Index: /trunk/doc/release.2015/ps1.analysis/analysis.tex =================================================================== --- /trunk/doc/release.2015/ps1.analysis/analysis.tex (revision 41346) +++ /trunk/doc/release.2015/ps1.analysis/analysis.tex (revision 41347) @@ -45,5 +45,5 @@ \def\Princeton{2} \def\DUR{3} -\def\MPIA{4} +\def\MPE{4} \def\CfA{5} @@ -61,5 +61,5 @@ L. Denneau,\altaffilmark{\IfA} P.~W. Draper,\altaffilmark{\DUR} -D. Farrow,\altaffilmark{\DUR,\MPIA} +D. Farrow,\altaffilmark{\DUR,\MPE} R. Jedicke,\altaffilmark{\IfA} K. W. Hodapp,\altaffilmark{\IfA} @@ -88,5 +88,6 @@ % \altaffiltext{\USNO}{US Naval Observatory, Flagstaff Station, Flagstaff, AZ 86001, USA} % \altaffiltext{\JHU}{Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA} -\altaffiltext{\MPIA}{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117 Heidelberg, Germany} +% \altaffiltext{\MPIA}{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117 Heidelberg, Germany} +\altaffiltext{\MPE}{Max-Planck-Institut f\"ur extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany} \begin{abstract} @@ -207,7 +208,7 @@ the analysis parameters to better suite the longer exposures. This program as well as the rest of the Pan-STARRS Image Processing -Pipeline (IPP) software suite is available for download from \url{http:ipp.ifa.hawaii.edu}}. - -\note{Generate a tarball of just the programs (skip certain directories)} +Pipeline (IPP) software suite is available for download from \url{http://ipp.ifa.hawaii.edu}}. + +% \note{Generate a tarball of just the programs (skip certain directories)} %Chambers et al. 2017 (Paper I) @@ -538,6 +539,6 @@ individual astrometric measurements is 16 milliarcseconds and the Pan-STARRS Data Release 2 (DR2) astrometric system is tied to the - Gaia DR1 coordinate frame with a systematic uncertainty of $\sim 5$ - milliarcseconds. } + Gaia DR1 \citep{2016AA...595A...4L} coordinate frame with a + systematic uncertainty of $\sim 5$ milliarcseconds. } \section{Basic Analysis} @@ -1473,4 +1474,27 @@ follow some of the observed PSF variations in the images. +Figure~\ref{fig:iq.exposure} illustrates the 2D variations in the PSF +shapes seen in PS1 data. This figure shows the FWHM, $e_1$, and $e_2$ +polarizations of the stars as a function of position in 4 exposures. +For images with good image quality, variations of the PSF shape due to +the optical aberrations can be see. The optical aberrations vary as +the active collimation and alignment are adjusted and as the focus +changes. These aberrations are coupled to the piston of the chips, +which have been adjusted to crudely follow the focal surface +\citep{chambers2017}. During regular operations, image with large +PSFs are usually caused by the atmosphere (seeing) or by telescope +tracking errors, both of which result in common shapes across the +field of the camera. In the figure, the top panel shows the +circularization of the PSF due to the atmosphere washes out the +lower-level variations caused by the optics. + +Examples of 2D PSF variations. + Each row represents an exposure. The left-most column shows the + distribution of FWHM across the camera; the median value in + arcseconds is given in the inset. The middle column gives the + $e_1$ polarization measured from second moments (see + Section~\ref{sec:lensing.params} while the right column gives the + $e_2$ polarization. + % \note{write up the fitting process to define the grid?} @@ -1498,4 +1522,19 @@ quality of the PSF fits. +% Figure 3: ** repaired PDF text ** +% pueo:psphot.iq.20200413/mana.sh : show.e12 (iq.exposures.pdf) +\begin{figure}[htbp] + \begin{center} + \includegraphics[width=\hsize]{{\picdir/iq.exposures}.\plotext} + \caption{\label{fig:iq.exposure} Examples of 2D PSF variations. + Each row represents an exposure. The left-most column shows the + distribution of FWHM across the camera; the median value in + arcseconds is given in the inset. The middle column gives the + $e_1$ polarization measured from second moments (see + Section~\ref{sec:lensing.params}) while the right column gives the + $e_2$ polarization. } + \end{center} +\end{figure} + For the PS1 GPC1 analysis, we used the \code{PS1_V1} model, which we found by experimentation to match well to the observed profiles @@ -1515,4 +1554,5 @@ % buonanno : 1983A&AS...51...83B +% Figure 4: % /data/kukui.3/eugene/psphot.20161214/mana.sh \begin{figure}[htbp] @@ -1575,4 +1615,21 @@ \subsubsection{Candidate PSF Source Selection} \label{sec:psf.source.selection} + +% Figure 5: +% /data/kukui.3/eugene/psphot.20161214/mana.sh +\begin{figure}[htbp] + \begin{center} + \includegraphics[width=\hsize]{{\picdir/moment.class}.\plotext} + \caption{\label{fig:moment.class} Illustration of PSF star selection + using the second moments. \textadd{Each point represents the + second moments in the $X_{\rm ccd}$ and $Y_{\rm ccd}$ directions + for sources measured in one chip (XY32) from a particular PS\,1 + exposure (o6065g0428o)}. The dominant clump is located in this + diagram \textadd{to identify the stars.} Galaxies tend to have a range of + sizes and thus spread out above the stars. Cosmic rays also have + a range of sizes, with one dimension smaller than the PSF. The + red circle represents the PSF star candidates. } + \end{center} +\end{figure} The first stage of determining the PSF model for an image is to @@ -1618,20 +1675,4 @@ most additional analyses and are marked with the flag bit \code{PM_SOURCE_MODE_SATURATED}. - -% /data/kukui.3/eugene/psphot.20161214/mana.sh -\begin{figure}[htbp] - \begin{center} - \includegraphics[width=\hsize]{{\picdir/moment.class}.\plotext} - \caption{\label{fig:moment.class} Illustration of PSF star selection - using the second moments. \textadd{Each point represents the - second moments in the $X_{\rm ccd}$ and $Y_{\rm ccd}$ directions - for sources measured in one chip (XY32) from a particular PS\,1 - exposure (o6065g0428o)}. The dominant clump is located in this - diagram \textadd{to identify the stars.} Galaxies tend to have a range of - sizes and thus spread out above the stars. Cosmic rays also have - a range of sizes, with one dimension smaller than the PSF. The - red circle represents the PSF star candidates. } - \end{center} -\end{figure} \subsubsection{Candidate PSF Source Model Fits} @@ -2039,5 +2080,5 @@ \code{PM_SOURCE_MODE_EXT_LIMIT} is set for the source. -\textmod{We decided to use $\delta M_{\rm KP}$ metric for this +\textmod{We decided to use the $\delta M_{\rm KP}$ metric for this assessment after we tested several possible star-galaxy separation statistics. We found that the Kron-PSF comparison was more reliable @@ -2084,23 +2125,37 @@ % apScale = 4.5 -Once a PSF model has been selected for an image, \ippprog{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 \textmod{the 3 -independent source model parameters (position in $X$ and $Y$ and flux -normalization) are allowed to vary in the fit. Note that we do {\em - not} allow the local sky to be fitted as a free parameters. Since -we have subtracted a model for the background, allowing the sky to be -again at this stage is redundant. In fact, in our testing, we found -that allowing the sky to float resulted in higher scatter for the flux -normalizations.} \ippprog{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. All sources for which a non-linear PSF model has been -attempted have the flag bit \code{PM_SOURCE_MODE_FITTED} set, -regardless of the quality of that fit. +\textadd{At this point, we have a PSF model for the image, we have an +assessment of the size (PSF-like, extended, or cosmic-ray) for each +object, and we have fitted the PSF model for the normalization to each +source (Section~\ref{sec:ensemble.fitting}). However, the positions +for the sources have been fixed to the position determined from the +peak detection stage (Section~\ref{sec:peaks}) or the centroid from +the analysis of the moments (Section~\ref{sec:moments}). A better +position, and thus a better normalization, can be determined by +simultaneously fitting for all three parameters. We therefore go +through the image and re-fit the PSF model to each source +one-at-a-time with all other sources subtracted based on the earlier +fit.} + +\textmod{This re-fitting analysis is performed for all of the sources + with signal-to-noise ratio greater than a user-defined limit. In + the PV3 analysis of the $3\pi$ survey data, this limit was set to a + signal-to-noise ratio of 20.0 for the \ippstage{chip} and + \ippstage{stack} analysis stages. In these fits, the dependent + parameters are fixed by the PSF model and only the 3 independent + source model parameters (position in $X$ and $Y$ and flux + normalization) are allowed to vary in the fit. Note that we do {\em + not} allow the local sky to be fitted as a free parameters. Since + we have subtracted a model for the background, allowing the sky to + be again at this stage is redundant. In fact, in our testing, we + found that allowing the sky to float resulted in higher scatter for + the flux normalizations. For the non-linear fitting, +\ippprog{psphot} again uses the Levenberg-Marquardt technique.} 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. All sources for which a non-linear PSF +model has been attempted have the flag bit +\code{PM_SOURCE_MODE_FITTED} set, regardless of the quality of that +fit. Since the PSF model describes the variation of the PSF across the @@ -2121,22 +2176,4 @@ 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 may be 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. Sources which are identified as members of a -blended group have the flag bit \code{PM_SOURCE_MODE_BLEND} set, while -those for which a blended PSF fit succeeds have the flag bit -\code{PM_SOURCE_MODE_BLEND_FIT} set. {\em Note that for DR1 \& DR2, - this option was not used because it tended to prevent galaxies from - being fitted as extended objects; the rules for identifying blended - stars and galaxies will be revisited in future re-analyses.} %% Once a solution has been achieved for a source, \ippprog{psphot} attempts to @@ -2226,45 +2263,72 @@ 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. -Sources for which a double-PSF model is fitted have the flag bit -\code{PM_SOURCE_MODE_PAIR} set. +\subsubsection{Double and Blended Sources} + +\textmod{In fields with high stellar density, the non-linear source fitting can +be adversely affected by close neighbors. We implemented two +modifications of the non-linear fitting code to address this issue for +different scales to the nearby neighbors. One version addresses the +case of nearby sources which are separately detected in the +peak-detection stage; the other version of the analysis attempts to +fit a pair of PSFs for sources which are apparently extended. {\em + Note that for DR1 \& DR2, neither of these options were used because + they tended to prevent galaxies from being fitted as extended + objects; these rules for distinguishing blended stars and galaxies will + be revisited in future re-analyses.} We outline the strategy below +although it was not used for these data releases.} + +{\TEXTADD Sources which are blended with other sources may be 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. Sources which are identified as members of a +blended group have the flag bit \code{PM_SOURCE_MODE_BLEND} set, while +those for which a blended PSF fit succeeds have the flag bit +\code{PM_SOURCE_MODE_BLEND_FIT} set. 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.} + +{\TEXTADD Sources which are judged to be non-PSF-like are confronted with two +possible alternative choices: double-star or extended source model +(see next section). For the double-star model, the assumption is made +that there are two neighboring PSF-like 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. Sources for which a double-PSF +model is fitted have the flag bit \code{PM_SOURCE_MODE_PAIR} set. } \subsubsection{Non-PSF Sources} \label{sec:nonlinear.galaxy.model} -Once every source (above the S/N cutoff) has been confronted with the +\textmod{Once every source (above the S/N cutoff) has been confronted with the 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 +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. -\ippprog{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. +{\TEXTADD The choice of extended source model or models is set by the user for a given +analysis. 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 @@ -2303,39 +2367,4 @@ \subsection{Faint Source Analysis} \label{sec:faint.psf.model} - -% pueo:/home/real/eugene/ppsim.20200407 -\begin{figure}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{completion.ppsim}.pdf} - \caption{\label{fig:complete.ppsim} Completeness as a function of - magnitude (blue curves) for different stellar densities in - simulated data. The curves are labeled with the logarithm of the - stellar density at the detection threshold of the low-density - image. The dotted red line shows the detection limit expected for - the sky level and seeing. The solid red curve shows the - completeness estimated for the low-density image based on - injection and recovery.} - \end{center} -\end{figure} - -% pueo:/home/real/eugene/ppsim.20200407 -\begin{figure}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{psphot.complete.pv3}.pdf} - \caption{\label{fig:complete.pv3} Completeness and bogus fraction - as a function of magnitude for different stellar densities in real - PS1 exposures. Each panel represents an exposure at different - Galactic latitudes towards anti-center, labeled by the density of - stars at the detection limit of the low-density exposure. In each - panel, the completeness (compared to deep stack data) and fraction - of false detections (bogus fraction) is shown for a series of - cuts. The gold curves show all detections in the exposures. The - dotted black curve shows the impact of cutting detections - identified by {\tt psphot} as cosmic rays. The blue curve - excludes cosmic rays and detections with {\tt PSF\_QF} $< 0.95$ - while the red curve excludes cosmic rays and detections with {\tt - PSF\_QF\_PERFECT} $< 0.95$.} - \end{center} -\end{figure} After a first pass through the image, in which the brighter sources @@ -2437,5 +2466,220 @@ actual source flux. -% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh +Aperture photometry attempts to avoid these problems, but introduces +other difficulties. In aperture photometry, if a large enough +aperture is chosen, the amount of flux which is lost will be a small +fraction of the total source flux. Even more importantly, as the +image conditions change, the amount lost will change by an even +smaller fraction, at least for a large aperture. +% +% This can be seen by +% the fact that the dominant variations in the image quality are in the +% focus, tracking and seeing. All of these errors initially affect the +% cores of the stellar images, rather than the wide wings. The wide +% wings are largely dominated by scattering in the optics and scattering +% in the atmosphere. The amplitude and distribution of these two +% scattering functions do not change significantly or quickly for a +% single telescope and site. +% +Aperture photometry can then be used to +correct the PSF photometry. + +The difficulty for aperture photometry is the need to make an accurate +measurement of the local background for each source. As the aperture +grows, errors in the measurement of the sky flux start to become +dominant. If the aperture is too small, then variations in the image +quality are dominant. The brighter is the source, the smaller is the +error introduced by the large size of the aperture. However, the +number of very bright stars is limited in any image, and of course the +brighter stars are more likely to suffer from non-linearity or +saturation. + +In order to thread the needle between these effects, \ippprog{psphot} +measures the aperture photometry on a modest-sized aperture, and then +uses the PSF model to extrapolate to a large aperture. When the PSF +fluxes are calculated, the aperture flux for the modest-sized aperture +is also determined. The aperture is a circular aperture with radius +set to a fixed multiple (\code{PSF_APERTURE_SCALE}) 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 aperture window radius is $4.5 \times \sigma_w$, +while the large reference aperture radius is set to 25 pixels +(\code{PSF_REF_RADIUS} = 6\farcs4). These corrected aperture +magnitudes are saved in the output catalogs as \code{AP_MAG}, the +uncorrected aperture magnitudes are saved as \code{AP_MAG_RAW}, and +the radius used to measure the raw aperture flux is saved as +\code{AP_MAG_RADIUS}. The corresponding flux and the flux error are +saved as \code{AP_FLUX} and \code{AP_FLUX_SIG}. + +% Figure 6: ** repaired PDF text ** +% pueo:/home/real/eugene/ppsim.20200407/tap_psphot_deteff.pro : all.complete +\begin{figure}[htbp] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{completion.ppsim}.pdf} + \caption{\label{fig:complete.ppsim} Completeness as a function of + magnitude (blue curves) for different stellar densities in + simulated data. The curves are labeled with the logarithm of the + stellar density at the detection threshold of the low-density + image. The dotted red line shows the detection limit expected for + the sky level and seeing. The solid red curve shows the + completeness estimated for the low-density image based on + injection and recovery.} + \end{center} +\end{figure} + +With these aperture magnitudes in hand, it is now possible to make an +average correction to the PSF magnitudes to bring the PSF and aperture +magnitudes to the same system. This correction is measured using the +same stars from which the PSF model is measured, as long as the PSF +magnitude error for the star is less than 0.03 mag. The correction is +calculated using the weighted average of the values $m_{\rm AP} - +m_{\rm PSF}$. Since the PSF may vary across the image, the correction +is determined as a function of position in the image. Like the PSF +model, the 2D variations of the aperture correction may be modeled as +a polynomial or via interpolation in a grid. For the $3\pi$ PV3 +analysis, a grid with a maximum of $6\times 6$ samples per GPC1 chip +image was used. The reported PSF magnitudes for all objects have this +aperture correction applied. \textadd{Note that an initial aperture correction was +measured during the initial steps of the analysis before the PSF model +was chosen. However, since the sources in the image were not yet +measured and subtracted, that aperture could be contaminated by +neighbors. The analysis here is performed one fairly bright star at a +time with all other sources subtracted in order to minimize such contamination.} + +% growth curve analysis in psphot: +% in psphotChoosePSF : call psphotMakeGrowthCurve +% in psphotMakeGrowthCurve : boolean GROWTH_FROM_SOURCES, use +%% pmGrowthCurveGenerateFromSources or +%% pmGrowthCurveGenerate (uses PSF model only) +%% GROWTH_FROM_SOURCES is set to TRUE for default recipe + +%% ApTrend: +%% in psphotApResid, called by psphotReadout near the end of the +%% analysis +%% ApTrend = f(x,y) for (apMag - psfMag) for psfMagErr <= 0.03 +%% apMag is growth curve corrected +%% psfMag is raw + +%% raw psfMag and raw apMag are measured +%% apMag = apMagRaw + growth curve correction (from apRadius to 25 pix +%% = PSF_REF_RADIUS) +%% psfMag = psfMagRaw + aperture trend ( + growth curve) + +% How important is this effect? Consider a typical bright source with a +% flux of (say) 40,000 counts in an image of background 1000 counts per +% pixel, with FWHM of 4 pixels. In principle, the flux of this source +% should be measurable with an accuracy of roughly 0.57\% +% ($\frac{\sqrt{40000 + 1000 \times 12}}{40000}$). However, the +% measurement of the sky is limited at some finite level by Poisson +% statistics. If we are required to use an aperture of (say) 25 pixels +% in radius (eg, 5 arcseconds for an 0.2 arcsec / pixel detector), and +% we have an annulus of twice this radius to measure the local sky, then +% we will have an error of XXX. +% +% \note{outline the variation of {\em ApResid} as a function of +% magnitude}. + +%%% \ippprog{psphot} measures the aperture correction ({\em ApResid}) for every PSF +%%% candidate source, then calculates the trend of this correction as a +%%% function of the magnitude. This trend is fitted with a line. The +%%% resulting function can be used to determine the effective aperture +%%% correction for an infinite flux source and the average bias inherent +%%% in the sky measurement for the image. The scatter of the +%%% PSF-candidate source measurements about this trend is a measure of how +%%% well we can measure photometry from the image by applying the specific +%%% PSF model. The slope of this trend is a measure of the bias in the +%%% local sky measurment for each source. In principal, the measured sky +%%% levels could be modified by this bias. More generally, the measured +%%% bias in a collection of images could be used to improve the model +%%% fitting or sky fitting portion of the software the remove the bias +%%% term. + +\subsection{Completeness \& Contamination} + +{\TEXTADD At the end of the \ippprog{psphot} analysis of the sources in the +image, an analysis is performed to test the detection efficiency. A +number of fake PSF sources are injected into the image and the peak +detection analysis (Section~\ref{sec:peaks}) is use to determine if +these sources would have been recovered. The PSF model fluxes are +measured for the source which are detected. For a given image, the +detection threshold is predicted based on the median image variance +and the seeing. A series of brightness bins straddling the threshold +are defined and a number of sources are injected with magnitudes +corresponding to each of these bin values. The \ippprog{psphot} +recipe value \code{EFF.NUM} specifies the number of sources in each +brightness bin (500 the PV3), and the value \code{@EFF.MAG} specifies +the bins as magnitudes above and below the threshold. For PV3, the 13 +magnitude offsets were (-2.0, -1.0, -0.5, -0.25, -0.1, -0.05, 0.0, +0.05, 0.1, 0.25, 0.5, 1.0, 2.0), providing fine sampling near the +limit, but more coarse coverage further away. Poisson noise +appropriate to the photon counts of the injected sources are included +in the image. Injected sources are uniformly distributed across the +image in $X$ and $Y$ pixel coordinates {\em without any consideration + of the masked regions}. This last point means the recovered +fraction in the bright bins can be used to test the masking fraction.} + +{\TEXTADD As the stellar density increases, the completeness suffers due to +crowding and confusion. Since the injection and recovery analysis of +the fake sources operates on the source-subtracted image and does not +attempt to fully discovery the sources, this analysis over-estimates +the completeness in crowded fields. To explore the completeness in +crowded field images, we generate a series of simulated images using a +Gaussian PSF with FWHM = 1\arcsec\ for a range of stellar densities. +We generate fake stars with fluxes as faint as $\frac{1}{5}$ of the +flux as the low-density detection limit, with densities ranging from +\approx 14,000 stars per square degree at low-density detection limit +to \approx 4.8 million stars per square degree at the low-density +detection limit. The latter is comparable to observed densities in +the Galactic plane. We run the \ippprog{psphot} analysis on these +simulated images and compare the detected stars to those injected to +calculate the completeness for each image as a function of the true +magnitude of the stars. Figure~\ref{fig:complete.ppsim} shows the measured +completeness for each of the six simulated images, labeled by the +logarithm of their faint-end stellar density. The red dashed line +shows the expected detection limit based on the background and seeing, +while the red curve shows the completeness curve calculated +automatically by \ippprog{psphot} using the injection and recovery +analysis.} + +{\TEXTADD For low-density fields, the completeness function determined by +injection and recovery is similar to that measured by the simulation, +with the 50\% completeness threshold roughly 0.3 magnitudes too faint. +As the stellar density increases, the true 50\% completeness magnitude +rises relative to the value estimated by injection and recovery.} + +{\TEXTADD Ideally, all sources detected by \ippprog{psphot} would correspond to +real astrophysical objects. In reality, many sources are detected in +the images which do not correspond to real sources in the sky. In the +very simplified simulations discussed above, which do not include +realistic detector artifacts, we find that the fraction of bogus +detections is extremely low, even at the very faint end. In real +data, bogus detections are due to a variety of typical instrumental +features including cosmic rays, diffraction spikes, satelite tracks, +glows, non-Gaussian noise, variance mis-estimation, etc. See paper III +for extensive discussion of instrumental artifacts in the Pan-STARRS images.} + +% Figure 7: ** repaired PDF text ** +% pueo:/home/real/eugene/psphot.complete.20200407/complete.sh : full.figure.all +\begin{figure}[htbp] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{psphot.complete.pv3}.pdf} + \caption{\label{fig:complete.pv3} Completeness and bogus fraction + as a function of magnitude for different stellar densities in real + PS1 exposures. Each panel represents an exposure at different + Galactic latitudes towards anti-center, labeled by the density of + stars at the detection limit of the low-density exposure. In each + panel, the completeness (compared to deep stack data) and fraction + of false detections (bogus fraction) is shown for a series of + cuts. The gold curves show all detections in the exposures. The + dotted black curve shows the impact of cutting detections + identified by {\tt psphot} as cosmic rays. The blue curve + excludes cosmic rays and detections with {\tt PSF\_QF} $< 0.95$ + while the red curve excludes cosmic rays and detections with {\tt + PSF\_QF\_PERFECT} $< 0.95$.} + \end{center} +\end{figure} + +% Figure 8: ** repaired PDF text ** +% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh : mkfigure \begin{figure*}[htbp] \begin{center} @@ -2460,241 +2704,5 @@ \end{figure*} -% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh -\begin{figure*}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{mag.resid.aper.v1}.\plotext} - \caption{\label{fig:mag.resid.aper} Aperture Photometry - demonstration. The plots show identical measurements to those in - Figure~\ref{fig:mag.resid.psf}, but for aperture photometry, as discussed in - Section~\ref{sec:aperture.correction}, rather than PSF photometry.} - \end{center} -\end{figure*} - -% on pueo ~eugene -% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh -\begin{figure}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{bright.mag.resid}.\plotext} - \caption{\label{fig:mag.resid.stdevs} Demonstration of photometric - accuracy using the image sequence from - Figure~\ref{fig:mag.resid.psf}. Using only bright stars (7 - 8 - magnitudes above the detection threshold), we calculate the - difference between the magnitudes in the first image and the other - 17 images. The plotted dots show for each pair the mean - difference vs the standard deviation of the difference. Red dots - show the PSF magnitudes and blue dots show aperture - magnitudes. Despite real transparency variations of 0.4 over the - 50 minutes of this sequence, magnitudes are consistent at the few - millimagnitude level. Aperture magnitudes have scatter in - the 2 - 7 millimagnitude range, while the PSF magnitudes have - scatter of 7 - 14 millimagntiudes. -} -\end{center} -\end{figure} - -% on pueo ~eugene/zpts.20200406/mana.sh -\begin{figure*}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{zpt.mjd.v0.i}.\plotext} - \caption{\label{fig:zpt.iband} Historical \ips-band zero points. - Blue dots are the individual exposure zero points, corrected to - airmass at the zenith. Red dots are the median of zero points - from images groups in bins of 10 nights. The grey line is a - spline fit to these median values. } -\end{center} -\end{figure*} - -% on pueo ~eugene/zpts.20200406/mana.sh -\begin{figure}[htbp] - \begin{center} - \includegraphics[width=\hsize,clip]{\picdir/{zptres.hist.v0.i}.\plotext} - \caption{\label{fig:zpt.resid.hist} Historical \ips-band zero-point - residual variations. Log-histogram (black line) of the - per-exposure zero points, corrected to the zenith, after - subtracting a spline fit to the median of image groups in bins of - 10 nights. The inset shows the core of the distribution. In - both, the red line is a Gaussian fit to the distribution. The - large negative tails are due to clouds and haze. } -\end{center} -\end{figure} - -Aperture photometry attempts to avoid these problems, but introduces -other difficulties. In aperture photometry, if a large enough -aperture is chosen, the amount of flux which is lost will be a small -fraction of the total source flux. Even more importantly, as the -image conditions change, the amount lost will change by an even -smaller fraction, at least for a large aperture. -% -% This can be seen by -% the fact that the dominant variations in the image quality are in the -% focus, tracking and seeing. All of these errors initially affect the -% cores of the stellar images, rather than the wide wings. The wide -% wings are largely dominated by scattering in the optics and scattering -% in the atmosphere. The amplitude and distribution of these two -% scattering functions do not change significantly or quickly for a -% single telescope and site. -% -Aperture photometry can then be used to -correct the PSF photometry. - -The difficulty for aperture photometry is the need to make an accurate -measurement of the local background for each source. As the aperture -grows, errors in the measurement of the sky flux start to become -dominant. If the aperture is too small, then variations in the image -quality are dominant. The brighter is the source, the smaller is the -error introduced by the large size of the aperture. However, the -number of very bright stars is limited in any image, and of course the -brighter stars are more likely to suffer from non-linearity or -saturation. - -In order to thread the needle between these effects, \ippprog{psphot} -measures the aperture photometry on a modest-sized aperture, and then -uses the PSF model to extrapolate to a large aperture. When the PSF -fluxes are calculated, the aperture flux for the modest-sized aperture -is also determined. The aperture is a circular aperture with radius -set to a fixed multiple (\code{PSF_APERTURE_SCALE}) 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 aperture window radius is $4.5 \times \sigma_w$, -while the large reference aperture radius is set to 25 pixels -(\code{PSF_REF_RADIUS} = 6\farcs4). These corrected aperture -magnitudes are saved in the output catalogs as \code{AP_MAG}, the -uncorrected aperture magnitudes are saved as \code{AP_MAG_RAW}, and -the radius used to measure the raw aperture flux is saved as -\code{AP_MAG_RADIUS}. The corresponding flux and the flux error are -saved as \code{AP_FLUX} and \code{AP_FLUX_SIG}. - -With these aperture magnitudes in hand, it is now possible to make an -average correction to the PSF magnitudes to bring the PSF and aperture -magnitudes to the same system. This correction is measured using the -same stars from which the PSF model is measured, as long as the PSF -magnitude error for the star is less than 0.03 mag. The correction is -calculated using the weighted average of the values $m_{\rm AP} - -m_{\rm PSF}$. Since the PSF may vary across the image, the correction -is determined as a function of position in the image. Like the PSF -model, the 2D variations of the aperture correction may be modeled as -a polynomial or via interpolation in a grid. For the $3\pi$ PV3 -analysis, a grid with a maximum of $6\times 6$ samples per GPC1 chip -image was used. The reported PSF magnitudes for all objects have this -aperture correction applied. \textadd{Note that an initial aperture correction was -measured during the initial steps of the analysis before the PSF model -was chosen. However, since the sources in the image were not yet -measured and subtracted, that aperture could be contaminated by -neighbors. The analysis here is performed one fairly bright star at a -time with all other sources subtracted in order to minimize such contamination.} - -% growth curve analysis in psphot: -% in psphotChoosePSF : call psphotMakeGrowthCurve -% in psphotMakeGrowthCurve : boolean GROWTH_FROM_SOURCES, use -%% pmGrowthCurveGenerateFromSources or -%% pmGrowthCurveGenerate (uses PSF model only) -%% GROWTH_FROM_SOURCES is set to TRUE for default recipe - -%% ApTrend: -%% in psphotApResid, called by psphotReadout near the end of the -%% analysis -%% ApTrend = f(x,y) for (apMag - psfMag) for psfMagErr <= 0.03 -%% apMag is growth curve corrected -%% psfMag is raw - -%% raw psfMag and raw apMag are measured -%% apMag = apMagRaw + growth curve correction (from apRadius to 25 pix -%% = PSF_REF_RADIUS) -%% psfMag = psfMagRaw + aperture trend ( + growth curve) - -% How important is this effect? Consider a typical bright source with a -% flux of (say) 40,000 counts in an image of background 1000 counts per -% pixel, with FWHM of 4 pixels. In principle, the flux of this source -% should be measurable with an accuracy of roughly 0.57\% -% ($\frac{\sqrt{40000 + 1000 \times 12}}{40000}$). However, the -% measurement of the sky is limited at some finite level by Poisson -% statistics. If we are required to use an aperture of (say) 25 pixels -% in radius (eg, 5 arcseconds for an 0.2 arcsec / pixel detector), and -% we have an annulus of twice this radius to measure the local sky, then -% we will have an error of XXX. -% -% \note{outline the variation of {\em ApResid} as a function of -% magnitude}. - -%%% \ippprog{psphot} measures the aperture correction ({\em ApResid}) for every PSF -%%% candidate source, then calculates the trend of this correction as a -%%% function of the magnitude. This trend is fitted with a line. The -%%% resulting function can be used to determine the effective aperture -%%% correction for an infinite flux source and the average bias inherent -%%% in the sky measurement for the image. The scatter of the -%%% PSF-candidate source measurements about this trend is a measure of how -%%% well we can measure photometry from the image by applying the specific -%%% PSF model. The slope of this trend is a measure of the bias in the -%%% local sky measurment for each source. In principal, the measured sky -%%% levels could be modified by this bias. More generally, the measured -%%% bias in a collection of images could be used to improve the model -%%% fitting or sky fitting portion of the software the remove the bias -%%% term. - -\subsection{Completeness \& Contamination} - -At the end of the \ippprog{psphot} analysis of the sources in the -image, an analysis is performed to test the detection efficiency. A -number of fake PSF sources are injected into the image and the peak -detection analysis (Section~\ref{sec:peaks}) is use to determine if -these sources would have been recovered. The PSF model fluxes are -measured for the source which are detected. For a given image, the -detection threshold is predicted based on the median image variance -and the seeing. A series of brightness bins straddling the threshold -are defined and a number of sources are injected with magnitudes -corresponding to each of these bin values. The \ippprog{psphot} -recipe value \code{EFF.NUM} specifies the number of sources in each -brightness bin (500 the PV3), and the value \code{@EFF.MAG} specifies -the bins as magnitudes above and below the threshold. For PV3, the 13 -magnitude offsets were (-2.0, -1.0, -0.5, -0.25, -0.1, -0.05, 0.0, -0.05, 0.1, 0.25, 0.5, 1.0, 2.0), providing fine sampling near the -limit, but more coarse coverage further away. Poisson noise -appropriate to the photon counts of the injected sources are included -in the image. Injected sources are uniformly distributed across the -image in $X$ and $Y$ pixel coordinates {\em without any consideration - of the masked regions}. This last point means the recovered -fraction in the bright bins can be used to test the masking fraction. - -As the stellar density increases, the completeness suffers due to -crowding and confusion. Since the injection and recovery analysis of -the fake sources operates on the source-subtracted image and does not -attempt to fully discovery the sources, this analysis over-estimates -the completeness in crowded fields. To explore the completeness in -crowded field images, we generate a series of simulated images using a -Gaussian PSF with FWHM = 1\arcsec for a range of stellar densities. -We generate fake stars with fluxes as faint as $\frac{1}{5}$ of the -flux as the low-density detection limit, with densities ranging from -\approx 14,000 stars per square degree at low-density detection limit -to \approx 4.8 million stars per square degree at the low-density -detection limit. The latter is comparable to observed densities in -the Galactic plane. We run the \ippprog{psphot} analysis on these -simulated images and compare the detected stars to those injected to -calculate the completeness for each image as a function of the true -magnitude of the stars. Figure~\ref{fig:complete.ppsim} shows the measured -completeness for each of the six simulated images, labeled by the -logarithm of their faint-end stellar density. The red dashed line -shows the expected detection limit based on the background and seeing, -while the red curve shows the completeness curve calculated -automatically by \ippprog{psphot} using the injection and recovery -analysis. - -For low-density fields, the completeness function determined by -injection and recovery is similar to that measured by the simulation, -with the 50\% completeness threshold roughly 0.3 magnitudes too faint. -As the stellar density increases, the true 50\% completeness magnitude -rises relative to the value estimated by injection and recovery. - -Ideally, all sources detected by \ippprog{psphot} would correspond to -real astrophysical objects. In reality, many sources are detected in -the images which do not correspond to real sources in the sky. In the -very simplified simulations discussed above, which do not include -realistic detector artifacts, we find that the fraction of bogus -detections is extremely low, even at the very faint end. In real -data, bogus detections are due to a variety of typical instrumental -features including cosmic rays, diffraction spikes, satelite tracks, -glows, non-Gaussian noise, variance mis-estimation, etc. See paper III -for extensive discussion of instrumental artifacts in the Pan-STARRS images. - -Figure~\ref{fig:complete.pv3} illustrates the completeness and bogus +{\TEXTADD Figure~\ref{fig:complete.pv3} illustrates the completeness and bogus detection fraction for a set of 4 real PS1 exposures from the $3\pi$ Survey. This figure uses \ips-band exposures with Galactic longitude @@ -2717,7 +2725,19 @@ also exclude detections with \ippmisc{PSF_QF_PERFECT} less than 0.95. This cut removes detections on residual persistent glows and -diffraction spikes. - -For the exposures at high-Galactic latitude, with a relatively low +diffraction spikes.} + +% Figure 9: ** repaired PDF text ** +% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh +\begin{figure*}[htbp] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{mag.resid.aper.v1}.\plotext} + \caption{\label{fig:mag.resid.aper} Aperture Photometry + demonstration. The plots show identical measurements to those in + Figure~\ref{fig:mag.resid.psf}, but for aperture photometry, as discussed in + Section~\ref{sec:aperture.correction}, rather than PSF photometry.} + \end{center} +\end{figure*} + +{\TEXTADD For the exposures at high-Galactic latitude, with a relatively low density of sources, the cosmic rays represent a significant contamination, as seen in the excess of bogus sources with \ips-band @@ -2730,5 +2750,5 @@ because the chance of having a source lie on the diffraction spikes or persistence glows is greatly increased at higher stellar densities. -The impact of the crowding on the completeness is also clear in this dataset. +The impact of the crowding on the completeness is also clear in this dataset.} \subsection{Stellar Photometry Example} @@ -2773,4 +2793,27 @@ the reported photometry for both PSF and aperture magnitudes. +% Figure 10: ** repaired PDF text ** +% on pueo ~eugene +% /data/kukui.1/eugene/psphot.examples.20190423/compare.sh : figure.resids +\begin{figure}[t] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{bright.mag.resid}.\plotext} + \caption{\label{fig:mag.resid.stdevs} Demonstration of photometric + accuracy using the image sequence from + Figure~\ref{fig:mag.resid.psf}. Using only bright stars (7 - 8 + magnitudes above the detection threshold), we calculate the + difference between the magnitudes in the first image and the other + 17 images. The plotted dots show for each pair the mean + difference vs the standard deviation of the difference. Red dots + show the PSF magnitudes and blue dots show aperture + magnitudes. Despite real transparency variations of 0.4 over the + 50 minutes of this sequence, magnitudes are consistent at the few + millimagnitude level. Aperture magnitudes have scatter in + the 2 - 7 millimagnitude range, while the PSF magnitudes have + scatter of 7 - 14 millimagntiudes. +} +\end{center} +\end{figure} + We believe the observed behavior at the faint end is primarily a result of the increased crowding. Aperture photometry is more @@ -2779,4 +2822,17 @@ with the aperture photometry degrading rapidly as the flux of the star decreases. + +% Figure 11: ** repaired PDF text ** +% on pueo ~eugene/zpts.20200406/mana.sh : go.zpt.stats i +\begin{figure*}[tb] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{zpt.mjd.v0.i}.\plotext} + \caption{\label{fig:zpt.iband} Historical \ips-band zero points. + Blue dots are the individual exposure zero points, corrected to + airmass at the zenith. Red dots are the median of zero points + from images groups in bins of 10 nights. The grey line is a + spline fit to these median values. } +\end{center} +\end{figure*} {\TEXTADD The figures above show the relative photometric accuracy for @@ -2832,7 +2888,7 @@ of the \ips-band zero points after subtracting a smoothly varying spline fit to the median of groups of 10 nights. A Gaussian fit to - this distribution has $\sigma = 28.4$ millimags. If we + this distribution has $\sigma = 26.6$ millimags. If we alternatively subtract a median zero point for each night, the - standard deviation is reduced to 18.9 millimags. These values can be + standard deviation is reduced to 17.6 millimags. These values can be compared to the results of \cite{2012ApJ...756..158S} in which only photometric nights were included, yielding a standard deviation of @@ -2842,4 +2898,19 @@ which are not expected from the normal effects of weather. We believe these are largely due to aperture correction errors.} + +% Figure 12: ** repaired PDF text ** +% on pueo ~eugene/zpts.20200406/mana.sh +\begin{figure}[b] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{zptres.hist.v0.i}.\plotext} + \caption{\label{fig:zpt.resid.hist} Historical \ips-band zero-point + residual variations. Log-histogram (black line) of the + per-exposure zero points, corrected to the zenith, after + subtracting a spline fit to the median of image groups in bins of + 10 nights. The inset shows the core of the distribution. In + both, the red line is a Gaussian fit to the distribution. The + large negative tails are due to clouds and haze. } +\end{center} +\end{figure} \subsection{Basic Analysis Summary} @@ -2907,12 +2978,53 @@ cut was defined by $|b| > b_{\rm min}$ where $b_{\rm min} = b_0 + r_b e^{\frac{-l^2}{2 \sigma_b^2}}$. For the PV3 analysis, $b_0 = -$20\degree, $r_b = $15\degree, $\sigma_b = $50\degree. \textadd{The Galactic plane cut is made on an object-by-object basis.} This contour -avoids the denser portions of the Galactic plane and bulge, limiting -the total time spent on the galaxy modeling analysis at the expense of -galaxy photometry in the plane (though Kron photometry is available -for those sources). - +$20\degree, $r_b = $15\degree, $\sigma_b = $50\degree. See +Figure~\ref{fig:galplanecut} for an illustration of the cut used for PV3. \textadd{The + Galactic plane cut is made on an object-by-object basis.} This +contour avoids the denser portions of the Galactic plane and bulge, +limiting the total time spent on the galaxy modeling analysis at the +expense of galaxy photometry in the plane (though Kron photometry is +available for those sources). + +% galaxy model fits performed based on limits set in psphotChooseAnalysisOptions.c + +% petrosian analysis performed on same objects as galaxy model fits +% if EXTENDED_SOURCE_PETROSIAN == TRUE (TRUE for PV3 stack - STACKPHOT) + +% galaxy model fits are performed on : +% all if (PSPHOT.EXT.FIT.ALL.SOURCES == TRUE) (FALSE for PV3 stack) +% (even so, if density is higher than PSPHOT.EXT.FIT.ALL.THRESH, skip) + +% only extended sources (based on EXT.NSIGMA) if EXT.NSIGMA.LIMIT.USE +% == TRUE (FALSE for PV3 stacks) + +% fit sources / measure petrosian to fixed flux limit if limits are +% defined (they are for PV3) + +% mag limits by filter, e.g., : petro 25, extfit 21.5 +% are translated to flux in counts and compared to Kron flux + +% SN limit is used only if fixed flux limits are not set +% SN limit set to EXTENDED_SOURCE_SN_LIM (10.0 for PV3) +% S/N limit for Kron flux, + +% S/N lim values set to 0.0 for all models in PV3 + +% galaxy coordinate limits: +% if |b| > 20.0 + 15.0 exp(-long^2 / (2 * 50^2)) + +\subsection{Radial Profiles} +\label{sec:radial.profile.v2} + +Galaxies with regular profiles, such as elliptical galaxies and +regular spiral galaxies, may be described as primarily a radial +surface brightness profile, with additional structure acting as a +perturbation on that profile. For many galaxies, the azimuthal shape +at a given isophotal level may be described as an elliptical contour. +To first order, a galaxy may be well described with a single elliptical +contour and radial profile. + +% Figure 13 % uses plots.sh in this directory -\begin{figure}[htbp] +\begin{figure}[b] \begin{center} \includegraphics[width=\hsize,clip]{\picdir/galplanecut.pdf} @@ -2923,41 +3035,17 @@ \end{figure} -% galaxy model fits performed based on limits set in psphotChooseAnalysisOptions.c - -% petrosian analysis performed on same objects as galaxy model fits -% if EXTENDED_SOURCE_PETROSIAN == TRUE (TRUE for PV3 stack - STACKPHOT) - -% galaxy model fits are performed on : -% all if (PSPHOT.EXT.FIT.ALL.SOURCES == TRUE) (FALSE for PV3 stack) -% (even so, if density is higher than PSPHOT.EXT.FIT.ALL.THRESH, skip) - -% only extended sources (based on EXT.NSIGMA) if EXT.NSIGMA.LIMIT.USE -% == TRUE (FALSE for PV3 stacks) - -% fit sources / measure petrosian to fixed flux limit if limits are -% defined (they are for PV3) - -% mag limits by filter, e.g., : petro 25, extfit 21.5 -% are translated to flux in counts and compared to Kron flux - -% SN limit is used only if fixed flux limits are not set -% SN limit set to EXTENDED_SOURCE_SN_LIM (10.0 for PV3) -% S/N limit for Kron flux, - -% S/N lim values set to 0.0 for all models in PV3 - -% galaxy coordinate limits: -% if |b| > 20.0 + 15.0 exp(-long^2 / (2 * 50^2)) - -\subsection{Radial Profiles} -\label{sec:radial.profile.v2} - -Galaxies with regular profiles, such as elliptical galaxies and -regular spiral galaxies, may be described as primarily a radial -surface brightness profile, with additional structure acting as a -perturbation on that profile. For many galaxies, the azimuthal shape -at a given isophotal level may be described as an elliptical contour. -To first order, a galaxy may be well described with a single elliptical -contour and radial profile. +% Figure 14 ** repaired PDF text ** +% on pueo ~eugene/sdss.psphot.2020414/mana.sh : go.figure +\begin{figure*}[htbp] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{petrosians.mags}.pdf} + \caption{\label{fig:petrosians} Comparison of PS1 ({\tt psphot}) and + SDSS Petrosian parameters for objects identified as galaxies by + SDSS. Panel (a) shows the difference in the measured Petrosian + magnitudes as a function of the Petrosian magnitude. Panel (b) + shows the magnitude difference as a function of the measured + difference in the Petrosian radius. } + \end{center} +\end{figure*} In order to facilitate the Petrosian photometry analysis below, \ippprog{psphot} @@ -3079,4 +3167,24 @@ available from the PSPS \ippdbtable{StackPetrosian} table.} +Our implementation of the Petrosian apertures and fluxes is designed +to match the SDSS implementation \citep{2002AJ....123..485S} and +therefore the measured parameters should be quite comparable between +the two surveys. Figure~\ref{fig:petrosians} compare the Petrosian +magnitudes and radii as measured by \ippprog{psphot} on the $3\pi$ +Survey observations and the values measured by SDSS for the same +objects. Objects identified by SDSS as galaxies ({\tt probPSF\_r} $< +0.5$) near the Galactic north pole ($\alpha$ = 180\degrees\ to +190\degrees, $\delta$ = 25\degrees\ to 35\degrees) are selected from +the PS1 $3\pi$ Survey dataset base on positional coincidence. The +figure shows the difference in the $r$-band Petrosian magnitudes as a +function of the Petrosian magnitude and as a function of the +difference in the measured Petrosian radii. Differences in the +measured magnitudes are driven by differences in the size estimates +from the two datasets and analysis methods. The PS1 analysis tends to +find larger radii for the same objects than the SDSS analysis, with +a mean difference of 0.3 arcseconds. The larger aperture results in +more flux captured in the aperture and thus brighter magnitudes for +the same object: the mean difference is -0.23 magnitude in the sense +of larger fluxes for the PS1 measurements. \subsection{Convolved Galaxy Model Fits} @@ -3270,23 +3378,35 @@ %% about the center of the pixel. do this? -In order to accurately compare the observed galaxy flux distribution +\textmod{In order to accurately compare the observed galaxy flux distribution to a model, it is necessary to integrate the pixel flux for a given -set of model parameter values. This could be done in a numerical -fashion, but in practice brute-force evaluation of the numerical -integral is computationally very expensive, requiring many evaluations -of the model function. Within \ippprog{psphot}, we bypass this -problem by defining a set of pre-calculated images for the central 9 -pixels (the $3 \times 3$ grid of pixels centered on the peak). These -pixel images are defined at higher resolution, with 11 subpixels per -real CCD pixel. The pre-calculated images are generated for a series -of values for the following parameters: S\'ersic index, effective -radius, axial ratio. We then select the closest image to our specific -case, and integrate over the true sub-pixels relevant for our position -and model. We have thus turned the problem from thousands of -evaluations of the full galaxy model to \approx 100 straight -additions, or up to $6 \times$ that number if we interpolate between -any of the parameters. - -\note{how much error does this approximation introduce?} +set of model parameter values. In the \ippprog{psphot} +implementation, we currently use a brute-force numerical evaluation of +the integral, dividing the central pixel into a grid of subpixels, +with the sampling set by the S\'ersic index of the model being +evaluated as $N_{\rm sub} = 2 Integer(6n / R_{\rm min})$ where $N_{\rm sub}$ +is subpixel scale $n$ is the S\'ersic index and $R_{\rm min}$ is the +size of the minor axis in pixel units. The value of $N_{\rm sub}$ is +constrained to be in the range 11 to 121, so the number of subpixels +evaluations ranges from 121 to $121^2 = 14,641$. Faster +approximations to this analysis were explored but they resulted in +unsatisfactory results. This is definitely an area where +\ippprog{psphot} could benefit from some of the lessons in the +literature \citep[e.g.][]{2013PASP..125..719H}.} + +%% This could be done in a numerical +%% fashion, but in practice brute-force evaluation of the numerical +%% integral is computationally very expensive, requiring many evaluations +%% of the model function. Within \ippprog{psphot}, we bypass this +%% problem by defining a set of pre-calculated images for the central 9 +%% pixels (the $3 \times 3$ grid of pixels centered on the peak). These +%% pixel images are defined at higher resolution, with 11 subpixels per +%% real CCD pixel. The pre-calculated images are generated for a series +%% of values for the following parameters: S\'ersic index, effective +%% radius, axial ratio. We then select the closest image to our specific +%% case, and integrate over the true sub-pixels relevant for our position +%% and model. We have thus turned the problem from thousands of +%% evaluations of the full galaxy model to \approx 100 straight +%% additions, or up to $6 \times$ that number if we interpolate between +%% any of the parameters. The convolved galaxy model fit results are available in one of three @@ -3294,5 +3414,4 @@ \ippdbtable{StackModelFitDeV}, \ippdbtable{StackModelFitSer} for the Exponential, DeVaucouleur, and S\'ersic models, respectively. - \subsection{Fixed Aperture Photometry} @@ -3377,5 +3496,5 @@ sets of measurements joined together for ease of access.} -\note{test SDSS radial apertures?} +% \note{test SDSS radial apertures?} % at least out to aperture # RADIAL_AP_MIN (= 4), but no further than @@ -3451,5 +3570,7 @@ earlier work were generally compact. -% /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% Figure 15: ** repaired PDF text ** +% was /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% is pueo:galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy \begin{figure}[htbp] \begin{center} @@ -3497,9 +3618,10 @@ accurate for the larger galaxies. -% /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% Figure 16 ** repaired PDF text ** +% was /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% is pueo:galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy \begin{figure*}[htbp] \begin{center} \includegraphics[width=\hsize,clip]{\picdir/{galaxy.exp.params}.\plotext} - \caption{\label{fig:exp.params} Parameter recovery for simulated galaxies with Exponential profiles. In each panel, we show @@ -3519,5 +3641,7 @@ \end{figure*} -% /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% Figure 17 ** repaired PDF text ** +% was /data/kukui.1/eugene/galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy +% is pueo:galaxies.20190425/tap_psphot_galaxies.pro : go.bigtest.ckgalaxy \begin{figure*}[htbp] \begin{center} @@ -3532,10 +3656,8 @@ \label{sec:psf.forced.fit} -\note{reference to multifit / cfht lens?} - Traditionally, projects which use multiple exposures to increase the depth and sensitivity of the observations have generated something equivalent to the stack images produced by the IPP analysis, -\textadd{as done for example by the CFHT Legacy Survey +\textadd{as done for example by the Canada-France-Hawaii Telescope (CFHT) Legacy Survey \citep{2006ApJ...647..116H} or the Cosmic Evolution Survey \citep[COSMOS][]{2007ApJS..172...99C}}. In theory, the photometry @@ -3641,6 +3763,57 @@ \ippdbtable{ForcedMeanObject} tables.} -\note{discuss the relative quality of average exposure, forced warp - average, and stack photometry. reference to Best et al} +% Figure 18 ** repaired PDF text ** +% on pueo ~eugene/sdss.psphot.2020414/photcompare.sh : go.figure +\begin{figure}[htbp] + \begin{center} + \includegraphics[width=\hsize,clip]{\picdir/{compare.mags}.pdf} + \caption{\label{fig:compare.mags} Comparison of {\tt psphot} average + chip photometry, average forced-warp photometry, and stack + photometry from $3\pi$ Survey data to average forced-warp + photometry from the Pan-STARRS\,1 Medium-Deep Survey field MD06 + At bright magnitudes, average chip photometry is the most + accurate while the stack photometry is degraded by the + highly-texturd PSF. At faint magnitudes, average chip magnitudes + are biased to artifically bright values.} + \end{center} +\end{figure} + +{\TEXTADD With the inclusion of the forced-warp photometry, we have three +distinct methods for measuring the PSF photometry of stars in the +Pan-STARRS survey data: the average of the \ippstage{chip}-stage +photometry from the individual exposures; the measurement from the +stacks, and the average of the forced-warp photometry described here. +It is worth considering which of these should be used in which +circumstance. Figure~\ref{fig:compare.mags} shows a comparison of +these three different methods to deeper data from the Medium Deep +Survey observations (MD06 field). Our conclusion from this and other +analysis is that the average \ippstage{chip}-stage photometry is the +best (most accurate) measurement for brighter objects, where the +signal-to-noise is roughly 10 or more. This is the photometry source +which was used for the global photometry solution discussed by +\cite{2012ApJ...756..158S} and used in the overall calibration (see +Paper V).} + +{\TEXTADD As can be clearly seen in the figure, the average from the forced-warp +photometry is slightly worse than the chip photometry, while the stack +PSF photometry is significantly degraded. We attribute the latter +effect to the highly-textured PSF observed in the stack images due to +the combination of variable PSFs in each exposure and significant +masking fraction in the PS1 camera. At the faint end, the chip +photometry is significantly worse that both average warp and stack +photometry. First, in order to have a measurement, a source must be +detected above the detection threshold in at least one of the +exposures, limiting the depth possible of the average chip +photometry. Second, at the faint end, only bright fluctuations will be +detected, resulting in a bright bias. This latter effect is clearly +seen in Figure~\ref{fig:compare.mags} as the average chip magnitudes +diverge from the deeper Medium Deep photometry measurements. As has +been noted elsewhere \citep{2018ApJS..234....1B}, the warp and stack +photometry is also degraded for objects which have significant proper +motion over the course of the $3\pi$ Survey since the position is held +constant for all epochs, while the average chip photometry is +calculated on detections which are cross-matched in the database. +Thus, warp and stack photometry should be avoided for sources with +proper motion greater than roughly 100 milliarcseconds per year.} \subsection{Forced Galaxy Models} @@ -3663,4 +3836,6 @@ the same time the best normalization corresponding to the best elliptical shape, and thus the best galaxy magnitude value. +\textadd{This technique is similar to the joint fitting of multiple + exposures performed by the CFHT Lensing Survey team \citep{2013MNRAS.429.2858M}.} For each warp image, the stack values for the major and minor axis are @@ -3894,5 +4069,8 @@ from the PSPS database \ippdbtable{ForcedWarpLensing} table while the average values calculated over the warps is found in the -\ippdbtable{ForcedMeanLensing} tables. +\ippdbtable{ForcedMeanLensing} tables. \textadd{Although the software used +here was not involved in any of the GRavitational lEnsing Accuracy +Testing (GREAT) challenges, it is similar to the code of the EPFL\_KSB +team \citep{2015MNRAS.450.2963M} and likely to perform similarly.} % \note{example of using the lensing elements for binaries?} @@ -4042,19 +4220,4 @@ \section{Conclusions} -\note{add lessons learned here} - -\begin{verbatim} -Suggestions for improvements / changes -* use more external knowledge: - ** Gaia or PS1 to select stars as PSF sources - ** pre-seed information about the very bright or very crowded - regions -* background model - ** allow the superpixel scale to change as a function of environment - ** do not use the lower-end model unless region is known to be dense -* use galactic latitude or local stellar density to smoothly - transition from double / multi-PSF to galaxy model fitting -\end{verbatim} - The Pan-STARRS Image Processing Pipeline has used the \ippprog{psphot} software to detect and characterize astronomical sources in images @@ -4069,4 +4232,36 @@ million PS\,1 exposures have been characterized (some representing repeated measurements of the same exposures). + +There is always room for improvement, however. A number of +possible improvements to \ippprog{psphot} have been identified which +could result in more reliable measurements for either stars or +galaxies. Here we discuss improvements beyond simply tuning +parameters for a specific dataset. + +In general, the improvements we identify share the characteristic of +making use of external information in the analysis. As described +above, essentially all operations of \ippprog{psphot}, except in the +context of forced photometry, approach each image with no prior +knowledge. This was necessary in the early stages of the Pan-STARRS +project when we had not yet observed the sky with our instrument and +comparable observations were only available in the SDSS Galactic cap +regions. However, the sky is now much better known, not only from +PS1, but also for example due to Gaia. + +Several improvements to the \ippprog{psphot} analysis could be made by +including as much information from external catalogs about the +positions and characteristics of sources in the images as possible. +For example, known stars (e.g., based on proper motions from Gaia or +colors and morphology from PS1) could be used for PSF sources. In +areas of high density, especially in known globular or even open +clusters, existing high-resolution imagery could be used to provide a +constraint on location of stars. External information could also be +used to control the scale on which the background is modelled: a finer +sampling is helpful in regions of known nebulosity and large galaxies +such as M31. Finally, the galactic latitude or the externally-defined +stellar density could be used to control the choice of fitting double +stars or galaxy models. This would be a step beyond the current +capability of choosing to fit galaxy models as a function of galactic +latitude. % PS2 reference: Index: /trunk/doc/release.2015/ps1.analysis/response.txt =================================================================== --- /trunk/doc/release.2015/ps1.analysis/response.txt (revision 41346) +++ /trunk/doc/release.2015/ps1.analysis/response.txt (revision 41347) @@ -1,4 +1,3 @@ ---------------------------------------------------------------------- Referee Report Reviewer's Comments: @@ -98,5 +97,5 @@ that the photometric goals are achieved -**** TBD : discuss relative quality of chip, forced, stack photometry +** added comparion discussion of chip, warp, stack photometry at the end of Sec 6.1 - Sec 7, where the image differencing detections and photometry is used @@ -126,5 +125,5 @@ in one place would be a useful service. -**** TBD : summarize the lessons learned +** added suggested improvements in conclusion Abstract: @@ -331,7 +330,6 @@ for a typical exposure. -**** TBD: SHOW SOME EXAMPLES of PSF variations - choose 3 exposures: 1 with good IQ, one with bad IQ, but round, one with bad IQ but not round, - plot some IQ stats (Mxx - Myy) / (Mxx + Myy) +** we have added a figure to show examples of the image quality + variations observed in PS1 in both good and bad seeing data. - Please state whether the PSF model is this set of formulae @@ -435,5 +433,7 @@ and presented as a future development effort. -**** TBD : wording of full PSF model section 4.6.6 +** reworded to explain that this step, unlike 4.6.2, does a + simultaneous fit to the position and normalization for sources + one-at-a-time. - Remind the reader that the 4 independent parameters includes a local sky @@ -455,5 +455,9 @@ range. -**** TBD: double-star mode: was this turned on for PV3? ppSim to show recovery +** In reviewing the code, we discovered that this approach to close + neighbors was turned off for PV3, similar to the blend fits + discussed above. We have moved both of these crowded field + analysis concepts to a single section, identified as deactivated + for PV3. Sec 4.7: @@ -558,5 +562,7 @@ compare well to those in the PS1 catalog? -**** TBD: compare Petrosian mags to SDSS for some example +** These agree to first order, but there is a tendency for the PS1 + measurements to have larger radii and smaller (brighter) + magnitudes. Added text and a figure to illustrate Sec 5.3: @@ -585,5 +591,10 @@ error of this approximation should be stated. -**** TBD: model central pixel errors for Sersic models +** In trying to answer this question, we realized that, while we + experimented with this technique, the as implemented psphot in fact + used brute-force numerical evaluation. These implementation + experiments did not pan out so we went ahead with something that + worked, even if it was slower. We have updated the text to + describe the actual implementation. Sec 5.4: @@ -688,5 +699,6 @@ and if not, which code would it be most similar to? -**** TBD : check on GREAT challenge to compare code +** psphot was not used in any of the GREAT challenges, but is similar + to the EPFL_KSB team's code. added this to the text - Define "KSB" and "HFK" references in-line