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:
...
...
@@ -71,7 +80,7 @@ A “total” magnitude :param:`MAG_ISOCOR` estimate is then
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.
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.
.. _flux_aper_def:
...
...
@@ -175,14 +184,14 @@ Similar to :param:`FLUX_AUTO`, :param:`FLUX_PETRO` provides an estimate of the
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
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 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 quantity :math:`N_{\rm P}r_{\rm P}` is called *Petrosian radius* in |SExtractor|\ [#petro_radius]_ and is provided 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}`.
...
...
@@ -204,46 +213,37 @@ This is generally a good approximation for photographic density on deep exposure
Photometric procedures described above remain unchanged, except that for each pixel we apply first the transformation
.. math::
:label: dtoi
I = I_0\,10^{D/\gamma} \ ,
\label{eq:dtoi}
I = I_0\,10^{D/\gamma},
where :math:`\gamma` (``MAG_GAMMA``) is the contrast index of the emulsion, :math:`D` the original pixel value from the background-subtracted image, and :math:`I_0` is computed from the magnitude zero-point :math:`m_0`:
One advantage of using a density-to-intensity transformation relative to the local sky background is that it corrects (to some extent) large-scale inhomogeneities in sensitivity (see :cite:`1996PhDT_68B` for details).
Magnitude uncertainties
-----------------------
.. math::
:label: m0toi0
An estimate of the error [#error]_ is available for each type of magnitude.
It is computed through
I_0 = \frac{\gamma}{\ln 10} \,10^{-0.4\, m_0}.
.. math:: \Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}
One advantage of using a density-to-intensity transformation relative to the local sky background is that it corrects (to some extent) large-scale inhomogeneities in sensitivity (see :cite:`1996PhDT_68B` for details).
where :math:`A` is the area (in pixels) over which the total flux
:math:`F` (in ADU) is summed, :math:`\sigma` the standard deviation of
noise (in ADU) estimated from the background, and g the detector gain
(GAIN parameter [#gain]_ , in :math:`e^- / \mbox{ADU}`).
For corrected-isophotal magnitudes, a term, derived from Eq. [eq:isocor] is quadratically added to take into account the error on the correction itself.
..
Magnitude uncertainties
-----------------------
In ``DETECT_TYPE PHOTO`` mode, things are slightly more complex.
Making the assumption that plate-noise is the major contributor to photometric errors, and that it is roughly constant in density, one can write:
In ``DETECT_TYPE PHOTO`` mode, things are slightly more complex.
Making the assumption that plate-noise is the major contributor to photometric errors, and that it is roughly constant in density, one can write:
.. math::
.. math::
:label: magerr_photo
\Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\,
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.
where :math:`I(x,y)` is the contribution of pixel :math:`(x,y)` to the total flux :eq:`dtoi`. ``GAIN`` is ignored in ``PHOTO`` mode.
..
Background
----------
...
...
@@ -253,12 +253,6 @@ total flux (Eq. [eq:dtoi]). ``GAIN`` is ignored in ``PHOTO`` mode.
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
it does not take into account the (complex) uncertainty on the local
background estimate.
.. [#gain]
Setting GAIN to 0 in the configuration file is equivalent to
:math:`g = +\infty`
.. [#petro_radius]
Some authors prefer to define the Petrosian radius as :math:`r_{\rm P}` instead of :math:`N_{\rm P}r_{\rm P}`.
