Doc: Moved FLUX_ISO and CLASS_STAR to isophotal measurement section (which is...

  PositionWin

  Photom

  Model

  ClassStar

.. [#thresh] For some isophotal measurements pixel values also have to exceed the local analysis threshold set with ``ANALYSIS_THRESH``.

.. [#psf_models] PSF models be computed using the |PSFEx|_ package.

The measurement (or catalog) parameter file

===========================================

In addition to the configuration file detailed above, |SExtractor| requires a file containing the list of measurements ("catalog parameters") that will be listed in the output catalog for every detection. This allows the software to compute only the measurements that are needed. The name of this catalog parameter file is traditionally suffixed with ``.param``, and must be specified using the :param:`PARAMETERS_NAME` config parameter. The full set of parameters can be queried with the command

In addition to the configuration file detailed above, |SExtractor| requires a file containing the list of measurements ("catalog parameters") that will be listed in the output catalog for every detection. This allows the software to compute only the measurements that are needed. The name of this catalog parameter file is traditionally suffixed with :file:`.param`, and must be specified using the :param:`PARAMETERS_NAME` config parameter. The full set of parameters can be queried with the command

.. code-block:: console

   {\tt MAG} = \left\{\begin{array}{ll}

   \mathrm{MAG\_ZEROPOINT} - 2.5 \log_{10} {\tt FLUX}\ &\mbox{if } {\tt FLUX} > 0\\

   99.0\ &\mbox{otherwise},

   99.0\ &\mbox{otherwise}.

   \end{array}\right.

Flux and magnitude uncertainties

   99.0\ &\mbox{otherwise}.

   \end{array}\right.

Setting ``PIXEL_SCALE`` to 0 instructs |SExtractor| to compute the pixel scale from the local Jacobian of the astrometric deprojection, based on the celestial |WCS| info in the |FITS| image header, if available.

Setting ``PIXEL_SCALE`` to 0 instructs |SExtractor| to compute the pixel scale from the local `Jacobian <https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant>`_ of the astrometric deprojection, based on the celestial |WCS|_ info :cite:`2002AA_395_1077C` in the |FITS| image header, if available.

.. _coord_suffix:

.. _world_coords:

:param:`_WORLD`

  Measurements are given in so-called “world coordinates”, converted from pixel coordinates using the local Jacobian of the transformation between both systems. This requires World Coordinate System (|WCS|_) metadata :cite:`2002AA_395_1061G` to be present in the FITS image header(s). Position angles are counted from the first world axis, positive towards the second world axis.

  Measurements are given in so-called “world coordinates”, converted from pixel coordinates using the local Jacobian of the transformation between both systems. This requires |WCS| metadata :cite:`2002AA_395_1061G` to be present in the FITS image header(s). Position angles are counted from the first world axis, positive towards the second world axis.

.. _sky_coords:

.. _focal_coords:

:param:`_FOCAL`

  Measurements are given in “focal plane coordinates”, which are actually projected coordinates, in degrees. This requires World Coordinate System (|WCS|_) metadata :cite:`2002AA_395_1061G` to be present in the FITS image header(s). The computation of focal plane coordinates from pixel coordinates is similar to that of :param:`_SKY` coordinates except that they are not de-projected and remain Cartesian. The main purpose of focal plane coordinates is to provide a common system for all the chips in a mosaic camera.

  Measurements are given in “focal plane coordinates”, which are actually projected coordinates, in degrees. This requires |WCS| metadata :cite:`2002AA_395_1061G` to be present in the FITS image header(s). The computation of focal plane coordinates from pixel coordinates is similar to that of :param:`_SKY` coordinates except that they are not de-projected and remain Cartesian. The main purpose of focal plane coordinates is to provide a common system for all the chips in a mosaic camera.

.. note::

  Conversion to :param:`_FOCAL` coordinates is available only for a limited subset of measurements.

  _`CXX_IMAGE`, pixel\ :sup:`-2`, :ref:`Isophotal image Cxx ellipse parameter <ellipse_iso_def>`

  _`CYY_IMAGE`, pixel\ :sup:`-2`, :ref:`Isophotal image Cyy ellipse parameter <ellipse_iso_def>`

  _`CXY_IMAGE`, pixel\ :sup:`-2`, :ref:`Isophotal image Cxy ellipse parameter <ellipse_iso_def>`

  _`ISOAREAF_IMAGE`, pixel\ :sup:`2`, :ref:`Isophotal area (filtered) above Detection threshold <isoarea_def>`

  _`ISOAREA_IMAGE`, pixel\ :sup:`2`, :ref:`Isophotal area above Analysis threshold <isoarea_def>`

  _`X2WIN_IMAGE`, pixel\ :sup:`2`, :ref:`Windowed image 2nd order central moment in x <moments_win_def>`

  _`Y2WIN_IMAGE`, pixel\ :sup:`2`, :ref:`Windowed image 2nd order central moment in y <moments_win_def>`

  _`XYWIN_IMAGE`, pixel\ :sup:`2`, :ref:`Windowed image 2nd order central cross-moment in xy <moments_win_def>`

.. _photometry:

Photometry

==========

Aperture photometry

===================

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>`.

Besides :ref:`isophotal <flux_iso_def>`, |PSF| and :ref:`model-fitting <models_def>` flux estimates, |SExtractor| can currently perform two types of flux measurements: :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: see :ref:`fluxes_and_magnitudes`.

An estimate of the error is available for each type of flux.

  {\tt FLUXERR} = \sqrt{\sum_{i\in{\cal A}}\, (\sigma_i^2 + \frac{p_i}{g_i})}

where :math:`{\cal A}` is the set of pixels defining the photometric aperture, and :math:`\sigma_i`, :math:`p_i`, :math:`g_i` respectively the standard deviation of noise (in ADU) estimated from the local background, :math:`p_i` the measurement image pixel value subtracted from the background, and :math:`g_i` the effective detector gain in :math:`e^- / \mbox{ADU}` at pixel :math:`i`. Note that this error estimate provides a lower limit of the true uncertainty, as it only takes into account photon and detector noise.

.. _flux_iso_def:

Isophotal flux: :param:`FLUX_ISO`

---------------------------------

: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

   {\tt FLUX\_ISO} = F_{\rm iso} = \sum_{i \in {\cal D}} p_i.

.. _mag_isocor_def:

Corrected isophotal magnitude: :param:`MAG_ISOCOR`

--------------------------------------------------

.. 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`:

.. math::

  :label: isocor

   \left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{F_{\rm iso}},

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:

.. math::

 :label: isocor2

   \eta \approx 1 - 0.1961 \frac{A\,t}{F_{\rm iso}} - 0.7512

   \left( \frac{A\,t}{F_{\rm iso}}\right)^2.

A “total” magnitude :param:`MAG_ISOCOR` estimate is then

.. math::

 :label: magisocor

   {\tt MAG\_ISOCOR} = {\tt MAG\_ISO} + 2.5 \log_{10} \eta.

Clearly the :param:`MAG_ISOCOR` 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.

where :math:`{\cal A}` is the set of pixels defining the photometric aperture, and :math:`\sigma_i`, :math:`p_i`, :math:`g_i` respectively the standard deviation of noise (in ADU) estimated from the local background, :math:`p_i` the measurement image pixel value subtracted from the background, and :math:`g_i` the effective detector gain in :math:`e^- / \mbox{ADU}` at pixel :math:`i`.

Note that this error estimate provides a lower limit of the true uncertainty, as it only takes into account photon and detector noise.

.. _flux_aper_def: