From 657e7d55047d4db21187e4a89c6913f0b59391a2 Mon Sep 17 00:00:00 2001 From: Emmanuel Bertin Date: Fri, 5 Jan 2018 19:36:55 +0100 Subject: [PATCH] Doc: added Petrosian photometry quantities in catalog parameter list. Doc: added description of aperture FLUXERR in photometry section. --- doc/src/Param.rst | 5 ++++ doc/src/Photom.rst | 62 +++++++++++++++++++++------------------------- 2 files changed, 33 insertions(+), 34 deletions(-) diff --git a/doc/src/Param.rst b/doc/src/Param.rst index a1ce15c..9b17bae 100644 --- a/doc/src/Param.rst +++ b/doc/src/Param.rst @@ -124,6 +124,11 @@ of their meaning. _`MAG_AUTO`, magnitude, :ref:`Kron-like automated aperture magnitude ` _`MAGERR_AUTO`, magnitude, :ref:`RMS error estimate for Kron-like automated aperture magnitude ` _`KRON_RADIUS`, ..., :ref:`Kron radius in units of A or B ` + _`FLUX_PETRO`, count, :ref:`Petrosian-like aperture flux ` + _`FLUXERR_PETRO`, count, :ref:`RMS error estimate for Petrosian-like aperture flux ` + _`MAG_PETRO`, magnitude, :ref:`Petrosian-like aperture magnitude ` + _`MAGERR_PETRO`, magnitude, :ref:`RMS error estimate for Petrosian-like aperture magnitude ` + _`PETRO_RADIUS`, ..., :ref:`Petrosian radius in units of A or B ` _`X_IMAGE`, pixel, :ref:`Pixel x coordinate ` of the :ref:`isophotal image centroid ` _`Y_IMAGE`, pixel, :ref:`Pixel y coordinate ` of the :ref:`isophotal image centroid ` _`X_FOCAL`, degree, :ref:`Focal plane x coordinate ` of :ref:`isophotal image centroid ` diff --git a/doc/src/Photom.rst b/doc/src/Photom.rst index 5b7b2e7..b6230e6 100644 --- a/doc/src/Photom.rst +++ b/doc/src/Photom.rst @@ -24,6 +24,15 @@ Magnitude uncertainties (error estimates) are computed using {\tt MAGERR} = \frac{2.5}{\ln 10}\frac{\tt FLUXERR}{\tt FLUX} +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})} + +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 {\tt MAG\_ISOCOR} = {\tt MAG\_ISO} + 2.5 \log_{10} \eta. -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 R_{\rm P}(r) = \frac{\sum_{0.9r < r_i < 1.1r} p^{(d)}_i}{\sum_{r_i < r} p^{(d)}_i} \frac{N_{r_i < r}}{N_{0.9r < r_i < 1.1r}}, 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`: -.. math:: 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 :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}\, \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 :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}`. -- GitLab