### 12 Astrometric Calibration

This recipe describes how to apply an astrometric calibration to an image. In this context an ‘astrometric calibration’ is a mathematical transformation relating the $x,y$ 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 $x,y$ 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:

(1)
finding suitable astrometric reference stars,
(2)
creating a preliminary astrometric calibration,
(3)
creating a final accurate astrometric calibration.

Each stage is described separately in individual sub-recipes below.

#### 12.1 Finding astrometric reference stars

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.

(1)
You need to extract a region of the Digitised Sky Survey (DSS) roughly corresponding to the region imaged in the CCD frame. The first part of the recipe in Section 9 gives exactly the procedure required. Either: repeat this procedure, load the image that you created when previously working through Section 9 into GAIA, or load file ngc1275dss.sdf into GAIA (the last is the required region, already extracted from the DSS).
(2)
Adjust the colour table until the image appears as in Figure 4. Click on the View menu and select the Colors… option. A panel will appear. Set the colour scale algorithm to Linear, the colormap to ramp and the intensity to neg. Then click on the Close button.

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.

(3)
Overlay the DSS image with objects selected from the USNO at ESO catalogue, following the second part of the recipe in Section 9.
(4)
The next step is to choose five stars in the image to act as reference stars. These stars should be:
• easily identified,
• reasonably bright,
• stars rather than galaxies (because star images have more precisely defined centres),
• isolated from other stars and galaxies (to avoid images which blend together),
• spread reasonably uniformly over the image,
• not very close to the edge of the image (later you will need to to identify the corresponding stars in the JKT image, and the two areas of sky are not exactly the same).

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.

(5)
Copy the selected stars to a new table dialogue box by clicking on the Options menu in the catalogue dialogue box and choosing the Extract selected item. A new catalogue dialogue box listing just the selected objects will appear. Henceforth you will work with this catalogue dialogue box.
(6)
To double-check which objects you have selected: click on the Graphics menu in the main window and choose Clear. All the catalogue object markers will disappear.

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.

(7)
It is useful to print out a copy of the image with the reference stars marked, for use in the next stage of the calibration. If you are using the colour table described above you will need to adjust it so that the star identifications are legible, typically by inverting the image to make the stars white against a dark background (as in Figure 10), rather than vice versa.
(8)
Print out a paper copy of the image by clicking on the File option (the rightmost option in the menu-bar along the top of the main window) and choose the Print... option, followed by Image.... Use the ensuing dialogue box to save the image as a postscript file, which you can then print.
(9)
Save the catalogue of selected objects. Click on the File menu in the USNO at ESO (1) dialogue box (the leftmost item in its menu-bar) and choose the Save as… option. You should specify a file-type of .lis so 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.

#### 12.2 Creating a preliminary transformation

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${}^{\circ }$. 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 file.

(1)
Load image ngc1275jkt.sdf into GAIA.
(2)
Adjust the colour table and magnification:
(a)
click the Auto Cut: button for 98% (in the bottom right of the control panel in the centre top of the window),
(b)
set the magnification: click the Scale: button (in the bottom left of the control panel in the centre top of the window) and set it to 1/2x,
(c)
set the colour table: click the Color Map: button (in the lower right of the control panel in the centre top of the window) and set it to heat. Also set the Intensity Map: button (directly below the Color Map: button) to default.
(3)
Rotate the image to the standard orientation. Click on the button marked with two horizontal arrows and then the one marked with two vertical arrows (these buttons are located on the bottom row of the control panel towards the top of the main window).

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.

(4)
Click on the Image-Analysis button on the menu-bar along the top of the main window. Choose the Astrometry calibration item and then Fit to star positions from the next menu. The Fit astrometry reference positions dialogue box shown in Figure 11 should appear.

(5)
Indicate the celestial coordinate system in which your star coordinates are expressed. You do so by specifying suitable values using the coordinate system:, Equinox: and Epoch: buttons. The coordinates will usually be FK5, equinox J2000 or for older catalogues FK4, equinox B1950. The epoch defaults to J2000 for FK5 coordinates and B1950 for FK4 coordinates. For the present recipe the defaults of FK5, equinox J2000 are correct.
(6)
To import the catalogue of selected reference stars click on the Grab button.

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).

(7)
You now need to measure the positions (in pixels) of these stars in the JKT image. Click on the first reference star in the list, make a mental note of its star name and click on the Edit button. The dialogue box shown in Figure 12 should appear.

(8)
Now click the Pick object... button. The dialogue box shown in Figure 13 should appear. The black box in the upper portion of the window displays a section of the main image centred on the position of the cursor. Referring back to your paper copy of the DSS image or Figure 10, position the cursor over the corresponding first reference star (the star names should match).

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).

(9)
Raise the object picker dialogue box (Figure 12). You should find that the pixel positions of the star have been copied into the X and Y fields.

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).

(10)
Repeat the procedure for the remaining reference stars. All the dialogue boxes remain open, so it is relatively simple to cycle through, measuring the positions of the remaining stars. Hint: double-clicking on a star in the reference star list is equivalent to clicking on it and then clicking the Edit button.
(11)
Once you have entered all your reference positions, close the dialogue boxes shown in Figures 12 and 13 by pressing the Close button in each one.
(12)
Click on the Marker menu on the menu-bar along the top of the Fit astrometry reference positions dialogue box (Figure 11), choose the Size option and set it to 21. This option makes the markers a convenient size when plotted on the JKT image. You may also need to set the Outline colour option to white (depending on which colour table you have set).

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 as before.

(13)
Once you are happy with the calibration, press the Accept button.
(14)
Finally, save the astrometric calibration by clicking the File menu button in the main window, and then the Save as… menu item. Use the resulting dialogue box to save the image (with the astrometric calibration) in a new file, perhaps called 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.

#### 12.3 Creating an accurate astrometric calibration

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.

(1)
Query the USNO at ESO catalogue to find the objects that overlay the JKT image, following the second part of the recipe in Section 9. Alternatively, you can load the example local catalogue ngc1275usno.tab.
(2)
Click on the Image-Analysis button on the menu-bar along the top of the main window. Choose the Astrometry calibration item and then Fit to star positions from the next menu. The Fit astrometry reference positions dialogue box (Figure 11) should appear.
(3)
Import the catalogue of reference stars by clicking on the Grab button and choosing the appropriate catalogue.
(4)
Click on the Clip button to remove reference stars which fall outside the image.
(5)
Delete all the catalogue objects which correspond to galaxies, nebulae, blended double-star images etc, none of which make good astrometric reference objects. The procedure to delete an object is:
• click on the symbol for the object in the main window, so that the object is highlighted in the catalogue window,
• click on the Delete button and then confirm that the object is to be deleted.
(6)
When you are happy that you have removed all unsuitable objects, clear the catalogue markers: click on the Graphics menu in the main window’s menu-bar and choose Clear.
(7)
Click on the Centroid button in the Fit astrometry reference positions dialogue box to refine the pixel positions for all the reference stars. New markers should be drawn over the JKT image showing the revised positions of the reference stars.
(8)
Click on the Fit/Test button and the revised calibration using all the reference stars will be created.

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.

(9)
Finally, save a version of the image with the revised calibration. Click on the File menu button in the main window, choose the Save as item and use the resulting dialogue box to save the image as a new file, perhaps called ngc1275jktast.sdf.

#### 12.4 Variations

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 $+{3}^{\circ }$). 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 deleted.