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

    r40577 r40695  
    6363\section{Introduction}
    6464
    65 The age of synoptic surveys has come.  As optical (and other
    66 wavelength) telescopes are surveying ever increasing areas to ever
    67 fainter flux limits with multiple repeats, there is a growing interest
    68 in the study of transient phenomena.  This technological progress is
    69 well matched with the current scientific emphases on large samples of
    70 supernovae (SN), microlenses, asteroids, and other transients and
    71 variable sources.
     65The past three decades have seen the increasing importance of
     66time-domain surveys in astronomy.  These include asteroid searches
     67such as the Lincoln Near-Earth Asteroid Research
     68\citep[LINEAR][]{2000Icar..148...21S}, the Lowell Observatory
     69Near-Earth Object Search \citep[LONEOS,][]{1995DPS....27.0110B}, the
     70Catalina Sky Survey \citep{2003DPS....35.3604L}, and ATLAS
     71\citep{2018PASP..130f4505T}; microlensing surveys such as MACHO
     72\citep{1993ASPC...43..291A} and Optical Gravitational Lens Experiment
     73\citep[OGLE,][]{1992AcA....42..253U}; and searches for supernovae and
     74other transient sources such as ASAS-SN \citep{2014ApJ...788...48S}, the
     75Palomar Transient Factory \citep[PTF,][]{2009PASP..121.1395L}, and the Robotic Optical
     76Transient Search Experiment \citep[ROTSE-I,][]{2000ApJ...542..251A}.
     77
     78The Pan-STARRS Observatory \citep{chambers2017} has been a leader in
     79the searches for both explosive transient / supernova and potentially
     80hazardous asteroids.  According to the statistics maintained by David
     81Bishop\footnote{http://www.rochesterastronomy.org/snimages/archives.html},
     82since 2009, 40\% of all supernova have been discovered by
     83Pan-STARRS\,1.  Similarly, 24\% of all Near Earth Objects (NEOs)
     84discovered to date have been found by
     85Pan-STARRS\footnote{https://cneos.jpl.nasa.gov/stats/site\_all.html}.
     86Since 2014, when Pan-STARRS shifted its primary mission to the search
     87for NEOs, this fraction has increased to 41\%. Both of these search
     88programs use nightly observations to hunt for features which have
     89changed, either between multiple images in a single night or between
     90the current image and an archival reference image.
    7291
    7392PSF-matched image differencing\footnote{We eschew the popular term
     
    88107of the convolution kernel as a linear combination of basis functions,
    89108which allows the least-squares problem to be reduced to a matrix
    90 equation.  \citet{2000A&AS..144..363A} showed how this can be expanded
     109equation.  \citet{2000AAS..144..363A} showed how this can be expanded
    91110to allow spatial variation of the kernel across the images.  Of
    92111course, the basis functions used for the kernel may be completely
     
    137156basis functions, $g_i(x,y) k_i(u,v)$, where the inclusion of
    138157$g_i(x,y)$ allows for spatial variation of the kernel.  In order to
    139 enforce conservation of flux \citep[following][]{2000A&AS..144..363A},
     158enforce conservation of flux \citep[following][]{2000AAS..144..363A},
    140159we specify that all of the kernel basis functions have zero sum,
    141160$\sum_{u,v} k_i(u,v) = 0\ \forall i$.  This may be achieved by scaling
     
    161180$\chi^2$ between wide and narrow kernels.  Setting $c_i \equiv 0$ and
    162181$p_i \equiv 0$ reduces the above equation to the
    163 \citet{2000A&AS..144..363A} formalism, but with the normalisation
     182\citet{2000AAS..144..363A} formalism, but with the normalisation
    164183($b_0$) included explicitly.  In practise, the above sum will only be
    165184over small regions (known as ``stamps''), and if we assume that the
    166185spatial variation is not large, then we can simply use the coordinates
    167186of the stamp centres for the $g_i(x,y)$; this allows a faster
    168 calculation \citep{2000A&AS..144..363A}.
     187calculation \citep{2000AAS..144..363A}.
    169188
    170189To simplify the equation, we write
     
    199218other special polynomial for the $f_i(x,y)$ and $g_i(x,y)$ is simple
    200219and convenient.  The kernel basis function sets of
    201 \citet{1998ApJ...503..325A} and \citet{2000A&AS..144..363A} are
     220\citet{1998ApJ...503..325A} and \citet{2000AAS..144..363A} are
    202221\begin{equation}
    203222g_i(x,y) k_i'(u,v) = \psi_i x^\ell y^m u^p v^q \exp((u^2+v^2)/2s_i^2)
     
    338357\subsection{Stamps}
    339358
    340 The choice of stamps is key to successful PSF-matching --- the
    341 convolution kernel is only as good as the stamps used to construct it.
    342 We use a merged list of sources from photometry of the two input
    343 images as the basis of our stamps list.  Sources with a flag
    344 indicating that it is anything other than a pristine astrophysical
    345 source are excluded.  At the present time, we make no effort to select
    346 sources of a particular color or range of colors.
     359Since we restrict the analysis of the kernel required for PSF matching
     360to the small ``stamps'' centered on bright stars, the choice of stamps
     361is key to successful PSF-matching.  The convolution kernel is only as
     362good as the stamps used to construct it.  We use a merged list of
     363sources from photometry of the two input images as the basis of our
     364stamps list.  Sources with a flag indicating that it is anything other
     365than a pristine astrophysical source are excluded.  At the present
     366time, we make no effort to select sources of a particular color or
     367range of colors.
    347368
    348369We exclude sources with any masked pixels that would affect the
     
    490511progressive software packages producing \citep[e.g.,
    491512  SWarp:][]{2002ASPC..281..228B} and using \citep[e.g.,
    492   SExtractor:][]{1996A&AS..117..393B} weight maps to characterise the
     513  SExtractor:][]{1996AAS..117..393B} weight maps to characterise the
    493514noise over the image.  Because of simplicity and lower calculation
    494515cost relative to weights or standard deviations, we prefer to
     
    9931014\clearpage
    9941015\bibliographystyle{apj}
    995 \bibliography{apj-jour,references}
     1016%\bibliography{apj-jour,references}
     1017\input{diffs.bbl}
    9961018
    9971019\end{document}
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