# public documents.sextractor_doc

## [/] [measure_photom.tex] - Rev 40

\section{Photometry}
\label{photometry}
{\sc SExtractor} has currently the possibility to compute four types of
magnitude: isophotal, {\em \index{corrected-isophotal} corrected-isophotal}, fixed-aperture and
{\em \index{adaptive-aperture} adaptive-aperture}. For all magnitudes, an additive zero-point''
correction can be applied with the {\tt MAG\_ZEROPOINT} keyword.
Note that for each {\tt MAG\_XXXX}, a \index{magnitude error} magnitude error estimate {\tt MAGERR\_XXXX},
a linear {\tt FLUX\_XXXX} measurement and its error estimate {\tt FLUXERR\_XXXX}
are also available.

\paragraph{Isophotal magnitudes} ({\tt MAG\_ISO}) are computed simply, using the
detection \index{threshold} threshold as the lowest isophote.

\paragraph{Corrected \index{isophotal magnitudes} isophotal magnitudes} ({\tt MAG\_ISOCOR}) can be considered
as a quick-and-dirty way for retrieving the fraction of flux lost by \index{isophotal magnitudes} isophotal magnitudes.
Although their use is now deprecated, they have been kept in {\sc SExtractor} 2.x and
above for compatibility with {\sc SExtractor} 1.
If we make the assumption that the intensity profiles of
the faint objects recorded on the plate are roughly Gaussian because
of \index{atmospheric blurring} atmospheric blurring, then the fraction $\eta = \frac{I_{\rm iso}}{I_{\rm tot}}$ of the total flux enclosed within a
$$\left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{I_{\rm iso}} \label{eqisocor}$$
where $A$ is the \index{area} area and $t$ the \index{threshold} threshold related to
this isophote. Eq. (\ref{eqisocor}) is not analytically invertible,
but a good approximation to $\eta$ (error $< 10^{-2}$ for $\eta > 0.4$) can be done with the second-order polynomial fit:
$$\eta \approx 1 - 0.1961 \frac{A\,t}{I_{\rm iso}} - 0.7512 \left( \frac{A\,t}{I_{\rm iso}}\right)^2 \label{eq:isocor}$$
A total'' magnitude $m_{\rm tot}$ estimate is then
$$m_{\rm tot} = m_{\rm iso} + 2.5 \log \eta$$
Clearly this cheap correction works best with \index{stars} 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.

\paragraph{Fixed-aperture magnitudes} ({\tt MAG\_APER}) estimate the
flux above the background within a circular aperture. The
diameter of the aperture in pixels ({\tt PHOTOM\_APERTURES}) is supplied
by the user (in fact it does not need to be an integer since each
normal'' pixel is subdivided in $5\times 5$ sub-pixels before measuring the flux
within the aperture). If {\tt MAG\_APER} is provided as a vector {\tt MAG\_APER[}$n${\tt ]},
at least $n$ \index{apertures} apertures must be specified with {\tt PHOTOM\_APERTURES}.

\paragraph{Automatic \index{aperture magnitudes} aperture magnitudes}
\label{chap:mag_auto}
({\tt MAG\_AUTO}) provides an estimate of the total magnitude'' by integrating
the source flux within an adaptively scaled aperture.
{\sc SExtractor}'s automatic aperture photometry routine is inspired by Kron's
first moment'' algorithm (1980). (1) We define an elliptical
aperture whose elongation $\epsilon$ and position angle $\theta$ are
defined by second order \index{moments} moments of the object's light distribution.
The ellipse is scaled to $R_{\rm max}.\sigma_{\rm iso}$ ($6 \sigma_{\rm iso}$,
which corresponds roughly to 2 isophotal radii'').
(2) Within this aperture we compute the first moment'':
$$r_1 = \frac{\sum r\,I(r)}{\sum I(r)}$$
Kron (1980) and Infante (1987) have shown that for \index{stars} stars and galaxy
profiles convolved with Gaussian seeing, $\ge 90\%$ of the flux is
expected to lie within a circular aperture of radius $k r_1$ if $k = 2$, almost independently of their magnitude. This picture remains
unchanged if we consider an ellipse with $\epsilon\, k r_1$ and $k r_1 / \epsilon$ as principal axes. $k = 2$ defines a sort of balance between
systematic and random errors. By choosing a larger $k = 2.5$, the \index{mean} 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 $R_{\rm min}$ (typically $R_{\rm min} = 3 - 4\, \sigma_{\rm iso}$). The user has full control over the parameters $k$
and $R_{\rm min}$ through the configuration parameters {\tt PHOT\_AUTOPARAMS};
by default, {\tt PHOT\_AUTOPARAMS} is set to {\tt 2.5,3.5}.

%------------------------------ Fig. phot -----------------------------
\begin{figure}[htbp]
\centerline{\includegraphics[width=15cm]{ps/simlostflux.ps}}
\caption{
Flux lost (expressed as a \index{mean} 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.
\gam{Add to figure Petrosian photometry and \index{mode} model-fit photometry.}
}
\label{figphot}
\end{figure}

Aperture magnitudes are sensitive to \index{crowding} crowding. In {\sc SExtractor}~1, {\tt MAG\_AUTO}
measurements were not very robust in that respect. It was therefore suggested to replace the
aperture magnitude by the \index{corrected-isophotal} corrected-isophotal one when an object is too close to its
\index{neighbour} \index{neighbours} neighbours (2 isophotal radii for instance).
This was done automatically when using the {\tt MAG\_BEST} magnitude:
${\tt MAG\_BEST} = {\tt MAG\_AUTO}$ when it is
sure that no \index{neighbour} neighbour can bias {\tt MAG\_AUTO} by more than 10\%,
or ${\tt MAG\_BEST} = {\tt MAG\_ISOCOR}$ otherwise.
Experience showed that the {\tt MAG\_ISOCOR} and {\tt MAG\_AUTO} magnitude would loose about
the same fraction of flux on \index{stars} stars or compact galaxy profiles: around 0.06 \% for default
extraction parameters. The use of {\tt MAG\_BEST} is now deprecated as {\tt MAG\_AUTO}
measurements are much more robust in versions 2.x of {\sc SExtractor}. The first improvement
is a crude subtraction of all the \index{neighbour} \index{neighbours} neighbours which have been detected around the measured source
The second improvement is an automatic correction of parts of the aperture that are suspected
to be contaminated by a \index{neighbour} neighbour. This is done by mirroring the opposite, cleaner side of the measurement
ellipse if available (the {\tt MASK\_TYPE CORRECT} option, which is also the default).
Figure \ref{figphot} shows the \index{mean} mean loss of flux measured with
isophotal (threshold $= 24.4\ \mbox{\rm magnitude\,arsec}^{-2}$), corrected
isophotal and automatic aperture photometries for simulated galaxy
$B_J$ on a typical Schmidt-survey plate \index{image} image.
The automatic adaptive aperture photometry leads to the lowest loss of flux.
\gam{Consider also Petrosian and \index{mode} model.}

\paragraph{Photographic photometry}
In {\tt DETECT\_TYPE PHOTO} \index{mode} mode, {\sc SExtractor}
assumes that the response of the detector, over the dynamic range of
the \index{image} image, is logarithmic. This is generally a good approximation for
photographic density on \index{deep exposures} deep exposures. Photometric procedures
described above remain unchanged, except that for each pixel we apply
first the transformation
$$I = I_0\,10^{D/\gamma} \ , \label{eq:dtoi}$$
where $\gamma$ ({\tt MAG\_GAMMA}) is the contrast index of the
emulsion, $D$ the original pixel value from the background-subtracted
\index{image} image, and $I_0$ is computed from the magnitude \index{zero-point} zero-point $m_0$:
$$I_0 = \frac{\gamma}{\ln 10} \,10^{-0.4\, m_0} \ .$$
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 Bertin 1996 for
details).

\paragraph{Errors on magnitude}
An estimate of the error\footnote{It is important to note that this
error provides a lower limit, since it does not take into account
the (complex) uncertainty on the \index{local background} local background estimate.} is
available for each type of magnitude. It is computed through
$$\Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}$$
where $A$ is the \index{area} area (in pixels) over which the total flux $F$ (in
ADU) is summed, $\sigma$ the \index{standard deviation} standard deviation of noise (in ADU)
estimated from the background, and g the detector \index{gain} gain ({\tt GAIN}
parameter\footnote{Setting {\tt GAIN} to 0 in the \index{configuration file} configuration file
is equivalent to $g = +\infty$} , in $e^- / \mbox{ADU}$). For
\index{corrected-isophotal} corrected-isophotal magnitudes, a term, derived from Eq.
on the correction itself.

In {\tt DETECT\_TYPE PHOTO} \index{mode} 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, we can write:
$$\Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\, \frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)} =2.5\,{\sigma\over \gamma}\, \frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}$$
where $I(x,y)$ is the contribution of pixel $(x,y)$ to the total flux
(Eq. \ref{eq:dtoi}). \gam{Which equality do we keep or both?}
The {\tt GAIN} is ignored in {\tt PHOTO} \index{mode} mode.

\paragraph{Background} is the last point relative to photometry.
The assumption made in \S \ref{chap:backest} --- that the
local'' background associated to an object can be interpolated
from the global \index{background map} background map --- is no longer valid
in crowded regions. An example is a \index{globular cluster} globular cluster superimposed
on a \index{bulge} bulge of galaxy. {\sc SExtractor} offers the possibility to
estimate locally the background used to compute magnitudes.
When this option is switched on ({\tt BACKPHOTO\_TYPE LOCAL} instead of
{\tt 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 {\tt BACKPHOTO\_SIZE}. A typical value is
{\tt BACKPHOTO\_SIZE}=24.