Astrometry allows you to determine true coordinates of objects (i.e. right ascension and declination) from their apparent position in an image (i.e. x,y). Iris can perform such transformations. The software contain sophisticated tools for quickly measuring the magnitude and position of asteroids, comets,... or estimating magnitudes of celestial objects.
In order to do that, it is necessary to get a few reference stars with precisely known sky coordinates. These positions may be obtained from information contained in different sources:
We take an example for demonstrate capacity of Iris in the Astrometric/Photometric applications. The task is the astromectric reduction of the galaxy NGC 2320 field (click here for download the image ngc2320.pic).
The equatorial coordinates of the center of the image are:
RA = 7 h 05 m
DEC = +50° 36'
The catalog used is the Tycho-2.
First define the catalog path in settings dialog box (File menu). The catalog is stored in a CD-ROM. The letter of the CD is "F". The catalog is localized in the subdirectory DATA.
Localization of the Tycho-2 catalog.
Open the Settings dialog box and complete item CR-ROM drive unit (here"f:") and catalog subdirectory (here "data").
Load the image
Open the dialog box Automatic astrometry of Analysis menu:
Complete the item's of this dialog box:
RA & DEC : Approximate coordinates of the field center (a precision of 1' is here sufficient to work properly). Note the format form (HHhMMmSSs for RA and DDdMM'SS" for DEC). For the example we have RA=7h05m and DEC=50d36'.
Pixel size X & Pixel size Y: Respectively the horizontal and vertical pixel size in millimeters. Here the pixel size is of 0.009 millimeter.
Focal length : The focal length of the telescope in millimeters. Note that the pixel size and the focal length have to be given with the same scale, e.g. in millimeters. Here F=530 mm.
Sigma detection : Coefficient that define the sensitivity detection of stars. The procedure detects stars with a level greater than Sigma detection times the noise level s in the background. If Sigma detection is too low, the number of detected stars may be much larger than the number of stars in the catalogue, which may give wrong matching. In the other hand, if Sigma detection is too high, the number of detected stars will be perhaps too low to allow a good matching. Typically we choose Sigma detection between 5 and 10 (detection of stars at 5s to 10s).
Sigma rejection : A coefficient used for remove detected stars for which the position difference between the observed and calculated data (O-C) is greater than Sigma rejection times the standard deviation of the (O-C) distribution (two pass analysis). It is very useful in some case to eliminate uncertain reference stars when making an astrometic analysis. Generally, Sigma rejection should be between 1.5 & 3 (avoid to eliminate too many stars with very low Sigma rejection values). But if Sigma rejection=0 where is no rejection and this is a correct option for standard situation.
Magnitude : Only for some catalog. Here the Tycho-2 astrometric catalog.
Then click the OK button. After some seconds we have the result:
The encircled objects are the detected stars.
Iris detect 574 stars in the input image (List #1), 21 Tycho-2 stars are present in the field (List #2). Iris find 12 common stars between list #1 and list #2. These12 stars are used for the astrometrical reduction of the image. The transformation equation between the image and the artidficial map of the sky (not used here) as well the RMS error of the reduction (here a fraction of arcsecond). Finally, Iris give the approximate V magnitude constant.
Some files are created in the working directory (ASCII format - edit with a word processing or the Output dialog box (File/Open)):
STAR.LST: The characteristics of detected stars in the image. Each line contains the following information:
Part of the STAR.LST file
POLX.POL & POLY.POL: Contains the coefficients of the polynoms (for astrometry reduction Iris fit a second order polynom for take into account optical distortion of the image) and many more informations that were used to calibrate the two fields both astrometically and photometrically. The 14 first lines of a .POL file contain the coefficients of the polynoms. The 15th line contains the correlation coefficient. The lines 16 to 19 contain the coordinates of the image window used for the computation. The 20th corresponds to the degree of the polynom. The 21st line is the magnitude constant. The lines 22 & 23 contain the equatorial coordinates (in decimal degrees) of the center of the image.
ERROR_X.LST & ERROR_Y.LST: Contains deviations from measured and calculated equatorial coordinates (respectively for AD and DEC) in the common list stars. This may allow you to detect pointing mistakes, or other problems (e.g. stars with high rate proper movement).
XY.LST & EQ.LST: Lists of common stars between detected in the input image and the catalogue (respectively in cartesian coordinates and equatorial coordinates).
Now you measure the precise equatorial coordinates of any stars in the image. This is done with the COMPUTE command. First select a star in the image with the mouse (draw a small rectangle, but be sure to include all the star flux), then, execute the console command COMPUTE (no parameters):
Iris return the precise coordinates of the object:
It also possible to open the contextual menu (right on the image) and run the COMPUTE command:
Select an other star, re-execute COMPUTE command, and so on.
The command REC2SKY
evaluate the equatorial coordinates of any point in the image. The format of
the command is:
REC2SKY [X] [Y]
[X] and [Y] are the coordinates of the pixel where you want to know the equatorial coordinates. In case of a star, x & y may come for example for the PSF command (contextual menu).
For example, to determine the celestial coordinates of a star which is near the cartesian coordinates (166.747, 255.477), run
>REC2SKY 166.747 255.477
SKY2REC is the symmetric command to REC2SKY. The function give the approximate image coordinates from the known equatorial coordinates. This is for example useful when one wants to localize an asteroid or a comet on an image. Note that SKY2REC will only use first order polynomial equation (the calculation is not so precise that COMPUTE / REC2SKY commands and not strictely symmetric). The syntax is: SKY2REC [RA] [DEC]
[RA] & [DEC] are the equatorial coordinates that are to be converted into apparent coordinates in the image. Example:
Use of the REC2SKY and SKY2REC commands.
If ou choose a rejection facteur the number of common stars is less, but the global précision improved:
It is possible to display the digital catalog map of the field. Open the Display a sky map dialobg box of Data base menu, then
The AD & DEC items are the equatorial coordinates of the field center (approximatively).
Note the fields about the image size in pixels (these fields are automaticalled filled if an image is in memory).
The Display sky map command produce an image where stars of the selected field are represented with intensities proportional to their magnitudes as read from the CD-ROM catalogue. You can click on a star to obtain informations.
Tycho-2 image of the NGC2320 field.
Here the reduction by using the GSC-ACT catalog. Note the superior number of stars the catalog is mode densified:
The sky map computed by using the GSC-ACT catalog:
A final note. The precise measurement of the
celestial coordinates of an object has many applications: identification, proper
motion of the stars, orbit calculation of asteroids and comets, etc. Iris implements
a proven astronomical reduction technique, which is widely used in specialized
observatories. It should be clear, however, that this is not enough to produce
a quality astrometric listing. The result depends on, among other things, the
precision of the measurements of the image, the number of stars used, the accuracy
of the catalogues employed and the quality of the image. All these parameters
show that in this field, experience is very significant.
Display coordinates circles
Here an image of a part of Ursa Major constellation captured with a EOS 20D and a Canon zoom lens (40 mm focal length- 20 seconds exposure @ ISO400). The image is scaled by a factor 0.25.
Fill the dialog box Automatic astrometry of Analysis menu in the following way:
The catalogue SKY2000 is used considering the image is of wide-field type. The approximate equatorial co-ordinates of the center of images are provided (Alpha = 11h15m, Delta = +58°). The pixels size of EOS 20D detector is 6.4 microns, but taking into account the reduction factor of the image, their equivalent size is 4 X 6.4 = 25.6 microns = 0.0256 mm.
Click OK to carry out the automatic reduction. Iris automatically finds the correspondence between stars present in the image and those of the catalogue.
At this stage the equatorial co-ordinates of an object in the image can be obtained by surrounding this one with a rectangle, then by typing COMPUTE command from the console or by run Compute command of contextual menu.
For draw equatorial circles run the commands D_ALPHA and D_DELTA. The first parameter is the coordinate (right ascension or declinaison). The second parameter is the intensity of the circle. For example:
>D_ALPHA 11H 600
>D_ALPHA 11H30 600
>D_ALPHA 12H 600
>D_DELTA 50d 600
>D_DELTA 55d 600
>D_DELTA 60d 600