Changeset 37865

Timestamp:

Jan 18, 2015, 1:13:42 PM (12 years ago)

Author:

eugene

Message:

insert the psphot manual text, needs cleanup

File:

• trunk/doc/release.2015/ps1.analysis/analysis.tex (modified) (1 diff)

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

@@ -105 +105 @@
 \section{INTRODUCTION}\label{sec:intro}
 
-\section{Pan-STARRS1}
-
-\section{Discussion}
-
-\section{Conclusion}
+The Pan-STARRS Image Processing Pipeline is responsible for the basic
+analysis of images from the Pan-STARRS telescopes Gigapixel Camera.
+The overall goals and requirements of the Image Processing Pipeline
+are described in the IPP System/Subsystem Design Description (SSDD;
+PSDC-430-XXX) and the IPP System Requirements Specification (SRS;
+PSDC-430-XXX).  Among the Pan-STARRS project survey goals is a
+repeated all-sky survey in 5 filters, {\it grizy}, beginning with a
+pre-survey with the prototype telescope PS-1.  The photometric and
+astrometric precision goals for the all-sky surveys, as well as the
+other survey components, are quite stringent:
+
+\begin{itemize}
+\item relative photometry: 10 millimagnitudes scatter for bright stars
+across the sky in the internal photometric system; 
+
+\item relative astrometry; 10 milliarcseconds scatter for individual
+stars between repeated images.
+
+\item absolute astrometry: 100 milliarcseconds scatter for all ICRS
+  reference stars (Tycho).
+\end{itemize}
+
+An additional constraint on the Pan-STARRS system comes from the high
+data rate.  The prototype telescope alone is expected to produce
+typically $\sim 700$ GB per night of imaging data.  These images will
+not be limited to high galactic latitudes, so large numbers of
+measurable stars can be expected in much of the data.  The combination
+of the high precision goals of the astrometric and photometric
+measurements and the high data rate (and a finite computing budget)
+mean that the process of detecting, classifying, and measuring the
+astronomical objects in the image data stream will be a significant
+challenge.  
+
+In order to achieve these ambitious goals, the object detection,
+classification, and measurement process must be both precise and
+efficient.  Not only is it necessary to make a careful measurement of
+the flux of individual objects, it is also critical to characterize
+the image point-spread-function, and its variations across the field
+and from image to image.  Since comparisons between images must be
+reliable, the measurements must be stable for both photometry and
+astrometry.
+
+\subsection{Comparable Programs}
+
+A variety of astronomical software packages perform the basic object
+detection, measurement, and classification tasks needed by the
+Pan-STARRS IPP.  Each of these programs have their own advantages and
+disadvantages.  Below we discuss some of the most widely used of these
+other packages, highlighting the features of the programs which are
+particularly desirable, and noting aspects of the programs which are
+problematic for the IPP.
+
+\begin{itemize}
+
+\item DoPhot : analytical fitted model with aperture corrections.
+  pro: well-tested, stable code.  con: limited range of models,
+  algorithm converges slowly to a PSF model, limited tests of PSF
+  validity, inflexible code base, fortran (P. Schechter)
+
+\item DAOPhot : Pixel-map PSF model with analytical component.  pro:
+  well-tested, high-quality photometry.  con: Difficult to use in an
+  automated fashion, does it handle 2D variations well? (P. Stetson)
+
+\item Sextractor : pure aperture measurement with rudimentary
+  object subtraction.  pro: fast, widely used, easy to automate.  con:
+  poor object separation in crowded regions, PSF-modeling is only
+  beta (psfex), what models are available? (E. Bertin)
+
+\item apphot : IRAF-based aperture photometry.  pro: widely used.
+  con: IRAF-based, aperture photometry. (???)
+
+\item galfit : detailed galaxy modeling.  not a multi-object PSF
+  analysis tool.  con: does not provide a PSF model, not easily
+  automated.  very detailed results in very slow processing.  only a
+  galaxy analysis program. (C. Impey)
+
+\item SDSS phot : con: tightly integrated into the SDSS software
+  environment.  (R. Lupton)
+
+\end{itemize}
+
+\note{discussion of these packages is insufficient: flesh out
+  discussion and add in the references.}
+
+\note{Add discussion of the lessons learned from experience with previous
+  analysis programs}
+
+The Pan-STARRS IPP team decided that none of the existing packages met
+all of their needs, particularly given the very challenging goals of
+the project.  We decided to redesign the photometry analysis from
+scratch, using the lessons learned from the existing photometry
+systems.  In the process, the object analysis software would be
+written using the data analysis C-code library written for the IPP,
+\code{psLib}, and the components of the photometry code would be
+integrated into the IPP's mid-level astronomy data analysis toolkit
+called \code{psModules}.  The result is 'PSPhot', which can be used
+either as a stand-alone C program, or as one of the high-level IPP
+components of \code{psModules}, available to programmers either via a
+C interface or through a SWIG interface in Perl (or potentially
+Python).
+
+\note{discuss the psphot program varients}
+
+\section{PSPhot Design Goals}
+
+PSPhot has a number of important requirements that it must meet, and a
+number of design goals which we believe will help to make usable in a
+wide range of circumstances.  The critical requirements of the
+Pan-STARRS IPP which drive the requirements for PSPhot:
+
+\begin{itemize}
+\item {\bf 10 millimagnitude photometric accuracy}.  For PSPhot, this
+  implies that the measured photometry of stellar objects must be
+  substantially better than this 10 mmag since the photometry error
+  per image is combined with an error in the flat-field calibration
+  and an error in measuring the atmospheric effects.  We have set a
+  goal for PSPhot of 3mmag photometric consistency for bright stars
+  between pairs of images obtained in photometric conditions at the
+  same pointing, ie to remove sensitivity to flat-field errors.  This
+  goal splits the difference between the three main contributors and
+  still allows some leeway.  This requirement must be met for
+  well-sampled images and images with only modest undersampling.
+
+\item {\bf 10 milliarcsecond astrometric accuracy}. Relative
+  astrometric calibration depends on the consistency of the individual
+  measurements.  The measurements from PSPhot must be sufficiently
+  representative of the true object position to enable astrometric
+  calibration at the 10mas level.  The error in the individual
+  measurements will be folded together with the errors introduced by
+  the optical system, the effects of seeing, and by the available
+  reference catalogs.  We have set a goal for PSPhot of 5mas
+  consistency between the true source postion and the measured
+  position given reasonable PSF variations under simulations.  This
+  level must be reached for images with 250 mas pixels, implying
+  PSPhot must introduce measurement errors less than 1/50th of a
+  pixel. \note{the choice of F32 parameters places a numerical limit
+  of 1e-7 on the accuracy of a pixel relative to the size of a chip
+  (since a single data value is used for X or Y).  For the $4800^2$
+  GPC chips, this yields a limit of about 0.25 milliarcsecond.}
+
+\item {\bf processing time of 45 seconds} This requirement depends
+  strongly on the hardware organization, the amount of time spent on
+  other analysis steps, the density of stars per image, and the depth
+  for a given type of image.  For the sources at the faint limit (eg,
+  $5\sigma$), the average density of sources is expected to be roughly
+  $3\times10^5$ per square degree, while sources at the 20 $\sigma$
+  level may have densities of $\sim 5\times10^4$ per square degree.
+  Allowing 30 seconds for the PSPhot portion of the analysis, of which
+  15 is used for careful analysis of the brighter sources, 10 seconds
+  is used for PSF modeling and other overheads, and the remaining 5
+  seconds is used for the PSF fitting of the faintest source implies
+  that the detailed modelling may take roughly 3msec per source, and
+  the basic PSF fitting may be allowed 150 usec per source.
+\end{itemize}
+
+The design goals for PSPhot are chosen to make the program flexible,
+general, and able to meet the unknown usages cases future projects may
+require:
+
+\begin{itemize}
+\item {\bf Flexible PSF model} Different image sources require
+  different ways of representing the PSF.  Ideally, both analytical
+  and pixel-based versions should be possible.
+
+\item {\bf PSF spatial variation} Most images result in some spatial
+  PSF variations at a certain level.  The PSF representation should
+  naturally incorporate 2-D variations.
+
+\item {\bf Flexible non-PSF models} PSPhot must be able to represent
+  PSF-like objects as well as non-PSF sources.  It must be easy to add
+  new object models as interesting representations of sources are
+  invented.
+
+\item {\bf Clean code base} PSPhot should incorporate a high-degree of
+  abstraction and encapsulation so that changes to the code structure
+  can be performed without pulling the code apart and starting from scratch.
+
+\item {\bf PSF validity tests} PSPhot should include the ability to
+  choose different types of PSF models for diffent situations, or to
+  provide the user with methods for assessing the different PSF models.
+
+\item {\bf Careful aperture corrections} PSPhot must carefully measure
+  and correct for the photometric and astrometric trends introduced by
+  using analytical PSF models.
+
+\item {\bf User Configurable} PSPhot should allow users to change the
+  options easily and to allow different approaches to the analysis.
+
+\end{itemize}
+
+\section{PSPhot Analysis Process}
+
+\subsection{Overview}
+
+The PSPhot analysis is divided into several major stages:
+
+\begin{itemize}
+\item {\bf Image preparation} Load data, characterize the image
+  background, load or construct noise and mask images.
+
+\item {\bf Initial object detection} Smooth, find peaks, measure basic
+  properties
+
+\item {\bf PSF determination} Select PSF candidates, perform model
+  fits, build PSF model from fits, select best PSF model class.
+
+\item {\bf Bright object analysis} Fit objects with PSFs, determine
+  PSF validity, subtract PSF-like objects, fit non-PSF model(s),
+  select best model class, subtract model.
+
+\item {\bf Low S/N sources} Detect low-level sources, measure
+  properties (aperture or PSF)
+
+\item {\bf Aperture corrections} Measure the curve-of-growth, spatial
+  aperture variations, and background-error corrections.  
+
+\item {\bf Output} Write out objects in selected format, write out
+  difference image, noise image, etc, as selected.
+\end{itemize}
+
+Note that a given run of PSPhot allows the user to perform many of
+these stages only if needed.  For example, the PSF model may already be
+available from external information, in which case the PSF modeling
+stage can be skipped.  Or, when used as a library function, the image
+may have already been loaded and the mask and weight images
+constructed.  In some implementations, it may be possible to skip the
+initial object detection stage because only supplied sources are
+measured.  These are only some of the possible configurations.  The
+use of these different configurations depends on the source of the
+image, the desired detail and speed of the processing, and the level
+of accuracy desired from the analysis.
+
+\subsection{Image Preparation}
+
+The first step is to prepare the image for detection of the
+astronomical objects.  We need three separate images: the measured
+flux, the corresponding variance image, and a mask defining which
+pixels are valid and which should be ignored.  For the stand-alone
+program, the input flux image is a required program argument.  When it
+is loaded, it is converted by default to 32-bit floating point
+representation.  In the function-call form of PSPhot, the image must
+be supplied by the user in 32-bit floating point format.  The noise
+and mask images may either be provided by the user, or they may be
+automatically generated from the input image, based on
+configuration-defined values for the image gain, read-noise,
+saturation, and so forth.  For the function-call form of the program,
+the flux image is provided in the API, and references to the mask and
+noise are provided in the configuration information.  As in the
+stand-alone C-program, the noise and mask may be constructed
+automatically by PSPhot.
+
+\note{describe the use of the covariance image}
+\note{describe the difference between 'bad' and 'suspect' pixels}
+
+For the mask, we use a 16-bit image in which a value of 0 represents a
+valid pixel.  We use each of the 16 bits to define different reasons a
+pixel should be ignored.  This allows us to optionally respect or
+ignore the mask depending on the circumstance.  For example, in some
+cases, we ignore saturated pixels completely while in other
+circumstances, it may be useful to know the flux value of the
+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.  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 (configuration keyword: \code{SATURATE}).  2) Pixels which
+are below a user-defined value are considered unresponsive and masked
+as dead.  3) Pixels which lie outside of a user-defined window are
+considered non-data pixels (eg, overscan) and are marked as invalid.
+The valid window is defined by the configuration variables
+\code{XMIN}, \code{XMAX}, \code{YMIN}, \code{YMAX}.
+
+\note{discuss the mask.config file, in which the mask meanings are assigned to bit values}
+
+The noise image, if not supplied is constructed by default from the
+flux image using the configuration supplied values of \code{GAIN} and
+\code{READ\_NOISE} to calculate the appropriate Poisson statistics for
+each pixel.  In this case, the image is assumed to represent the
+readout from a single detector, with well-defined gain and read noise
+characteristics.  In some obvious cases, this assumption will not be
+valid.  For example, if the input flux image is the result of an image
+stack with significantly variable number of input measurements per
+pixel, it will be necessary to supply a noise image which accurately
+represents the noise as a function of position in the image.
+
+\subsection{Initial Object Detection}
+
+The objects are initially detected by finding the location of local
+peaks in the image.  The flux and variance images are smoothed with a
+small circularly symmetric kernel using a two-pass 1D Gaussian
+(\note{KEYWORD?}).  The smoothed flux and variance images are combined
+to generate a significance image in signal-to-noise units
+\note{including correction for the covariance, if known}. At this
+stage, the goal is only to detect the brighter sources, above a user
+defined S/N limit (configuration keyword: \code{PEAK\_NSIGMA}).  The
+detection efficiency for the brighter sources is not strongly
+dependent on the form of this smoothing function.
+
+The local peaks in the smoothed image are found by first detecting
+local peaks in each row.  For each peak, the neighboring pixels are
+then examined and the peak is accepted or rejected depending on a set
+of simple rules.  First, any peak which is greater than all 8
+neighboring pixels is kept.  Any peak which is lower than any of the 8
+neighboring pixels is rejected.  Any peak which has the same value as
+any of the other 8 pixels is kept if the pixel $X$ and $Y$ coordinates
+are greater than or equal to the other equal value pixels.  This
+simple rule set means that a flat-topped region will maintain peaks at
+the maximum $X$ and $Y$ corners of the region.
+
+\subsection{Footprints}
+
+\note{need to describe the process of generating the source footprints
+  and then culling the insignificant peaks}
+
+\subsubsection{Moments and related}
+
+\note{disucss the Kron mags}
+
+\note{this section is wrong: we no longer use S/N clipping, but a
+  Gaussian window function, chosed based on the measured moment}
+
+Once a collection of peaks have been identified, basic properties of
+the objects are measured.  First, the local sky flux is measured
+within a square annulus with user-defined dimensions
+(\code{INNER\_RADIUS} and \code{OUTER\_RADIUS}), using the sample
+median.  This local background value is then used to calculate the
+object first and second moments within a small user-defined aperture
+(\code{MOMENT\_RADIUS}).  The first-order moments are a good
+representation of the object position, while the second-order moments
+are a measure of the object shape.  The second-order moments are
+somewhat sensitive to the size of the aperture and the accuracy of the
+background measurement.  The moment calculation is only performed
+using pixels which exceed a S/N of 1.  If, in the process of
+calculating the source moments, the S/N limits reject all but \note{3}
+or fewer of the source pixels, the peak is identified as being
+suspect, and is not used for further analysis.  If the measured
+centroid coordinates differ from the peak coordinates be a large
+amount (\code{MOMENT\_RADIUS}), then the peak is again identified as
+being of poor quality and is rejected.  In both of these cases, it is
+likely that the `peak' was identified in a region of flat flux
+distribution or many saturated or edge pixels.
+
+\subsubsection{Determination of the Peak Coordinates and Errors}
+
+\note{this section is wrong: it is a poor estimator of the source
+  position errors.  we gave up a reverted to using the FWHM / (S/N)}
+
+We use the 9 pixels which include the source peak to fit for the
+position and position errors.  We model the peak of the sources as a
+2D quadratic polynomial, and use a very simple bi-quadratic fit to
+these pixels.  We use the following function to describe the peak
+
+\[ f(x,y) = C_{00} + C_{10}x + C_{01} y + C_{11} x y + C_{20} x^2 + C_{02} y^2 \]
+
+and write the Chi-Square equation:
+
+\[ \chi^2 = \sum_{i,j} (F_{i,j} - f(x,y))^2 / \sigma_{i,j}^2 \]
+
+By approximating the error per pixel as the error on just the peak,
+and pulling that term out of the above equation, and recognizing that
+the values x,y in the 3x3 grid centered on the peak pixel have values
+of only 0 or 1, we can greatly simplify the chi-square equation to a
+square matrix equation with the following values:
+
+%% fix this:
+\begin{verbatim}
+| 9 0 0 0 6 6 | C_00 | = \sum F_{i,j}
+| 0 6 0 0 0 0 | C_10 | = \sum F_{i,j} x
+| 0 0 6 0 0 0 | C_01 | = \sum F_{i,j} y
+| 0 0 0 6 0 0 | C_11 | = \sum F_{i,j} x y
+| 6 0 0 0 6 4 | C_20 | = \sum F_{i,j} x^2
+| 6 0 0 0 4 6 | C_02 | = \sum F_{i,j} y^2
+\end{verbatim}
+
+The inverse of the 3x3 matrix terms for $C_{00}$, $C_{20}$, and $C_{02}$ is:
+\begin{verbatim}
+| +5/9 -1/3 -1/3 | 
+| -1/3 +1/2    0 | 
+| -1/3    0 +1/2 | 
+\end{verbatim}
+
+which can be used to determine the errors on the coefficients: 
+
+\begin{eqnarray}
+\sigma^2_{00} & = & \sigma^2 (5/9) \\
+\sigma^2_{10} & = & \sigma^2 (1/6) \\
+\sigma^2_{01} & = & \sigma^2 (1/6) \\
+\sigma^2_{11} & = & \sigma^2 (1/6) \\
+\sigma^2_{20} & = & \sigma^2 (1/2) \\
+\sigma^2_{02} & = & \sigma^2 (1/2) \\
+\end{eqnarray}
+
+The location of the peak is determined from the minimum of the
+bi-quadratic function above, and is given by:
+
+\begin{eqnarray}
+Det    & = & 4 C_{20} C_{02} - C_{11}^2 \\
+x_{min} & = & (C_{11} C_{01} - 2 C_{02} C_{10}) / Det \\
+y_{min} & = & (C_{11} C_{10} - 2 C_{20} C_{01}) / Det \\
+\end{eqnarray}
+
+Applying error propagation to the above, we find:
+
+\begin{eqnarray}
+\sigma_{Det}^2  & = & \sigma_{11}^2 (4 C_{11}^2) + \sigma_{20}^2 (16 C_{02}^2) + \sigma_{02}^2 (16 C_{20}^2) \\
+\sigma_{xn}^2   & = & \sigma_{11}^2 C_{01}^2 + \sigma_{01}^2 C_{11}^2 + \sigma_{02}^2 (4 C_{10}^2) + \sigma_{10}^2 (4 C_{02}^2) \\
+\sigma_{yn}^2   & = & \sigma_{11}^2 C_{10}^2 + \sigma_{10}^2 C_{11}^2 + \sigma_{20}^2 (4 C_{01}^2) + \sigma_{01}^2 (4 C_{20}^2) \\
+\sigma_{x}^2    & = & x^2 (\sigma_{xn}^2 / xn^2 + \sigma_{Det}^2 / Det^2) \\
+\sigma_{y}^2    & = & y^2 (\sigma_{yn}^2 / yn^2 + \sigma_{Det}^2 / Det^2) \\
+\end{eqnarray}
+
+\subsection{PSF Determination}
+
+\subsubsection{PSF Model vs Object Model}
+
+PSPhot uses an analytical model to represent the shape and flux of an
+object.  An important concept within the PSPhot code is the
+distinction between a model which describes an object on an image and
+a model with describes the point-spread-function (PSF) across an
+image.
+
+Any object in an image may be represented by some analytical model,
+for example, a 2-D elliptical Gaussian:
+\begin{eqnarray}
+f(x,y) & = & I_o exp (-z) + S  \\
+    R  & = & \frac{(x - x_o)^2}{2\sigma_x^2} + \frac{(y -
+    y_o)^2}{2\sigma_y^2} + \sigma_{\rm xy}(x - x_o)(y - y_o)
+\end{eqnarray}
+The object model will have a variety of model parameters, in this case
+the centroid coordinates ($x_o, y_o$), the elliptical shape parameters
+($\sigma_x, \sigma_y, \sigma_{\rm xy}$), the model normalization
+($I_o$) and the local value of the background ($S$).  A specific
+object will have a particular set of values for these different
+parameters.
+
+The point-spread-function (PSF) of an image describes the shape of all
+unresolved objects in the image.  In a typical image, the shape of
+point sources is not well described by a single functional form;
+rather, the shape will vary as a function of position in the image.
+The PSF model therefore must describe the parameter variation as a
+function of the position of the object on the image.  Note that the
+object model consists of a certain number of parameters which are
+defined by the PSF model, and another set of parameters which are
+independent from object to object.  For the case of the elliptical
+Gaussian model, the PSF parameters would be the shape terms
+($\sigma_x, \sigma_y, \sigma_{\rm xy}$) while the independent
+parameters would be the centroid, normalization and local sky values
+($x_o, y_o, I_o, S$).  PSPhot uses a 2-D polynomial to specify the
+variation in the PSF parameters as a function of position in the
+image.  In the case of the elliptical Gaussian, this implies that the
+parameters are each a function of the object centroid coordinates:
+\begin{eqnarray}
+\sigma_x    & = & f_1(x,y) \\
+\sigma_y    & = & f_2(x,y) \\
+\sigma_{xy} & = & f_3(x,y) \\
+\end{eqnarray}
+
+PSPhot uses a single structure to represent the object model and
+another structure to represent the PSF model.  The object model
+structure consists of the collection of measured object model
+parameters, carried as a \code{psLib} vector (\code{psVector}) along
+with an equal-length vector with the parameter errors.  The structure
+also includes an integer giving the identifier of the model used in
+the particular case, as well as model fit statistics such as the
+Chi-Square of the fit and the magnitude representation of the ratio
+between the model flux and an aperture flux (see below for more
+details on this value).
+
+The PSPhot representation of the PSF consists of an array of
+polynomials, each representing the variation in the object model PSF
+parameters (\code{psArray} of \code{psPolynomial2D}).  The PSF model
+structure also includes the same integer used to identify which model
+corresponds to particular instance of the PSF.  At the moment, the
+number of PSF parameters is a fixed number (4) fewer than the number
+of parameters of the corresponding object model.  For example, the
+elliptical Gaussian model uses 7 parameters to represent the object and
+3 for the PSF model.  
+
+PSPhot is written so that the object detection, measurement, and
+classification code does not depend on the specific form of the
+available object model functions.  Access to the characteristics of
+the models is provided through a simple function abstraction method.
+Throughout PSPhot, there are many places where it is necessary for the
+code to refer to an aspect of the object or PSF model.  Often, these
+quantities are needed deep within other parts of the code.  For
+example, when attempting to fit the pixel flux values for an object,
+it is necessary to generate a guess for the model parameters.  Or, in
+order to limit the domain of the fit, it is necessary to determine an
+isophotal radius for a model.  
+
+In order to avoid having the code depend on the specific form of a
+model, the function calls needed in these types of circumstances are
+abstracted, and a method is provided to return the necessary function
+to the higher-level software.  For example, each model type has its
+own function to define an initial guess for the model, or a function
+to determine the radius for a given flux level.  These are then
+registered as part of the model function code.  Another function is
+then used to return the appropriate function for a specific model
+type.  For example, the \code{psModelLookup\_GetFunction} will return
+the \code{psModelLookup} function for a given model type.  This
+mechanism makes it very easy to add new model functions into the
+PSPhot code base.  To add a new model function, the programmer simply
+defines a new model name (a string), the set of all necessary model
+lookup functions, and places the reference to the model code at the
+appropriate location in the psModelInit.c routine.
+
+When a new model is provided to PSPhot, it is not necessary to specify
+the intended use of the object model function (ie, PSF-like object,
+galaxy, comet, etc).  Any model can be used for the PSF model, or to
+describe the flux distributions of the non-PSF objects.  The code
+currently uses a fixed translation between the object model parameters
+and the PSF model parameters.  It also defines a specific order for
+the 4 independent parameters.  
+
+\note{the code may also require that two of the PSF-like parameters
+represent the shape in some way}.
+
+\subsubsection{PSF Candidate Object Selection}
+
+The first stage of determining the PSF model for an image is to
+identify a collection of objects in the image which are {\em likely}
+to be PSF-like.  PSPhot uses the object moments to make the initial
+guess at a collection of PSF-like objects.  At this point, the program
+has measured the second order moments for all objects identified by
+their peaks, as well as an approximate signal-to-noise ratio.  All
+objects with a S/N ratio greater than a user-defined parameter
+(\code{PSF\_SHAPE\_NSIGMA} ???) are selected by PSPhot, though objects
+which have more than a certain number of saturated pixels are excluded
+at this stage.  PSPhot then examines the 2-D plane of $\sigma_x,
+\sigma_y$ in search of a concentrated clump of objects.  To do this,
+it constructs an artificial image with pixels representing the value
+of $\sigma_x, \sigma_y$, using a user-defined scale for the size of a
+pixel in this artificial image (note that the units of the $\sigma_x,
+\sigma_y$ plane are the size of the second-moment in pixels in the
+original image).  A typical value for the bin size is approximately
+0.1 image pixels.  The binned $\sigma_x, \sigma_y$ plane is then
+examined to find a peak which has a significance greater than XXX.
+Unless the image is extremely sparse, such a peak will be well-defined
+and should represent the objects which are all very similar in shape.
+Other objects in the image will tend to land in very different
+locations, failing to produce a single peak.  To avoid detecting a
+peak from the unresolved cosmic rays, objects which have
+second-moments very close to 0 are ignored.  The only danger is if the
+PSF is very small and too many of these objects are rejected as cosmic
+rays.
+
+Once a peak has been detected in this plane, the centroid and second
+moments of this peak are measured.  All objects which land within XXX
+$\sigma$ of this centroid are selected as likely PSF-like objects in
+the image.  
+
+\subsubsection{PSF Candidate Object Model Fits}
+
+All candidate PSF objects are then fitted with the selected object
+model, allowing all of the parameters (PSF and independent) to vary in
+the fit.  PSPhot uses the Levenberg-Marqardt process for the
+non-linear fitting.  Non-linear fitting can be very computationally
+intensive, particularly for if the starting parameters are far from
+the minimization values.  PSPhot uses the first and second moments to
+make a good guess for the centroid and shape parameters for the PSF
+models.  \note{still true? In order to minimize the impact of close
+  neighbors, the noise values used in the fit are enhanced by a
+  fraction of the deviation of the particular pixel value from the
+  model guess.}  Any objects which fail to converge in the fit are
+flagged as invalid.
+
+\note{does the noise enhancement introduce too much bias?}
+
+\note{discuss the convergence criteria, model parameter guesses}
+
+For the resulting collection of object model parameters, the
+PSF-dependent parameters of the models are all fitted as a function of
+position to a 2-D polynomial.  The order of this polynomial is (should
+be?) a user-defined parameter.  The fitting process for these
+polynomials is iterative, and rejects the $3-\sigma$ outliers in each
+of three passes.  This fitting technique results in a robust
+measurement of the variation of the PSF model parameters as a function
+of position without being excessively biased by individual objects
+which fail drastically.  Objects whose model parameters are rejected
+by this iterative fitting technique are also marked as invalid and
+ignored in the later PSF model fitting stages.
+
+All of the PSF-candidate objects are then re-fitted using the PSF
+model to specify the dependent model parameter values for each object.
+For example, in the case of the elliptical Gaussian model, the shape
+parameters ($\sigma_x, \sigma_y, \sigma_{xy}$) for each object are
+set by the coordinates of the object centroid and fixed (not allowed
+to vary) in the fitting procedure.  The resulting fitted models are
+then used to determine a metric which tests the quality of the PSF
+model for this particular image.  
+
+The metric used by PSPhot to assess the PSF model is the scatter in
+the differences between the aperture and fit magnitudes for the PSF
+objects.  The difference between the aperture and fit magnitudes ({\em
+ApResid}) is a critical parameter for any PSF modeling software which
+uses an analytical model to represent the flux distribution of the
+objects in an image.  An approximate correction is measured here, with
+a more detailed correction measured after all object analysis is
+performed.  The PSF model with the best consistency of the aperture
+correction is judged to be the best model.
+
+\subsubsection{Basic Deblending}
+
+The collection of identified peaks is examined to find peaks which are
+'blended', that is, they are close enough together to make the
+analysis of one of the sources difficult if performed in isolation.
+Saturated stars also result in additional peaks which are likely to be
+invalid; it is useful to restrict a saturated star to a single primary
+position with associated neighboring peaks.
+
+The deblending process first searches for any peaks which are within
+the image cell of another peak.  All such groups are examined,
+starting with the brightest source.  An isophot is found about the
+primary peak which is at least \code{DEBLEND\_SKY\_NSIGMA} times the sky
+sigma above the local background and which is otherwise
+\code{DEBLEND\_PEAK\_FRACTION} of the primary peak central pixel flux.
+Any secondary sources which are contained within this isophot are
+considered to be blended peaks associated with the primary peak.  
+
+\subsection{Bright Source Analysis}
+
+After a PSF model has been determined, PSPhot performs the analysis of
+the bright objects in the image.  In this stage, all of the objects
+with an estimated signal to noise (based on the moments analysis)
+greater than a user-set threshold are analysed and subtracted from the
+image.  An optional successive stage then finds fainter sources and
+measures them as well (see Faint Source Analysis,
+Section~\ref{faintsources}).  In the bright source analysis stage, two
+major varients are available.  In the primary version, all objects are
+examined (in decending order of brightness) and an appropriate models
+is determined for each object which is then subtracted; in the
+alternate version, the objects are examined (in decending order of
+brightness) and the PSF-like objects subtracted first, then the
+extended objects are analysed on a second pass.
+
+\subsubsection{Fast Ensemble PSF Fitting}
+
+Before the detailed analysis of the objects is performed, it is
+convenient to subtract off all of the sources, at least as well as
+possible at this stage.  We make the assumption that all sources are
+PSF-like.  We also assume their position can be taken as the peak of a
+2D quadratic function fitted to the peak pixel and its surrounding 8
+pixels.  A single linear fit is used to simultaneously measure all
+source fluxes.  Since the local sky has been subtracted, this
+measurement assumes the local sky is zero.  
+
+\[
+\chi^2 = \sum_{\rm pixels} (F_{x,y} - \sum_{\rm sources} A_i PSF[x,y])^2
+\]
+
+Minimizing this equation with respect to each of the $A_i$ values
+results in a matrix equation:
+\[ M_{i,j} \bar{A_i} = \bar{F_j}\]
+where $\bar{A_i}$ is the vector of $A_i$ values, the elements of
+$M_{i,j}$ consist of the dot product of the unit-flux PSF for source
+$i$ and source $i$, and $\bar{F_j}$ is the dot product of the
+unit-flux PSF for source $i$ with the pixels corresponding to source
+$i$.  The dot products are calculated only using pixels within the
+source apertures.  Since most sources have no overlap with most other
+sources, this matrix equation results in a very sparse, mostly
+diagonal square matrix.  The dimension is the number of sources,
+likely to be 1000s or 10,000s.  Such a matrix does not lend itself to
+direct inversion.  However, an interative solution quickly yields a
+result with sufficient accuracy.  In the iterative solution, a guess
+at the solution is made; the guess is multiplied by the matrix, and
+the result compared with the observed vector $\bar{F_j}$.  The
+difference is used to modify the initial guess. This proces is
+repeated several times to achieve a good convergence.  
+
+Once a solution set for $A_i$ is found, all of the objects are
+subtracted from the by applying these values to the unit-flux PSF.
+
+\subsubsection{PSF Model applied to detected objects}
+
+Once a PSF model has been selected for an image, PSPhot attempts to
+fit all of the detected objects, above a user-defined signal-to-noise
+ratio (\note{KEYWORD}) with the PSF model.  For these fits, the
+dependent parameters are fixed by the PSF model and only the 4
+independent object model parameters are allowed to vary in the fit.
+PSPhot again uses the Levenberg-Marqardt process for the non-linear
+fitting.  The objects are fitted in their S/N order, starting with the
+brightest and working down to the user-specified limit.
+
+Once a solution has been achieved, PSPhot attempts to judge the
+quality of the PSF model as a representation of the object shape.  To
+do this, it calculates the next step of the minimization {\em allowing
+the shape parameters to vary}.  This step, essentially the
+Gauss-Newton minimization distance from the current local minimum,
+should be very small if the object is well represented by the PSF, but
+large if the PSF is not a good representation of the object flux.  The
+model quality is judged by the change in the two shape parameters
+which represent the 2D size of the object.  For the case of the
+elliptical Gaussian, these two parameters are $\sigma_x$ and
+$\sigma_y$.  For a generic model, the shape parameters may be defined
+differently, but the should always be two parameters which scale the
+object size in two dimensions (what about a polar-coordinate form?)
+Currently, PSPhot requires the two relevant shape parameters to be the
+first two dependent parameters in the list of model parameters (ie,
+parameters 4 \& 5).
+
+The expected distribution of the variation of the two shape parameters
+will be a function of the signal-to-noise of the object in question
+and the value of the shape parameter itself.  The expected standard
+deviation on the shape parameter is, eg, $\sigma_x / {\rm SN}$.  If
+the object is well-represented by the PSF, then the shape parameter
+values should be close to their minimization value.  We can thus ask,
+for each object, given the measured amplitude of the Gauss-Newton
+step, how many standard deviations from the expected value (of 0.0) is
+this particular value?  Objects for which the variation in the shape
+parameters is a large positive number of standard deviations are
+likely to be better represented by a larger flux distribution than the
+PSF (eg, a Galaxy or Comet, etc).  Objects for which the variation in
+the shape parameters is a large negative number of standard deviations
+are likely to be better represented by a smaller flux distribution
+than the PSF (ie, a cosmic ray or other defect).  A user-defined
+number of standard deviations is used to select these two cases, and
+to flag the object as a likely galaxy (really meaning 'extended') or
+as a likely defect.  
+
+At this stage of the analysis, PSPhot uses two additional indicators
+to identify good and poor PSF fits.  The first of these is the
+signal-to-noise ratio.  It is possible for the peak finding algorithm
+to identify peaks in locations which are not actually a normal peak.
+Some of these cases are in the edges of saturated, bleeding columns
+from bright stars, in the nearly flat halos of very bright stars, and
+so on.  In these cases, a local peak exists, with a lower nearby sky
+region.  However, the fitted PSF model cannot converge on the peak
+because it is very poorly defined (perhaps only existing in the
+smoothed image).  The fit can either fail to converge or it can
+converge on a fit with very low or negative peak flux / flux
+normalization.  PSPhot will flag any non-convergent PSF fit and any
+object with PSF S/N ratio lower than a user-defined cutoff.  It is
+also useful to identify very poor fits by setting a maximum Chi-Square
+cutoff for objects.  
+
+As the objects are fitted to the PSF model, those which survive the
+exclusion stage are subtracted from the image.  The subtraction
+process modifies the image pixels (removing the fitted flux, though
+not the locally fitted background) but does not modify the mask or the
+noise images.  The signal-to-noise ratio in the image after
+subtraction represents the significance of the remaining flux.  If the
+subtractions are sufficiently accurate models of the PSF flux
+distribution, the remaining flux should be below 1 $\sigma$
+significance.  In practice the cores of bright stars are poorly
+represented and may have larger residual significance. \note{in future
+work, we may choose to enhance the noise to minimize detection of
+objects in the residuals of brighter objects}.
+
+\subsubsection{Blended Sources}
+
+Sources which are blended with other sources are fitted together as a set of
+PSFs.  A single multi-object fit is performed on all blended peaks.
+The resulting fits are evaluated independently and any which are
+determined to be PSFs are subtracted from the image.
+
+\subsubsection{Double Sources}
+
+Sources which are judged to be non-PSF-like are confronted with two
+possible alternative choices.  First, the object is fitted with a
+double-source model.  In this pass, the assumption is made that there
+are two neighboring sources, but the peaks are blended together, or
+otherwise not distinguished.  The initial guess for the two peaks is
+made by splitting the flux of the single source in half and locating
+the two starting peaks at +/- 2 pixels from the original peak along
+the direction of the semi-major axis of the sources, as measured from
+the second moments.  In order for the two-source model to be accepted,
+both sources must be judged as a valid PSF source.  Otherwise, the
+double-PSF model is rejected and the source is fitted with the
+available non-PSF model or models.
+
+\note{better description of the acceptance criteria; the FLT model is
+  tried before the DBL is accepted or rejected}. 
+
+\subsubsection{Non-PSF Objects}
+
+Once every object (above the S/N cutoff) has been confronted with the
+PSF model, the objects which are thought to be galaxies (extended) can
+now be fit with appropriate models for the galaxies (or other likely
+extended shapes).  Again, the fitting stage starts with the brightest
+sources (as judged by the rough S/N measured from the moments
+aperture) and working to a user defined S/N limit.  
+
+PSPhot will use the user-selected galaxy model to attempt the galaxy
+model fits.  In the configuration system, the keyword \code{GAL\_MODEL}
+is set to the model of interest.  All suspected extended objects 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 object parameters can be accurately guessed from the first and
+second moments.  The power-law slope can be guessed by measuring the
+isophotal level at two elliptical radii and comparing the ratio to
+that expected.
+
+For each of the galaxy models (in fact for all object models), a
+function is defined which examines the fit results and determines if
+the fit can be consider as a success or a failure.  The exact criteria
+for this decision will depend on the details of the model, and so this
+level of abstraction is needed.  For example, in some case, the range
+of valid values for each of the parameters must be considered in the
+fit assessment.  In other cases, we may choose to use only the
+parameter errors and the fit Chi-Square value.
+
+All galaxy model fits which are successful are then subtracted from
+the image as is done for the successful PSF model fits.  Of course,
+the background flux is retained, with the result that only the object
+is subtracted from the image.  Again, the noise image is (currently)
+not modified.  
+
+\note{we have no code yet to select the best of several models for a
+  given objects.  The relative value of the Chi-Square is the obvious
+  test in this case}.
+
+\subsection{Faint Sources}
+
+\note{this is not done : should use the ensemble PSF fitting to fit
+  just the new significant peaks}
+
+After a first pass through the image, in which the brighter sources
+above a high threshold level have been detected, measured, and
+subtracted, PSPhot optionally begins a second pass at the image.  In
+this stage, the new peaks are detected on the image with the bright
+objects subtracted.  In this pass, the peak detection process uses the
+noise image to test the validity of the individual peaks.  All peaks
+with a significance greater than a user-defined minimum threshold are
+accepted as objects of potential interest.  
+
+The objects which are measured in this faint-object stage are clearly
+low significance detections.  A typical threshold for the bright
+object analysis would S/N of 5 - 10.  The lower limit cutoff for the
+faint object analysis would typically be S/N of 2 - 4.  In this stage,
+PSPhot can perform one of three types of analysis.  The difference
+between these options is one of speed vs detail.
+
+In the first option, PSPhot can repeat the analysis described above in
+sections XXX and XXX, performing a PSF fit followed by a non-PSF fit
+to the objects which are not PSF-like, and subtracting them.  The
+advantage of this option is that the faint objects are treated
+identically to the bright objects, and all potential parameters are
+measured, even for marginally extended sources.  The disadvantage of
+this option is that the low signal-to-noise of the objects in this
+stage limits the amount of information which can be extracted from
+them.  The marginal gain may not be worth the large expense of
+processing time.
+
+In the second option, PSPhot can perform only the PSF model fit to the
+remaining peaks, but ignore any further questions of the shape of the
+objects.  The advantage of this option is that it is substantially
+faster than performing the more complex (and less stable)
+multi-parameter non-linear fits on all faint objects.  On the
+downside, less information is learned about the objects.
+
+Finally, PSPhot can simply ignore the fitting process and instead
+glean information about the fainter sources on the basis of the peak
+characteristics.  In this option, the image is smoothed with the PSF
+model, and the peak for each object is measured.  The peak flux and
+the local peak curvature theoretically give sufficient information to
+recover the object flux, the centroid coordinates, and the centroid
+errors.  The advantage of the stage is speed, especially for the very
+faintest levels: if the lower limit is not sufficiently faint, the
+time spent in performing the smoothing (3 FFTs) cannot make up for the
+time which would have been spent applying the PSF model to the peaks.
+The downside of this method is an increased sensitivity to the local
+sky model (the local sky must be correctly subtracted) and fewer
+constraints on the quality of the detection (no Chi-Square is
+measured, for example).
+
+\note{In the ideal case, if we were only interested in detecting PSFs,
+and we had a good model for the PSF, we could optimally find the
+sources by smoothing the image and the noise image with the PSF model.
+\em write out the description of Nick's optimal PSF finding}.
+
+PSPhot allows the user to select between these three options for the
+analysis of the faint sources.  Three separate user-controlled
+signal-to-noise ratio limits are defined.  One specifies the depth to
+which the PSF / non-PSF analysis is performed.  A second (which must
+be smaller) specifies the depth to which only the PSF is fitted.  A
+third specifies the depth to which the analysis is performed using on
+the peak statistics.  If two of these are identical, then certain of
+these options are simply skipped.  For example, if the peak analysis
+threshold is set to the same value as the PSF-only threshold, no peak
+analysis is performed.
+
+\subsection{Aperture Correction Measurement}
+
+The important concept here is that an analytical model will always
+fail to describe the flux of the objects at some level.  In the end,
+all astronomical photometry is in some sense a relative measurement
+between two images.  Whether the goal is calibration of a science
+image taken at one location to a standard star image at another
+location, or the goal is simply the repetitive photometry of the same
+star at the same location in the image, it is always necessary to
+compare the photometry between two images.  If this measurement is to
+be consistent, then the measurement must represent the flux of the
+stars in the same way regardless of the conditions under which the
+images were taken, at least within some range of normal image
+conditions.  So, for example, two images with different image quality,
+or with different tracking and focus errors, will have different PSF
+models.  Since an analytical model will always fail to represent the
+flux of the star at some level, the measured flux of the same object
+in the two images will be different (even assuming all other
+atmospheric and instrumental effects have been corrected).  The
+amplitude of the error will by determined by how inconsistently the
+models represent the actual object flux.  For example, if the first
+image PSF model flux is consistently 10\% too low and the second is 5\%
+too high, then the comparison between the two images will be in error
+by 15\%.  
+
+Aperture photometry avoids these problems, by trading for 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 object 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.  
+
+The difficulty for aperture photometry is the need to make an accurate
+measurement of the local background for each object.  As the aperture
+grows, errors in the measurement of the sky flux start to become
+dominant.  If the aperture is too small, then variation in the image
+quality are dominant.  The brighter is the object, 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.  
+
+\note{this discussion sucks: put in some more details of my point:
+  amplitude of systematic vs random sky errors}
+
+How important is this effect?  Consider a typical bright object 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 object
+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}.
+
+PSPhot measures the aperture correction ({\em ApResid}) for every PSF
+candidate object, 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 object and the average bias inherent
+in the sky measurement for the image.  The scatter of the
+PSF-candidate object 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 object.  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.
+
+PSPhot allows a collection of PSF model functions to be tried on all
+PSF candidate objects.  For each model test, the above corrected
+ApResid scatter is measured.  The PSF model function with the smallest
+value for the ApResid scatter is then used by PSPhot as the best PSF
+model for this image.  The number of models to be tested is specified
+by the configuration keyword \code{PSF\_MODEL\_N}.  The configuration
+variables \code{PSF\_MODEL\_0}, \code{PSF\_MODEL\_1}, through
+\code{PSF\_MODEL\_N - 1} specify the names of the models which should be
+tested.
+
+\subsubsection{Types of Object / PSF models currently available}
+
+\note{the discussion of the model types needs to be extended}
+
+\begin{itemize}
+\item GAUSS  : Pure elliptical Gaussian
+\item PGAUSS : polynomial approximation to a Gaussian (PGAUSS)
+\item QGAUSS : power law with variable exponential term
+\item SGAUSS : 
+\end{itemize}
+
+\note{discuss the stability issues with the galaxy model(s)}
+
+\subsection{Output Options}
+
+\note{need to discuss tests}
+
+\note{need to discuss failings and holes}
+
+\section{Alternative Scenarios}
+
+\subsection{Trailed Sources}
+
+\subsection{Fixed / Known-position Sources}
+
+\subsection{Difference Images}
+
+The noise map for a difference image must be generated from the two
+images use to construct the difference.  Otherwise, the low sky level
+will automatically result in inconsistent interpretation of the noise.
+
+For a difference image, both positive and negative objects will be
+present.  The basic peak detection algorithm will only trigger for the
+positive sources.  One solution is to simply apply PSPhot to both the
+difference image and its negative value.  \note{do we want to code in
+an automatic switch to get both positive and negative excursions in
+the single pass?}.
+
+In the case of a difference image, the PSF model construction stage
+will probably fail for lack of valid sources.  It is better in these
+cases to provide PSF model from some other source.  For example, the
+two images which are combined to generate the difference image
+represent the PSF.  Presumably, one or both have been convolved with a
+PSF-matching kernel.  The images which result from the convolution
+should be used to measure the PSF model.  
+
+The object classification scheme defaults to the galaxy models for
+objects which are not well represented by the PSF model.  In a
+properly-constructed difference image, galaxies are unlikely to remain
+behind as significant sources.  Most real objects in the difference
+image will be PSF-like and will consist of photometrically variable
+objects (flare stars, supernovae, etc) or astrometrically variable
+objects (high-proper motion stars or solar-system objects).  There are
+three likely classes of objects which will not be well represented by
+the PSF model.  1) Fast-moving solar-system objects will appear as
+short streaks.  For example, a fast solar system object would have an
+apparent rate of 0.5 degrees per hour, translating to 15 arcseconds in
+a 30 second exposure.  Even a main belt asteroid at roughly 1 AU would
+have reflect motion of approximately 1 degree per day, equivalent to
+1.25 arcsec in a 30 second exposure, and could be noticeably smeared
+and non-PSF-like.  A trailed-star model can be used to characterize
+these types of objects.  2) Small offset stars, either due to
+atmospheric / color effects or modest proper motion will appear as PSF
+dipoles in the difference images.  The positive and the negative
+images will have stellar profiles, but they will be significantly
+offset and will not subtract well.  The two components may not have
+the same amplitude.  A PSF-dipole model can be used to fit these types
+of objects, with free parameters of the two centroids and the two
+fluxes.  3) Comets will appear in the difference images as a non-PSF
+objects.  Their 2-D structure includes both the flux from the coma
+(with a typical power-law profile) and flux from the tail (with a more
+complex flux distribution).  A comet flux model can be used to
+characterize these objects in difference images.  A major difficulty
+in applying these three types of models is in making a robust test of
+which model should be used.  This problem is akin to the issue of
+selecting and distinguishing between multiple galaxy models, as
+discussed in the section on Galaxy models.
+
+\section{PSPhot Structures and Data Elements}
+
+The following structures are described in detail in the document
+`Pan-STARRS PS-1 Image Processing Pipeline Modules Supplementary
+Design Requirements' (psModules SDRS; PSDC-430-012).
+
+\begin{verbatim}
+ pmModel
+ pmModelGroup
+ pmGrowthCurve
+ pmPSF
+ pmPSFTry
+ pmSource
+ pmPeak
+ pmMoments
+\end{verbatim}
+
+\note{psphot is supposed to operate on individual readouts, and use
+  the techniques used by ppImage to extract header-related metadata.
+  currently, psphot uses an alternative to the psReadout until the
+  ppImage code can be folded together with psphot}. 
+
+\subsection{Top-Level APIs}
+
+\begin{verbatim}
+psMetadata     *psphotArguments (int *argc, char **argv);
+\end{verbatim}
+Load the command-line arguments, parse the configuration file, and
+place the configuration information on a single metadata structure.
+This function searches for the following command line option flags,
+and places their corresponding values on the output metadata with the
+given name.  These options override any such values in the
+configuration file.
+\begin{verbatim}
+-mask (filename)      : MASK_IMAGE
+-weight (filename)    : WEIGHT_IMAGE
+-resid (filename)     : RESID_IMAGE
+-region [x0:x1,y0:y1] : ANALYSIS_REGIONP
+-photcode (code)      : PHOTCODE
+-psf (filename)       : PSF_INPUT_FILE
+-modeltest x y        : TEST_FIT_X, TEST_FIT_Y
+-model (name)         : TEST_FIT_MODEL
+-fitmode (name)       : TEST_FIT_MODE
+-fitset (name)        : TEST_FIT_SET
+\end{verbatim}
+
+The following option flags can be used to set any option:
+\begin{verbatim}
+-D  (key) (value)      : any string value
+-Df (key) (value)      : any F32 value
+-Di (key) (value)      : any S32 value
+\end{verbatim}
+
+The function next examines the remaining command-line arguments and
+complains if there are not exactly 3 arguments, reporting the program
+usage.  It sets default configuration variables, and then loads the
+configuration file specified as the third command-line option.
+Finally, it sets the \code{IMAGE} and \code{OUTPUT\_FILE} config
+options to arguments 1 and 2, respecitively.
+
+\begin{verbatim}
+eamReadout     *psphotSetup (psMetadata *config);
+\end{verbatim}
+This function examines the configuration data in \code{config} and
+loads the image into memory.  It constructs the weight and mask images
+if they have not been specified, or loads the specified images.  The
+weight image is built based on the read noise and gain of the image,
+as extracted from the header or from the configuration options
+directly.  It defines the mask based on the selection image region,
+the values for saturation and the \code{min\_VALID\_PIXEL}.  
+
+\begin{verbatim}
+bool            psphotModelTest (eamReadout *imdata, psMetadata *config);
+\end{verbatim}
+This function is an optional test mode for psphot.  If the test mode
+has been selected, this function will attempt to fit a single object
+with the requested model.  It writes out subimage containing the
+source, the difference, the mask, and the weight.  This function may
+load a PSF model or fit a floating model.
+
+\begin{verbatim}
+psStats        *psphotImageStats (eamReadout *imdata, psMetadata *config);
+\end{verbatim}
+Measure the basic image properties: median sky, expected sky sigma
+
+\begin{verbatim}
+psPolynomial2D *psphotImageBackground (eamReadout *imdata, psMetadata *config, psStats *sky);
+\end{verbatim}
+Model the image background as a 2D polynomial and subtract from the
+image.   The should use a more sophisticated model and return the
+subtracted image.
+
+\begin{verbatim}
+psArray        *psphotFindPeaks (eamReadout *imdata, psMetadata *config, psStats *sky);
+\end{verbatim}
+Create a smoothed image and find all local peaks above the threshold
+level (uses: \code{PEAKS\_SMOOTH\_SIGMA, PEAKS\_SMOOTH\_NSIGMA,
+PEAKS\_NSIGMA\_LIMIT, PEAKS\_OUTPUT\_FILE})
+
+\begin{verbatim}
+psArray        *psphotSourceStats (eamReadout *imdata, psMetadata *config, psArray *allpeaks);
+\end{verbatim}
+Create the basic source structures for all peaks, define the initial
+pixels, measure the local sky (sky offset) and the source moments.
+
+\begin{verbatim}
+bool            psphotRoughClass (psArray *sources, psMetadata *config);
+\end{verbatim}
+Find the PSF clump and make the first cut source identifications
+
+\begin{verbatim}
+bool            psphotBasicDeblend (psArray *sources, psMetadata *config, psStats *sky);
+\end{verbatim}
+Find all blended peaks and tag, group with single primary source.
+
+\begin{verbatim}
+pmPSF          *psphotChoosePSF (psMetadata *config, psArray *sources, psStats *sky);
+\end{verbatim}
+Try each of the selected PSF models on a subset of likely PSF stars.
+Measure the metric (aperture residual scatter) for each PSF model and
+choose the best model.  
+
+\begin{verbatim}
+bool            psphotEnsemblePSF (eamReadout *imdata, psMetadata *config, psArray *sources, pmPSF *psf, psStats *sky);
+\end{verbatim}
+Perform simultaneous fitting to all sources in the array using a
+linear fitting process which assumes all sources are PSFs and their
+positions are fixed.  Set the positions based on the bilinear
+interpolation of the peak implied by the 3x3 square of pixels
+containing the peak.  Local sky is also assumed to be correctly subtracted.
+
+\begin{verbatim}
+bool            psphotFullFit (eamReadout *imdata, psMetadata *config, psArray *sources, pmPSF *psf, psStats *sky);
+\end{verbatim}
+Fit all sources in sequence starting from the brightest, and
+subtracting the sources as they are fitted.  This function only
+attempts single PSF and single EXT models and chooses between them.
+The sources are assumed to have been subtracted in advance (ie, using
+psphotEnsembleFit).  The models which do not succeed are re-subtracted
+using the prior model.
+
+\begin{verbatim}
+bool            psphotBlendFit (eamReadout *imdata, psMetadata *config, psArray *sources, pmPSF *psf, psStats *sky);
+\end{verbatim}
+Fit all sources in sequence starting from the brightest, and
+subtracting the sources as they are fitted.  This function attempts a
+multi-source fit for blended sources, or a single PSF if it is not a
+blend, followed by both EXT and DBL models and chooses between them.
+The sources are assumed to have been subtracted in advance (ie, using
+psphotEnsembleFit).  The models which do not succeed are re-subtracted
+using the prior model.
+
+\begin{verbatim}
+bool            psphotReplaceUnfit (psArray *sources);
+\end{verbatim}
+After models have been attempted for all sources, this function
+replaces the sources which were temporarily subtracted, but which did
+not succeed or converge on a good solution.
+
+\begin{verbatim}
+bool            psphotApplyPSF (eamReadout *imdata, psMetadata *config, psArray *sources, pmPSF *psf, psStats *sky);
+\end{verbatim}
+Attempt to fit the PSF model to all sources in brightness order,
+subtracting the resulting model if successful.  Only attempts single
+PSF models.   
+
+\begin{verbatim}
+bool            psphotFitExtended (eamReadout *imdata, psMetadata *config, psArray *sources, psStats *skyStats);
+\end{verbatim}
+Attempt to fit the PSF model to all sources in brightness order,
+subtracting the resulting model if successful.  Only attempts single
+EXT models.
+
+\begin{verbatim}
+bool            psphotApResid (eamReadout *imdata, psArray *sources, psMetadata *config, pmPSF *psf);
+ \end{verbatim}
+Measure the curve-of-growth and the aperture correction trend.
+
+\begin{verbatim}
+void            psphotOutput (eamReadout *imdata, psMetadata *config, psArray *sources, pmPSF *psf, psStats *sky);
+\end{verbatim}
+Write out data in various formats as selected.
+
+\section{User's Guide}
+
+\subsection{Configuration Parameters}
+
+\begin{verbatim}
+FAINT_SN_LIM
+FIT_MAX_CHI
+FIT_MIN_SN
+FIT_NSIGMA
+FIT_PADDING
+FIT_RADIUS
+GAIN
+GAL_MODEL
+GAL_MOMENTS_RADIUS
+INNER_RADIUS
+INPUT
+MASK
+NOISE
+NSUBSET
+OUTER_RADIUS
+OUTPUT
+OUTPUT_MODE
+PEAK_NSIGMA
+PSF_MODEL_N
+PSF_MOMENTS_RADIUS
+PSF_SHAPE_NSIGMA
+RDNOISE
+SATURATE
+SMOOTH_NSIGMA
+SMOOTH_SIGMA
+XMAX
+XMIN
+YMAX
+YMIN
+\end{verbatim}
+
+\subsection{Command-Line Arguments and Options}
+
+\subsection{Input \& Output Data Formats} 
+
+\section{Sample Tests}
+
+\section{Further Work to be Completed}
+
+\begin{itemize}
+\item convert to pmCell as input data
+\item loop over all readouts in a pmCell
+\item write out multiple files?
+\item better method for defining the recipe?
+\item additional options for image background
+\item image background should return a background image
+\end{itemize}
 
 \end{document}