The :param:`CLASS_STAR` classifier has been superseded by the :param:`SPREAD_MODEL` estimator (see :ref:`spread_model_def`), which offers better performance by making explicit use of the full, variable |PSF| model.
A good discrimination between stars and galaxies is essential for both galactic and extragalactic statistical studies.
The common assumption is that galaxy images look more extended or fuzzier than those of stars (or |QSO|\ s).
The :param:`CLASS_STAR` classifier relies on a `multilayer feed-forward neural network <https://en.wikipedia.org/wiki/Multilayer_perceptron>`_ trained using `supervised learning <https://en.wikipedia.org/wiki/Supervised_learning>`_ to estimate the *a posteriori* probability :cite:`Richard1991,Saerens2002` of a |SExtractor| detection to be a point source or an extended object.
|SExtractor| provides the :param:`CLASS_STAR` catalog parameter for separating both types of sources.
The :param:`CLASS_STAR` classifier relies on a `multilayer feed-forward neural network <https://en.wikipedia.org/wiki/Multilayer_perceptron>`_ trained using `supervised learning <https://en.wikipedia.org/wiki/Supervised_learning>`_ to estimate the *a posteriori* probability :cite:`Richard1991,Saerens2002` of a |SExtractor| detection to be a point source or an extended object.
Below is a shortened description of the estimator, see :cite:`1996AAS_117_393B` for more details.
The :param:`SPREAD_MODEL` estimator has been developed as a star/galaxy classifier for the DESDM pipeline :cite:`2012SPIE_8451E_0DM`, and has also been used in other surveys :cite:`2012ApJ_757_83D,2013AA_554A_101B`.
:param:`SPREAD_MODEL` indicates which of the best fitting local PSF model resampled at the current position :math:`\tilde{\boldsymbol{\phi}}` (representing a point source) or a slightly ``fuzzier'' resampled model :math:`\tilde{\boldsymbol{G}}` (representing a galaxy) matches best the image data.
Besides PSF and model-fitting flux estimates, |SExtractor| can currently perform four types of flux measurements: isophotal, *corrected-isophotal*, fixed-aperture and *adaptive-aperture*.
Besides |PSF| and :ref:`model-fitting <models_def>` flux estimates, |SExtractor| can currently perform four types of flux measurements: :ref:`isophotal <flux_iso_def>`, :ref:`corrected-isophotal <mag_isocor_def>`, :ref:`fixed-aperture <flux_aper_def>` and :ref:`adaptive-aperture <flux_auto_def>`.
For every :param:`FLUX_` measurement, an error estimate :param:`FLUXERR_`, a magnitude :param:`MAG_` and a magnitude error estimate :param:`MAGERR_` are also available.
The ``MAG_ZEROPOINT`` configuration parameter sets the magnitude zero-point
of magnitudes:
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...
@@ -25,30 +25,33 @@ Magnitude uncertainties (error estimates) are computed using
.. _flux_iso_def:
Isophotal flux
--------------
Isophotal flux: :param:`FLUX_ISO`
---------------------------------
:param:`FLUX_ISO` is computed simply by integrating pixels values 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 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:`MAG_ISOCOR` can be considered as a quick-and-dirty way for retrieving the fraction of flux lost by isophotal magnitudes.
Although their use is now deprecated, they have been kept in |SExtractor| v2.x and above for compatibility with |SExtractor| v1.
If we make the assumption that the intensity profiles of the faint objects recorded in the frame are roughly Gaussian because of atmospheric blurring, then the fraction :math:`\eta = \frac{I_{\rm iso}}{I_{\rm tot}}` of the total flux enclosed within a particular isophote reads :cite:`1990MNRAS_246_433M`:
.. note::
Corrected isophotal magnitudes are now deprecated; they remain in |SExtractor| v2.x for compatibility with |SExtractor| v1.
:param:`MAG_ISOCOR` magnitudes are a quick-and-dirty way of retrieving the fraction of flux lost by isophotal magnitudes.
If one makes the assumption that the intensity profiles of faint objects recorded in the frame are roughly Gaussian because of atmospheric blurring, then the fraction :math:`\eta = \frac{F_{\rm iso}}{F_{\rm tot}}` of the total flux enclosed within a particular isophote reads :cite:`1990MNRAS_246_433M`:
where :math:`A` is the area and :math:`t` the threshold related to this isophote.
:eq:isocor is not analytically invertible, but a good approximation to :math:`\eta` (error :math:`< 10^{-2}` for :math:`\eta > 0.4`) can be done with the second-order polynomial fit:
...
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@@ -56,57 +59,71 @@ where :math:`A` is the area and :math:`t` the threshold related to this isophote
Clearly this cheap correction works best with stars; and although it is shown to give tolerably accurate results with most disk galaxies, it fails with ellipticals because of the broader wings of their profiles.
Clearly this cheap correction works best with stars; and although it gives reasonably accurate results with most disk galaxies, it breaks down for ellipticals because of the broader wings in the profiles.
.. _flux_aper_def:
Fixed-aperture flux
-------------------
:param:`FLUX_APER` estimates the flux above the background within 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 “normal” 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 ``PHOTOM_APERTURES``.
Fixed-aperture flux: :param:`FLUX_APER`
---------------------------------------
:param:`FLUX_APER` estimates the flux above the background within 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.
.. _flux_auto_def:
Automatic aperture flux
-----------------------
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`.
#. An elliptical aperture is defined whose elongation :math:`\epsilon` and position angle :math:`\theta` are defined by second order moments of the object’s light distribution. The ellipse is scaled to :math:`R_{\rm max}.\sigma_{\rm iso}`
(:math:`6 \sigma_{\rm iso}`, which corresponds roughly to 2 isophotal
“radii”).
#. Within this aperture the “first moment” is computed:
#. 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:
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`.
:param:`FLUX_AUTO` is the flux above the background summed over the Kron ellipse:
.. math::
:label: flux_auto
{\tt FLUX\_AUTO} = \sum_{i\in\cal K} p_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`):
: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 their magnitude.
This picture remains unchanged if one considers an ellipse with :math:`\epsilon\, k r_1` and :math:`k r_1 / \epsilon` as principal axes.
: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%.
When Signal to Noise is low, it may appear that an erroneously small aperture is taken by the algorithm.
That’s why we have to bound the smallest accessible aperture to :math:`R_{\rm min}` (typically :math:`R_{\rm min} = 3 - 4\,\sigma_{\rm iso}`).
The user has full control over the parameters :math:`k` and :math:`R_{\rm min}` through the configuration parameters ``PHOT_AUTOPARAMS``; by default, ``PHOT_AUTOPARAMS`` is set to ``2.5,3.5``.
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``.
.. figure:: ps/simlostflux.ps
..
.. figure:: ps/simlostflux.ps
:alt: Flux lost (expressed as a mean magnitude difference) with different faint-object photometry techniques as a function of total magnitude (see text). Only isolated galaxies (no blends) of the simulations have been considered.
:width: 15.00000cm
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@@ -117,17 +134,18 @@ The user has full control over the parameters :math:`k` and :math:`R_{\rm min}`
.. hint::
Aperture magnitudes are sensitive to crowding.
In |SExtractor|v1, :param:`MAG_AUTO` measurements were not very robust in that respect.
In |SExtractor|v1, :param:`MAG_AUTO` measurements were not very robust in that respect.
It was therefore suggested to replace the aperture magnitude by the corrected-isophotal one when an object is too close to its neighbors (2 isophotal radii for instance).
This was done automatically when using the :param:`MAG_BEST` magnitude: :math:`{\tt MAG\_BEST} = {\tt MAG\_AUTO}` when it is sure that no neighbor can bias :param:`MAG_AUTO` by more than 10%, and :math:`{\tt MAG\_BEST} = {\tt MAG\_ISOCOR}` otherwise.
This was done automatically when using the :param:`MAG_BEST` magnitude: :param:`MAG_BEST`\=\ :param:`MAG_AUTO` when it is sure that no neighbor can bias :param:`MAG_AUTO` by more than 10%, and :math:`{\tt MAG\_BEST} = {\tt MAG\_ISOCOR}` otherwise.
Experience showed that the :param:`MAG_ISOCOR` and :param:`MAG_AUTO` magnitude would loose about the same fraction of flux on stars or compact galaxy profiles: around 0.06 % for default extraction parameters.
The use of :param:`MAG_BEST` is now deprecated as :param:`MAG_AUTO` measurements are much more robust in versions 2.x of |SExtractor|.
The first improvement is a crude subtraction of all the neighbors that have been detected around the measured source (``MASK_TYPE BLANK`` option).
The second improvement is an automatic correction of parts of the aperture that are suspected to be contaminated by a neighbor.
This is done by mirroring the opposite, cleaner side of the measurement ellipse if available (``MASK_TYPE CORRECT`` option, which is also the default).
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.
..
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.
Photographic photometry
...
...
@@ -177,14 +195,15 @@ where :math:`I(x,y)` is the contribution of pixel :math:`(x,y)` to the
total flux (Eq. [eq:dtoi]). ``GAIN`` is ignored in ``PHOTO`` mode.
Background
----------
..
Background
----------
Background is the last point relative to photometry. The assumption made in §[chap:backest] — that the "local" background associated to an object can be interpolated from the global background map — is no longer valid in crowded regions.
An example is a globular cluster superimposed to a bulge of galaxy.
SExtractor offers the possibility to estimate locally the background used to compute magnitudes.
When this option is switched on (``BACKPHOTO_TYPE LOCAL`` instead of ``GLOBAL``), the "photometric" background is estimated within a "rectangular annulus" around the isophotal limits of the object.
The thickness of the annulus (in pixels) can be specified by the user with ``BACKPHOTO_SIZE``. A typical value is ``BACKPHOTO_SIZE``=``24``.
Background is the last point relative to photometry. The assumption made in §[chap:backest] — that the "local" background associated to an object can be interpolated from the global background map — is no longer valid in crowded regions.
An example is a globular cluster superimposed to a bulge of galaxy.
SExtractor offers the possibility to estimate locally the background used to compute magnitudes.
When this option is switched on (``BACKPHOTO_TYPE LOCAL`` instead of ``GLOBAL``), the "photometric" background is estimated within a "rectangular annulus" around the isophotal limits of the object.
The thickness of the annulus (in pixels) can be specified by the user with ``BACKPHOTO_SIZE``. A typical value is ``BACKPHOTO_SIZE``=``24``.
.. [#error]
It is important to note that this error provides a lower limit, since
The following parameters are derived from the spatial distribution :math:`\cal S` of pixels detected above the analysis threshold (see :ref:`description<isophotal_measurements>`).
The following quantities are derived from the spatial distribution :math:`\cal S` of pixels detected above the analysis threshold (see :ref:`description<isophotal_measurements>`).
.. important::
Unless otherwise noted, pixel values :math:`I_i` are taken from the (filtered) detection image.
Unless otherwise noted, in this section pixel values :math:`p_i` above the local background are taken from the (filtered) detection image.
.. note::
Unless otherwise noted, all parameter names given below are only prefixes.
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@@ -25,12 +25,12 @@ These coordinates define two corners of a rectangle which encloses the detected
.. math::
:label: xminymax
\begin{aligned}
\begin{eqnarray}
{\tt XMIN} & = & \min_{i \in {\cal S}} x_i,\\
{\tt YMIN} & = & \min_{i \in {\cal S}} y_i,\\
{\tt XMAX} & = & \max_{i \in {\cal S}} x_i,\\
{\tt YMAX} & = & \max_{i \in {\cal S}} y_i,
\end{aligned}
\end{eqnarray}
where :math:`x_i` and :math:`y_i` are respectively the x-coordinate and y-coordinate of pixel :math:`i`.
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...
@@ -45,12 +45,12 @@ Barycenter coordinates generally define the position of the “center” of a so
:param:`A` and :param:`B` can be computed directly from the 2nd-order moments, using the following equations derived from :eq:`varproj` after some algebra:
Note that :param:`A` and :param:`B` are exactly halves the :math:`a` and :math:`b` parameters computed by the COSMOS image analyser :cite:`1980SPIE_264_208S`.
Actually, :math:`a` and :math:`b` are defined in :cite:`1980SPIE_264_208S` as the semi-major and semi-minor axes of an elliptical shape with constant surface brightness, which would have the same 2nd-order moments as the analyzed object.
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@@ -176,10 +172,10 @@ These parameters [#elongation]_ are directly derived from :param:`A` and :param:
where :math:`{\sigma_B}_i` is the local background noise and :math:`g_i` the local gain — conversion factor — for pixel :math:`i` (see :ref:`effect_of_weighting` for more details). Semi-major axis :param:`ERRA`, semi-minor axis :param:`ERRB`, and position angle :param:`ERRTHETA` of the :math:`1\sigma` position error ellipse are computed from the covariance matrix exactly like for :ref:`basic shape parameters<shape_iso_def>`:
