:`N_{\rm P}r_{\rm P}`, where :math:`r_{\rm P}` is the *Petrosian radius* defined by
.. math::
:label: petrosian_radius
R_{\rm P}(r_{\rm p}) \equiv 0.2
:math:`r_{\rm P}` is provided in |SExtractor| by the :param:`PETRO_RADIUS` catalog parameter.
The Petrosian factor :math:`N_{\rm P}` is set to 2.0 by default.
Very noisy objects may sometimes end up with a Petrosian ellipse being too small.
For this reason, |SExtractor| imposes a minimum size for the Petrosian radius, which cannot be less than :math:`r_{\rm P,min}`.
The user has full control over the parameters :math:`N_{\rm P}` and :math:`r_{\rm P,min}` through the ``PHOT_PETROPARAMS`` configuration parameters. ``PHOT_PETROPARAMS`` is set by default to ``2.0,3.5``.
The Petrosian flux is the sum of pixel values from the measurement image, subtracted from the local background, inside the Petrosian ellipse:
.. math::
:label: flux_petro
{\tt FLUX\_PETRO} = \sum_{i\in\cal P} p_i.
Photographic photometry
-----------------------
......
doc/src/references.bib
View file @ 040b827f
......@@ -24,6 +24,39 @@
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2001AJ_121_2358B,
author = {{Blanton}, M.~R. and {Dalcanton}, J. and {Eisenstein}, D. and
{Loveday}, J. and {Strauss}, M.~A. and {SubbaRao}, M. and {Weinberg}, D.~H. and
{Anderson}, Jr., J.~E. and {Annis}, J. and {Bahcall}, N.~A. and
{Bernardi}, M. and {Brinkmann}, J. and {Brunner}, R.~J. and
{Burles}, S. and {Carey}, L. and {Castander}, F.~J. and {Connolly}, A.~J. and
{Csabai}, I. and {Doi}, M. and {Finkbeiner}, D. and {Friedman}, S. and
{Frieman}, J.~A. and {Fukugita}, M. and {Gunn}, J.~E. and {Hennessy}, G.~S. and
{Hindsley}, R.~B. and {Hogg}, D.~W. and {Ichikawa}, T. and {Ivezi{\'c}}, {\v Z}. and
{Kent}, S. and {Knapp}, G.~R. and {Lamb}, D.~Q. and {Leger}, R.~F. and
{Long}, D.~C. and {Lupton}, R.~H. and {McKay}, T.~A. and {Meiksin}, A. and
{Merelli}, A. and {Munn}, J.~A. and {Narayanan}, V. and {Newcomb}, M. and
{Nichol}, R.~C. and {Okamura}, S. and {Owen}, R. and {Pier}, J.~R. and
{Pope}, A. and {Postman}, M. and {Quinn}, T. and {Rockosi}, C.~M. and
{Schlegel}, D.~J. and {Schneider}, D.~P. and {Shimasaku}, K. and
{Siegmund}, W.~A. and {Smee}, S. and {Snir}, Y. and {Stoughton}, C. and
{Stubbs}, C. and {Szalay}, A.~S. and {Szokoly}, G.~P. and {Thakar}, A.~R. and
{Tremonti}, C. and {Tucker}, D.~L. and {Uomoto}, A. and {Vanden Berk}, D. and
{Vogeley}, M.~S. and {Waddell}, P. and {Yanny}, B. and {Yasuda}, N. and
{York}, D.~G.},
title = "{The Luminosity Function of Galaxies in SDSS Commissioning Data}",
journal = {AJ},
eprint = {astro-ph/0012085},
keywords = {Galaxies: Fundamental Parameters, Galaxies: Photometry, Galaxies: Statistics},
year = 2001,
month = may,
volume = 121,
pages = {2358-2380},
doi = {10.1086/320405},
adsurl = {http://adsabs.harvard.edu/abs/2001AJ....121.2358B},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2013AA_554A_101B,
author = {{Bouy}, H. and {Bertin}, E. and {Moraux}, E. and {Cuillandre}, J.-C. and {Bouvier}, J. and {Barrado}, D. and {Solano}, E. and {Bayo}, A.},
title = "{Dynamical analysis of nearby clusters. Automated astrometry from the ground: precision proper motions over a wide field}",
......@@ -236,6 +269,20 @@ archivePrefix = "arXiv",
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{1976ApJ_209L_1P,
author = {{Petrosian}, V.},
title = "{Surface brightness and evolution of galaxies}",
journal = {ApJL},
keywords = {Astronomical Models, Galactic Evolution, Luminous Intensity, Red Shift, Surface Properties, Big Bang Cosmology, Cosmology, Hubble Diagram, Iterative Solution, Point Sources},
year = 1976,
month = oct,
volume = 209,
pages = {L1-L5},
doi = {10.1086/182253},
adsurl = {http://adsabs.harvard.edu/abs/1976ApJ...209L...1P},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{1856MNRAS_17_12P,
author = {{Pogson}, N.},
title = "{Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857}",
......@@ -288,6 +335,30 @@ ISSN={1045-9227},
month={Sep}
}
@ARTICLE{2001AJ_122_1104Y,
author = {{Yasuda}, N. and {Fukugita}, M. and {Narayanan}, V.~K. and {Lupton}, R.~H. and
{Strateva}, I. and {Strauss}, M.~A. and {Ivezi{\'c}}, {\v Z}. and
{Kim}, R.~S.~J. and {Hogg}, D.~W. and {Weinberg}, D.~H. and
{Shimasaku}, K. and {Loveday}, J. and {Annis}, J. and {Bahcall}, N.~A. and
{Blanton}, M. and {Brinkmann}, J. and {Brunner}, R.~J. and {Connolly}, A.~J. and
{Csabai}, I. and {Doi}, M. and {Hamabe}, M. and {Ichikawa}, S.-I. and
{Ichikawa}, T. and {Johnston}, D.~E. and {Knapp}, G.~R. and
{Kunszt}, P.~Z. and {Lamb}, D.~Q. and {McKay}, T.~A. and {Munn}, J.~A. and
{Nichol}, R.~C. and {Okamura}, S. and {Schneider}, D.~P. and
{Szokoly}, G.~P. and {Vogeley}, M.~S. and {Watanabe}, M. and
{York}, D.~G.},
title = "{Galaxy Number Counts from the Sloan Digital Sky Survey Commissioning Data}",
journal = {AJ},
eprint = {astro-ph/0105545},
keywords = {Cosmology: Observations},
year = 2001,
month = sep,
volume = 122,
pages = {1104-1124},
doi = {10.1086/322093},
adsurl = {http://adsabs.harvard.edu/abs/2001AJ....122.1104Y},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@INPROCEEDINGS{2002ASPC_281_228B,
author = {{Bertin}, E. and {Mellier}, Y. and {Radovich}, M. and {Missonnier}, G. and
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment