| Line 1... |
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\section{Photometry}
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\section{Photometry}
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\label{photometry}
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\label{photometry}
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{\sc SExtractor} has currently the possibility to compute four types of
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{\sc SExtractor} has currently the possibility to compute four types of
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magnitude: isophotal, {\em corrected-isophotal}, fixed-aperture and
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magnitude: isophotal, {\em \index{corrected-isophotal} corrected-isophotal}, fixed-aperture and
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{\em adaptive-aperture}. For all magnitudes, an additive ``zero-point''
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{\em \index{adaptive-aperture} adaptive-aperture}. For all magnitudes, an additive ``zero-point''
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correction can be applied with the {\tt MAG\_ZEROPOINT} keyword.
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correction can be applied with the {\tt MAG\_ZEROPOINT} keyword.
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Note that for each {\tt MAG\_XXXX}, a magnitude error estimate {\tt MAGERR\_XXXX},
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Note that for each {\tt MAG\_XXXX}, a \index{magnitude error} magnitude error estimate {\tt MAGERR\_XXXX},
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a linear {\tt FLUX\_XXXX} measurement and its error estimate {\tt FLUXERR\_XXXX}
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a linear {\tt FLUX\_XXXX} measurement and its error estimate {\tt FLUXERR\_XXXX}
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are also available.
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are also available.
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\paragraph{Isophotal magnitudes} ({\tt MAG\_ISO}) are computed simply, using the
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\paragraph{Isophotal magnitudes} ({\tt MAG\_ISO}) are computed simply, using the
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detection threshold as the lowest isophote.
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detection \index{threshold} threshold as the lowest isophote.
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\paragraph{Corrected isophotal magnitudes} ({\tt MAG\_ISOCOR}) can be considered
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\paragraph{Corrected \index{isophotal magnitudes} isophotal magnitudes} ({\tt MAG\_ISOCOR}) can be considered
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as a quick-and-dirty way for retrieving the fraction of flux lost by isophotal magnitudes.
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as a quick-and-dirty way for retrieving the fraction of flux lost by \index{isophotal magnitudes} isophotal magnitudes.
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Although their use is now deprecated, they have been kept in {\sc SExtractor} 2.x and
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Although their use is now deprecated, they have been kept in {\sc SExtractor} 2.x and
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above for compatibility with {\sc SExtractor} 1.
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above for compatibility with {\sc SExtractor} 1.
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If we make the assumption that the intensity profiles of
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If we make the assumption that the intensity profiles of
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the faint objects recorded on the plate are roughly Gaussian because
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the faint objects recorded on the plate are roughly Gaussian because
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of atmospheric blurring, then the fraction $\eta =
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of \index{atmospheric blurring} atmospheric blurring, then the fraction $\eta =
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\frac{I_{\rm iso}}{I_{\rm tot}}$ of the total flux enclosed within a
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\frac{I_{\rm iso}}{I_{\rm tot}}$ of the total flux enclosed within a
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particular isophote reads (see Maddox~et~al.~1990):
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particular isophote reads (see Maddox~et~al.~1990):
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\begin{equation}
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\begin{equation}
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\left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{I_{\rm iso}} \label{eqisocor}
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\left(1-\frac{1}{\eta}\right ) \ln (1-\eta) = \frac{A\,t}{I_{\rm iso}} \label{eqisocor}
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\end{equation}
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\end{equation}
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where $A$ is the area and $t$ the threshold related to
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where $A$ is the \index{area} area and $t$ the \index{threshold} threshold related to
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this isophote. Eq. (\ref{eqisocor}) is not analytically invertible,
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this isophote. Eq. (\ref{eqisocor}) is not analytically invertible,
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but a good approximation to $\eta$ (error $< 10^{-2}$ for $\eta >
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but a good approximation to $\eta$ (error $< 10^{-2}$ for $\eta >
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0.4$) can be done with the second-order polynomial fit:
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0.4$) can be done with the second-order polynomial fit:
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\begin{equation} \eta \approx 1 - 0.1961 \frac{A\,t}{I_{\rm iso}} - 0.7512
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\begin{equation} \eta \approx 1 - 0.1961 \frac{A\,t}{I_{\rm iso}} - 0.7512
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\left( \frac{A\,t}{I_{\rm iso}}\right)^2 \label{eq:isocor} \end{equation}
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\left( \frac{A\,t}{I_{\rm iso}}\right)^2 \label{eq:isocor} \end{equation}
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A ``total'' magnitude $m_{\rm tot}$ estimate is then
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A ``total'' magnitude $m_{\rm tot}$ estimate is then
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\begin{equation}
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\begin{equation}
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m_{\rm tot} = m_{\rm iso} + 2.5 \log \eta
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m_{\rm tot} = m_{\rm iso} + 2.5 \log \eta
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\end{equation}
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\end{equation}
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Clearly this cheap correction works best with stars; and although it
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Clearly this cheap correction works best with \index{stars} stars; and although it
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is shown to give tolerably accurate results with most disk galaxies,
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is shown to give tolerably accurate results with most disk galaxies,
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it fails with ellipticals because of the broader wings of their
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it fails with ellipticals because of the broader wings of their
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profiles.
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profiles.
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\paragraph{Fixed-aperture magnitudes} ({\tt MAG\_APER}) estimate the
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\paragraph{Fixed-aperture magnitudes} ({\tt MAG\_APER}) estimate the
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flux above the background within a circular aperture. The
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flux above the background within a circular aperture. The
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diameter of the aperture in pixels ({\tt PHOTOM\_APERTURES}) is supplied
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diameter of the aperture in pixels ({\tt PHOTOM\_APERTURES}) is supplied
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by the user (in fact it does not need to be an integer since each
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by the user (in fact it does not need to be an integer since each
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``normal'' pixel is subdivided in $5\times 5$ sub-pixels before measuring the flux
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``normal'' pixel is subdivided in $5\times 5$ sub-pixels before measuring the flux
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within the aperture). If {\tt MAG\_APER} is provided as a vector {\tt MAG\_APER[}$n${\tt ]},
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within the aperture). If {\tt MAG\_APER} is provided as a vector {\tt MAG\_APER[}$n${\tt ]},
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at least $n$ apertures must be specified with {\tt PHOTOM\_APERTURES}.
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at least $n$ \index{apertures} apertures must be specified with {\tt PHOTOM\_APERTURES}.
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\paragraph{Automatic aperture magnitudes}
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\paragraph{Automatic \index{aperture magnitudes} aperture magnitudes}
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\label{chap:mag_auto}
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\label{chap:mag_auto}
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({\tt MAG\_AUTO}) provides an estimate of the ``total magnitude'' by integrating
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({\tt MAG\_AUTO}) provides an estimate of the ``total magnitude'' by integrating
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the source flux within an adaptively scaled aperture.
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the source flux within an adaptively scaled aperture.
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{\sc SExtractor}'s automatic aperture photometry routine is inspired by Kron's
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{\sc SExtractor}'s automatic aperture photometry routine is inspired by Kron's
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``first moment'' algorithm (1980). (1) We define an elliptical
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``first moment'' algorithm (1980). (1) We define an elliptical
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aperture whose elongation $\epsilon$ and position angle $\theta$ are
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aperture whose elongation $\epsilon$ and position angle $\theta$ are
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defined by second order moments of the object's light distribution.
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defined by second order \index{moments} moments of the object's light distribution.
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The ellipse is scaled to $R_{\rm max}.\sigma_{\rm iso}$ ($6 \sigma_{\rm iso}$,
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The ellipse is scaled to $R_{\rm max}.\sigma_{\rm iso}$ ($6 \sigma_{\rm iso}$,
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which corresponds roughly to 2 isophotal ``radii'').
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which corresponds roughly to 2 isophotal ``radii'').
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(2) Within this aperture we compute the ``first moment'':
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(2) Within this aperture we compute the ``first moment'':
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\begin{equation}
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\begin{equation}
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r_1 = \frac{\sum r\,I(r)}{\sum I(r)}
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r_1 = \frac{\sum r\,I(r)}{\sum I(r)}
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\end{equation}
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\end{equation}
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Kron (1980) and Infante (1987) have shown that for stars and galaxy
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Kron (1980) and Infante (1987) have shown that for \index{stars} stars and galaxy
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profiles convolved with Gaussian seeing, $\ge 90\%$ of the flux is
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profiles convolved with Gaussian seeing, $\ge 90\%$ of the flux is
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expected to lie within a circular aperture of radius $k r_1$ if $k =
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expected to lie within a circular aperture of radius $k r_1$ if $k =
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2$, almost independently of their magnitude. This picture remains
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2$, almost independently of their magnitude. This picture remains
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unchanged if we consider an ellipse with $\epsilon\, k r_1$ and $k r_1 /
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unchanged if we consider an ellipse with $\epsilon\, k r_1$ and $k r_1 /
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\epsilon$ as principal axes. $k = 2$ defines a sort of balance between
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\epsilon$ as principal axes. $k = 2$ defines a sort of balance between
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systematic and random errors. By choosing a larger $k = 2.5$, the mean
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systematic and random errors. By choosing a larger $k = 2.5$, the \index{mean} mean
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fraction of flux lost drops from about 10\% to 6\%. When Signal to
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fraction of flux lost drops from about 10\% to 6\%. When Signal to
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Noise is low, it may appear that an erroneously small aperture is
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Noise is low, it may appear that an erroneously small aperture is
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taken by the algorithm. That's why we have to bound the smallest
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taken by the algorithm. That's why we have to bound the smallest
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accessible aperture to $R_{\rm min}$ (typically $R_{\rm min} = 3 - 4\,
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accessible aperture to $R_{\rm min}$ (typically $R_{\rm min} = 3 - 4\,
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\sigma_{\rm iso}$). The user has full control over the parameters $k$
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\sigma_{\rm iso}$). The user has full control over the parameters $k$
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| Line 78... |
Line 78... |
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%------------------------------ Fig. phot -----------------------------
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%------------------------------ Fig. phot -----------------------------
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\begin{figure}[htbp]
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\begin{figure}[htbp]
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\centerline{\includegraphics[width=15cm]{ps/simlostflux.ps}}
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\centerline{\includegraphics[width=15cm]{ps/simlostflux.ps}}
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\caption{
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\caption{
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Flux lost (expressed as a mean magnitude difference) with different
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Flux lost (expressed as a \index{mean} mean magnitude difference) with different
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faint-object photometry techniques as a function of total magnitude (see text).
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faint-object photometry techniques as a function of total magnitude (see text).
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Only isolated galaxies (no blends) of the simulations have been
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Only isolated galaxies (no blends) of the simulations have been
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considered.
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considered.
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\gam{Add to figure Petrosian photometry and model-fit photometry.}
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\gam{Add to figure Petrosian photometry and \index{mode} model-fit photometry.}
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}
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}
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\label{figphot}
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\label{figphot}
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\end{figure}
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\end{figure}
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Aperture magnitudes are sensitive to crowding. In {\sc SExtractor}~1, {\tt MAG\_AUTO}
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Aperture magnitudes are sensitive to \index{crowding} crowding. In {\sc SExtractor}~1, {\tt MAG\_AUTO}
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measurements were not very robust in that respect. It was therefore suggested to replace the
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measurements were not very robust in that respect. It was therefore suggested to replace the
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aperture magnitude by the corrected-isophotal one when an object is too close to its
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aperture magnitude by the \index{corrected-isophotal} corrected-isophotal one when an object is too close to its
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neighbours (2 isophotal radii for instance).
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\index{neighbour} \index{neighbours} neighbours (2 isophotal radii for instance).
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This was done automatically when using the {\tt MAG\_BEST} magnitude:
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This was done automatically when using the {\tt MAG\_BEST} magnitude:
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${\tt MAG\_BEST} = {\tt MAG\_AUTO}$ when it is
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${\tt MAG\_BEST} = {\tt MAG\_AUTO}$ when it is
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sure that no neighbour can bias {\tt MAG\_AUTO} by more than 10\%,
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sure that no \index{neighbour} neighbour can bias {\tt MAG\_AUTO} by more than 10\%,
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or ${\tt MAG\_BEST} = {\tt MAG\_ISOCOR}$ otherwise.
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or ${\tt MAG\_BEST} = {\tt MAG\_ISOCOR}$ otherwise.
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Experience showed that the {\tt MAG\_ISOCOR} and {\tt MAG\_AUTO} magnitude would loose about
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Experience showed that the {\tt MAG\_ISOCOR} and {\tt MAG\_AUTO} magnitude would loose about
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the same fraction of flux on stars or compact galaxy profiles: around 0.06 \% for default
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the same fraction of flux on \index{stars} stars or compact galaxy profiles: around 0.06 \% for default
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extraction parameters. The use of {\tt MAG\_BEST} is now deprecated as {\tt MAG\_AUTO}
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extraction parameters. The use of {\tt MAG\_BEST} is now deprecated as {\tt MAG\_AUTO}
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measurements are much more robust in versions 2.x of {\sc SExtractor}. The first improvement
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measurements are much more robust in versions 2.x of {\sc SExtractor}. The first improvement
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is a crude subtraction of all the neighbours which have been detected around the measured source
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is a crude subtraction of all the \index{neighbour} \index{neighbours} neighbours which have been detected around the measured source
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(the {\tt MASK\_TYPE BLANK} option).
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(the {\tt MASK\_TYPE BLANK} option).
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The second improvement is an automatic correction of parts of the aperture that are suspected
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The second improvement is an automatic correction of parts of the aperture that are suspected
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to be contaminated by a neighbour. This is done by mirroring the opposite, cleaner side of the measurement
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to be contaminated by a \index{neighbour} neighbour. This is done by mirroring the opposite, cleaner side of the measurement
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ellipse if available (the {\tt MASK\_TYPE CORRECT} option, which is also the default).
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ellipse if available (the {\tt MASK\_TYPE CORRECT} option, which is also the default).
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Figure \ref{figphot} shows the mean loss of flux measured with
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Figure \ref{figphot} shows the \index{mean} mean loss of flux measured with
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isophotal (threshold $= 24.4\ \mbox{\rm magnitude\,arsec}^{-2}$), corrected
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isophotal (threshold $= 24.4\ \mbox{\rm magnitude\,arsec}^{-2}$), corrected
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isophotal and automatic aperture photometries for simulated galaxy
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isophotal and automatic aperture photometries for simulated galaxy
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$B_J$ on a typical Schmidt-survey plate image.
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$B_J$ on a typical Schmidt-survey plate \index{image} image.
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The automatic adaptive aperture photometry leads to the lowest loss of flux.
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The automatic adaptive aperture photometry leads to the lowest loss of flux.
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\gam{Consider also Petrosian and model.}
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\gam{Consider also Petrosian and \index{mode} model.}
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\paragraph{Photographic photometry}
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\paragraph{Photographic photometry}
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In {\tt DETECT\_TYPE PHOTO} mode, {\sc SExtractor}
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In {\tt DETECT\_TYPE PHOTO} \index{mode} mode, {\sc SExtractor}
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assumes that the response of the detector, over the dynamic range of
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assumes that the response of the detector, over the dynamic range of
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the image, is logarithmic. This is generally a good approximation for
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the \index{image} image, is logarithmic. This is generally a good approximation for
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photographic density on deep exposures. Photometric procedures
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photographic density on \index{deep exposures} deep exposures. Photometric procedures
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described above remain unchanged, except that for each pixel we apply
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described above remain unchanged, except that for each pixel we apply
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first the transformation
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first the transformation
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\begin{equation}
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\begin{equation}
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I = I_0\,10^{D/\gamma} \ ,
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I = I_0\,10^{D/\gamma} \ ,
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\label{eq:dtoi}
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\label{eq:dtoi}
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\end{equation}
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\end{equation}
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where $\gamma$ ({\tt MAG\_GAMMA}) is the contrast index of the
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where $\gamma$ ({\tt MAG\_GAMMA}) is the contrast index of the
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emulsion, $D$ the original pixel value from the background-subtracted
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emulsion, $D$ the original pixel value from the background-subtracted
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image, and $I_0$ is computed from the magnitude zero-point $m_0$:
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\index{image} image, and $I_0$ is computed from the magnitude \index{zero-point} zero-point $m_0$:
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\begin{equation}
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\begin{equation}
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I_0 = \frac{\gamma}{\ln 10} \,10^{-0.4\, m_0} \ .
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I_0 = \frac{\gamma}{\ln 10} \,10^{-0.4\, m_0} \ .
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\end{equation}
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\end{equation}
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One advantage of using a density-to-intensity transformation relative
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One advantage of using a density-to-intensity transformation relative
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to the local sky background is that it corrects (to some extent)
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to the local sky background is that it corrects (to some extent)
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| Line 136... |
Line 136... |
details).
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details).
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\paragraph{Errors on magnitude}
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\paragraph{Errors on magnitude}
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An estimate of the error\footnote{It is important to note that this
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An estimate of the error\footnote{It is important to note that this
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error provides a lower limit, since it does not take into account
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error provides a lower limit, since it does not take into account
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the (complex) uncertainty on the local background estimate.} is
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the (complex) uncertainty on the \index{local background} local background estimate.} is
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available for each type of magnitude. It is computed through
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available for each type of magnitude. It is computed through
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\begin{equation}
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\begin{equation}
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\Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}
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\Delta m = 1.0857\, \frac{\sqrt{A\,\sigma^2 + F/g}}{F}
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\end{equation}
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\end{equation}
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where $A$ is the area (in pixels) over which the total flux $F$ (in
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where $A$ is the \index{area} area (in pixels) over which the total flux $F$ (in
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ADU) is summed, $\sigma$ the standard deviation of noise (in ADU)
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ADU) is summed, $\sigma$ the \index{standard deviation} standard deviation of noise (in ADU)
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estimated from the background, and g the detector gain ({\tt GAIN}
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estimated from the background, and g the detector \index{gain} gain ({\tt GAIN}
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parameter\footnote{Setting {\tt GAIN} to 0 in the configuration file
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parameter\footnote{Setting {\tt GAIN} to 0 in the \index{configuration file} configuration file
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is equivalent to $g = +\infty$} , in $e^- / \mbox{ADU}$). For
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is equivalent to $g = +\infty$} , in $e^- / \mbox{ADU}$). For
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corrected-isophotal magnitudes, a term, derived from Eq.
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\index{corrected-isophotal} corrected-isophotal magnitudes, a term, derived from Eq.
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\ref{eq:isocor} is quadratically added to take into account the error
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\ref{eq:isocor} is quadratically added to take into account the error
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on the correction itself.
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on the correction itself.
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In {\tt DETECT\_TYPE PHOTO} mode, things are slightly more complex. Making the
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In {\tt DETECT\_TYPE PHOTO} \index{mode} mode, things are slightly more complex. Making the
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assumption that plate-noise is the major contributor to photometric
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assumption that plate-noise is the major contributor to photometric
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errors, and that it is roughly constant in density, we can write:
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errors, and that it is roughly constant in density, we can write:
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\begin{equation}
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\begin{equation}
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\Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\,
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\Delta m = 1.0857 \,\ln 10\, {\sigma\over \gamma}\,
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\frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
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\frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
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=2.5\,{\sigma\over \gamma}\,
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=2.5\,{\sigma\over \gamma}\,
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\frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
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\frac{\sqrt{\sum_{x,y}{I^2(x,y)}}}{\sum_{x,y}I(x,y)}
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\end{equation}
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\end{equation}
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where $I(x,y)$ is the contribution of pixel $(x,y)$ to the total flux
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where $I(x,y)$ is the contribution of pixel $(x,y)$ to the total flux
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(Eq. \ref{eq:dtoi}). \gam{Which equality do we keep or both?}
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(Eq. \ref{eq:dtoi}). \gam{Which equality do we keep or both?}
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The {\tt GAIN} is ignored in {\tt PHOTO} mode.
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The {\tt GAIN} is ignored in {\tt PHOTO} \index{mode} mode.
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\paragraph{Background} is the last point relative to photometry.
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\paragraph{Background} is the last point relative to photometry.
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The assumption made in \S \ref{chap:backest} --- that the
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The assumption made in \S \ref{chap:backest} --- that the
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``local'' background associated to an object can be interpolated
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``local'' background associated to an object can be interpolated
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from the global background map --- is no longer valid
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from the global \index{background map} background map --- is no longer valid
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in crowded regions. An example is a globular cluster superimposed
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in crowded regions. An example is a \index{globular cluster} globular cluster superimposed
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on a bulge of galaxy. {\sc SExtractor} offers the possibility to
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on a \index{bulge} bulge of galaxy. {\sc SExtractor} offers the possibility to
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estimate locally the background used to compute magnitudes.
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estimate locally the background used to compute magnitudes.
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When this option is switched on ({\tt BACKPHOTO\_TYPE LOCAL} instead of
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When this option is switched on ({\tt BACKPHOTO\_TYPE LOCAL} instead of
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{\tt GLOBAL}), the ``photometric'' background is
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{\tt GLOBAL}), the ``photometric'' background is
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estimated within a ``rectangular annulus'' around the isophotal
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estimated within a ``rectangular annulus'' around the isophotal
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limits of the object. The thickness of the annulus (in pixels)
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limits of the object. The thickness of the annulus (in pixels)
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