Index: trunk/doc/release.2015/ps1.analysis/analysis.tex =================================================================== --- trunk/doc/release.2015/ps1.analysis/analysis.tex (revision 40559) +++ trunk/doc/release.2015/ps1.analysis/analysis.tex (revision 40584) @@ -184,5 +184,5 @@ The photometric and astrometric precision goals for the Pan-STARRS\,1 -surveys were quite stringent: photmetric accuracy of 10 +surveys were quite stringent: photometric accuracy of 10 millimagnitudes, relative astrometric accuracy of 10 milliarcseconds and absolute astrometric accuracy of 100 milliarcseconds with respect @@ -252,11 +252,10 @@ In the process, the source analysis software was written using the data analysis C-code library written for the IPP, \code{psLib} -\citep{psLib}. Components of the photometry code were integrated into -the IPP's mid-level astronomy data analysis toolkit called -\code{psModules} \citep{psModules}. The resulting software, -`\code{psphot}', can be used either as a stand-alone C program, or as -a set of library functions which may be integrated into other programs - -% \note{add refs to the psLib and psModules ADDs} : ref to online docs? +\citep{magnier2017.datasystem}. Components of the photometry code +were integrated into the IPP's mid-level astronomy data analysis +toolkit called \code{psModules} \citep{magnier2017.datasystem}. The +resulting software, `\code{psphot}', can be used either as a +stand-alone C program, or as a set of library functions which may be +integrated into other programs Several variants of \code{psphot} have been used in the PS1 PV3 @@ -703,16 +702,24 @@ \begin{figure}[htbp] \begin{center} - \includegraphics[width=\hsize]{{pics/FWHM.smooth.trend.ps1}.\plotext} - \caption{\label{fig:moments.window} Example of the biases encountered when measuring the second - moments. A simulated image was generated using the PS1 PSF - profile. Each panel corresponds to a different value of - $\sigma_w$, as marked. The solid red line is the true FWHM of the - PSF used to generate the stars. The blue solid line is the FWHM - of the window function ($2.35\sigma_w$). The gray dots are the - FWHM derived from the measured second moments for stars in the - image. The dotted blue line is the target (65\% of the window - function). In this example, we would choose $\sigma_w$ between - 0.5 and 0.8 arcseconds so the dotted blue line would match the - bright end of the gray dots.} +% \includegraphics[width=0.6\hsize]{{pics/FWHM.smooth.trend.ps1}.\plotext} + \includegraphics[width=0.95\hsize]{{pics/FWHM.smooth.trend.ps1}.png} + \caption{\label{fig:moments.window} Example of the biases + encountered when measuring the second moments. A simulated image + was generated using the PS1 PSF profile. Each panel corresponds + to a different value of $\sigma_w$, corresponding to the window + FWHM values as marked. The solid red line is the true FWHM of the + PSF used to generate the stars (1.4 arcsec in all cases). The + blue solid line is the FWHM of the window function. The gray dots + are the FWHM derived from the measured second moments for stars in + the image. The median of this distribution (mag $< -10$) is + listed as ``obs''. The ratio of the median FWHM to the FWHM of + the window function is listed as ``ratio'', while the ratio of the + median FWHM to the true stellar FWHM is listed as ``bias''. The + dotted blue line is the target (65\% of the window function). In + this example, we would choose $\sigma_w$ between 0.5 and 0.8 + arcseconds so the dotted blue line would match the bright end of + the gray dots. See discussion in the text for the choice of + target window. +} \end{center} \end{figure} @@ -726,11 +733,11 @@ appropriate aperture in which the moments are measured. We also apply a ``window function'', down-weighting the pixels by a Gaussian, -centered on the object, with size $\sigma_W$ chosen to be large +centered on the object, with size $\sigma_w$ chosen to be large compared to the PSF size, $\sigma_{\rm PSF}$. This window function reduces the noise of the measurement of the moments by suppressing the noisy pixels at high radial distance as well as by reducing the -contaminating effects of neighboring stars. The choice of $\sigma_W$ +contaminating effects of neighboring stars. The choice of $\sigma_w$ and the aperture is an iterative process: for a given value of -$\sigma_W$, the PSF stars will have a measured value of the PSF size, +$\sigma_w$, the PSF stars will have a measured value of the PSF size, $\sigma^{\prime}_{\rm PSF}$ which different from the true value due to the effect of the window function. The measured value of the PSF size @@ -743,9 +750,10 @@ radial profile of the PS1 PSF model with $\sigma_{\rm PSF}$ corresponding to a FWHM of 1.4 arcseconds. As the window function -$\sigma_W$ is increased, the measured FWHM for the bright simulated -stars rises to meet the truth value. For small values of $\sigma_W$, +$\sigma_w$ is increased, the measured FWHM for the bright simulated +stars rises to meet the truth value. For small values of $\sigma_w$, fainter stars are biased to low measured values of the FWHM. For -large values of $\sigma_W$, the faint stars are biased to higher -values and the scatter increases. +large values of $\sigma_w$, the faint stars are biased to higher +values and the scatter increases. We attempt to minimize the scatter +and trends with magnitude at the cost of overall bias. In a real image, we do not know the true value of the PSF size. If we @@ -763,10 +771,10 @@ brightness. -To choose the value of $\sigma_W$, we try a sequence of values +To choose the value of $\sigma_w$, we try a sequence of values spanning a range guaranateed to contain any reasonable seeing values. The values are specified in the \code{psphot} recipe as \code{PSF.SIGMA.VALUES} and have the following values for PS1 PV3: (1, 2, 3, 4.5, 6, 9, 12, 18) pixels $\approx$ (0.26, 0.51, 0.77, 1.15, -1.54, 2.3, 3.1, 4.6) arcseconds. For each of these $\sigma_W$ values, +1.54, 2.3, 3.1, 4.6) arcseconds. For each of these $\sigma_w$ values, we then select candidate PSF stars based on the distribution of the measured $\sigma^{\prime}_{\rm PSF}$ in the two principal directions: @@ -776,5 +784,5 @@ \frac{\sigma_{x} + \sigma{y}}{2 \sigma_w}$, i.e., the ratio of the window size to the observed PSF size. We interpolate to find a value -of $\sigma_W$ for which $\rho_\sigma$ is expected to be 0.65. We use +of $\sigma_w$ for which $\rho_\sigma$ is expected to be 0.65. We use an aperture with a radius of 4$\sigma_w$ to select the pixels for the measurement of the moments. @@ -849,4 +857,5 @@ \subsubsection{PSF Model vs Source Model} +\label{sec:Source.Model} The point-spread-function (PSF) of an image describes the shape of all @@ -1007,10 +1016,10 @@ selected by \code{psphot}, though sources which have more than a certain number of saturated pixels are excluded at this stage. The -program then examines the 2-D plane of $\sigma_x, \sigma_y$ in search +program then examines the 2-D plane of $M_{x,x}, M_{y,y}$ in search of a concentrated clump of sources (see Figure~\ref{fig:moment.class}). To do this, it constructs an -artificial image with pixels representing the value of $\sigma_x, -\sigma_y$, using $0.1 \sigma_w$ as the size of a pixel in this -artificial image. The binned $\sigma_x, \sigma_y$ plane is then +artificial image with pixels representing the value of $M_{x,x}, +M_{y,y}$, using $0.1 \sigma^2_w$ as the size of a pixel in this +artificial image. The binned $M_{x,x}, M_{y,y}$ plane is then examined to find a significant peak. Unless the image is extremely sparse, such a peak will be well-defined and should represent the @@ -1027,6 +1036,4 @@ % (\sigma_x^2) not \sigma_x,\sigma_y) -\note{re-work wording above reflecting comment above} - Once a peak has been detected in this plane, the centroid and second moments of this peak are measured. All sources which land within 2 @@ -1037,6 +1044,6 @@ \begin{center} \includegraphics[width=\hsize]{{pics/moment.class}.\plotext} - \caption{\label{fig:moment.class} Illustration of PSF star selection using the FWHM derived - from the second moments in $X_{\rm ccd}$ and $Y_{\rm ccd}$ + \caption{\label{fig:moment.class} Illustration of PSF star selection + using the second moments in $X_{\rm ccd}$ and $Y_{\rm ccd}$ directions. The dominant clump is located in this diagram. Galaxies tend to have a range of sizes and thus spread out above @@ -1088,5 +1095,5 @@ \begin{table} \caption{\label{tab:psf.order.nstars} Minimum number of stars required - for a given order of the PSF 2D variations.}\vspace{-0.5cm} + for a given order of the PSF 2D variations.} % \vspace{-0.5cm} \begin{center} \begin{tabular}{llll} @@ -1215,108 +1222,68 @@ PSF. -\subsubsection{Full PSF Model Fitting} - -% \note{review the discussion below} - -Once a PSF model has been selected for an image, \code{psphot} attempts to -fit all of the detected sources, above a user-defined signal-to-noise -ratio with the PSF model. For these fits, the dependent parameters -are fixed by the PSF model and only the 4 independent source model -parameters are allowed to vary in the fit. \code{psphot} again uses -Levenberg-Marquardt minimization for the non-linear fitting. The -sources are fitted in their S/N order, starting with the brightest and -working down to the user-specified limit, with the other sources -subtracted as discussed above. - -\note{code review for the next bit} - -Once a solution has been achieved for a source, \code{psphot} attempts to -judge the quality of the PSF model as a representation of the source -shape. To do this, it calculates the next step of the minimization -{\em allowing the shape parameters to vary}. This step, essentially -the Gauss-Newton minimization distance from the current local minimum, -should be very small if the source is well represented by the PSF, but -large if the PSF is not a good representation of the source flux. The -model quality is judged by the change in the two shape parameters -which represent the 2D size of the source. For the case of the -elliptical Gaussian, these two parameters are $\sigma_x$ and -$\sigma_y$. For a generic model, the shape parameters may be defined -differently, but there should always be two parameters which scale the -source size in two dimensions. Currently, \code{psphot} requires the two -relevant shape parameters to be the first two dependent parameters in -the list of model parameters (ie, parameters 4 \& 5). - -The expected distribution of the variation of the two shape parameters -will be a function of the signal-to-noise of the source in question -and the value of the shape parameter itself. The expected standard -deviation on the shape parameter is, eg, $\sigma_x / {\rm S/N}$. If -the source is well-represented by the PSF, then the shape parameter -values should be close to their minimization value. We can thus ask, -for each source, given the measured amplitude of the Gauss-Newton -step, how many standard deviations from the expected value (of 0.0) is -this particular value? Sources for which the variation in the shape -parameters is a large positive number of standard deviations are -likely to be better represented by a larger flux distribution than the -PSF (eg, a Galaxy or Comet, etc). Sources for which the variation in -the shape parameters is a large negative number of standard deviations -are likely to be better represented by a smaller flux distribution -than the PSF (ie, a cosmic ray or other defect). A user-defined -number of standard deviations is used to select these two cases, and -to flag the source as a likely galaxy (really meaning 'extended') or -as a likely defect. - -At this stage of the analysis, \code{psphot} uses two additional indicators -to identify good and poor PSF fits. The first of these is the -signal-to-noise ratio. It is possible for the peak finding algorithm -to identify peaks in locations which are not actually a normal peak. -Some of these cases are in the edges of saturated, bleeding columns -from bright stars, in the nearly flat halos of very bright stars, and -so on. In these cases, a local peak exists, with a lower nearby sky -region. However, the fitted PSF model cannot converge on the peak -because it is very poorly defined (perhaps only existing in the -smoothed image). The fit can either fail to converge or it can -converge on a fit with very low or negative peak flux / flux -normalization. \code{psphot} will flag any non-convergent PSF fit and any -source with PSF S/N ratio lower than a user-defined cutoff. It is -also useful to identify very poor fits by setting a maximum Chi-Square -cutoff for sources. - -As the sources are fitted to the PSF model, those which survive the -exclusion stage are subtracted from the image. The subtraction -process modifies the image pixels (removing the fitted flux, though -not the locally fitted background) but does not modify the mask or the -variance images. The signal-to-noise ratio in the image after -subtraction represents the significance of the remaining flux. If the -subtractions are sufficiently accurate models of the PSF flux -distribution, the remaining flux should be below 1 $\sigma$ -significance. In practice the cores of bright stars are poorly -represented and may have larger residual significance. - -\subsubsection{Blended Sources} - -Sources which are blended with other sources are fitted together as a set of -PSFs. A single multi-source fit is performed on all blended peaks. -The resulting fits are evaluated independently and any which are -determined to be PSFs are subtracted from the image. - -\subsubsection{Double Sources} - -Sources which are judged to be non-PSF-like are confronted with two -possible alternative choices. First, the source is fitted with a -double-source model. In this pass, the assumption is made that there -are two neighboring sources, but the peaks are blended together, or -otherwise not distinguished. The initial guess for the two peaks is -made by splitting the flux of the single source in half and locating -the two starting peaks at +/- 2 pixels from the original peak along -the direction of the semi-major axis of the sources, as measured from -the second moments. In order for the two-source model to be accepted, -both sources must be judged as a valid PSF source. Otherwise, the -double-PSF model is rejected and the source is fitted with the -available non-PSF model or models. +\subsubsection{Radial Profile Wings} + +We attempt to measure the radial profile of sources in order to find +the radius at which the flux of the source is matches the sky. In +this analysis, a series of up to 25 radial bins with power-law spacing +are defined and the flux of the source in each annulus is measured. +The ``sky radius'' is defined to be the radius at which the (robust +median) flux in the annulus is within 1 $\sigma$ of the local sky +level. If this limit is not reached before the slope of the flux from +one annulus to the next is less than a user-defined limit, then the +annulus at which the slope reaches this limit is used to define the +sky radius. These values are saved in the output smf / cmf files, but +not sent to the PSPS. The sky radius value is used below in the +calculation of the Kron magnitude. + +\subsubsection{Kron Magnitudes} +\label{sec:kron.mags} + +Preliminary Kron radius and flux values \citep{1980ApJS...43..305K} +are calculated soon after sources are detected +(Section~\ref{sec:moments}). However, these preliminary values are +not accurate due to the window-functions applied. After sources have +been characterized and the PSF model is well-determined, the Kron +parameters are re-calculated more carefully. In this version of the +calculation, following the algorithm described by \cite{sextractor}, +the image is first smoothed by Gaussian kernel with $\sigma = 1.7$ +pixels, corresponding to a FWHM of 1.0\arcsec\ in the PS1 stack +images. Next, the Kron radius is determined in an iterative process: +the first radial moment is measured using the pixels in an aperture +6$\times$ the first radial moment from the previous iteration. On the +first iteration, the sky radius is used in place of the first radial +moment. By default, 2 iterations are performed. The Kron radius is +defined to be 2.5$\times$ the first radial moment. The Kron flux is +the sum of pixel fluxes within the Kron radius. We also calculate the +flux in two related annular apertures: the Kron inner flux is the sum +of pixel values for the annulus $R_1 < r < 2.5 R_1$, while the Kron +outer flux is the sum of pixel values for $2.5 R_1 < r < 4 R_1$. + +Two details in the calculation above should be noted. First, for +faint sources, noise in the measurement of the 1st radial moment may +result in an excessively small aperture for the successive +calculations. The window used for the calculations is constrained to +be at least the size of the aperture based on the PSF stars +(Section~\ref{sec:moments}). At the other extreme, noise may make the radius +grow excessively, resulting in an unrealistically low effective +surface brightness. The aperture is constrained to be less than a +maximum value defined such that the minimum surface brightness is +1/2$times$ the effective surface brightness of a point source detected at the +$5\sigma$ limit. + +Second, the measurement of the 1st radial moment includes a filter to +reduce contamination from outlier pixels. Pairs of pixels on +opposites sides of the central pixel are considered together. The +geometric mean of the two fluxes is used to replace the flux values. +If the source has 180\degree\ symmetry, this operation has no impact. +However, if one of the two pixels is unusually high, the value will be +surpressed by the matched pixel on the other side. This trick has the +effect of reducing the impact of pixels which include flux from near +neighbors. + +\note{give a test example} \subsubsection{Source Size Assessment} \label{sec:source.size} - -\note{is this in the right place?} After the PSF model has been fitted to all sources, and the Kron flux @@ -1353,39 +1320,195 @@ \note{how are / were these parameters set?} +\subsubsection{Full PSF Model Fitting} + +% \note{review the discussion below} + +% gaussSigma = MOMENTS_GAUSS_SIGMA from recipe (initially) +% gaussSigma = Sigma used for window function, $\sigma_w$ + +% fitRadius, apRadius = (fitScale, apScale) * gaussSigma +% fitScale = 7.0 +% apScale = 4.5 + +Once a PSF model has been selected for an image, \code{psphot} +attempts to fit all of the detected sources, with signal-to-noise +ratio greater than a user-defined limit, with the PSF model. In the +PV3 analysis of the $3\pi$ survey data, this limit was set to a +signal-to-noise ratio of 20.0 for all analysis stages. In these fits, +the dependent parameters are fixed by the PSF model and only the 4 +independent source model parameters are allowed to vary in the fit. +\code{psphot} again uses Levenberg-Marquardt minimization for the +non-linear fitting. The sources are fitted in their S/N order, +starting with the brightest and working down to the user-specified +limit, with the other sources subtracted as discussed above. + +For the PSF model fitting, only pixels within a circular aperture +scaled based on the seeing are used. The radius of the circular +aperture is set to be a fixed multiple of $\sigma_w$, the width of the +Gaussian window function determined based on the analysis of the +second moments (see Section~\ref{sec:moments}). For the PV3 $3\pi$ +analysis, the PSF fit window radius is $7 \times \sigma_w$. + +Sources which are blended with other sources are fitted together as a +set of PSFs. Blended objects are identified by first searching for +objects for which the PSF fit windows overlap. For a group of such +neighboring objects, a contour is determined in the flux image at +$25\%$ of the peak of the brightest source in the group. All objects +lying within this contour are treated as blends of this brightest +source. If other objects in this group exist, the brightest object +not already assigned to a blend is used to define the contour for +blends of this next object. All objects in the image are tested as +possible blends. A single multi-source fit is performed on each group +of blended peaks. + +%% Once a solution has been achieved for a source, \code{psphot} attempts to +%% judge the quality of the PSF model as a representation of the source +%% shape. To do this, it calculates the next step of the minimization +%% {\em allowing the shape parameters to vary}. This step, essentially +%% the Gauss-Newton minimization distance from the current local minimum, +%% should be very small if the source is well represented by the PSF, but +%% large if the PSF is not a good representation of the source flux. The +%% model quality is judged by the change in the two shape parameters +%% which represent the 2D size of the source. For the case of the +%% elliptical Gaussian, these two parameters are $\sigma_x$ and +%% $\sigma_y$. For a generic model, the shape parameters may be defined +%% differently, but there should always be two parameters which scale the +%% source size in two dimensions. Currently, \code{psphot} requires the two +%% relevant shape parameters to be the first two dependent parameters in +%% the list of model parameters (ie, parameters 4 \& 5). +%% +%% The expected distribution of the variation of the two shape parameters +%% will be a function of the signal-to-noise of the source in question +%% and the value of the shape parameter itself. The expected standard +%% deviation on the shape parameter is, eg, $\sigma_x / {\rm S/N}$. If +%% the source is well-represented by the PSF, then the shape parameter +%% values should be close to their minimization value. We can thus ask, +%% for each source, given the measured amplitude of the Gauss-Newton +%% step, how many standard deviations from the expected value (of 0.0) is +%% this particular value? Sources for which the variation in the shape +%% parameters is a large positive number of standard deviations are +%% likely to be better represented by a larger flux distribution than the +%% PSF (eg, a Galaxy or Comet, etc). Sources for which the variation in +%% the shape parameters is a large negative number of standard deviations +%% are likely to be better represented by a smaller flux distribution +%% than the PSF (ie, a cosmic ray or other defect). A user-defined +%% number of standard deviations is used to select these two cases, and +%% to flag the source as a likely galaxy (really meaning 'extended') or +%% as a likely defect. + +After the PSF model is fitted to each object, \code{psphot} makes an +assessment of the quality of the PSF fits. First, it checks that the +non-linear fitting process has converged with a valid fit. The fit +for an object can fail if there are too few valid pixels, due to +masking or proximity to an edge, or if the parameters are driven to +extreme values which are not permitted. In addition, it is possible +for the peak finding algorithm to identify peaks in locations which +are not actually a normal peak. Some of these cases are in the edges +of saturated, bleeding columns from bright stars, in the nearly flat +halos of very bright stars, and so on. In these cases, a local peak +exists, with a lower nearby sky region. However, the fitted PSF model +cannot converge on the peak because it is very poorly defined (perhaps +only existing in the smoothed image). In these cases, \code{psphot} +flags the object with the bad bit \code{PM_SOURCE_MODE_FAIL}. It is +also possible in this type of case for the fit to result in a very low +or negative value for the flux normalization parameter. Source for +which the peak is less than 0.02 are also marked as failing the +non-linear PSF fit (\code{PM_SOURCE_MODE_FAIL}). + +Poor fits are also identified by the signal-to-noise and the $\chi^2$ +value of the resulting fit. If a source has a PSF S/N ratio lower +than a user-defined cutoff (set to 2.0 for the PV3 analysis of the +$3\pi$ survey), the non-linear PSF fit will be rejected. If the +Chi-Square per degree of freedom is greater than a user-defined limit +(set to 50.0 for the PV3 analysis of the $3\pi$ survey), the +non-linear PSF fit will be rejected. These sources are marked with +the flag bit (\code{PM_SOURCE_MODE_POOR}). + +Sources which are pass the above tests are marked as having a valid +non-linear PSF model fit (\code{PM_SOURCE_MODE_SATSTAR}). Among these +sources, those for which the peak flux is greater than the saturation +limit are marked as saturated stars (\code{PM_SOURCE_MODE_SATSTAR}). +These model fits should be consisdered with caution, but the fluxes +and positions may have some validity (see Section~\ref{Saturation}). + +As the sources are fitted to the PSF model, those which survive the +exclusion stage are subtracted from the image. The subtraction +process modifies the image pixels (removing the fitted flux, though +not the locally fitted background) but does not modify the mask or the +variance images. The signal-to-noise ratio in the image after +subtraction represents the significance of the remaining flux. If the +subtractions are sufficiently accurate models of the PSF flux +distribution, the remaining flux should be below 1 $\sigma$ +significance. In practice the cores of bright stars are poorly +represented and may have larger residual significance. + +For sources in groups of blended stars, the resulting fits are +evaluated independently. Any which are determined to be valid PSF +fits are subtracted from the image and kept for future analysis. + +\subsubsection{Double and Extended Sources} + +Sources which are judged to be non-PSF-like are confronted with two +possible alternative choices. First, the source is fitted with a +double-source model. In this pass, the assumption is made that there +are two neighboring sources, but the peaks are not resolved. The +initial guess for the two peaks is made by splitting the flux of the +single source in half and locating the two starting peaks at +/- 2 +pixels from the original peak along the direction of the semi-major +axis of the sources, as measured from the second moments. In order +for the two-source model to be accepted, both sources must be judged +as a valid PSF source. Otherwise, the double-PSF model is rejected +and the source is fitted with the available non-PSF model or models. + \subsubsection{Non-PSF Sources} Once every source (above the S/N cutoff) has been confronted with the -PSF model, the sources which are thought to be galaxies (extended) can -now be fit with appropriate models for the galaxies (or other likely -extended shapes). Again, the fitting stage starts with the brightest -sources (as judged by the rough S/N measured from the moments -aperture) and working to a user defined S/N limit. - -\code{psphot} will use the user-selected galaxy model to attempt the galaxy -model fits. In the configuration system, the keyword \code{GAL_MODEL} -is set to the model of interest. All suspected extended sources are -fitted with the model, allowing all of the parameters to float. The -initial parameter guesses are critical here to achieving convergence -on the model fits in a reasonable time. The moments and the pixel -flux distribution are used to make the initial parameter guess. Many -of the source parameters can be accurately guessed from the first and -second moments. The power-law slope can be guessed by measuring the -isophotal level at two elliptical radii and comparing the ratio to -that expected. - -For each of the galaxy models (in fact for all source models), a -function is defined which examines the fit results and determines if -the fit can be consider as a success or a failure. The exact criteria -for this decision will depend on the details of the model, and so this -level of abstraction is needed. For example, in some case, the range -of valid values for each of the parameters must be considered in the -fit assessment. In other cases, we may choose to use only the -parameter errors and the fit Chi-Square value. - -All galaxy model fits which are successful are then subtracted from -the image as is done for the successful PSF model fits. Of course, -the background flux is retained, with the result that only the source -is subtracted from the image. Again, the variance image is (currently) -not modified. +PSF model, the sources which are thought to be extended (resolved) can +now be fit with an appropriate model (e.g., galaxy profile or other +likely extended shapes). Again, the fitting stage starts with the +brightest sources (as judged by the rough S/N measured from the +moments aperture) and working to a user defined S/N limit. + +\code{psphot} will use the user-selected extended source model to +attempt these fits. In the configuration system, the keyword +\code{EXT_MODEL} is set to the model of interest. All suspected +extended sources are fitted with the model, allowing all of the +parameters to float. The initial parameter guesses are critical here +to achieving convergence on the model fits in a reasonable time. The +moments and the pixel flux distribution are used to make the initial +parameter guess. Many of the source parameters can be accurately +guessed from the first and second moments. The power-law slope can be +guessed by measuring the isophotal level at two elliptical radii and +comparing the ratio to that expected. + +For each type of extended source model (in fact for all source +models), a function is defined which examines the fit results and +determines if the fit can be consider as a success or a failure. The +exact criteria for this decision depends on the details of the model, +and so this level of abstraction is needed. For example, in some +case, the range of valid values for each of the parameters must be +considered in the fit assessment. In other cases, we may choose to +use only the parameter errors and the fit Chi-Square value. + +All extended source model fits which are successful are then +subtracted from the image as is done for the successful PSF model +fits. The background flux is retained, with the result that only the +source is subtracted from the image. At this stage, the variance +image is not modified. + +For the single exposure (\ippstage{camera}) and \ippstage{stack} image +analysis, these galaxy model fits are only used internally to generate +a clean object-subtracted residual image. For the PV3 analysis of the +$3\pi$ survey, these model fits were saved in the output catalog +files, but not loaded to the public database. The \code{QGAUSS} +extended source model was used for the PV3 analysis (see +Section~\ref{sec:Source.Model}). The convolved galaxy model fits (see +Section~\ref{sec:galaxy.conv.fit}) and the forced galaxy model fits +(see Section~\ref{sec:galaxy.forced.fit}) provide more reliable and +physically-motivated galaxy models. + +For the difference image analysis, a trailed object model is used for +the extended sources; these model fit parameters are passed to the +Moving Object Processing System \citep[MOPS][]{2013PASP..125..357D}. \subsection{Faint Source Analysis} @@ -1518,67 +1641,6 @@ Petrosian flux is contained. -\subsubsection{Radial Profile Wings} - -We attempt to measure the radial profile of sources in order to find -the radius at which the flux of the source is matches the sky. In -this analysis, a series of up to 25 radial bins with power-law spacing -are defined and the flux of the source in each annulus is measured. -The ``sky radius'' is defined to be the radius at which the (robust -median) flux in the annulus is within 1 $\sigma$ of the local sky -level. If this limit is not reached before the slope of the flux from -one annulus to the next is less than a user-defined limit, then the -annulus at which the slope reaches this limit is used to define the -sky radius. These values are saved in the output smf / cmf files, but -not sent to the PSPS. The sky radius value is used below in the -calculation of the kron magnitude. - -\subsubsection{Kron Magnitudes} -\label{sec:kron.mags} - -Preliminary Kron radius and flux values \citep{1980ApJS...43..305K} -are calculated soon after sources are detected -(Section~\ref{sec:moments}). However, these preliminary values are -not accurate due to the window-functions applied. After sources have -been characterized and the PSF model is well-determined, the Kron -parameters are re-calculated more carefully. In this version of the -calculation, following the algorithm described by \cite{sextractor}, -the image is first smoothed by Gaussian kernel with $\sigma = 1.7$ -pixels, corresponding to a FWHM of 1.0\arcsec\ in the PS1 stack -images. Next, the Kron radius is determined in an iterative process: -the first radial moment is measured using the pixels in an aperture -6$\times$ the first radial moment from the previous iteration. On the -first iteration, the sky radius is used in place of the first radial -moment. By default, 2 iterations are performed. The Kron radius is -defined the be 2.5$\times$ the first radial moment. The Kron flux is -the sum of pixel fluxes within the Kron radius. We also calculate the -flux in two related annular apertures: the Kron inner flux is the sum -of pixel values for the annulus $R_1 < r < 2.5 R_1$, while the Kron -outer flux is the sum of pixel values for $2.5 R_1 < r < 4 R_1$. - -Two details in the calculation above should be noted. First, for -faint sources, noise in the measurement of the 1st radial moment may -result in an excessively small aperture for the successive -calculations. The window used for the calculations is constrained to -be at least the size of the aperture based on the PSF stars -(Section~\ref{sec:moments}). At the other extreme, noise may make the radius -grow excessively, resulting in an unrealistically low effective -surface brightness. The aperture is constrained to be less than a -maximum value defined such that the minimum surface brightness is -1/2$times$ the effective surface brightness of a source detected at the -$5\sigma$ limit. - -Second, the measurement of the 1st radial moment includes a filter to -reduce contamination from outlier pixels. Pairs of pixels on -opposites sides of the central pixel are considered together. The -geometric mean of the two fluxes is used to replace the flux values. -If the source has 180\degree\ symmetry, this operation has no impact. -However, if one of the two pixels is unusually high, the value will be -surpressed by the matched pixel on the other side. This trick has the -effect of reducing the impact of pixels which include flux from near -neighbors. - -\note{give a test example} - \subsubsection{Convolved Galaxy Model Fits} +\label{sec:galaxy.conv.fit} In the galaxy model fittting stage, sources which meet certain @@ -1874,4 +1936,41 @@ tested. +\begin{table*} +\begin{center} +\caption{\label{tab:measurements} \nocode{psphot} measurements performed} % \vspace{-0.5cm} +\begin{tabular}{lcccc} +\hline +\hline +{\bf Measurement} & {\bf Camera} & {\bf Stack} & {\bf Forced Warp} & {\bf Diff} \\ +\hline + Background & Y & Y & Y & N$^1$ \\ + Peaks & Y & Y & N & Y \\ + Footprints & Y & Y & N & Y \\ + Moments & Y & Y & Y & Y \\ + PSF Model & Y & Y & Y & N$^2$ \\ + Bright Star Profile & Y & Y & N & Y \\ + Non-Linear PSF Fits & Y & Y & N & N \\ + Source-Size Tests & Y & Y & N & Y \\ + Unconvolved Galaxy Model & Y & Y & N & N \\ + Unconvolved Streak Model & N & N & N & Y \\ + Linear PSF Fits & Y & Y & Y & Y \\ + Radial Profiles & Y & Y & N & Y \\ + Petrosian Fluxes & N & Y & Y & N \\ + Kron Fluxes & Y & Y & Y & Y \\ + Convolved Galaxy Models & N & Y & N & N \\ + Fixed Aperture Photometry & N & Y & Y & N \\ + Convolved, Fixed Apertures & N & Y & N & N \\ + Aperture Corrections & Y & Y & Y & N \\ + Forced PSF Fluxes & N & N & Y & N \\ + Forced Galaxy Models & N & N & Y & N \\ + Lensing Parameters & N & Y & Y & N \\ +\hline +\hline +\multicolumn{5}{l}{$^1$ Background subtraction is performed by {\tt ppSub} before calling {\tt psphot}} \\ +\multicolumn{5}{l}{$^2$ PSF modeling is perfom by {\tt ppSub} on the input warps before calling {\tt psphot}} \\ +\end{tabular} +\end{center} +\end{table*} + \subsection{Output Formats} @@ -1973,7 +2072,6 @@ is marked as completed. -\subsection{Forced Photometry : PSFs} - -\subsection{Forced Photometry : galaxies} +\subsection{Forced Galaxy Models} +\label{sec:galaxy.forced.fit} The convolved galaxy models are also re-measured on the @@ -2149,2 +2247,3 @@ * background model description (see waters) +