# public documents.sextractor_doc

## [/] [measure_photom.tex] - Diff between revs 22 and 25

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\section{Photometry}
\section{Photometry}
\label{photometry}
\label{photometry}
{\sc SExtractor} has currently the possibility to compute four types of
{\sc SExtractor} has currently the possibility to compute four types of
magnitude: isophotal, {\em corrected-isophotal}, fixed-aperture and
magnitude: isophotal, {\em \index{corrected-isophotal} corrected-isophotal}, fixed-aperture and
{\em adaptive-aperture}. For all magnitudes, an additive zero-point''
{\em \index{adaptive-aperture} adaptive-aperture}. For all magnitudes, an additive zero-point''
correction can be applied with the {\tt MAG\_ZEROPOINT} keyword.
correction can be applied with the {\tt MAG\_ZEROPOINT} keyword.
Note that for each {\tt MAG\_XXXX}, a magnitude error estimate {\tt MAGERR\_XXXX},
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}
a linear {\tt FLUX\_XXXX} measurement and its error estimate {\tt FLUXERR\_XXXX}
are also available.
are also available.
 
 
\paragraph{Isophotal magnitudes} ({\tt MAG\_ISO}) are computed simply, using the
\paragraph{Isophotal magnitudes} ({\tt MAG\_ISO}) are computed simply, using the
detection threshold as the lowest isophote.
detection \index{threshold} threshold as the lowest isophote.
 
 
\paragraph{Corrected isophotal magnitudes} ({\tt MAG\_ISOCOR}) can be considered
\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 isophotal magnitudes.
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
Although their use is now deprecated, they have been kept in {\sc SExtractor} 2.x and
above for compatibility with {\sc SExtractor} 1.
above for compatibility with {\sc SExtractor} 1.
If we make the assumption that the intensity profiles of
If we make the assumption that the intensity profiles of
the faint objects recorded on the plate are roughly Gaussian because
the faint objects recorded on the plate are roughly Gaussian because
of atmospheric blurring, then the fraction $\eta = of \index{atmospheric blurring} atmospheric blurring, then the fraction$\eta =
\frac{I_{\rm iso}}{I_{\rm tot}}$of the total flux enclosed within a \frac{I_{\rm iso}}{I_{\rm tot}}$ of the total flux enclosed within a
particular isophote reads (see Maddox~et~al.~1990):
particular isophote reads (see Maddox~et~al.~1990):
\left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{I_{\rm iso}} \label{eqisocor}
\left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{I_{\rm iso}} \label{eqisocor}
where $A$ is the area and $t$ the threshold related to
where $A$ is the \index{area} area and $t$ the \index{threshold} threshold related to
this isophote. Eq. (\ref{eqisocor}) is not analytically invertible,
this isophote. Eq. (\ref{eqisocor}) is not analytically invertible,
but a good approximation to $\eta$ (error $< 10^{-2}$ for $\eta > but a good approximation to$\eta$(error$< 10^{-2}$for$\eta >
0.4$) can be done with the second-order polynomial fit: 0.4$) can be done with the second-order polynomial fit:
 \eta \approx 1 - 0.1961 \frac{A\,t}{I_{\rm iso}} - 0.7512
 \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} 
\left( \frac{A\,t}{I_{\rm iso}}\right)^2 \label{eq:isocor} 
A total'' magnitude $m_{\rm tot}$ estimate is then
A total'' magnitude $m_{\rm tot}$ estimate is then
  m_{\rm tot} = m_{\rm iso} + 2.5 \log \eta
  m_{\rm tot} = m_{\rm iso} + 2.5 \log \eta
Clearly this cheap correction works best with stars; and although it
Clearly this cheap correction works best with \index{stars} stars; and although it
is shown to give tolerably accurate results with most disk galaxies,
is shown to give tolerably accurate results with most disk galaxies,
it fails with ellipticals because of the broader wings of their
it fails with ellipticals because of the broader wings of their
profiles.
profiles.
 
 
\paragraph{Fixed-aperture magnitudes} ({\tt MAG\_APER}) estimate the
\paragraph{Fixed-aperture magnitudes} ({\tt MAG\_APER}) estimate the
flux above the background within a circular aperture. The
flux above the background within a circular aperture. The
diameter of the aperture in pixels ({\tt PHOTOM\_APERTURES}) is supplied
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
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
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 ]},
within the aperture). If {\tt MAG\_APER} is provided as a vector {\tt MAG\_APER[}$n${\tt ]},
at least $n$ apertures must be specified with {\tt PHOTOM\_APERTURES}.
at least $n$ \index{apertures} apertures must be specified with {\tt PHOTOM\_APERTURES}.
 
 
\paragraph{Automatic aperture magnitudes}
\paragraph{Automatic \index{aperture magnitudes} aperture magnitudes}
\label{chap:mag_auto}
\label{chap:mag_auto}
({\tt MAG\_AUTO}) provides an estimate of the total magnitude'' by integrating
({\tt MAG\_AUTO}) provides an estimate of the total magnitude'' by integrating
the source flux within an adaptively scaled aperture.
the source flux within an adaptively scaled aperture.
{\sc SExtractor}'s automatic aperture photometry routine is inspired by Kron's
{\sc SExtractor}'s automatic aperture photometry routine is inspired by Kron's
first moment'' algorithm (1980). (1) We define an elliptical
first moment'' algorithm (1980). (1) We define an elliptical
aperture whose elongation $\epsilon$ and position angle $\theta$ are
aperture whose elongation $\epsilon$ and position angle $\theta$ are
defined by second order moments of the object's light distribution.
defined by second order \index{moments} moments of the object's light distribution.
The ellipse is scaled to $R_{\rm max}.\sigma_{\rm iso}$ ($6 \sigma_{\rm iso}$,
The ellipse is scaled to $R_{\rm max}.\sigma_{\rm iso}$ ($6 \sigma_{\rm iso}$,
which corresponds roughly to 2 isophotal radii'').
which corresponds roughly to 2 isophotal radii'').
(2) Within this aperture we compute the first moment'':
(2) Within this aperture we compute the first moment'':
      r_1 = \frac{\sum r\,I(r)}{\sum I(r)}
      r_1 = \frac{\sum r\,I(r)}{\sum I(r)}
Kron (1980) and Infante (1987) have shown that for stars and galaxy
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
profiles convolved with Gaussian seeing, $\ge 90\%$ of the flux is
expected to lie within a circular aperture of radius $k r_1$ if $k = expected to lie within a circular aperture of radius$k r_1$if$k =
2$, almost independently of their magnitude. This picture remains 2$, almost independently of their magnitude. This picture remains
unchanged if we consider an ellipse with $\epsilon\, k r_1$ and $k r_1 / unchanged if we consider an ellipse with$\epsilon\, k r_1$and$k r_1 /
\epsilon$as principal axes.$k = 2$defines a sort of balance between \epsilon$ as principal axes. $k = 2$ defines a sort of balance between
systematic and random errors. By choosing a larger $k = 2.5$, the mean
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
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
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
taken by the algorithm. That's why we have to bound the smallest
accessible aperture to $R_{\rm min}$ (typically $R_{\rm min} = 3 - 4\, accessible aperture to$R_{\rm min}$(typically$R_{\rm min} = 3 - 4\,
\sigma_{\rm iso}$). The user has full control over the parameters$k$ \sigma_{\rm iso}$). The user has full control over the parameters $k$
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%------------------------------ Fig. phot -----------------------------
%------------------------------ Fig. phot -----------------------------
\begin{figure}[htbp]
\begin{figure}[htbp]
\centerline{\includegraphics[width=15cm]{ps/simlostflux.ps}}
\centerline{\includegraphics[width=15cm]{ps/simlostflux.ps}}
\caption{
\caption{
              Flux lost (expressed as a mean magnitude difference) with different
              Flux lost (expressed as a \index{mean} mean magnitude difference) with different
              faint-object photometry techniques as a function of total magnitude (see text).
              faint-object photometry techniques as a function of total magnitude (see text).
              Only isolated galaxies (no blends) of the simulations have been
              Only isolated galaxies (no blends) of the simulations have been
              considered.
              considered.
\gam{Add to figure Petrosian photometry and model-fit photometry.}
\gam{Add to figure Petrosian photometry and \index{mode} model-fit photometry.}
              }
              }
\label{figphot}
\label{figphot}
\end{figure}
\end{figure}
 
 
Aperture magnitudes are sensitive to crowding. In {\sc SExtractor}~1, {\tt MAG\_AUTO}
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
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
aperture magnitude by the \index{corrected-isophotal} corrected-isophotal one when an object is too close to its
neighbours (2 isophotal radii for instance).
\index{neighbour} \index{neighbours} neighbours (2 isophotal radii for instance).
This was done automatically when using the {\tt MAG\_BEST} magnitude:
This was done automatically when using the {\tt MAG\_BEST} magnitude:
${\tt MAG\_BEST} = {\tt MAG\_AUTO}$ when it is
${\tt MAG\_BEST} = {\tt MAG\_AUTO}$ when it is
sure that no neighbour can bias {\tt MAG\_AUTO} by more than 10\%,
sure that no \index{neighbour} neighbour can bias {\tt MAG\_AUTO} by more than 10\%,
or ${\tt MAG\_BEST} = {\tt MAG\_ISOCOR}$ otherwise.
or ${\tt MAG\_BEST} = {\tt MAG\_ISOCOR}$ otherwise.
Experience showed that the {\tt MAG\_ISOCOR} and {\tt MAG\_AUTO} magnitude would loose about
Experience showed that the {\tt MAG\_ISOCOR} and {\tt MAG\_AUTO} magnitude would loose about
the same fraction of flux on stars or compact galaxy profiles: around 0.06 \% for default
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}
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
measurements are much more robust in versions 2.x of {\sc SExtractor}. The first improvement
is a crude subtraction of all the neighbours which have been detected around the measured source
is a crude subtraction of all the \index{neighbour} \index{neighbours} neighbours which have been detected around the measured source
(the {\tt MASK\_TYPE BLANK} option).
(the {\tt MASK\_TYPE BLANK} option).
The second improvement is an automatic correction of parts of the aperture that are suspected
The second improvement is an automatic correction of parts of the aperture that are suspected
to be contaminated by a neighbour. This is done by mirroring the opposite, cleaner side of the measurement
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).
ellipse if available (the {\tt MASK\_TYPE CORRECT} option, which is also the default).
Figure \ref{figphot} shows the mean loss of flux measured with
Figure \ref{figphot} shows the \index{mean} mean loss of flux measured with
isophotal (threshold $= 24.4\ \mbox{\rm magnitude\,arsec}^{-2}$), corrected
isophotal (threshold $= 24.4\ \mbox{\rm magnitude\,arsec}^{-2}$), corrected
isophotal and automatic aperture photometries for simulated galaxy
isophotal and automatic aperture photometries for simulated galaxy
$B_J$ on a typical Schmidt-survey plate image.
$B_J$ on a typical Schmidt-survey plate \index{image} image.
The automatic adaptive aperture photometry leads to the lowest loss of flux.
The automatic adaptive aperture photometry leads to the lowest loss of flux.
\gam{Consider also Petrosian and model.}
\gam{Consider also Petrosian and \index{mode} model.}
 
 
\paragraph{Photographic photometry}
\paragraph{Photographic photometry}
In {\tt DETECT\_TYPE PHOTO} mode, {\sc SExtractor}
In {\tt DETECT\_TYPE PHOTO} \index{mode} mode, {\sc SExtractor}
assumes that the response of the detector, over the dynamic range of
assumes that the response of the detector, over the dynamic range of
the image, is logarithmic. This is generally a good approximation for
the \index{image} image, is logarithmic. This is generally a good approximation for
photographic density on deep exposures. Photometric procedures
photographic density on \index{deep exposures} deep exposures. Photometric procedures
described above remain unchanged, except that for each pixel we apply
described above remain unchanged, except that for each pixel we apply
first the transformation
first the transformation
  I = I_0\,10^{D/\gamma} \ ,
  I = I_0\,10^{D/\gamma} \ ,
\label{eq:dtoi}
\label{eq:dtoi}
where $\gamma$ ({\tt MAG\_GAMMA}) is the contrast index of the
where $\gamma$ ({\tt MAG\_GAMMA}) is the contrast index of the
emulsion, $D$ the original pixel value from the background-subtracted
emulsion, $D$ the original pixel value from the background-subtracted
image, and $I_0$ is computed from the magnitude zero-point $m_0$:
\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} \ .
  I_0 = \frac{\gamma}{\ln 10} \,10^{-0.4\, m_0} \ .
One advantage of using a density-to-intensity transformation relative
One advantage of using a density-to-intensity transformation relative
to the local sky background is that it corrects (to some extent)
to the local sky background is that it corrects (to some extent)
Line 136... Line 136...
details).
details).
 
 
\paragraph{Errors on magnitude}
\paragraph{Errors on magnitude}
An estimate of the error\footnote{It is important to note that this
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
  error provides a lower limit, since it does not take into account
the (complex) uncertainty on the local background estimate.} is
the (complex) uncertainty on the \index{local background} local background estimate.} is
available for each type of magnitude. It is computed through
available for each type of magnitude. It is computed through
\Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}
\Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}
where $A$ is the area (in pixels) over which the total flux $F$ (in
where $A$ is the \index{area} area (in pixels) over which the total flux $F$ (in
ADU) is summed, $\sigma$ the standard deviation of noise (in ADU)
ADU) is summed, $\sigma$ the \index{standard deviation} standard deviation of noise (in ADU)
estimated from the background, and g the detector gain ({\tt GAIN}
estimated from the background, and g the detector \index{gain} gain ({\tt GAIN}
parameter\footnote{Setting {\tt GAIN} to 0 in the configuration file
parameter\footnote{Setting {\tt GAIN} to 0 in the \index{configuration file} configuration file
is equivalent to $g = +\infty$} , in $e^- / \mbox{ADU}$). For
is equivalent to $g = +\infty$} , in $e^- / \mbox{ADU}$). For
corrected-isophotal magnitudes, a term, derived from Eq.
\index{corrected-isophotal} corrected-isophotal magnitudes, a term, derived from Eq.
\ref{eq:isocor} is quadratically added to take into account the error
\ref{eq:isocor} is quadratically added to take into account the error
on the correction itself.
on the correction itself.
 
 
In {\tt DETECT\_TYPE PHOTO} mode, things are slightly more complex. Making the
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
assumption that plate-noise is the major contributor to photometric
errors, and that it is roughly constant in density, we can write:
errors, and that it is roughly constant in density, we can write:
  \Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\,
  \Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\,
  \frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
  \frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
=2.5\,{\sigma\over \gamma}\,
=2.5\,{\sigma\over \gamma}\,
\frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
\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
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?}
(Eq. \ref{eq:dtoi}). \gam{Which equality do we keep or both?}
The {\tt GAIN} is ignored in {\tt PHOTO} mode.
The {\tt GAIN} is ignored in {\tt PHOTO} \index{mode} mode.
 
 
\paragraph{Background} is the last point relative to photometry.
\paragraph{Background} is the last point relative to photometry.
The assumption made in \S \ref{chap:backest} --- that the
The assumption made in \S \ref{chap:backest} --- that the
local'' background associated to an object can be interpolated
local'' background associated to an object can be interpolated
from the global background map --- is no longer valid
from the global \index{background map} background map --- is no longer valid
in crowded regions. An example is a globular cluster superimposed
in crowded regions. An example is a \index{globular cluster} globular cluster superimposed
on a bulge of galaxy. {\sc SExtractor} offers the possibility to
on a \index{bulge} bulge of galaxy. {\sc SExtractor} offers the possibility to
estimate locally the background used to compute magnitudes.
estimate locally the background used to compute magnitudes.
When this option is switched on ({\tt BACKPHOTO\_TYPE LOCAL} instead of
When this option is switched on ({\tt BACKPHOTO\_TYPE LOCAL} instead of
{\tt GLOBAL}), the photometric'' background is
{\tt GLOBAL}), the photometric'' background is
estimated within a rectangular annulus'' around the isophotal
estimated within a rectangular annulus'' around the isophotal
limits of the object. The thickness of the annulus (in pixels)
limits of the object. The thickness of the annulus (in pixels)