ccstd: Transform to and from standard astrometric coordinates

Package: imcoords

Usage

ccstd input output database solutions

Parameters

input: The input coordinate files. Coordinates may be entered by hand by setting input to "STDIN".

output: The output coordinate files. The number of output files must be one or equal to the number of input files. Results may be printed on the terminal by setting output to "STDOUT".

database: The text database file written by the ccmap task which contains the desired plate solutions. If database is undefined ccstd computes the standard coordinates or pixel and celestial coordinates using the current values of the xref, yref, xmag ymag, xrotation, yrotation, lngref, latref, and projection parameters.

solutions: The database record containing the desired plate solution. The number of records must be one or equal to the number of input coordinate files. Solutions is either the user name supplied to ccmap, the name of the image input to ccmap for which the plate solution is valid, or the name of the coordinate file that the ccmap task used to compute the plate solution. The quantities stored in solutions always supersede the values of the parameters xref, yref, xmag, ymag, xrotation, yrotation, lngref, latref, and projection.

geometry = "geometric"

The type of geometric transformation. The geometry parameter is only requested if database is defined. The options are:

linear: Transform the pixel coordinates to standard coordinates or vice versa using the linear part of the plate solution. only.

geometric: Transform the pixel coordinates to standard coordinates or vice versa using the full plate solution.

forward = yes: Transform from pixel and celestial coordinates to standard coordinates ? If forward is "no" then the plate solution is inverted and standard coordinates are transformed to pixel and celestial coordinates.

polar = no: Convert to and from polar standard coordinates instead of Cartesian standard coordinates?

xref = INDEF, yref = INDEF: The pixel coordinates of the reference point. If database is undefined then xref and yref default to 0.0 and 0.0, otherwise these parameters are ignored.

xmag = INDEF, ymag = INDEF: The x and y scale factors in arcseconds per pixel. If database is undefined xmag and ymag default to 1.0 and 1.0 arcseconds per pixel, otherwise these parameters are ignored.

xrotation = INDEF, yrotation = INDEF: The x and y rotation angles in degrees measured counter-clockwise with respect to the x and y axes. If database is undefined then xrotation and yrotation are interpreted as the rotation of the coordinates with respect to the x and y axes and default to 0.0 and 0.0 degrees. For example xrotation and yrotation values of 30.0 and 30.0 degrees will rotate a point 30 degrees counter-clockwise with respect to the x and y axes. To flip the x axis coordinates in this case either set the angles to 210.0 and 30.0 degrees or leave the angles at 30.0 and 30.0 and set the xmag parameter to a negative value. If database is defined these parameters are ignored. The ccmap task computes the x and y rotation angles of the x and y axes, not the rotation angle of the coordinates. An celestial coordinate system rotated 30 degrees counter-clockwise with respect to the pixel coordinate system will produce xrotation and yrotation values o 330.0 and 330.0 or equivalently -30.0 and -30.0 degrees in the database file not 30.0 and 30.0.

lngref = INDEF, latref = INDEF: The celestial coordinates of the reference point, e.g. the ra and dec of the reference point for equatorial systems, galactic longitude and latitude of the reference for galactic systems. If database is undefined lngref and latref default to 0.0 and 0.0, otherwise these parameters are ignored.

lngunits = "", latunits = "": The units of the input or output ra / longitude and dec / latitude coordinates. The options are "hours", "degrees", "radians" for ra / longitude coordinates, and "degrees" and "radians" for dec / latitude systems. If lngunits and latunits are undefined they default to the values in the database records. If database is undefined then lngunits and latunits default to "hours" and "degrees" respectively.

projection = "tan": The sky projection geometry. The options are "tan", "sin", "arc" and "lin". If database is undefined then the value of the projection parameter is used, otherwise this parameter is ignored.

xcolumn = 1, ycolumn = 2: The columns in the input coordinate file containing the x and y coordinates if the forward parameter is "yes", or the corresponding standard coordinates xi and eta if the forward parameter is "no".

lngcolumn = 3, latcolumn = 4: The columns in the input coordinate file containing the celestial coordinates if the forward parameter is "yes", or the corresponding standard coordinates xi and eta if the forward parameter is "no".

lngformat = "", latformat = "": The default output format of the transformed coordinates in lngcolumn and latcolumn. If forward = yes then the default output format is "%10.3f". Otherwise the defaults are "%12.2h" for output coordinates in hours, "%11.1h" for output coordinates in degrees, and "%13.7g" for output coordinates in radians.

xformat = "", yformat = "": The default output format of the transformed coordinates in xcolumn and ycolumn. The default is "%10.3f".

min_sigdigits = 7: The minimum precision of the output coordinates.

Description

CCSTD transforms the list of input coordinates in the text file input and writes the transformed coordinates to the text file output. The input coordinates are read from and the output coordinates written to, the columns xcolumn, ycolumn, lngcolumn, and latcolumn in the input and output files. The format of the output coordinates can be specified using the xformat, yformat, lngformat and latformat parameters. If the output formats are unspecified the coordinates are written out with reasonable default formats, e.g. "%10.3f" for standard coordinates, "%12.2h" and "11.1h" for celestial coordinates in hours or degrees, and "%13.7g" for celestial coordinates in radians. All the remaining fields in the input file are copied to the output file without modification. Blank lines and comment lines are also passed to the output file unaltered.

The plate solution can either be read from record solutions in the database file database written by CCMAP, or specified by the user via the xref, yref, xmag, ymag, xrotation, yrotation, lngref, latref, and projection parameters. lngunits and latunits define the units of the input celestial coordinates. If undefined they default to the values in the database or to the quantities "hours" and "degrees" respectively. The standard coordinates are always written and read in units of arcseconds.

If the forward parameter is "yes", the input coordinates are assumed to be pixel coordinates and celestial coordinates. The pixel coordinates are transformed to standard coordinates using the plate solution, and celestial coordinates are transformed to standard coordinates using the position of the reference point lngref, latref, and the projection specified by projection. If forward is "no", then the input coordinates are assumed to be standard coordinates and those in xcolumn and ycolumn are transformed to pixel coordinates by inverting the plate solution, and those in lngcolumn and latcolumn are transformed to celestial coordinates using the position of the reference point and the specified projection.

The plate solution computed by CCMAP has the following form where x and y are the pixel coordinates and xi and eta are the corresponding fitted standard coordinates in arcseconds per pixel. The observed standard coordinates are computed by applying the appropriate sky projection to the celestial coordinates.

 xi = f (x, y)
eta = g (x, y)

The functions f and g are either power series, Legendre, or Chebyshev polynomials whose order and region of validity were set by the user when CCMAP was run. The plate solution is arbitrary and does not correspond to any physically meaningful model. However the first order terms can be given the simple geometrical interpretation shown below.

 xi = a + b * x + c * y
eta = d + e * x + f * y
  b = xmag * cos (xrotation)
  c = ymag * sin (yrotation)
  e = -xmag * sin (xrotation)
  f = ymag * cos (yrotation)
  a = xi0 - b * xref - c * yref = xshift
  d = eta0 - e * xref - f * yref = yshift
  xi0 = 0.0
  eta0 = 0.0

xref, yref, xi0, and eta0 are the origins of the reference and output coordinate systems respectively. xi0 and eta0 are both 0.0 by default. xmag and ymag are the x and y scales in arcsec / pixel, and xrotation and yrotation are the x and y axes rotation angles measured counter-clockwise from original x and y axes.

If the CCMAP database is undefined then CCSTD computes a linear plate solution using the parameters xref, yref, xmag, ymag, xrotation, yrotation, lngref, latref, lngunits, latunits and projection as shown below. Note that in this case xrotation and yrotation are interpreted as the rotation of the coordinates not the rotation of the coordinate axes.

 xi = a + b * x + c * y
eta = d + e * x + f * y
  b = xmag * cos (xrotation)
  c = -ymag * sin (yrotation)
  e = xmag * sin (xrotation)
  f = ymag * cos (yrotation)
  a = xi0 - b * xref - c * yref = xshift
  d = eta0 - e * xref - f * yref = yshift
  xi0 = 0.0
  eta0 = 0.0

Linear plate solutions are evaluated in the forward and reverse sense using the appropriate IRAF mwcs system routines. Higher order plate solutions are evaluated in the forward sense using straight-forward evaluation of the polynomial terms, in the reverse sense by applying Newton's method to the plate solution.

Formats

A format specification has the form "%w.dCn", where w is the field width, d is the number of decimal places or the number of digits of precision, C is the format code, and n is radix character for format code "r" only. The w and d fields are optional. The format codes C are as follows:

b       boolean (YES or NO)
c       single character (c or '\c' or '\0nnn')
d       decimal integer
e       exponential format (D specifies the precision)
f       fixed format (D specifies the number of decimal places)
g       general format (D specifies the precision)
h       hms format (hh:mm:ss.ss, D = no. decimal places)
m       minutes, seconds (or hours, minutes) (mm:ss.ss)
o       octal integer
rN      convert integer in any radix N
s       string (D field specifies max chars to print)
t       advance To column given as field W
u       unsigned decimal integer
w       output the number of spaces given by field W
x       hexadecimal integer
z       complex format (r,r) (D = precision)

Conventions for w (field width) specification:

    W =  n      right justify in field of N characters, blank fill
        -n      left justify in field of N characters, blank fill
        0n      zero fill at left (only if right justified)
absent, 0       use as much space as needed (D field sets precision)

Escape sequences (e.g. "\n" for newline):

\b      backspace   (not implemented)
     formfeed
\n      newline (crlf)
\r      carriage return
\t      tab
\"      string delimiter character
\'      character constant delimiter character
\\      backslash character
\nnn    octal value of character

Examples

%s          format a string using as much space as required
%-10s       left justify a string in a field of 10 characters
%-10.10s    left justify and truncate a string in a field of 10 characters
%10s        right justify a string in a field of 10 characters
%10.10s     right justify and truncate a string in a field of 10 characters

%7.3f       print a real number right justified in floating point format
%-7.3f      same as above but left justified
%15.7e      print a real number right justified in exponential format
%-15.7e     same as above but left justified
%12.5g      print a real number right justified in general format
%-12.5g     same as above but left justified

%h          format as nn:nn:nn.n
%15h        right justify nn:nn:nn.n in field of 15 characters
%-15h       left justify nn:nn:nn.n in a field of 15 characters
%12.2h      right justify nn:nn:nn.nn
%-12.2h     left justify nn:nn:nn.nn

%H          / by 15 and format as nn:nn:nn.n
%15H        / by 15 and right justify nn:nn:nn.n in field of 15 characters
%-15H       / by 15 and left justify nn:nn:nn.n in field of 15 characters
%12.2H      / by 15 and right justify nn:nn:nn.nn
%-12.2H     / by 15 and left justify nn:nn:nn.nn

\n          insert a newline

Examples

1. Compute the standard coordinates in arcseconds per pixel given a list of
pixel and equatorial coordinates and the position of the reference point in
pixel and equatorial coordinates.

cl> type coords
13:29:47.297  47:13:37.52  327.50  410.38
13:29:37.406  47:09:09.18  465.50   62.10
13:29:38.700  47:13:36.23  442.01  409.65
13:29:55.424  47:10:05.15  224.35  131.20
13:30:01.816  47:12:58.79  134.37  356.33

cl> ccstd coords STDOUT "" xref=256.5 yref=256.5 lngref=13:29:48.1 \
latref = 47:11:53.4 xcol=3 ycol=4 lngcol=1 latcol=2
  -8.180   104.120    71.000   153.880
-109.087  -164.189   209.000  -194.400
 -95.753   102.854   185.510   153.150
  74.688  -108.235   -32.150  -125.300
 139.745    65.441  -122.130    99.830

2. Repeat the previous example but output the results in polar coordinates.
The first and third columns contain the radius coordinate in arcseconds,
the second and fourth columns contain the position angle in degrees measured
counter-clockwise with respect to the standard coordinates.

cl> ccstd coords STDOUT "" xref=256.5 yref=256.5 lngref=13:29:48.1 \
latref = 47:11:53.4 xcol=3 ycol=4 lngcol=1 latcol=2 polar+
104.441    94.492   169.470    65.231
197.124   236.400   285.434   317.073
140.526   132.952   240.560    39.542
131.504   304.608   129.359   255.609
154.309    25.093   157.740   140.737

3. Compute the plate solution and use it to evaluate the Cartesian and
polar standard coordinates for the input coordinate list used in example 1.

cl> ccmap coords coords.db xcol=3 ycol=4 lngcol=1 latcol=2 inter-
Coords File: coords  Image:
    Database: coords.db  Record: coords
Refsystem: j2000  Coordinates: equatorial FK5
    Equinox: J2000.000 Epoch: J2000.00000000 MJD: 51544.50000
Insystem: j2000  Coordinates: equatorial FK5
    Equinox: J2000.000 Epoch: J2000.00000000 MJD: 51544.50000
Coordinate mapping status
    Ra/Dec or Long/Lat fit rms: 0.229  0.241   (arcsec  arcsec)
Coordinate mapping parameters
    Sky projection geometry: tan
    Reference point: 13:29:48.129  47:11:53.37  (hours  degrees)
    Reference point: 318.735  273.900  (pixels  pixels)
    X and Y scale: 0.764  0.767  (arcsec/pixel  arcsec/pixel)
    X and Y axis rotation: 179.110  358.958  (degrees  degrees)

cl> type coords.db
# Mon 10:29:13 24-Nov-97
begin   coords
        xrefmean        318.7460000000001
        yrefmean        273.9320000000001
        lngmean         13.49670238888889
        latmean         47.19815944444444
        coosystem       j2000
        projection      tan
        lngref          13.49670238888889
        latref          47.19815944444444
        lngunits        hours
        latunits        degrees
        xpixref         318.7352667484295
        ypixref         273.9002619912411
        geometry        general
        function        polynomial
        xishift         247.3577084680361
        etashift        -206.1795977453246
        xmag            0.7641733802338992
        ymag            0.7666917500560622
        xrotation       179.1101291109185
        yrotation       358.9582148846163
        wcsxirms        0.2288984454992771
        wcsetarms       0.2411034140453112
        xirms           0.2288984454992771
        etarms          0.2411034140453112
        surface1        11
                        3.      3.
                        2.      2.
                        2.      2.
                        0.      0.
                        134.3700000000001       134.3700000000001
                        465.5000000000002       465.5000000000002
                        62.1    62.1
                        410.3800000000001       410.3800000000001
                        247.3577084680361       -206.1795977453246
                        -0.7640812161068504     -0.011868034832272
                        -0.01393966623835092    0.7665650170136847
        surface2        0

cl> ccstd coords STDOUT coords.db coords xcol=3 ycol=4 lngcol=1 latcol=2
  -8.471   104.146    -8.599   104.517
-109.378  -164.163  -109.188  -164.100
 -96.044   102.880   -96.084   102.598
  74.397  -108.210    74.107  -108.269
 139.454    65.467   139.721    65.376

cl> ccstd coords STDOUT coords.db coords xcol=3 ycol=4 lngcol=1 latcol=2 \
polar+
104.490    94.650   104.870    94.704
197.264   236.325   197.106   236.361
140.744   133.032   140.565   133.122
131.317   304.509   131.202   304.391
154.056    25.148   154.259    25.075

4. Use the previous plate solution to transform the pixel and equatorial
coordinates to standard coordinates but enter the plate solution by hand.

cl> ccstd coords STDOUT "" xref=318.735 yref=273.900 lngref=13:29:48.129 \
latref=47:11:53.37 xmag=.764 ymag=.767 xrot=180.890 yrot=1.042 xcol=3    \
ycol=4 lngcol=1 latcol=2
  -8.475   104.150    -8.599   104.559
-109.382  -164.159  -109.161  -164.165
 -96.048   102.884   -96.064   102.640
  74.393  -108.206    74.092  -108.313
 139.450    65.471   139.688    65.401

cl> ccstd coords STDOUT "" xref=318.735 yref=273.900 lngref=13:29:48.129 \
latref=47:11:53.37 xmag=.764 ymag=.767 xrot=180.890 yrot=1.042 xcol=3    \
ycol=4 lngcol=1 latcol=2 polar+
104.494    94.652   104.912    94.702
197.263   236.324   197.145   236.378
140.750   133.032   140.582   133.105
131.311   304.509   131.230   304.374
154.054    25.150   154.240    25.089

Note that there are minor differences between the results of examples 3 and
4 due to precision differences in the input, and that the angles input
to ccstd in example 4 are the coordinate rotation angles not the axes
rotation angles as printed by ccmap. The difference is exactly 180 degrees
in both cases.

5. Use the plate solution computed in example 3 to convert a list
of standard coordinates into the equivalent pixel and celestial coordinates.

cl> type stdcoords
  -8.471   104.146    -8.599   104.517
-109.378  -164.163  -109.188  -164.100
 -96.044   102.880   -96.084   102.598
  74.397  -108.210    74.107  -108.269
 139.454    65.467   139.721    65.376

cl> ccstd stdcoords STDOUT coords.db coords xcol=3 ycol=4 lngcol=1 latcol=2  \
forward-

13:29:47.30 47:13:37.5   327.499   410.381
13:29:37.41 47:09:09.2   465.500    62.101
13:29:38.70 47:13:36.2   442.010   409.650
13:29:55.42 47:10:05.1   224.350   131.200
13:30:01.82 47:12:58.8   134.370   356.330