Index: trunk/doc/pslib/psLibADD.tex =================================================================== --- trunk/doc/pslib/psLibADD.tex (revision 3721) +++ trunk/doc/pslib/psLibADD.tex (revision 3772) @@ -1,3 +1,3 @@ -%%% $Id: psLibADD.tex,v 1.72 2005-04-19 23:44:43 eugene Exp $ +%%% $Id: psLibADD.tex,v 1.73 2005-04-27 19:59:04 eugene Exp $ \documentclass[panstarrs]{panstarrs} @@ -14,5 +14,5 @@ \project{Pan-STARRS Image Processing Pipeline} \organization{Institute for Astronomy} -\version{10} +\version{11} \docnumber{PSDC-430-006} @@ -41,4 +41,5 @@ 09 & 2005 Feb 14 & Frozen for Cycle 5 \\ \hline 10 & 2005 Apr 19 & Frozen for Cycle 6 \\ \hline +11 & 2005 Apr 27 & Update for Cycle 6 \\ \hline \RevisionsEnd @@ -1553,6 +1554,4 @@ the quarternion for this transformation. -\tbd{can we drop this, since we do this with the quaternion?} - The relevant trigonometric relationships are: % @@ -1611,7 +1610,7 @@ \phi_p & = & 90^\circ + 0^\circ.6406161\, T + 0^\circ.0003041\, T^2 + 0^\circ.0000051\, T^3 \end{eqnarray} -where $T$ is $($MJD$_{\rm out} -$ MJD$_{\rm in})/36525$ is the difference -between the two epochs, in Julian centuries. - +where $T$ is $($MJD$_{\rm out} -$ MJD$_{\rm in})/36525$ is the +difference between the two epochs, in Julian centuries. This +precession form shall be used to implement \code{PS_PRECESS_ROUGH}. \subsubsection{Suggested test cases} @@ -1648,11 +1647,10 @@ There are two reference implementatins for the code to account for the motion of the Earth in space. The first are the sample routines -provided by the IERS to accompany chaper 5 of IERS Bulletin 32. This -document and the code can be downloaded from -http://maia.usno.navy.mil/conv2003.html . The second reference -implementation is the SOFA software package managed by the IAU and -available at http://www.iau-sofa.rl.ac.uk Only the 2003-04-29 version -of SOFA should be used. The IERS code requires a few of the rotation -matrix utility routines from SOFA. +provided by the IERS to accompany chaper 5 of IERS Bulletin +32.\footnote{http://maia.usno.navy.mil/conv2003.html} The second +reference implementation is the SOFA software package managed by the +IAU.\footnote{http://www.iau-sofa.rl.ac.uk} Only the 2003-04-29 +version of SOFA should be considered. The IERS code requires a few of +the rotation matrix utility routines from SOFA. Both implementations are in FORTRAN 77. The SOFA code has a more @@ -1663,5 +1661,6 @@ reference for psLib should be the IERS code. Note that the IERS code calculates the transform from terrestrial to celestial coordinates, -while the SOFA code calculates its inverse. +while the SOFA code calculates its inverse. This code may be using as +a comparison for testing purposes. \subsubsection{Coordinate Systems} @@ -1711,13 +1710,13 @@ The X axes of the intermediate coordinate systems are known as the -Celestial and Terrestrial Ephemeris Origins. (CEO and TEO). Both are defined -to be non-rotating origins. A non-rotating origin is a point on the equator -whose instantaneous motion is always orthogonal to the equator -(Kaplan 2003 IAU XXV Joint Discussion 16 -\footnote{http://aa.usno.navy.mil/kaplan/NROs\%5BJD16proc\%5D.pdf}). -Thus the CEO is defined by its position in the GCRS at some epoch and by the -motion of the CIP in the GCRS since that date. Similarly the TEO is -defined by its position in the ITRS at some epoch and the motion of the -CIP in the ITRS since that date. +Celestial and Terrestrial Ephemeris Origins. (CEO and TEO). Both are +defined to be non-rotating origins. A non-rotating origin is a point +on the equator whose instantaneous motion is always orthogonal to the +equator (Kaplan 2003 IAU XXV Joint Discussion +16\footnote{http://aa.usno.navy.mil/kaplan/NROs\%5BJD16proc\%5D.pdf}). +Thus the CEO is defined by its position in the GCRS at some epoch and +by the motion of the CIP in the GCRS since that date. Similarly the +TEO is defined by its position in the ITRS at some epoch and the +motion of the CIP in the ITRS since that date. \subsubsection{ICRS - GCRS} @@ -1793,5 +1792,5 @@ This section is largely a summary of Chapter 5 of IERS Technical Note -32 \footnote{http://maia.usno.navy.mil/conv2003.html} (hereafter +32\footnote{http://maia.usno.navy.mil/conv2003.html} (hereafter IERS32), which is a description of the implementation of the Resoltions of the XXIVth General Assembly of the IAU, available from @@ -1807,4 +1806,6 @@ accurate to the 0.2 mas level. For higher accuracy the user must apply corrections to the model, which are tabulated by the IERS. + +\subparagraph{IAU 200A Precession/Nutation Model : {\tt psEOC\_PrecessionModel}} The IAU 2000A precession-nutation model may be calculated in the @@ -1855,7 +1856,7 @@ The constants $p_j$, $w_{i,j,k}$, $(a_{{\rm s},j})_i$, and $(a_{{\rm c},j})_i$ are given in the ASCII files: -tab5.2a.txt \footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2a.txt} (for $X$), -tab5.2b.txt \footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2b.txt} (for $Y$), and -tab5.2c.txt \footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2c.txt} (for $s+XY/2$). +tab5.2a.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2a.txt} (for $X$), +tab5.2b.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2b.txt} (for $Y$), and +tab5.2c.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2c.txt} (for $s+XY/2$). Note that the expansion is given for $s+XY/2$, since this series converges more rapidly than the one for $s$ alone. @@ -1876,10 +1877,12 @@ A FORTRAN reference implementation for the precession/nutation model -is available from the IERS -\footnote{http://maia.usno.navy.mil/conv2000/chapter5/XYS2000A.f}. -The psLib results should agree with the reference implementation to within -the limits of numerical precision. - -Next, corrections to $X$, and $Y$ may be obtained from the IERS as +is available from the +IERS.\footnote{http://maia.usno.navy.mil/conv2000/chapter5/XYS2000A.f} +The psLib results should agree with the reference implementation to +within the limits of numerical precision. + +\subparagraph{Corrections to the Model : {\tt psEOC\_PrecessionCorr}} + +Corrections to $X$, and $Y$ may be obtained from the IERS as part of Bulletin A, or B. It is recommended to use the values published daily by USNO in the table @@ -1895,24 +1898,28 @@ the result as instantaneous values. -The final step is to use $X$, $Y$, and $s$ to calculate the rotation -matrix from the CIP/CEO system to the GCRS using IERS32 equation (10), -reproduced below: - -\begin{equation} +\subparagraph{Spherical Rotation from Polar Coordinates : {\tt psSphereRot\_CEOtoGCRS}} + +In order to relate the values $X$, $Y$, and $s$ to the rotation +components, the rotation matrix below must be used. The definitions +of $X$, $Y$, and $s$ transform from the CIP/CEO system to the GCRS +using IERS32 equation (10), reproduced below: + +\begin{equation} +\label{CEOtoGCRS} \begin{pmatrix}1-aX^2& -aXY& X\cr -aXY& 1-aY^2& Y\cr -X& -Y& 1-a(X^2+Y^2)\cr \end{pmatrix} \cdot R_3(s), \end{equation} -where $R_3$ denotes a rotation about the Z axis, -$a = 1/(1+\sqrt{1 - X^2 + Y^2})$, -and $X$ and $Y$ are expressed in radians. -A FORTRAN reference implementation for this calculation is given -by the IERS \footnote{http://maia.usno.navy.mil/conv2000/chapter5/BPN2000.f}. - -Note that above we gave the expression for the transform toward celestial -coordinates (upward in figure X), in order to match the IERS reference code. -The inverse transform may be found by inverting the resulting rotation. - -\paragraph{Rotation of the Earth} +where $R_3$ denotes a rotation about the Z axis, $a = 1/(1+\sqrt{1 - +(X^2 + Y^2})$, and $X$ and $Y$ are expressed in radians. A FORTRAN +reference implementation for this calculation is given by the +IERS.\footnote{http://maia.usno.navy.mil/conv2000/chapter5/BPN2000.f} + +Note that above we gave the expression for the transform toward +celestial coordinates (upward in Figure~\ref{earthrot}), in order to +match the IERS reference code. The inverse transform may be found by +inverting the resulting rotation. + +\paragraph{Earth Rotation} The transform from the CIP/CEO to CIP/TEO coordinate systems is a @@ -1931,11 +1938,14 @@ motion''. Similarly to precession/nutation, the instantaneous position of the CIP in the ITRS is specified by the quantites $x_p$, and $y_p$, -and a third quantity, $s'$, gives the position of the TEO with respect -to the ITRS. The values of $x_p$ and $y_p$ are published daily by the -IERS\footnote{http://maia.usno.navy.mil/ser7/finals2000A.daily}, with +and a third quantity, $s'$, which give the position of the TEO with +respect to the ITRS. The values of $x_p$ and $y_p$ are published +daily by the +IERS,\footnote{http://maia.usno.navy.mil/ser7/finals2000A.daily} with a format described by their \code{readme.finals2000A}\footnote{http://maia.usno.navy.mil/ser7/readme.finals2000A}. The UT1$-$UTC, and the precession/nutation corrections (discussed elsewhere in this document) come from this same source. + +\subparagraph{Polar Motion from Bulletin : {\tt psEOC\_GetPolarMotion}} The polar motion coordinates should be interpolated using a third @@ -1953,5 +1963,7 @@ The tidal effects should be included by using the Ray tidal model given in IERS Gazette \#13. The definition of this correction is -provided below. +provided below (Section~\ref{Raymodel}). + +\subparagraph{Polar Motion Nutation Correction : {\tt psEOC\_NutationCorr}} By definition of the CIP, nutation terms with periods less than 2 days @@ -1966,4 +1978,6 @@ over this century by $s' = -4.7 \times 10^{-5} t$ in arcseconds. There is no need to apply short timescale corrections to $s'$. + +\subparagraph{Spherical Rotation from Polar Motion : {\tt psSphereRot\_ITRStoTEO}} The transform from the ITRS to the CIP/TEO frame can be constructed by @@ -2009,5 +2023,5 @@ correction from the Ray Tidal Model applied. -\subsubsection{Ray Tidal Model} +\subsubsection{Ray Tidal Model : {\tt psEOC\_PolarTideCorr}} The Ray Model tidal corrections to X, Y, and dT are given by the the