This recipe describes how to apply an astrometric calibration to an image. In this context an ‘astrometric calibration’ is a mathematical transformation relating the positions of pixels in the image array to celestial coordinates on the sky. Applying an astrometric calibration is just another term for creating a World Coordinate System (WCS; see Section 4.1) for the image, with the World Coordinates being celestial coordinates.
GAIA provides numerous options for astrometric calibration, only one of which will be used here (though Section 12.4, below, gives a few hints about what else is available). In most of the techniques stars occurring in the image are used as fiducial marks and a transformation is defined between their pixel positions measured in the image and their celestial coordinates obtained from an astrometric reference catalogue. The most interactive (and problematic) part of the procedure is identifying a given object in the image with the corresponding entry in an astrometric reference catalogue.
The principal information which you need to know about an image before attempting astrometric calibration is the approximate position on the sky corresponding to the centre of the image and the size of the field of view. The former can usually be obtained from examining the auxiliary information included with the image (see Section 4). The latter may also be found in the auxiliary information or from the documentation for the instrument or telescope. If you have no prior information whatsoever about the region of sky observed then astrometric calibration will usually be impossible.
In this recipe an astrometric calibration will be created for the V band CCD image of NGC 1275 obtained with the JKT which was used in the recipe in Section 8. The field of view of this image is about six minutes of arc in each axis.
The process of creating the astrometric calibration divides naturally into three stages:
Each stage is described separately in individual sub-recipes below.
The purpose of this stage is to find a small number of astrometric reference stars, imaged on the CCD frame, which can be used to define the preliminary astrometric calibration. Traditionally finding reference stars is a long-winded task involving consulting printed atlases and catalogues. However, the on-line resources available to GAIA allow the process to be automated and simplified. Proceed as follows.
ngc1275dss.sdfinto GAIA (the last is the required region, already extracted from the DSS).
Set the magnification by clicking on the Scale: button (in the bottom left of the control panel in the centre top of the window) and setting it to 2x.
Figure 10 shows five suitable stars in the DSS example image. To select the stars: hold down the
shift key and click on each star in turn (without releasing the
shift key). As you do so the
selected star is highlighted in both the image and the catalogue windows. You can add as many
stars as you like, but five is adequate.
Re-plot the selected objects by clicking on the Plot button towards the bottom of the new catalogue dialogue box. Label the chosen objects by clicking on the Options menu in the catalogue dialogue box menu-bar and choosing Label all objects.
.lisso that the catalogue is saved in the ‘ASCII Header’ format (see Section 4.2).
You now have a list of suitable reference stars. You can quit GAIA at this point, but it is better to proceed directly to the next stage of the recipe.
This stage of the recipe uses the five reference stars identified in the previous stage as ‘fiducial marks’ to define a preliminary astrometric calibration. However, before starting, a superficial glance at the DSS image (for example in Figure 4) and the JKT image (Figure 1) reveals that they are rotated with respect to each other by 180. Sometimes uncalibrated images show such gross rotations with respect to the standard orientation, sometimes they do not (the ‘standard orientation’ has north at the top, east to the left and Right Ascension increasing from right to left, that is ‘the wrong way round’). If they do then it is best to rotate them before attempting the astrometric calibration.
This recipe assumes that GAIA is still running and that the catalogue of reference stars created in the
previous stage is still available. If not, then start GAIA and load either the local catalogue of reference
stars that you created in the previous stage, or file
ngc1275usno.tab, which is the equivalent example
It should now be straightforward to identify objects in the JKT image with the corresponding objects in your print-out of the DSS image (created in the previous stage) or in Figure 10.
A selection box allowing you to specify the catalogue required will appear. The selected reference stars will usually be the first catalogue in the list.
Once the catalogue has been imported the reference stars should be listed under ‘Reference positions’ in the Fit astrometry reference positions dialogue box (Figure 11).
If there are any other significant features visible in the box, you should reduce the size of the box using the ‘zoom buttons’ (‘Z’ and ‘z’) immediately below the image box.
Once you are happy with the sample size, re-position the cursor over the star and press the left mouse button. The pixel coordinates at the centre of the feature are displayed in the Image X: and Image Y: fields within the object picker dialogue box (Figure 12).
The star is now fully specified, so press the Enter button. After confirmation, this will amend the details of the star in the list of reference stars in the Fit astrometry reference positions dialogue box (Figure 11).
Now click the Fit/Test button in the same dialogue box. GAIA uses the known celestial coordinates and measured positions of the reference stars to define an astrometric calibration. It then uses this calibration to work out the pixel positions corresponding to each of your reference coordinates, and displays markers in the main image at these pixel positions. You should find that a marker is drawn more-or-less on top of each of your reference stars.
If the markers are not properly aligned then you have probably measured the wrong star or entered an incorrect Right Ascension or Declination value. You should correct the reference positions, and then press the Fit/Test button again. To correct the reference positions: Edit the details of the offending star, as above, then press Fit/Test again to re-calculate the astrometric calibration.
Cheat: you can load a file containing the celestial coordinates and measured positions for the
five stars marked in Figure 10. Click on the File menu in the menu-bar along the top of the Fit
astrometry reference positions dialogue box (Figure 11) and choose the Read positions from a file…
option. A file-picker appears. Use it to load file
refstars.prelim. Then click the Fit/Test button
ngc1275jktpre.sdf. This is most simply done by entering the new file name in the Selection box, and pressing OK. Do not worry if a message is displayed saying that the WCS could only be saved as an AST native representation.
In some cases the approximate astrometric calibration derived in the previous stage will be adequate. However, it is possible to use additional astrometric reference stars to refine it. Assuming that you already have an approximate astrometric calibration proceed as follows.
If any unsuitable objects remain amongst the reference stars, or the fit is in some other way unsatisfactory, then repeat the steps above to remove the offending objects and repeat the fit.
When the fit is acceptable click the Accept button.
The preceding recipe has described just one of the numerous different ways to apply an astrometric calibration to an image using GAIA. Many images already contain an approximate astrometric calibration and in such cases you can skip the first two stages of the recipe and proceed directly to the third to create an accurate astrometric calibration.
Comparison images retrieved from the SuperCOSMOS surveys rather than the DSS already have an object catalogue attached, making it un-necessary to retrieve a separate catalogue from the USNO PMM (but remember that the SuperCOSMOS surveys are currently only available south of Declination ). Alternatively, you may not need to retrieve an object catalogue because you already know accurate celestial coordinates for a set of reference stars in your image; they might, for example, be listed in a scientific paper associated with the image. If you know an approximate astrometric calibration (typically, the orientation, plate scale and approximate central coordinates) for an image then you can simply type in the values (use the Astrometry calibration item from the Image-Analysis menu and choose the Type in known calibration… option).
If you have a series of similar images all overlapping the same area of sky, you could determine an astrometric calibration for the first using the method described. For the remaining images you can copy the WCS for the first image and then tweak it to fit the host image (use the Transfer button in the Fit astrometry reference positions dialogue box).
You can transfer a set of reference stars, with measured positions, from a DSS or SuperCOSMOS
calibration image to the target image, then move the markers for the stars onto the corresponding
objects in the target image (move the cursor to the appropriate reference star marker, hold down the
left mouse button, move the cursor to the required position and then release the mouse button) and
measure the positions in the target image (click on the Centroid button). A reference star can be deleted
by positioning the cursor over the appropriate marker, holding down the
Control key and
clicking on the left mouse button. After confirmation the corresponding reference star is