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Changeset 39865


Ignore:
Timestamp:
Dec 14, 2016, 7:13:40 PM (10 years ago)
Author:
eugene
Message:

add figures, updates to analysis

Location:
trunk/doc/release.2015
Files:
4 added
4 edited

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

    r39857 r39865  
    1 % \documentclass[iop,floatfix]{emulateapj}
     1\documentclass[iop,floatfix]{emulateapj}
    22% \documentclass[iop,floatfix,onecolumn]{emulateapj}
    33% \pdfoutput=1
    44
    55% see latex.readme.txt for notes on using the PS1 template
    6 \documentclass[12pt,preprint]{aastex}
     6%\documentclass[12pt,preprint]{aastex}
    77%\documentclass[manuscript]{aastex}
    88%\documentclass[preprint2]{aastex}
    … …  
    3535\def\CfA{2}
    3636\def\MPIA{3}
    37 \def\Princeton{3}
     37\def\Princeton{2}
    3838\def\USNO{4}
    3939\def\JHU{1}
    … …  
    4242\author{
    4343Eugene A. Magnier,\altaffilmark{\IfA}
    44 IPP Team,
    45 %PS Builder List
     44R. H. Lupton,\altaffilmark{\Princeton}
     45W.~E. Sweeney,\altaffilmark{\IfA}
     46K.~C. Chambers,\altaffilmark{\IfA}
     47H.~A. Flewelling,\altaffilmark{\IfA}
     48M. E. Huber,\altaffilmark{\IfA}
     49P.~A. Price,\altaffilmark{\Princeton}
     50C. Z. Waters,\altaffilmark{\IfA}
     51PS1 Builders
    4652% W.~S. Burgett,\altaffilmark{\IfA}
    4753% K.~C. Chambers,\altaffilmark{\IfA}
    … …  
    7480\altaffiltext{\IfA}{Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu HI 96822}
    7581% \altaffiltext{\CfA}{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138}
    76 % \altaffiltext{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA}
     82\altaffiltext{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA}
    7783% \altaffiltext{\USNO}{US Naval Observatory, Flagstaff Station, Flagstaff, AZ 86001, USA}
    7884% \altaffiltext{\JHU}{Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA}
    … …  
    299305The PSPhot analysis is divided into several major stages:
    300306
    301 \begin{itemize}
     307\begin{enumerate}
    302308\item {\bf Image preparation} Load data, characterize the image
    303309  background, load or construct variance and mask images.
    … …  
    324330\item {\bf Output} Write out objects in selected format, write out
    325331  difference image, variance image, etc, as selected.
    326 \end{itemize}
     332\end{enumerate}
    327333
    328334PSPhot is highly configurable.  Users may choose via the configuration
    … …  
    378384  al. paper} for additional information).
    379385
    380 \begin{table}
     386\begin{table*}
    381387\caption{\label{tab:mask_values} PSPhot / GPC1 Mask Image Pixel Values}\vspace{-0.5cm}
    382388\begin{center}
    … …  
    406412\end{tabular}
    407413\end{center}
    408 \end{table}
     414\end{table*}
    409415
    410416The variance image, if not supplied is constructed by default from the
    … …  
    437443pixels are used to measure the local background for each background
    438444grid point, thus over-sampling the background spatial variations by a
    439 factor of 2.  In the interest of speed, 10,000 randomly selected
    440 {\em unmasked} pixels in these regions are sampled to determine the
    441 background.  \note{flesh out the details here}.  Bilinear
    442 interpolation is used to generate a full-resolution image from the grid of
    443 background points, and this image is then subtracted from the science
    444 image.  The background image and the background standard deviation
    445 image are kept in memory from which the values of \code{SKY} and
    446 \code{SKY_SIGMA} are calculated for each object in the output catalog.
     445factor of 2.  In the interest of speed, 10,000 randomly selected {\em
     446  unmasked} pixels in these regions are sampled to determine the
     447background.  Bilinear interpolation is used to generate a
     448full-resolution image from the grid of background points, and this
     449image is then subtracted from the science image.  The background image
     450and the background standard deviation image are kept in memory from
     451which the values of \code{SKY} and \code{SKY_SIGMA} are calculated for
     452each object in the output catalog.  See also the discussion in
     453\note{Waters et al REF}.
    447454
    448455\subsection{Initial Object Detection}
    … …  
    527534\end{eqnarray}
    528535
     536\begin{figure}[htbp]
     537  \begin{center}
     538  \includegraphics[width=\hsize,angle=0,clip]{peaks.ps}
     539  \caption{Illustration of peak finding and culling peaks within a
     540    footprint.  Insignificant peaks within the footprint of a brighter
     541    peak are ignored in further processing. }
     542  \end{center}
     543\end{figure}
     544
    529545\subsubsection{Footprints}
    530546
    … …  
    558574\subsubsection{Centroid and higher-order Moments}
    559575
     576\begin{figure}[htbp]
     577  \begin{center}
     578  \includegraphics[width=\hsize,angle=0,clip]{FWHM.smooth.trend.ps1.ps}
     579  \caption{Example of the biases encountered when measuring the second
     580    moments.  A simulated image was generated using the PS1 PSF
     581    profile.  Each panel corresponds to a different value of
     582    $\sigma_w$, as marked.  The solid red line is the true FWHM of the
     583    PSF used to generate the stars.  The blue solid line is the FWHM
     584    of the window function ($2.35\sigma_w$).  The gray dots are the
     585    FWHM derived from the measured second moments for stars in the
     586    image.  The dotted blue line is the target (65\% of the window
     587    function).  In this example, we would choose $\sigma_w$ between
     588    0.5 and 0.8 arcseconds so the dotted blue line would match the
     589    bright end of the gray dots.}
     590  \end{center}
     591\end{figure}
     592
    560593Once a collection of peaks has been identified, a number of basic
    561594properties of the objects related to the first and second moments are
    … …  
    566599appropriate aperture in which the moments are measured.  We also apply
    567600a ``window function'', down-weighting the pixels by a Gaussian of size
    568 $\sigma_W$ which is chosen to be large compared to the PSF size.  The
    569 choice of the window function $\sigma_W$ and the aperture is an
     601$\sigma_W$ which is chosen to be large compared to the PSF size,
     602$\sigma_{\rm PSF}$.  This
     603window function reduces the noise of the measurement of the first and
     604second moments by suppressing the noisy pixels at high radial distance
     605as well as by reducing the contaminating effects of neighboring stars.
     606The choice of the window function $\sigma_W$ and the aperture is an
    570607iterative process: for a given value of $\sigma_W$, the PSF stars will
    571 have a measured value of $\sigma$ which is smaller than the true value
    572 due to the window function.  \note{generate examples to illustrate
    573   this}.
     608have a measured value of $\sigma_{\rm PSF}$ which is modified by the effect of
     609the window function.  In addition, depending on the size of the window
     610function compared to the true PSF size, the measured value of the PSF
     611size, $\sigma_{\rm PSF}$, will be biased high or low depending on the
     612signal-to-noise of the object. 
     613
     614These effects are illustrated in Figure~\ref{fig:moment.window} using
     615simulated data.  An image was generated with a PSF model matching the
     616radial profile of the PS1 PSF model with a FWHM of 1.4 arcseconds.  As
     617the window function $\sigma_W$ is increased, the measured FWHM for the
     618bright simulated stars rises to meet the truth value.  For small
     619values of $\sigma_W$, fainter stars are biased to low measured values
     620of the FWHM.  For large values of $\sigma_W$, the faint stars are
     621biased to higher values and the scatter increases.
     622
     623In a real image, we do not know the true value of the PSF size.  If we
     624simply choose a very large window function and rely on bright stars,
     625our estimate of the PSF size will be quite noisy.  Compounding this
     626problem are the two additional facts that (1) we do not know which are
     627the real stars (as opposed to bright galaxies or possible image
     628artifacts) and (2) the brighter stars are themselves subject to
     629additional biases due to saturation and other non-linear effects
     630(c.f., ``the Brighter-Fatter'' effect, REF).  To make a robust
     631choice for the window function $sigma_w$, we choose a value
     632such that the measured value of $\sigma_{\rm PSF}$ is 65\% of
     633$\sigma_w$.  The resulting second moment values are biased somewhat
     634low (\approx 75\% of the truth value for the PS1 PSF profile), but are
     635relatively unbiased as a function of brightness.
    574636
    575637To choose the value of $\sigma_W$, we try values of (1, 2, 3, 4.5, 6,
    576 9, 12, 18) pixels \note{list arcseconds}.  For each of these values,
    577 we then select candidate PSF stars based on the distribution of the
    578 measured $\sigma_{x,x}, \sigma_{y,y}$ values.  For each test value of
    579 $\sigma_w$, determine the ratio $f = \frac{\sigma_{x,x} +
    580   \sigma{y,y}}{2 \sigma_w}$, i.e., the ratio of the window size to the
    581 observed PSF size.  We interpolate to find a value of $\sigma_W$ for
    582 which $f$ is expected to be 0.65.  \note{what is the expected ratio of
    583   $\sigma_x$ to the true value?}.  We call this value the
    584 \code{MOMENTS_GAUSS_SIGMA}.  We use an aperture with a radius of
    585 \code{PSF_MOMENTS_RADIUS} = 4$\times$ \code{MOMENTS_GAUSS_SIGMA} to
    586 select the pixels for the measurement.
     6389, 12, 18) pixels $\approx$ (0.26, 0.51, 0.77, 1.15, 1.54, 2.3, 3.1,
     6394.6) arcseconds.  For each of these values, we then select candidate
     640PSF stars based on the distribution of the measured $\sigma_{x,x},
     641\sigma_{y,y}$ values.  For each test value of $\sigma_w$, we determine
     642the ratio $f = \frac{\sigma_{x,x} + \sigma{y,y}}{2 \sigma_w}$, i.e.,
     643the ratio of the window size to the observed PSF size.  We interpolate
     644to find a value of $\sigma_W$ for which $f$ is expected to be 0.65.
     645We call this value the \code{MOMENTS_GAUSS_SIGMA}.  We use an aperture
     646with a radius of \code{PSF_MOMENTS_RADIUS} = 4$\times$
     647\code{MOMENTS_GAUSS_SIGMA} to select the pixels for the measurement.
    587648
    588649Once \code{PSF_MOMENTS_SIGMA} has been determined, moments are
    … …  
    656717for example, a 2-D elliptical Gaussian:
    657718\begin{eqnarray}
    658 f(x,y) & = & I_o exp (-z) + S  \\
     719f(x,y) & = & I_o e^{-z} + S  \\
    659720    z  & = & \frac{x^2}{2\sigma_x^2} + \frac{y^2}{2\sigma_y^2} + \sigma_{\rm xy} x y \\
    660721    x  & = & x_{\rm ccd} - x_o \\
    661     y  & = & y_{\rm ccd} - y_o \\
     722    y  & = & y_{\rm ccd} - y_o
    662723\end{eqnarray}
    663724The object model will have a variety of model parameters, in this case
    … …  
    680741\sigma_{\rm xy}$) while the independent parameters would be the
    681742centroid, normalization and local sky values ($x_o, y_o, I_o, S$).
    682 PSPhot uses a 2-D polynomial to specify the variation in the PSF
    683 parameters as a function of position in the image \note{or an
    684   interpolated map}.  In the case of the elliptical Gaussian, this
    685 implies that the parameters are each a function of the object centroid
     743Thus these parameters are each a function of the object centroid
    686744coordinates:
    687745\begin{eqnarray}
    … …  
    690748\sigma_{xy} & = & f_3(x,y) \\
    691749\end{eqnarray}
    692 
    693 \note{PV3 config values: we used 6x6 map not 3x3 (PV2) or 3rd order
    694   polynomial (PV1)}
     750PSPhot represents the variation in the PSF parameters as a function of
     751position in the image in two possible ways, specified by the
     752configuration.  The first option is to use a 2-D polynomial which is
     753fitted to the measured parameter values across the image.  The second
     754option is to use a grid of values which are measured for objects
     755within a subregion of the image.  In the latter case, the value at a
     756specific coordinate in the image is determined by interpolation
     757between the nearest grid points.  The order of the polynomial or the
     758sampling size of the grid is dynamically determined depending on the
     759number of available of PSF stars.  In the case of the PV3 analysis,
     760the grid of values was used, with a maximum of $6\times 6$ samples per
     761GPC1 chip image.  For the earlier PV2 analysis, the maximum grid
     762sampling was $3\times 3$ per GPC1 chip image.  For the PV1 analysis,
     763the polynomial representation was used, with up to 3rd order terms.
     764The higher order representation was used for PV3 in order to follow
     765some of the observed PSF variations in the images
     766
     767% XXX specify the rule for the polynomial order and grid scale
     768% XXX discuss the improvements in the astrometric modeling PV1 - PV3
    695769
    696770PSPhot uses a single structure to represent the object model and
    … …  
    760834their peaks, as well as an approximate signal-to-noise ratio.  All
    761835objects with a S/N ratio greater than a user-defined parameter
    762 (\code{PSF_SHAPE_NSIGMA} ???) are selected by PSPhot, though objects
    763 which have more than a certain number of saturated pixels are excluded
    764 at this stage.  PSPhot then examines the 2-D plane of $\sigma_x,
    765 \sigma_y$ in search of a concentrated clump of objects.  To do this,
    766 it constructs an artificial image with pixels representing the value
    767 of $\sigma_x, \sigma_y$, using a user-defined scale for the size of a
    768 pixel in this artificial image (note that the units of the $\sigma_x,
    769 \sigma_y$ plane are the size of the second-moment in pixels in the
    770 original image).  A typical value for the bin size is approximately
    771 0.1 image pixels.  The binned $\sigma_x, \sigma_y$ plane is then
    772 examined to find a peak which has a significance greater than XXX.
    773 Unless the image is extremely sparse, such a peak will be well-defined
    774 and should represent the objects which are all very similar in shape.
    775 Other objects in the image will tend to land in very different
    776 locations, failing to produce a single peak.  To avoid detecting a
    777 peak from the unresolved cosmic rays, objects which have
     836(\code{PSF_SHAPE_NSIGMA} = 20.0) are selected by PSPhot, though
     837objects which have more than a certain number of saturated pixels are
     838excluded at this stage.  PSPhot then examines the 2-D plane of
     839$\sigma_x, \sigma_y$ in search of a concentrated clump of objects (see
     840Figure~\ref{fig:moment.class}).  To
     841do this, it constructs an artificial image with pixels representing
     842the value of $\sigma_x, \sigma_y$, using a user-defined scale for the
     843size of a pixel in this artificial image (note that the units of the
     844$\sigma_x, \sigma_y$ plane are the size of the second-moment in pixels
     845in the original image).  A typical value for the bin size is
     846approximately 0.1 image pixels.  The binned $\sigma_x, \sigma_y$ plane
     847is then examined to find a peak which has a significance greater than
     848XXX.  Unless the image is extremely sparse, such a peak will be
     849well-defined and should represent the objects which are all very
     850similar in shape.  Other objects in the image will tend to land in
     851very different locations, failing to produce a single peak.  To avoid
     852detecting a peak from the unresolved cosmic rays, objects which have
    778853second-moments very close to 0 are ignored.  The only danger is if the
    779854PSF is very small and too many of these objects are rejected as cosmic
    … …  
    785860the image. 
    786861
     862\begin{figure}[htbp]
     863  \begin{center}
     864  \includegraphics[width=\hsize,angle=0,clip]{moment.class.ps}
     865  \caption{\label{fig:moment.class} Illustration of PSF star selection using the FWHM derived
     866    from the second moments in $X_{\rm ccd}$ and $Y_{\rm ccd}$
     867    directions.  The dominant clump is located in this diagram.
     868    Galaxies tend to have a range of sizes and thus spread out above
     869    the stars.  Cosmic rays also have a range of sizes, with one
     870    dimension smaller than the PSF.  The red circle represents the PSF
     871    star candidates. }
     872  \end{center}
     873\end{figure}
     874
    787875\subsubsection{PSF Candidate Object Model Fits}
    788876
    789877All candidate PSF objects are then fitted with the selected object
    790878model, allowing all of the parameters (PSF and independent) to vary in
    791 the fit.  PSPhot uses the Levenberg-Marqardt method \note{REF, link to
    792   psLibADD} for the non-linear fitting.  Non-linear fitting can be
    793 very computationally intensive, particularly for if the starting
    794 parameters are far from the minimization values.  PSPhot uses the
    795 first and second moments to make a good guess for the centroid and
     879the fit.  PSPhot uses the Levenberg-Marquardt minimization technique
     880\note{link to psLibADD} for the non-linear fitting.  Non-linear
     881fitting can be very computationally intensive, particularly for if the
     882starting parameters are far from the minimization values.  PSPhot uses
     883the first and second moments to make a good guess for the centroid and
    796884shape parameters for the PSF models.  Any objects which fail to
    797885converge in the fit are flagged as invalid.
    … …  
    830918\subsection{Bright Source Analysis}
    831919
    832 \subsubsection{Very Bright Stars}
    833 \note{flesh out}
    834 
    835 The PSF modeling code fails to fit the wings of highly saturated stars
    836 if the core of the star is too contaminated by saturated pixels. For
    837 stars with estimated instrumental magnitudes brighter than XXX, we fit
    838 and subtract a radial profile modeled with a spline (?).
     920%% \subsubsection{Very Bright Stars}
     921%%
     922%% The PSF modeling code fails to fit the wings of highly saturated stars
     923%% if the core of the star is too contaminated by saturated pixels. For
     924%% stars with estimated instrumental magnitudes brighter than XXX, we fit
     925%% and subtract a radial profile modeled with a spline (?).
    839926
    840927\subsubsection{Fast Ensemble PSF Fitting}
    … …  
    881968\subsubsection{PSF Model applied to detected objects}
    882969
     970\note{review the discussion below}
     971
    883972Once a PSF model has been selected for an image, PSPhot attempts to
    884973fit all of the detected objects, above a user-defined signal-to-noise
    … …  
    886975dependent parameters are fixed by the PSF model and only the 4
    887976independent object model parameters are allowed to vary in the fit.
    888 PSPhot again uses the Levenberg-Marqardt process for the non-linear
     977PSPhot again uses Levenberg-Marquardt minimization for the non-linear
    889978fitting.  The objects are fitted in their S/N order, starting with the
    890979brightest and working down to the user-specified limit.
    891980
    892 Once a solution has been achieved, PSPhot attempts to judge the
    893 quality of the PSF model as a representation of the object shape.  To
    894 do this, it calculates the next step of the minimization {\em allowing
    895   the shape parameters to vary}.  This step, essentially the
    896 Gauss-Newton minimization distance from the current local minimum,
     981Once a solution has been achieved for an object, PSPhot attempts to
     982judge the quality of the PSF model as a representation of the object
     983shape.  To do this, it calculates the next step of the minimization
     984{\em allowing the shape parameters to vary}.  This step, essentially
     985the Gauss-Newton minimization distance from the current local minimum,
    897986should be very small if the object is well represented by the PSF, but
    898987large if the PSF is not a good representation of the object flux.  The
    … …  
    9521041represented and may have larger residual significance.
    9531042
    954 \note{I am not sure the above discussion is still (PV3) true.  To be reviewed.}
    955 
    9561043\subsubsection{Blended Sources}
    9571044
    … …  
    10441131not modified. 
    10451132
    1046 \note{we have no code yet to select the best of several models for a
    1047   given objects.  The relative value of the Chi-Square is the obvious
    1048   test in this case}.
    1049 
    10501133\subsection{Faint Sources}
    10511134
    … …  
    10601143
    10611144The objects which are measured in this faint-object stage are clearly
    1062 low significance detections.  A typical threshold for the bright
    1063 object analysis would S/N of 5 - 10.  \note{PV3 value is 20.0?}  The
    1064 lower limit cutoff for the faint object analysis would typically be
    1065 S/N of 2 - 4.  \note{PV3 value is 5.0?}  Objects detected in the faint
    1066 object stage are fitted with the PSF model using the linear, ensemble
    1067 fitting process.
     1145low significance detections.  The PV3 threshold for the bright object
     1146analysis is a signal-to-noise of 20.  The lower limit cutoff for the
     1147faint object analysis in PV3 is a signal-to-noise of 5.0.  Objects
     1148detected in the faint object stage are fitted with the PSF model using
     1149the linear, ensemble fitting process.
    10681150
    10691151\subsection{Aperture Correction Measurement}
    … …  
    11141196number of very bright stars is limited in any image, and of course the
    11151197brighter stars are more likely to suffer from non-linearity or
    1116 saturation. 
     1198saturation.  PSPhot measures the aperture correction ({\em ApResid})
     1199for every PSF candidate object and applies this correction to the PSF
     1200model photometry.
    11171201
    11181202% How important is this effect?  Consider a typical bright object with a
    … …  
    11301214% magnitude}.
    11311215
    1132 PSPhot measures the aperture correction ({\em ApResid}) for every PSF
    1133 candidate object, then calculates the trend of this correction as a
    1134 function of the magnitude.  This trend is fitted with a line.  The
    1135 resulting function can be used to determine the effective aperture
    1136 correction for an infinite flux object and the average bias inherent
    1137 in the sky measurement for the image.  The scatter of the
    1138 PSF-candidate object measurements about this trend is a measure of how
    1139 well we can measure photometry from the image by applying the specific
    1140 PSF model.  The slope of this trend is a measure of the bias in the
    1141 local sky measurment for each object.  In principal, the measured sky
    1142 levels could be modified by this bias.  More generally, the measured
    1143 bias in a collection of images could be used to improve the model
    1144 fitting or sky fitting portion of the software the remove the bias
    1145 term.
     1216%%% PSPhot measures the aperture correction ({\em ApResid}) for every PSF
     1217%%% candidate object, then calculates the trend of this correction as a
     1218%%% function of the magnitude.  This trend is fitted with a line.  The
     1219%%% resulting function can be used to determine the effective aperture
     1220%%% correction for an infinite flux object and the average bias inherent
     1221%%% in the sky measurement for the image.  The scatter of the
     1222%%% PSF-candidate object measurements about this trend is a measure of how
     1223%%% well we can measure photometry from the image by applying the specific
     1224%%% PSF model.  The slope of this trend is a measure of the bias in the
     1225%%% local sky measurment for each object.  In principal, the measured sky
     1226%%% levels could be modified by this bias.  More generally, the measured
     1227%%% bias in a collection of images could be used to improve the model
     1228%%% fitting or sky fitting portion of the software the remove the bias
     1229%%% term.
    11461230
    11471231PSPhot allows a collection of PSF model functions to be tried on all
    … …  
    11541238\code{PSF_MODEL_N - 1} specify the names of the models which should be
    11551239tested.
     1240
     1241Several likely PSF model classes are available within \code{psphot}:
     1242\begin{itemize}
     1243\item Gaussian : $f = I_0 e^{-z}$
     1244\item Pseudo-Gaussian : $f = I_0 (1 + z + \frac{1}{2} z^2 + \frac{1}{6} z^3)^{-1}$ \code{[PGAUSS]}
     1245\item Variable Power-Law : $f = I_0 (1 + z + z^{\alpha})^{-1}$ \code{[RGAUSS]}
     1246\item Steep Power-Law : $f = I_0 (1 + \kappa z + z^{2.25})^{-1}$ \code{[QGAUSS]}
     1247\item PS1 Power-Law : $f = I_0 (1 + \kappa z + z^{1.67})^{-1}$ \code{[PS1_V1]}
     1248\end{itemize}
     1249where $z \propto r^2$ ($z = \frac{x^2}{2\sigma_x^2} +
     1250\frac{y^2}{2\sigma_y^2} + \sigma_{\rm xy} x y $).  The Pseudo-Gaussian
     1251is a Taylor expansion of the Gaussian and is used by Dophot
     1252\citep{dophot}.  The latter profiles are similar to the Moffat profile
     1253form \citep{moffat,buonanno}, with small differences.  For the PS1
     1254GPC1 analysis, we used the \code{PS1_V1} model, which we found by
     1255experimentation to match well to the observed profiles generated by
     1256PS1.  Using a fixed power-law exponent results in somewhat faster
     1257profile fitting compared to the variable power-law exponent model.
     1258
     1259% moffat : 1969A&A.....3..455M
     1260% buonanno : 1983A&AS...51...83B
     1261
     1262\begin{figure}[htbp]
     1263  \begin{center}
     1264  \includegraphics[width=\hsize,angle=0,clip]{radial.profiles.ps}
     1265  \caption{Radial profiles of stellar images from PS1.  These two
     1266    profiles illustrate the radial trend of the PS1 PSFs for a star
     1267    with FWHM 0.9 arcsec (red) and 2.2 arcsec (blue).  The black line
     1268    shows the PSF model with radial trend of the form $(1 + \kappa r^2 + r^{3.33})^{-1}$.}
     1269  \end{center}
     1270\end{figure}
    11561271
    11571272\subsection{Radial Profiles}
    … …  
    13801495
    13811496The PSF-convolved galaxy model fitting analysys uses the
    1382 Levenberg-Marquardt method to determine the best fit.  In this
     1497Levenberg-Marquardt minimization method to determine the best fit.  In this
    13831498process, the $\chi^2$ value to be minimized is:
    13841499\[
    … …  
    16041719Figures Needed for this document:
    16051720
    1606 * illustration of peak & col for footprint
    1607 * measured moments vs gauss window size for PS1 profile
    1608 * PS1 PSF profiles (good and bad seeing)
    1609 * Mxx vs Myy plane for selecting PSF stars (etc)
    1610 * example of a very bright star, subtracted?
    1611 * CR masking example?
    16121721* aperture - PSF model example
    1613 * make of the sky with galaxy region illustrated?
    1614 
     1722* map of the sky with galaxy region illustrated?
    16151723* plots showing the quality of the data?
    16161724
    16171725Tables needed:
    16181726
    1619 * table of mask image bit values
    16201727* table of models?
    16211728
    16221729Work still needed:
    16231730
    1624 * Figures
    16251731* Tables
    16261732* refereces for other programs
    16271733
    1628 * moments & gauss sigma issue
    1629 * words on the 2d maps
    1630 * PS1 PSF profile discussion
     1734* authors
    16311735* PSF residual map
    16321736* section 3.5.3 Model applied to detected objects needs to be reviewed
    … …  
    16391743* reduce coding description?
    16401744* put engineering docs (psLib, psModules) on public website
     1745
     1746% example of 2 image figure:
     1747\begin{figure}
     1748  \centering
     1749  \begin{minipage}{0.45\hsize}
     1750    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt_trail.png}
     1751  \end{minipage}%
     1752  \begin{minipage}{0.45\hsize}
     1753    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt_trail.png}
     1754  \end{minipage}
     1755  \caption{Example of a profile cut along the y-axis through a bright star on exposure o5677g0123o OTA11 in cell xy60 (left panel) and on the subsequent exposure o5677g0124o (right panel).  In both figures, the green points show the image corrected with all appropriate detrending steps, but without burntool applied, illustrating the amplitude of the persistence trails.  The red points show the same data after the burntool correction, which reduces the impact of these features.  Both exposures are in the \gps{} filter with exposure times of 43s}
     1756\end{figure}
     1757

  • trunk/doc/release.2015/ps1.analysis/plots.sh

    r39857 r39865  
     1
     2macro choose.seed
     3
     4  for i 0 100
     5    rndseed $i
     6    peak.and.col
     7    echo $i
     8    cursor
     9  end
     10end
    111
    212macro peak.and.col
     13
     14  # using 3 gives a pretty look
     15  rndseed 3
    316
    417  $scale = 50.0
    … …  
    619  $Ia = 500; $Xa = 100
    720  $Ib = 100 ; $Xb = 50
    8   $Ic = 30  ; $Xc = 180
     21  $Ic = 20  ; $Xc = 180
    922
    1023  create x 0 200
    … …  
    2235 
    2336  clear -s
    24   section a 0.0 0.5 1.0 0.5
    25   lim x yo; box; plot x yo -x hist
     37  resize 1200 600
     38  label -fn helvetica 24
     39  section a 0.0 0.5 1.0 0.45
     40  lim x yo; box -lw 2 -xpad 0.5 -labels 0100 -ticks 1100; plot x yo -x hist -lw 2
     41  label -y "Raw Counts"
    2642
    27   section b 0.0 0.0 1.0 0.5
    28   lim x yo; box; plot x ym -x hist
     43  section b 0.0 0.0 1.0 0.55
     44  lim x yo; box -lw 2 +xpad 0.5 -xpad 3.5 -labelpadx 3.0 -ticks 1100; plot x ym -x hist
     45  label -y "Smoothed Counts" -x "Pixel Coordinate"
    2946
    3047  set yd = 500 - ym
    … …  
    3249  $dX = 5
    3350  peak x ym {$Xa - $dX} {$Xa + $dX}
    34   line -c red $peakpos {$peakval + 10} to $peakpos $YMAX
     51  line -c red $peakpos {$peakval - 10} to $peakpos 400; textline 90 350 "Primary Peak"
    3552
    3653  peak x ym {$Xb - $dX} {$Xb + $dX}
    37   line -c red $peakpos {$peakval + 10} to $peakpos $YMAX
     54  line -c red $peakpos {$peakval + 10} to $peakpos 350; textline 30 400 "Significant Peak"
    3855
    3956  peak x ym {$Xc - $dX} {$Xc + $dX}
    40   line -c red $peakpos {$peakval + 10} to $peakpos $YMAX
     57  line -c red $peakpos {$peakval + 10} to $peakpos 250; textline 160 300 "Insignificant Peak"
    4158
    4259  $dX = 5
    4360  peak x yd $Xb {$Xb + 2*$dX}
    44   line -c blue $peakpos {ym[$peakpos] - 10} to $peakpos $YMIN
     61  line -c blue $peakpos {ym[$peakpos] - 10} to $peakpos 150; textline 50 100 "Col"
    4562
    4663  peak x yd {$Xc - 2*$dX} $Xc
    47   line -c blue $peakpos {ym[$peakpos] - 10} to $peakpos $YMIN
     64  line -c blue $peakpos {ym[$peakpos] + 10} to $peakpos 150; textline 170 190 "Col"
     65
     66  png -name peaks.png
     67  ps  -name peaks.ps
    4868
    4969end

  • trunk/doc/release.2015/ps1.calibration/calibration.tex

    r39855 r39865  
    11801180* bright-end photometry residuals [running cdhist code, but is the density too low?]
    11811181
     1182* careful discussion of calibration wrt scolnic et al
     1183
    11821184\end{verbatim}
    11831185

  • trunk/doc/release.2015/ps1.datasystem/datasystem.tex

    r39848 r39865  
    853853
    854854\end{document}
     855
     856Figures needed for this document:
     857
     858*
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