Changeset 39960 for trunk/doc/release.2015/ps1.analysis/analysis.tex

Timestamp:

Jan 28, 2017, 2:55:27 PM (9 years ago)

Author:

eugene

Message:

updates to the analysis paper

File:

• trunk/doc/release.2015/ps1.analysis/analysis.tex (modified) (10 diffs)

trunk/doc/release.2015/ps1.analysis/analysis.tex

@@ -103 +103 @@
 \section{INTRODUCTION}\label{sec:intro}
 
+\begin{verbatim}
+here is a list of things to do:
+* clear out \note entries
+  * explain use of covariance
+  * add example for sky model
+  * Kaiser optimal detection reference
+  * find a brighter-fatter reference
+* define more tests and generate examples
+  * simulation example of background subtraction at different densities
+  * real example of oversubtracted galaxy
+* check all references
+* fix the \code macro to work with alternate concepts
+  * DONE : the use of \textbf style formats was a problem : expects \textbf{foobar}
+\end{verbatim}
+
 This is the fourth in a series of seven papers describing the
 Pan-STARRS1 Surveys, the data reduction techiques and the resulting
@@ -163 +178 @@
     from early users of the data products are welcome during the
     submission and refereeing process.}}
+
+\end{document}
 
 \section{Background}
@@ -227 +244 @@
 
 When the IPP development was starting, the existing photometry
-packages either did not meet the accuracy requirements or
-required too much human intervention to be considered for the needs of
-PS1.  In the case of the SDSS Photo tool, the software was judged to
-be too tightly integrated to the architecture of SDSS to be easily
-re-integrated into the Pan-STARRS pipeline.  A new photometry analysis
-package was developed using lessons learned from the existing
-photometry systems.  In the process, the source analysis software was
-written using the data analysis C-code library written for the IPP,
-\code{psLib}.  Components of the photometry code were integrated into
+packages either did not meet the accuracy requirements or required too
+much human intervention to be considered for the needs of PS1.  In the
+case of the SDSS Photo tool, the software was judged to be too tightly
+integrated to the architecture of SDSS to be easily re-integrated into
+the Pan-STARRS pipeline.  A new photometry analysis package was
+developed using lessons learned from the existing photometry systems.
+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}.  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}
-
-The main version of \code{psphot} is a stand-alone program which is run on a
-single image, or a group of related images representing the data read
-from a camera in a single exposure.  The images are expected to have
-already been detrended so that pixel values are linearly related to
-the flux.  The gain may be specified by the configuration system, or a
-variance image may be supplied.  A mask may also be supplied to mark
-good, bad, and suspect pixels.  Several variants of psphot have also
-been used in the PS1 PV3 analysis.  \note{ppImage version is an
-  integrated library call}
-
-The version called \code{psphotStack} accepts a set of images, each
+\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?
+
+Several variants of \code{psphot} have been used in the PS1 PV3
+analysis.  The main variant of \code{psphot} operates on a single
+image, or a group of related images representing the data read from a
+camera in a single exposure.  The images are expected to have already
+been detrended so that pixel values are linearly related to the flux.
+The gain may be specified by the configuration system, or a variance
+image may be supplied.  A mask may also be supplied to mark good, bad,
+and suspect pixels.  This variant of \code{psphot} can be called as a
+stand-alone program, also called \code{psphot}.  In standard IPP
+operations, this variant is used as a library call within the analysis
+program \code{ppImage} during the \ippstage{chip} analysis stage.
+
+The variant called \code{psphotStack} accepts a set of images, each
 representing the same patch of sky in a different filter, nominally
 the full $grizy$ filter set for the analysis of the PS1 PV3 stack
@@ -265 +284 @@
 photometry.
 
-Another version of \code{psphot} used in the PV3 analysis is called
-\code{psphotFullForce}.  In this version, a set of image all representing the
+Another variant of \code{psphot} used in the PV3 analysis is called
+\code{psphotFullForce}.  In this variant, a set of image all representing the
 same pixels are processed together, with the positions of sources to
-be analysed loaded from a supplied file.  In this version of the
+be analysed loaded from a supplied file.  In this variant of the
 analysis, sources are not discovered -- only the supplied sources are
 considered.  PSF models are determined for each exposure and the
@@ -389 +408 @@
 case the PSF modeling stage can be skipped.
 
-{\bf A note on nomenclature:} 
+% {\bf A note on nomenclature:  ???} 
 
 \subsection{Image Preparation}
@@ -415 +434 @@
 saturated pixel.  In addition, the mask pixels are used to define the
 pixels available during a model fit, and which should be ignored for
-that specific fit (\code{MARK = 0x8000}).  The initial mask, if not
-supplied by the user, is constructed by default from the image by
-applying three rules: 1) Pixels which are above a specified saturation
-level are marked as saturated.  The level is specified by the camera
-format keyword \code{CELL.SATURATION}, which may specify a value or
-define a header keyword which in turn specifies the value in the image
-header.  In the case of PS1 PV3, the header keyword \code{MAXLIN}
-specifies the saturation level for each chip. \note{refer to detrend
-  paper here?  what are GPC1 saturation levels?}. 2) Pixels which are
-below a user-defined value are considered unresponsive and masked as
-dead.  (camera format keyword \code{CELL.BAD} = 0 for PS1 PV3).  3)
-Pixels which lie outside of a user-defined coordinate window are
-considered non-data pixels (eg, overscan) and are marked as invalid.
-(psphot recipe keywords \code{XMIN}, \code{XMAX}, \code{YMIN},
-\code{YMAX}, all set to 0 for PS1 PV3 -- invalid pixels were specified
-for PS1 PV3 with a supplied mask image, see \cite{waters2017}.
+that specific fit by setting a special bit (\code{MARK = 0x8000}).
+The initial mask, if not supplied by the user or library calls, is
+constructed by default from the image by applying three rules: 1)
+Pixels which are above a specified saturation level are marked as
+saturated.  The level is specified by the camera format keyword
+\code{CELL.SATURATION}, which may specify a value or define a header
+keyword which in turn specifies the value in the image header.  In the
+case of PS1 PV3, the header keyword \code{MAXLIN} specifies the
+saturation level for each chip (see \cite{waters2017}). 2) Pixels
+which are below a user-defined value are considered unresponsive and
+masked as dead.  (camera format keyword \code{CELL.BAD} = 0 for PS1
+PV3).  3) Pixels which lie outside of a user-defined coordinate window
+are considered non-data pixels (eg, overscan) and are marked as
+invalid.  (psphot recipe keywords \code{XMIN}, \code{XMAX},
+\code{YMIN}, \code{YMAX}, all set to 0 for PS1 PV3 -- invalid pixels
+were specified for PS1 PV3 with a supplied mask image, see
+\cite{waters2017}.
 
 The library functions used by \code{psphot} understand two types of
@@ -888 +908 @@
 some of the observed PSF variations in the images
 
-\note{need to describe fitting the pixel residual image}
-
 \note{write up the fitting process to define the grid?}
-
-\notespecify the rule for the polynomial order and grid scale}
-
-\note{discuss the improvements in the astrometric modeling PV1 - PV3}
 
 Several analytical functions which are likely candidates to describe
@@ -940 +954 @@
   \end{center}
 \end{figure}
+
+Once the smooth component of the PSF has been fitted with an
+analytical model, a pixel representation of the residuals is
+generated.  This representation is constructed as an image of the
+expected residuals for any position in the image.  The value of each
+pixel in the image model is determined from 2D fits to the measured
+residuals of the PSF stars.  Pixel values in this model are only
+defined for pixels with 
+
+The residual model is calculated using the residuals for all PSF
+stars.  The residuals (and their errors) for each star are
+renormalized by the flux of the star to put them on a consistent flux
+scale.  For each PSF star, all pixels within a user-specified radius
+(PSF.RESIDUALS.RADIUS = 9) are selected for the measurement.  For a
+given pixel in the model, the pixel values from the PSF stars are
+interpolated to the center of the model pixel. 
+
+Pixels for a given star which are more than XX sigma
+(PSF.RESIDUALS.NSIGMA = 3.0) deviant from the median value of the
+pixels from all stars are rejected.  
+
+If no spatial variation is allowed, the mean or median value is
+calculated for the model pixel based on the user-specified mean
+statistic (\code{PSF.RESIDUALS.STATISTIC = ROBUST_MEDIAN}).
+
+If spatial variation is requested, then the pixel values are fitted to
+a linear model:
+\[
+R[(x_{\rm mod},y_{\rm mod})][(x_{\rm ccd},y_{\rm ccd})] = R_o[(x_{\rm
+      mod},y_{\rm mod})] + R_x[(x_{\rm
+      mod},y_{\rm mod})] x_{\rm ccd} + R_y[(x_{\rm
+      mod},y_{\rm mod})] y_{\rm ccd}
+\]
+where $R[(x_{\rm mod},y_{\rm mod})][(x_{\rm ccd},y_{\rm ccd})]$ is the
+value for model pixel $(x_{\rm mod},y_{\rm mod})$ for a star with
+centroid at image pixel $(x_{\rm ccd},y_{\rm ccd})$.  The parameters
+$R_o, R_x, R_y$ are determined for each pixel in the model $[(x_{\rm
+    mod},y_{\rm mod})]$.
 
 \subsubsection{Candidate PSF Source Selection}
@@ -969 +1021 @@
 ignored.
 
+% \note{is the pixel scale $0.1 \sigma_w$ or PSF_CLUMP_GRID_SCALE = 0.2?}
+% psphotSourceStats sets PSF_CLUMP_GRID_SCALE to 0.1 \sigma_w^2, set
+% to 0.2 by default (before \sigma_w is known).
+% pmSource uses PSF_CLUMP_GRID_SCALE.  note that the image is in Mxx
+% (\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 XXX
-$\sigma$ of this centroid are selected as likely PSF-like sources in
-the image.  
-
-\note{work out the logic for selecting the PSF stars}
+moments of this peak are measured.  All sources which land within 2
+pixels of this centroid are selected as candidate PSF sources in the
+image.
 
 \begin{figure}[htbp]
@@ -1021 +1079 @@
 sources and ignored in the later PSF model fitting stages.
 
-%% table of orders:
-%% N stars | max order | max Ncells
-%%  16   |  1; //  4 cells, 4 per cell
-%%  54   |  2; //  9 cells, 6 per cell
-%% 128   |  3; // 16 cells, 8 per cell
-%% 300   |  4; // 25 cells, 12 per cell
-%% 576   |  5; // 36 cells, 16 per cell
+The order of the fit or number of grid samples is modified if the
+number of stars available for the fit is insufficient to justify the
+highest value.  Regardness of the requested order, if the number of
+stars is below the following limits, the order is limited as shown in
+Table~\ref{tab:psf.order.nstars}.  Note that the number of grid cells
+in one dimension is one greater than the equivalent polynomial order.
+
+\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}
+\begin{center}
+\begin{tabular}{lcl}
+\hline
+\hline
+{\bf Minimum Number of Stars} & {\bf Order} & {\bf Number of Grid Cells} \\
+\hline
+ 16 &  1 &  4 &   4 \\
+ 54 &  2 &  9 &   6 \\
+128 &  3 & 16 &   8 \\
+300 &  4 & 25 &  12 \\
+576 &  5 & 36 &  16 \\
+\hline
+\end{tabular}
+\end{center}
+\end{table}
+
 
 All of the PSF-candidate sources are then re-fitted using the PSF