Changeset 3564 for trunk/doc/pslib/psLibSDRS_Astrom.tex

Timestamp:

Mar 30, 2005, 11:14:48 AM (21 years ago)

Author:

eugene

Message:

serious reorg for release 13

File:

• trunk/doc/pslib/psLibSDRS_Astrom.tex (modified) (4 diffs)

trunk/doc/pslib/psLibSDRS_Astrom.tex

@@ -270 +270 @@
 \code{TRUE} if they are all correctly assigned, otherwise \code{FALSE}.
 
-\subsubsection{Coordinate Transformations}
+\subsubsection{Detector Coordinate Transformations}
 
 \begin{figure}
@@ -322 +322 @@
 \end{verbatim}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% add psExposure to metadata?
-% add grommit to metadata?
-% add photsystem data to metadata?
-% add statistics to metadata?
-
-\subsubsection{Observatory data}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Astrometry}
+
+Astrometry is a basic functionality required for the IPP that will be
+used repeatedly, both for low-precision (roughly where is my favorite
+object?) and high-precision (what is the proper motion of this star?).
+As such, it must be flexible, yet robust.
+
+\subsubsection{Coordinate frames}
+\label{sec:coordinateFrames}
+
+There are five coordinate frames that we need to worry about for the
+purposes of astrometry:
+\begin{itemize}
+\item Cell: $(x,y)$ in pixels --- raw coordinates;
+\item Chip: $(X,Y)$ in pixels --- the location on the silicon;
+\item Focal Plane: $(p,q)$ in microns --- the location on the focal plane;
+\item Tangent Plane: $(l,m)$ in arcsec from the telescope boresight; and
+\item Sky: (RA,Dec) --- ICRS.
+\end{itemize}
+
+The following steps are required to convert from the cell coordinates to
+the sky:
+\begin{itemize}
+\item Cell $\longleftrightarrow$ Chip: two 2D polynomials, $(X,Y) = f(x,y)$;
+\item Chip $\longleftrightarrow$ FP: two 2D polynomials, $(p,q) = g(X,Y)$;
+\item FP $\longleftrightarrow$ TP: two 4D polynomials, $(l,m) =
+h(p,q,m,c)$, where $m$ and $c$ are the magnitude and color of the
+object, respectively; and
+\item TP $\longleftrightarrow$ Sky:  transformation to the sky using
+pre-computed coefficients for each pointing.
+\end{itemize}
+
+Note that the transformation between the Focal Plane and the Tangent
+Plane is a four-dimensional polynomial, in order to account for any
+possible dependencies in the astrometry on the stellar magnitude and
+color; the former serves as a check for charge transfer
+inefficiencies, while the latter will correct chromatic refraction,
+both through the atmosphere and the corrector lenses.
+
+We require structures to contain each of the above transformations as
+well as the pixel data.
+
+\subsubsection{Position Finding}
+
+We require functions to return the structure containing given
+coordinates.  For example, we want the chip that corresponds to the
+focal plane coordinates $(p,q) = (-1.234,+5.678)$.  These routines
+handle the one-to-many problem --- i.e., for one given focal plane
+coordinate, there are many chips that this coordinate may be
+correspond to; these functions will select the correct one. 
+%
+\begin{verbatim}
+psCell *psCellInFPA (const psPlane *coord, const psFPA *fpa);
+psChip *psChipInFPA (const psPlane *coord, const psFPA *fpa);
+psCell *psCellInChip(const psPlane *coord, const psChip *chip);
+\end{verbatim}
+
+\subsubsection{Conversion Functions}
+
+We require functions to convert between the various coordinate frames
+(Section~\ref{sec:coordinateFrames}).  The hierarchy of the coordinate
+frames and the transformations between each are shown in
+Figure~\ref{fig:coco}.  The functions that employ the transformations
+are shown in Figure~\ref{fig:cocoFunc}.  In addition to
+transformations between each adjoining coordinate frame in the
+hierarchy, we also require higher-level functions to convert between
+the Cell and Sky coordinate frames; these will simply perform the
+intermediate steps.
+
+\begin{figure}
+\psfig{file=coordinateFrames,height=7in,angle=-90}
+\caption{The coordinate systems in the \PS{} IPP, and the relation
+between each by transformations contained in the appropriate
+structures.}
+\label{fig:coco}
+\end{figure}
+
+\begin{figure}
+\psfig{file=coordinateConv,height=7in,angle=-90}
+\caption{Conversion between coordinate systems by PSLib.}
+\label{fig:cocoFunc}
+\end{figure}
+
+We specify the following functions to convert between coordinates in
+one type of frame to another type of frame.  The first group consist
+of unambiguous transformations: from the coordinates in a low-level
+frame to the coordinates in the containing higher-level frame, of
+which only one exists.  In all of these functions, the output
+coordinate structure may be \code{NULL} or may be supplied by the
+calling function.  In the former case, the structure must be
+allocated; in the latter case, the supplied structure must be used.
+
+\begin{verbatim}
+psPlane *psCoordCellToChip (psPlane *out, const psPlane *in, const psCell *cell);
+% astrometry comes from cell (no need for parent)
+\end{verbatim}
+which converts coordindates \code{in} on the specified \code{cell} to
+the coordinates on the parent chip.
+
+\begin{verbatim}
+psPlane *psCoordChipToFPA (psPlane *out, const psPlane *in, const psChip *chip);
+% astrometry comes from chip (no need for parent)
+\end{verbatim}
+which converts the coordinates \code{in} on the specified \code{chip}
+to the coordinates on the parent FPA.
+
+\begin{verbatim}
+psPlane *psCoordFPAToTP(psPlane *out, const psPlane *in, float color, float mag, const psFPA *fpa);
+% astrometry comes from FPA (no need for parent)
+\end{verbatim}
+which converts coordinates \code{in} on the specified focal plane
+\code{fpa} to tangent plane coordinates, applying the appropriate
+distortion terms.  The \code{color} and magnitude (\code{mag}) of the
+source is necessary in order to perform the distortion between the
+focal plane and the tangent plane.
+
+\begin{verbatim}
+psSphere *psCoordTPToSky(psSphere *out, const psPlane *in, const psGrommit *grommit);
+\end{verbatim}
+which converts the tangent plane coordinates \code{in} to (RA,Dec) on
+the sky, based on the environmental information specified by
+\code{grommit}.
+
+% astrometry comes from cell
+\begin{verbatim}
+psPlane *psCoordCellToFPA(psPlane *out, const psPlane *in, const psCell *cell);
+\end{verbatim}
+which performs the single-step conversion between Cell coordinates
+\code{in} and FPA coordinates.
+
+% astrometry comes from cell,chip,fpa (PARENT IS NEEDED HERE)
+\begin{verbatim}
+psSphere *psCoordCellToSky(psSphere *out, const psPlane *in, float color, float mag, const psCell *cell);
+\end{verbatim}
+which converts coordinates on the specified cell to (RA,Dec).  This
+transformation must be performed using the intermediate stage
+transformations of Cell to Chip, Chip to FPA, FPA to Tangent Plane,
+Tangent Plane to Sky.  The information needed for each of these
+transformations is available in the \code{.parent} elements of
+\code{psCell} and \code{psChip}, and the \code{psFPA.exposure}
+element.  The \code{color} and magnitude (\code{mag}) of the source is
+necessary in order to perform the distortion between the focal plane
+and the tangent plane.
+
+% astrometry comes from cell (no need for parent)
+\begin{verbatim}
+psSphere *psCoordCellToSkyQuick(psSphere *out, const psPlane *in, const psCell *cell);
+\end{verbatim}
+which uses the 'quick-and-dirty' transformation to convert coordinates
+on the specified cell to (RA,Dec).  This transformation should use the
+locally linear transformation specified by the element
+\code{psCell.toTP}.  Although the accuracy of this transformation
+is lower than the complete transformation above, the calculation is
+substantially faster as it only involves linear transformations.
+
+The following functions convert from high-level frames to the
+coordinates of contained lower-level frames.  
+
+\begin{verbatim}
+psPlane *psCoordSkyToTP(psPlane *out, const psSphere *in, const psGrommit *grommit);
+\end{verbatim}
+which converts (RA,Dec) coordinates \code{in} to tangent plane coords
+based on the enviromental information supplied by \code{grommit}.
+
+\begin{verbatim}
+psPlane *psCoordTPToFPA(psPlane *out, const psPlane *in, float color, float mag, const psFPA *fpa);
+\end{verbatim}
+which converts the tangent plane coordinates \code{in} to focal plane
+coordinates.  The \code{color} and magnitude (\code{mag}) of the
+source is necessary in order to perform the distortion between the
+focal plane and the tangent plane.
+
+\begin{verbatim}
+psPlane *psCoordFPAToChip (psPlane *out, const psPlane *in, const psChip *chip);
+\end{verbatim}
+which converts the specified FPA coordinates \code{in} to the
+coordinates on the given Chip.  The specified chip need not contain
+the input coordinate.  To find the chip which contains a particular
+coordinate, the function \code{psChipInFPA}, defined above, should be
+used.
+
+\begin{verbatim}
+psPlane *psCoordChipToCell (psPlane *out, const psPlane *in, const psCell *cell);
+\end{verbatim}
+which converts the specified Chip coordinate \code{in} to the
+coordinate on the given Cell.  The specified Cell need not contain the
+input coordinate.  To find the cell which contains a particular
+coordinate, the function \code{psCellInChip}, defined above, should be
+used.
+
+\begin{verbatim}
+psPlane *psCoordSkyToCell(psPlane *out, const psSphere *in, float color, float mag, psCell *cell);
+\end{verbatim}
+which directly converts (RA,Dec) \code{in} to coordinates on the
+specified cell.  The specified cell need not contain the input
+coordinates.  The \code{color} and magnitude (\code{mag}) of the
+source is necessary in order to perform the distortion between the
+focal plane and the tangent plane.
+
+\begin{verbatim}
+psPlane *psCoordSkyToCellQuick(psPlane *out, const psSphere *in, psCell *cell);
+\end{verbatim}
+which directly converts (RA,Dec) \code{in} to coordinates on the
+specified cell.  The specified cell need not contain the input
+coordinates.  This transformation should use the locally linear
+transformation specified by the element \code{psCell.toTP}.
+Although the accuracy of this transformation is lower than the
+complete transformation above, the calculation is substantially faster
+as it only involves linear transformations.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Astrometry and World Coordinate System}
+
+The FITS World Coordinate System (WCS) headers are commonly employed
+with astronomical images in order to relate pixels to celestial (or
+otherwise) coordinates.  Since it is a FITS standard, we must be able
+to read and write from WCS into our internal format.  For the time
+being, we will consider only celestial WCS (i.e., no spectral
+wavelength calibrations, etc).  Because WCS does not support the
+multiple layers that we have built for \PS{}, we will use a simple
+internal representation: a transformation, which handles any
+distortions (i.e., goes directly from the coordinate frame of the
+image to the tangent plane); and the projection.
+
+\begin{verbatim}
+bool psAstrometryReadWCS(psPlaneTransform **transform, // Output transformation
+                         psProjection **projection, // Output projection
+                         psMetadata *header // Input FITS header
+                         );
+bool psAstrometryWriteWCS(psMetadata *header, // Output FITS header
+                          psPlaneTransform *transform, // Input transformation
+                          psProjection *projection, // Input projection
+                          double color, // Mean color to use
+                          double magnitude, // Mean magnitude to use
+                          );
+bool psAstrometrySimplify(psPlaneTransform **transform, // Output transformation
+                          psProjection **projection, // Output projection
+                          psCell *cell // Cell for which to generate transform and projection
+                          );
+\end{verbatim}                  
+
+\code{pmReadAstrometry} shall parse the specified FITS \code{header},
+returning new instances of the \code{transform} and \code{projection}
+that represent the WCS.  The function shall return \code{true} if it
+was able to successfully generate the outputs; otherwise it shall
+return \code{false}.
+
+\code{pmWriteAstrometry} shall add WCS keywords to the supplied FITS
+\code{header} that implement the given \code{transform} and
+\code{projection}.  The function shall return \code{true} if it was
+able to successfully generate the output; otherwise it shall return
+\code{false}.
+
+\code{pmSimplifyAstrometry} shall take a \code{cell} and simplify the
+internal astrometric representation (\code{cell->toFPA} or equivalent,
+\code{cell->parent->parent->toTangentPlane} and
+\code{cell->parent->parent->grommit}) to a single \code{transform} and
+\code{projection}.  This allows the subsequent use of
+\code{pmWriteAstrometry} in the case that we have only the
+multi-layered \PS{} internal astrometric representation.  The function
+shall return \code{true} if it was able to successfully generate the
+output; otherwise it shall return \code{false}.
+
+\subsection{Observatory data}
 
 We need a container for the observatory data that doesn't change per
@@ -350 +609 @@
 \end{verbatim}
 
-\subsubsection{Exposure information}
+\subsection{Exposure information}
 
 We need several quantities from the telescope in order to make a
@@ -388 +647 @@
 \end{verbatim}
 
-\subsubsection{Environmental Information}
-
-A-priori astrometric transformations between the tangent plane and the
-sky require several pieces of information describing the current
-environmental conditions.  These quantities are consistent from image
-to image, and may vary only slowly with time.  Pre-computing these
-quantities for exposures means that subsequent transformations are
-faster.  The structure below carries the environment data of interest.
-For historical reasons, this structure is known colloquially as ``the
-Grommit''.
-
-\begin{verbatim}
-typedef struct {
-    const double latitude;              ///< geodetic latitude (radians)
-    const double sinLat, cosLat;        ///< sine and cosine of geodetic latitude
-    const double abberationMag;         ///< magnitude of diurnal aberration vector
-    const double height;                ///< height (HM)
-    const double temperature;           ///< ambient temperature (TDK)
-    const double pressure;              ///< pressure (PMB)
-    const double humidity;              ///< relative humidity (RH)
-    const double wavelength;            ///< wavelength (WL)
-    const double lapseRate;             ///< lapse rate (TLR)
-    const double refractA, refractB;    ///< refraction constants A and B (radians)
-    const double longitudeOffset;       ///< longitude + ... (radians)
-    const double siderealTime;          ///< local apparent sidereal time (radians)
-} psGrommit;
-\end{verbatim}
-
-The \code{psGrommit} is calculated from telescope information for the
-particular exposure, \code{exp}:
-\begin{verbatim}
-psGrommit *psGrommitAlloc(const psExposure *exp);
-\end{verbatim}
-
-\subsubsection{Fixed Pattern}
-
-The fixed pattern is a correction to the general astrometric solution
-formed by summing the residuals from many observations.  The intent is
-to correct for higher-order distortions in the camera system on a
-coarse grid (larger than individual pixels, but smaller than a single
-cell).  Hence, in addition to the offsets, we need to specify the size
-and scale of the grid in $x$ and $y$, as well as the origin of the
-grid.
-
-\begin{verbatim}
-typedef struct {
-    int nX, nY;                         ///< Number of elements in x and y
-    double x0, y0;                      ///< Position of 0,0 corner on focal plane
-    double xScale, yScale;              ///< Scale of the grid
-    double **x, **y;                    ///< The grid of offsets in x and y
-} psFixedPattern;
-\end{verbatim}
-
-The constructor for \code{psFixedPattern} shall be:
-\begin{verbatim}
-psFixedPattern *psFixedPatternAlloc(double x0,        double y0, 
-                                    double xScale,    double yScale,
-                                    const psImage *x, const psImage *y);
-\end{verbatim}
-Here, \code{x0}, \code{y0}, \code{xScale} and \code{yScale} have the
-same meaning as in the \code{psFixedPattern} structure.  Note that the
-values of the fixed pattern offsets are specified as images, the
-values from which need to be copied into the \code{double **x} and
-\code{double **y} of \code{psFixedPattern}, and that the number of
-elements may be derived from the size of the images.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection{Astrometry}
-
-Astrometry is a basic functionality required for the IPP that will be
-used repeatedly, both for low-precision (roughly where is my favorite
-object?) and high-precision (what is the proper motion of this star?).
-As such, it must be flexible, yet robust.  Accordingly, we will wrap
-the StarLink Astronomy Libraries (SLALib), which has already been
-developed.  \tbd{SLAlib functions will be replaced in the next
-release}.
-
-\subsubsection{Coordinate frames}
-\label{sec:coordinateFrames}
-
-There are five coordinate frames that we need to worry about for the
-purposes of astrometry:
-\begin{itemize}
-\item Cell: $(x,y)$ in pixels --- raw coordinates;
-\item Chip: $(X,Y)$ in pixels --- the location on the silicon;
-\item Focal Plane: $(p,q)$ in microns --- the location on the focal plane;
-\item Tangent Plane: $(l,m)$ in arcsec from the telescope boresight; and
-\item Sky: (RA,Dec) --- ICRS.
-\end{itemize}
-
-The following steps are required to convert from the cell coordinates to
-the sky:
-\begin{itemize}
-\item Cell $\longleftrightarrow$ Chip: two 2D polynomials, $(X,Y) = f(x,y)$;
-\item Chip $\longleftrightarrow$ FP: two 2D polynomials, $(p,q) = g(X,Y)$;
-\item FP $\longleftrightarrow$ TP: two 4D polynomials, $(l,m) =
-h(p,q,m,c)$, where $m$ and $c$ are the magnitude and color of the
-object, respectively; and
-\item TP $\longleftrightarrow$ Sky:  transformation to the sky using
-pre-computed coefficients for each pointing.
-\end{itemize}
-
-Note that the transformation between the Focal Plane and the Tangent
-Plane is a four-dimensional polynomial, in order to account for any
-possible dependencies in the astrometry on the stellar magnitude and
-color; the former serves as a check for charge transfer
-inefficiencies, while the latter will correct chromatic refraction,
-both through the atmosphere and the corrector lenses.
-
-We require structures to contain each of the above transformations as
-well as the pixel data.
-
-\subsubsection{Position Finding}
-
-We require functions to return the structure containing given
-coordinates.  For example, we want the chip that corresponds to the
-focal plane coordinates $(p,q) = (-1.234,+5.678)$.  These routines
-handle the one-to-many problem --- i.e., for one given focal plane
-coordinate, there are many chips that this coordinate may be
-correspond to; these functions will select the correct one. 
-%
-\begin{verbatim}
-psCell *psCellInFPA (const psPlane *coord, const psFPA *fpa);
-psChip *psChipInFPA (const psPlane *coord, const psFPA *fpa);
-psCell *psCellInChip(const psPlane *coord, const psChip *chip);
-\end{verbatim}
-
-\subsubsection{Conversion Functions}
-
-We require functions to convert between the various coordinate frames
-(Section~\ref{sec:coordinateFrames}).  The hierarchy of the coordinate
-frames and the transformations between each are shown in
-Figure~\ref{fig:coco}.  The functions that employ the transformations
-are shown in Figure~\ref{fig:cocoFunc}.  In addition to
-transformations between each adjoining coordinate frame in the
-hierarchy, we also require higher-level functions to convert between
-the Cell and Sky coordinate frames; these will simply perform the
-intermediate steps.
-
-\begin{figure}
-\psfig{file=coordinateFrames,height=7in,angle=-90}
-\caption{The coordinate systems in the \PS{} IPP, and the relation
-between each by transformations contained in the appropriate
-structures.}
-\label{fig:coco}
-\end{figure}
-
-\begin{figure}
-\psfig{file=coordinateConv,height=7in,angle=-90}
-\caption{Conversion between coordinate systems by PSLib.}
-\label{fig:cocoFunc}
-\end{figure}
-
-We specify the following functions to convert between coordinates in
-one type of frame to another type of frame.  The first group consist
-of unambiguous transformations: from the coordinates in a low-level
-frame to the coordinates in the containing higher-level frame, of
-which only one exists.  In all of these functions, the output
-coordinate structure may be \code{NULL} or may be supplied by the
-calling function.  In the former case, the structure must be
-allocated; in the latter case, the supplied structure must be used.
-
-\begin{verbatim}
-psPlane *psCoordCellToChip (psPlane *out, const psPlane *in, const psCell *cell);
-% astrometry comes from cell (no need for parent)
-\end{verbatim}
-which converts coordindates \code{in} on the specified \code{cell} to
-the coordinates on the parent chip.
-
-\begin{verbatim}
-psPlane *psCoordChipToFPA (psPlane *out, const psPlane *in, const psChip *chip);
-% astrometry comes from chip (no need for parent)
-\end{verbatim}
-which converts the coordinates \code{in} on the specified \code{chip}
-to the coordinates on the parent FPA.
-
-\begin{verbatim}
-psPlane *psCoordFPAToTP(psPlane *out, const psPlane *in, float color, float mag, const psFPA *fpa);
-% astrometry comes from FPA (no need for parent)
-\end{verbatim}
-which converts coordinates \code{in} on the specified focal plane
-\code{fpa} to tangent plane coordinates, applying the appropriate
-distortion terms.  The \code{color} and magnitude (\code{mag}) of the
-source is necessary in order to perform the distortion between the
-focal plane and the tangent plane.
-
-\begin{verbatim}
-psSphere *psCoordTPToSky(psSphere *out, const psPlane *in, const psGrommit *grommit);
-\end{verbatim}
-which converts the tangent plane coordinates \code{in} to (RA,Dec) on
-the sky, based on the environmental information specified by
-\code{grommit}.
-
-\begin{verbatim}
-psPlane *psCoordCellToFPA(psPlane *out, const psPlane *in, const psCell *cell);
-% astrometry comes from cell
-\end{verbatim}
-which performs the single-step conversion between Cell coordinates
-\code{in} and FPA coordinates.
-
-\begin{verbatim}
-psSphere *psCoordCellToSky(psSphere *out, const psPlane *in, float color, float mag, const psCell *cell);
-% astrometry comes from cell,chip,fpa (PARENT IS NEEDED HERE)
-\end{verbatim}
-which converts coordinates on the specified cell to (RA,Dec).  This
-transformation must be performed using the intermediate stage
-transformations of Cell to Chip, Chip to FPA, FPA to Tangent Plane,
-Tangent Plane to Sky.  The information needed for each of these
-transformations is available in the \code{.parent} elements of
-\code{psCell} and \code{psChip}, and the \code{psFPA.exposure}
-element.  The \code{color} and magnitude (\code{mag}) of the source is
-necessary in order to perform the distortion between the focal plane
-and the tangent plane.
-
-\begin{verbatim}
-psSphere *psCoordCellToSkyQuick(psSphere *out, const psPlane *in, const psCell *cell);
-% astrometry comes from cell (no need for parent)
-\end{verbatim}
-which uses the 'quick-and-dirty' transformation to convert coordinates
-on the specified cell to (RA,Dec).  This transformation should use the
-locally linear transformation specified by the element
-\code{psCell.toTP}.  Although the accuracy of this transformation
-is lower than the complete transformation above, the calculation is
-substantially faster as it only involves linear transformations.
-
-The following functions convert from high-level frames to the
-coordinates of contained lower-level frames.  
-
-\begin{verbatim}
-psPlane *psCoordSkyToTP(psPlane *out, const psSphere *in, const psGrommit *grommit);
-\end{verbatim}
-which converts (RA,Dec) coordinates \code{in} to tangent plane coords
-based on the enviromental information supplied by \code{grommit}.
-
-\begin{verbatim}
-psPlane *psCoordTPToFPA(psPlane *out, const psPlane *in, float color, float mag, const psFPA *fpa);
-\end{verbatim}
-which converts the tangent plane coordinates \code{in} to focal plane
-coordinates.  The \code{color} and magnitude (\code{mag}) of the
-source is necessary in order to perform the distortion between the
-focal plane and the tangent plane.
-
-\begin{verbatim}
-psPlane *psCoordFPAToChip (psPlane *out, const psPlane *in, const psChip *chip);
-\end{verbatim}
-which converts the specified FPA coordinates \code{in} to the
-coordinates on the given Chip.  The specified chip need not contain
-the input coordinate.  To find the chip which contains a particular
-coordinate, the function \code{psChipInFPA}, defined above, should be
-used.
-
-\begin{verbatim}
-psPlane *psCoordChipToCell (psPlane *out, const psPlane *in, const psCell *cell);
-\end{verbatim}
-which converts the specified Chip coordinate \code{in} to the
-coordinate on the given Cell.  The specified Cell need not contain the
-input coordinate.  To find the cell which contains a particular
-coordinate, the function \code{psCellInChip}, defined above, should be
-used.
-
-\begin{verbatim}
-psPlane *psCoordSkyToCell(psPlane *out, const psSphere *in, float color, float mag, psCell *cell);
-\end{verbatim}
-which directly converts (RA,Dec) \code{in} to coordinates on the
-specified cell.  The specified cell need not contain the input
-coordinates.  The \code{color} and magnitude (\code{mag}) of the
-source is necessary in order to perform the distortion between the
-focal plane and the tangent plane.
-
-\begin{verbatim}
-psPlane *psCoordSkyToCellQuick(psPlane *out, const psSphere *in, psCell *cell);
-\end{verbatim}
-which directly converts (RA,Dec) \code{in} to coordinates on the
-specified cell.  The specified cell need not contain the input
-coordinates.  This transformation should use the locally linear
-transformation specified by the element \code{psCell.toTP}.
-Although the accuracy of this transformation is lower than the
-complete transformation above, the calculation is substantially faster
-as it only involves linear transformations.
-
-\subsubsection{Additional functions}
-
-We require additional functions to perform general functions which
-will be useful for astrometry.  Given coordinates on the sky, we
-need to get the airmass, the parallactic angle, and an estimate of
-the atmospheric refraction.
-
-\begin{verbatim}
-float psGetAirmass(const psSphere *coord, psTime *lst, float height);
-\end{verbatim}
-which returns the airmass for a given position and local sidereal time
-(\code{lst}).
-
-\begin{verbatim}
-float psGetParallactic(const psSphere *coord, double siderealTime);
-\end{verbatim}
-which returns the parallactic angle for a given position and sidereal time.
-
-\begin{verbatim}
-float psGetRefraction(float colour,            ///< Colour of object
-                      psPhotSystem colorPlus,  ///< Colour reference
-                      psPhotSystem colorMinus, ///< Colour reference
-                      const psExposure *exp);  ///< Telescope pointing information
-\end{verbatim}
-which provides an estimate of the atmospheric refraction, along the parallactic angle.
-
-\begin{verbatim}
-double psGetParallaxFactor(const psExposure *exp)
-\end{verbatim}
-Calculate the parallax factor for the given exposure.  \tbd{Why do we need this?}.
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection{Astrometry and World Coordinate System}
-
-The FITS World Coordinate System (WCS) headers are commonly employed
-with astronomical images in order to relate pixels to celestial (or
-otherwise) coordinates.  Since it is a FITS standard, we must be able
-to read and write from WCS into our internal format.  For the time
-being, we will consider only celestial WCS (i.e., no spectral
-wavelength calibrations, etc).  Because WCS does not support the
-multiple layers that we have built for \PS{}, we will use a simple
-internal representation: a transformation, which handles any
-distortions (i.e., goes directly from the coordinate frame of the
-image to the tangent plane); and the projection.
-
-\begin{verbatim}
-bool psAstrometryReadWCS(psPlaneTransform **transform, // Output transformation
-                         psProjection **projection, // Output projection
-                         psMetadata *header // Input FITS header
-                         );
-bool psAstrometryWriteWCS(psMetadata *header, // Output FITS header
-                          psPlaneTransform *transform, // Input transformation
-                          psProjection *projection, // Input projection
-                          double color, // Mean color to use
-                          double magnitude, // Mean magnitude to use
-                          );
-bool psAstrometrySimplify(psPlaneTransform **transform, // Output transformation
-                          psProjection **projection, // Output projection
-                          psCell *cell // Cell for which to generate transform and projection
-                          );
-\end{verbatim}                  
-
-\code{pmReadAstrometry} shall parse the specified FITS \code{header},
-returning new instances of the \code{transform} and \code{projection}
-that represent the WCS.  The function shall return \code{true} if it
-was able to successfully generate the outputs; otherwise it shall
-return \code{false}.
-
-\code{pmWriteAstrometry} shall add WCS keywords to the supplied FITS
-\code{header} that implement the given \code{transform} and
-\code{projection}.  The function shall return \code{true} if it was
-able to successfully generate the output; otherwise it shall return
-\code{false}.
-
-\code{pmSimplifyAstrometry} shall take a \code{cell} and simplify the
-internal astrometric representation (\code{cell->toFPA} or equivalent,
-\code{cell->parent->parent->toTangentPlane} and
-\code{cell->parent->parent->grommit}) to a single \code{transform} and
-\code{projection}.  This allows the subsequent use of
-\code{pmWriteAstrometry} in the case that we have only the
-multi-layered \PS{} internal astrometric representation.  The function
-shall return \code{true} if it was able to successfully generate the
-output; otherwise it shall return \code{false}.
-