Doc: Fixed a few things and removed duplicates.

position, or shape, several variants of the same measurement are

available:

.. _fluxes_and_magnitudes:

Fluxes and magnitudes

~~~~~~~~~~~~~~~~~~~~~

Fluxes may be expressed in linear (ADU) units or as Pogson :cite:`1856MNRAS_17_12P` magnitudes. Flux measurements in ADUs are prefixed with :param:`FLUX_`, for example: :param:`FLUX_AUTO`, :param:`FLUX_ISO`, etc. Magnitudes are prefixed with :param:`MAG_` e.g., :param:`MAG_AUTO`, :param:`MAG_ISO`, ... In

|SExtractor| the magnitude :math:`m` of a source is derived from the flux

:math:`f`:

Fluxes may be expressed in counts (|ADU|\ s) or as Pogson :cite:`1856MNRAS_17_12P` magnitudes.

Flux measurements in |ADU|\ s are prefixed with :param:`FLUX_`, for example: :param:`FLUX_AUTO`, :param:`FLUX_ISO`, etc.

Magnitudes are prefixed with :param:`MAG_` e.g., :param:`MAG_AUTO`, :param:`MAG_ISO`, ...

The ``MAG_ZEROPOINT`` configuration parameter sets the magnitude zero-point of magnitudes:

.. math::

 :label: mag

   m = \left\{\begin{array}{ll}

   m_{ZP} -2.5 \log_{10} f\ &\mbox{if } f > 0\\

   99.0 &\mbox{otherwise},

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

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

   99.0\ &\mbox{otherwise},

   \end{array}\right.

where :math:`m_{ZP}` is the magnitude zero-point set with the

``MAG_ZEROPOINT`` configuration parameter.

Flux and magnitude uncertainties

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Flux uncertainties follow a scheme similar to that of fluxes. Flux uncertainties are prefixed with :param:`FLUXERR_`, as in :param:`FLUXERR_AUTO` or :param:`FLUXERR_ISO`. Magnitude uncertainties start with :param:`MAGERR_`, for instance: :param:`MAGERR_AUTO`, :param:`MAGERR_ISO`,... Magnitude uncertainties :math:`\sigma_m` are derived from the estimated 1-\ :math:`\sigma` flux error :math:`\sigma_f`:

Flux uncertainties (error estimates) follow a scheme similar to that of fluxes.

They are prefixed with :param:`FLUXERR_`, as in :param:`FLUXERR_AUTO` or :param:`FLUXERR_ISO`.

Magnitude uncertainties start with :param:`MAGERR_`, for instance: :param:`MAGERR_AUTO`, :param:`MAGERR_ISO`,...

They are computed using

.. math::

 :label: magerr

   \sigma_m = \left\{\begin{array}{ll}

   (2.5/\ln 10) (\sigma_f/f)\ &\mbox{if } f > 0\\

   99.0 &\mbox{otherwise}.

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

   \frac{2.5}{\ln 10}({\tt FLUXERR}/{\tt FLUX})\ &\mbox{if } {\tt FLUX} > 0\\

   99.0\ &\mbox{otherwise}.

   \end{array}\right.

Pixel values and Surface brightnesses

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Pixel values (averaged or not) :math:`p` are expressed in counts (|ADU|\ s).

There is no specific prefix (:param:`THRESHOLD`, :param:`BACKGROUND`, :param:`FLUX_MAX`, etc.).

Surface brightnesses are given in magnitudes per square arcsecond, and prefixed with :param:`MU_` e.g., :param:`MU_THRESHOLD`, :param:`MU_MAX`, ...

The conversion to surface brightness relies on the ``MAG_ZEROPOINT`` and the ``PIXEL_SCALE`` configuration parameters:

.. math::

 :label: mu

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

   \mathrm{MAG\_ZEROPOINT} - 2.5 \log_{10} (p \times {\rm PIXEL\_SCALE}\,^2)\ &\mbox{if } p > 0\\

   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.

.. _coord_suffix:

Positions and shapes

==========

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:

.. math::

 :label: mag

   {\tt MAG} = \mathrm{MAG\_ZEROPOINT} - 2.5 \log_{10} {\tt FLUX}

Magnitude uncertainties (error estimates) are computed using

.. math::

 :label: magerr

   {\tt MAGERR} = \frac{2.5}{\ln 10}\frac{\tt FLUXERR}{\tt FLUX}

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.

For aperture fluxes, the flux uncertainty is computed using

.. math::

  :label: fluxerr

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

  {\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.

  {\tt FLUX\_PETRO} = \sum_{i\in\cal P} p_i.

.. [#petro_radius]

   Some authors prefer to define the Petrosian radius as :math:`r_{\rm P}` instead of :math:`N_{\rm P}r_{\rm P}`.

Photographic photometry

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

In both ``LOCAL`` and ``GLOBAL`` modes, the :param:`BACKGROUND` catalog parameter gives the value of the background estimated at the centroid of the object.

.. [#petro_radius]

   Some authors prefer to define the Petrosian radius as :math:`r_{\rm P}` instead of :math:`N_{\rm P}r_{\rm P}`.

.. |ADU| replace:: :abbr:`ADU (Analog-to-Digital Unit)`

.. _ADU: https://en.wikipedia.org/wiki/Analog-to-digital_converter

.. |ATLAS| replace:: :program:`ATLAS`

.. _ATLAS: http://math-atlas.sourceforge.net