diff --git a/doc/src/Photom.rst b/doc/src/Photom.rst index c7ac789dbae416fab4f812173b47543ba3567c71..5b7b2e79ac81fce9c3033437244e86c9a2518a1f 100644 --- a/doc/src/Photom.rst +++ b/doc/src/Photom.rst @@ -30,7 +30,7 @@ Magnitude uncertainties (error estimates) are computed using Isophotal flux: :param:`FLUX_ISO` --------------------------------- -:param:`FLUX_ISO` is computed simply by integrating pixels values :math:`p_i` within the detection footprint, with the additional constraint that the background-subtracted, filtered value of detection image pixels must exceed the threshold set with the ``ANALYSIS_THRESH`` configuration parameter: +:param:`FLUX_ISO` is computed simply by integrating the background-subracted pixels values :math:`p_i` from the measurement image within the detection footprint, with the additional constraint that the background-subtracted, filtered value of detection image pixels must exceed the threshold set with the ``ANALYSIS_THRESH`` configuration parameter: .. math:: :label: fluxiso @@ -78,7 +78,7 @@ Clearly this cheap correction works best with stars; and although it gives reaso Fixed-aperture flux: :param:`FLUX_APER` --------------------------------------- -:param:`FLUX_APER` estimates the flux above the background within a circular aperture. +:param:`FLUX_APER` estimates the flux from the measurement image above the background inside a circular aperture. The diameter of the aperture in pixels is defined by the ``PHOTOM_APERTURES`` configuration parameter. It does not have to be an integer: each "regular" pixel is subdivided in :math:`5\times 5` sub-pixels before measuring the flux within the aperture. If :param:`FLUX_APER` is provided as a vector :param:`FLUX_APER[n]`, at least :math:`n` apertures must be specified with the ``PHOTOM_APERTURES`` configuration parameter. @@ -89,40 +89,49 @@ Automatic aperture flux: :param:`FLUX_AUTO` ------------------------------------------- :param:`FLUX_AUTO` provides an estimate of the “total flux” by integrating pixel values within an adaptively scaled aperture. -|SExtractor|’s automatic aperture photometry routine is inspired by Kron’s “first moment” algorithm :cite:`1980ApJS_43_305K`. +|SExtractor|’s automatic aperture photometry routine derives from Kron’s “first moment” algorithm :cite:`1980ApJS_43_305K`: -#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution `, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`. - The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis). -#. Within this elliptical aperture :math:`{\cal E}`, Kron's "first moment" is computed: +#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution `, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`. +#. The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis). +#. Inside this elliptical aperture :math:`{\cal E}`, an analog of Kron's "first moment" is computed: .. math:: - :label: kron_r1 - - r_1 = \frac{\sum_{i\in\cal E} d_i\,p_i}{\sum_{i\in\cal E} p_i}, + :label: kron_radius -where :math:`d_i` and :math:`p_i` are respectively the Euclidean distance to the (isophotal) centroid and the pixel value above the local background at image pixel :math:`i`. -:cite:`1980ApJS_43_305K` and :cite:`1987AA_183_177I` have shown that for stars and galaxy profiles convolved with Gaussian seeing, :math:`\ge 90\%` of the flux is expected to lie within a circular aperture of radius :math:`k r_1` if :math:`k = 2`, almost independently of the magnitude. -Experiments have shown :cite:`1996AAS_117_393B` that this conclusion remains unchanged if one replaces the circular aperture with a "Kron ellipse" :math:`{\cal K}`, which is simply the ellipse :math:`{\cal E}` above, scaled such that the principle axes become :math:`\sqrt{a/b}\,k r_1` and :math:`\sqrt{b/a}\,k r_1`. + r_{\rm Kron} = \frac{\sum_{i\in\cal E} r_i\,p^{(d)}_i}{\sum_{i\in\cal E} p^{(d)}_i}, -:param:`FLUX_AUTO` is the flux above the background summed over the Kron ellipse: +where :math:`p^{(d)}_i` is the pixel value *in the detection image*. :math:`r_i` is what we shall call the "reduced pseudo-radius" at pixel :math:`i` .. math:: - :label: flux_auto + :label: reduced_radius - {\tt FLUX\_AUTO} = \sum_{i\in\cal K} p_i. + r_i \equiv \sqrt{{\tt CXX\_IMAGE} \times \Delta x_i^2 + {\tt CYY\_IMAGE} \times \Delta y_i^2 + {\tt CXY\_IMAGE} \times \Delta x_i \Delta y_i}, -The quantity :math:`kr_1` is known as the *Kron radius*, and is provided in |SExtractor| by the :param:`KRON_RADIUS` catalog parameter in units of :param:`A_IMAGE` (or :param:`B_IMAGE`): +where :math:`\Delta x_i` and :math:`\Delta y_i` are the pixel coordinates relative to the detection centroid: .. math:: - :label: kron_radius - {\tt KRON\_RADIUS} = \frac{1}{\sqrt{{\tt A\_IMAGE}\times{\tt B\_IMAGE}}}\,k\,r_1. + \begin{aligned} + \Delta x_i & = x_i - {\tt X\_IMAGE}\\ + \Delta y_i & = y_i - {\tt Y\_IMAGE}. + \end{aligned} + + +:cite:`1980ApJS_43_305K` and :cite:`1987AA_183_177I` have shown that for stars and galaxy profiles convolved with Gaussian seeing, :math:`\ge 90\%` of the flux is expected to lie inside a circular aperture of radius :math:`k r_{\rm Kron}` with :math:`k = 2`, almost independently of the magnitude. +Experiments have shown :cite:`1996AAS_117_393B` that this conclusion remains unchanged if one replaces the circular aperture with the "Kron elliptical aperture" :math:`{\cal K}` with reduced pseudo-radius :math:`k r_{\rm Kron}`. +:param:`FLUX_AUTO` is the sum of pixel values from the measurement image, subtracted from the local background, inside the Kron ellipse: +.. math:: + :label: flux_auto + + {\tt FLUX\_AUTO} = \sum_{i\in\cal K} p_i. + +The quantity :math:`k r_{\rm Kron}`, known as the *Kron radius* (which in |SExtractor| is actually a "reduced pseudo-radius") is provided by the :param:`KRON_RADIUS`. :math:`k = 2` defines a sort of balance between systematic and random errors. By choosing a larger :math:`k = 2.5`, the mean fraction of flux lost drops from about 10% to 6%, at the expense of |SNR| in the measurement. -Very noisy objects may sometimes end up with a Kron radius being too small, even smaller that the isophotal footprint of the object itself. For this reason, |SExtractor| imposes a minimum size for the Kron radius, which must be larger than :math:`\sqrt{ab}\, r_{\rm min}` -The user has full control over the parameters :math:`k` and :math:`r_{\rm min}` through the ``PHOT_AUTOPARAMS`` configuration parameters. ``PHOT_AUTOPARAMS`` is set by default to ``2.5,3.5``. +Very noisy objects may sometimes end up with a Kron ellipse being too small, even smaller that the isophotal footprint of the object itself. For this reason, |SExtractor| imposes a minimum size for the Kron radius, which cannot be less than :math:`r_{\rm Kron,min}`. +The user has full control over the parameters :math:`k` and :math:`r_{\rm Kron,min}` through the ``PHOT_AUTOPARAMS`` configuration parameters. ``PHOT_AUTOPARAMS`` is set by default to ``2.5,3.5``. .. .. figure:: ps/simlostflux.ps @@ -149,6 +158,43 @@ The user has full control over the parameters :math:`k` and :math:`r_{\rm min}` Figure [figphot] shows the mean loss of flux measured with isophotal (threshold 24.4 magnitude.arsec\ :sup:`-2`), corrected isophotal and automatic aperture photometry for simulated galaxies on a typical Schmidt-survey B\ :sub:`J` plate image. The automatic adaptive aperture photometry leads to the lowest loss of flux. +.. _flux_petro_def: + +Petrosian aperture flux: :param:`FLUX_PETRO` +-------------------------------------------- + +Similar to :param:`FLUX_AUTO`, :param:`FLUX_PETRO` provides an estimate of the “total flux” by integrating pixel values within an adaptively scaled elliptical aperture. :param:`FLUX_PETRO`\ 's algorithm derives from Petrosian’s photometric estimator :cite:`1976ApJ_209L_1P,2001AJ_121_2358B,2001AJ_122_1104Y`: + +#. An elliptical aperture is :ref:`defined by the second order moments of the object’s light distribution `, with semi-major axis :math:`a={\tt A\_IMAGE}`, semi-minor axis :math:`b={\tt B\_IMAGE}`, and position angle :param:`THETA_IMAGE`. +#. The ellipse's major and minor axes are multiplied by 6 (which corresponds roughly to twice the size of the isophotal footprint on each axis). +#. Within this elliptical aperture :math:`{\cal E}`, the *Petrosian ratio* :math:`R_{\rm P}(r)` is computed: + +.. math:: + :label: petrosian_ratio + + 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 + +.. 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 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}`. +The user has full control over the parameters :math:`N_{\rm P}` and :math:`r_{\rm P,min}` through the ``PHOT_PETROPARAMS`` configuration parameters. ``PHOT_PETROPARAMS`` is set by default to ``2.0,3.5``. + +The Petrosian flux is the sum of pixel values from the measurement image, subtracted from the local background, inside the Petrosian ellipse: + +.. math:: + :label: flux_petro + + {\tt FLUX\_PETRO} = \sum_{i\in\cal P} p_i. + Photographic photometry ----------------------- diff --git a/doc/src/references.bib b/doc/src/references.bib index ae608d560dc9e3c7256989d1e389bf11130dd03f..c66c5b2ecbfd95624b9b7159946c5d33328cac82 100644 --- a/doc/src/references.bib +++ b/doc/src/references.bib @@ -24,6 +24,39 @@ adsnote = {Provided by the SAO/NASA Astrophysics Data System} } +@ARTICLE{2001AJ_121_2358B, + author = {{Blanton}, M.~R. and {Dalcanton}, J. and {Eisenstein}, D. and + {Loveday}, J. and {Strauss}, M.~A. and {SubbaRao}, M. and {Weinberg}, D.~H. and + {Anderson}, Jr., J.~E. and {Annis}, J. and {Bahcall}, N.~A. and + {Bernardi}, M. and {Brinkmann}, J. and {Brunner}, R.~J. and + {Burles}, S. and {Carey}, L. and {Castander}, F.~J. and {Connolly}, A.~J. and + {Csabai}, I. and {Doi}, M. and {Finkbeiner}, D. and {Friedman}, S. and + {Frieman}, J.~A. and {Fukugita}, M. and {Gunn}, J.~E. and {Hennessy}, G.~S. and + {Hindsley}, R.~B. and {Hogg}, D.~W. and {Ichikawa}, T. and {Ivezi{\'c}}, {\v Z}. and + {Kent}, S. and {Knapp}, G.~R. and {Lamb}, D.~Q. and {Leger}, R.~F. and + {Long}, D.~C. and {Lupton}, R.~H. and {McKay}, T.~A. and {Meiksin}, A. and + {Merelli}, A. and {Munn}, J.~A. and {Narayanan}, V. and {Newcomb}, M. and + {Nichol}, R.~C. and {Okamura}, S. and {Owen}, R. and {Pier}, J.~R. and + {Pope}, A. and {Postman}, M. and {Quinn}, T. and {Rockosi}, C.~M. and + {Schlegel}, D.~J. and {Schneider}, D.~P. and {Shimasaku}, K. and + {Siegmund}, W.~A. and {Smee}, S. and {Snir}, Y. and {Stoughton}, C. and + {Stubbs}, C. and {Szalay}, A.~S. and {Szokoly}, G.~P. and {Thakar}, A.~R. and + {Tremonti}, C. and {Tucker}, D.~L. and {Uomoto}, A. and {Vanden Berk}, D. and + {Vogeley}, M.~S. and {Waddell}, P. and {Yanny}, B. and {Yasuda}, N. and + {York}, D.~G.}, + title = "{The Luminosity Function of Galaxies in SDSS Commissioning Data}", + journal = {AJ}, + eprint = {astro-ph/0012085}, + keywords = {Galaxies: Fundamental Parameters, Galaxies: Photometry, Galaxies: Statistics}, + year = 2001, + month = may, + volume = 121, + pages = {2358-2380}, + doi = {10.1086/320405}, + adsurl = {http://adsabs.harvard.edu/abs/2001AJ....121.2358B}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + @ARTICLE{2013AA_554A_101B, author = {{Bouy}, H. and {Bertin}, E. and {Moraux}, E. and {Cuillandre}, J.-C. and {Bouvier}, J. and {Barrado}, D. and {Solano}, E. and {Bayo}, A.}, title = "{Dynamical analysis of nearby clusters. Automated astrometry from the ground: precision proper motions over a wide field}", @@ -236,6 +269,20 @@ archivePrefix = "arXiv", adsnote = {Provided by the SAO/NASA Astrophysics Data System} } +@ARTICLE{1976ApJ_209L_1P, + author = {{Petrosian}, V.}, + title = "{Surface brightness and evolution of galaxies}", + journal = {ApJL}, + keywords = {Astronomical Models, Galactic Evolution, Luminous Intensity, Red Shift, Surface Properties, Big Bang Cosmology, Cosmology, Hubble Diagram, Iterative Solution, Point Sources}, + year = 1976, + month = oct, + volume = 209, + pages = {L1-L5}, + doi = {10.1086/182253}, + adsurl = {http://adsabs.harvard.edu/abs/1976ApJ...209L...1P}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + @ARTICLE{1856MNRAS_17_12P, author = {{Pogson}, N.}, title = "{Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857}", @@ -288,6 +335,30 @@ ISSN={1045-9227}, month={Sep} } +@ARTICLE{2001AJ_122_1104Y, + author = {{Yasuda}, N. and {Fukugita}, M. and {Narayanan}, V.~K. and {Lupton}, R.~H. and + {Strateva}, I. and {Strauss}, M.~A. and {Ivezi{\'c}}, {\v Z}. and + {Kim}, R.~S.~J. and {Hogg}, D.~W. and {Weinberg}, D.~H. and + {Shimasaku}, K. and {Loveday}, J. and {Annis}, J. and {Bahcall}, N.~A. and + {Blanton}, M. and {Brinkmann}, J. and {Brunner}, R.~J. and {Connolly}, A.~J. and + {Csabai}, I. and {Doi}, M. and {Hamabe}, M. and {Ichikawa}, S.-I. and + {Ichikawa}, T. and {Johnston}, D.~E. and {Knapp}, G.~R. and + {Kunszt}, P.~Z. and {Lamb}, D.~Q. and {McKay}, T.~A. and {Munn}, J.~A. and + {Nichol}, R.~C. and {Okamura}, S. and {Schneider}, D.~P. and + {Szokoly}, G.~P. and {Vogeley}, M.~S. and {Watanabe}, M. and + {York}, D.~G.}, + title = "{Galaxy Number Counts from the Sloan Digital Sky Survey Commissioning Data}", + journal = {AJ}, + eprint = {astro-ph/0105545}, + keywords = {Cosmology: Observations}, + year = 2001, + month = sep, + volume = 122, + pages = {1104-1124}, + doi = {10.1086/322093}, + adsurl = {http://adsabs.harvard.edu/abs/2001AJ....122.1104Y}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} @INPROCEEDINGS{2002ASPC_281_228B, author = {{Bertin}, E. and {Mellier}, Y. and {Radovich}, M. and {Missonnier}, G. and