ASTROMETRY - PHOTOMETRY TUTORIAL
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. In Iris, 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.
Download the file N2320.ZIP, decompress the image N2320.FIT and display:
Image of the field of the galaxy NGC 2320 (the supernova 2000B is present in the image). Instrumentation: Takahashi FSQ-106 refractor (F=530mm) and Audine CCD camera with KAF-401E chip. The result is the simple sum of 4 x 60 seconds exposure (240 seconds cumulative integration time) in binning 1x1 (pixel of 9 microns). The observation was made in Toulouse (France) and a very polluted sky. Note that the image is not flat-fielded.
The equatorial coordinates of the center of the image are:
RA = 7 h 05 m
DEC = +50° 36'
Activate the dialog box Astrometry/Photometry... from the Data base menu:
The automatic Astrometry/Photometry dialog box of Iris.
Complete the item's of this dialog box:
RA & DEC : approximate coordinates of the field center (a precision of 1' is sufficient here for the algorithm 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. Here 9 microns for each side or 0.009 millimeters.
Focal length : the focal length of the telescope. Note that the pixel size and the focal length have to be given with the same scale, e.g. in millimeters. For the example we have F=530 mm.
Sigma detection : coefficient that define the detection level of stars in the in memory image. 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 : this is a coefficient used to removes 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 MicroCat catalogue. This is the limit magnitude of stars extracted from the catalogue. Here we select Magnitude=16, the fainter stars of MicroCat.
Finally, select the catalogue, MicroCat in this example (insert the CD-ROM in your unit!). Then click the OK button. After some seconds we have the result:
The encircled stars are detected automaticaly (this is equivalent to the FIND_STAR command). Note that satured stars and very faint stars are not selected.
Iris detect 497 stars in the input image (L1 list), 464 in the same MicroCat field (L2 list ). Then, Iris searches for common stars between the MicroCat map (or GSC, USNO maps) and the detected stars in the input image (matching operation). Here we have common 332 stars (COM list). Iris computes the 2nd-degree polynoms that links the two maps. Finaly Iris computes the astrometric and photometric analysis of all detected stars. The result will be in the file STAR.LST that is automatically created. The software return also the magnitude constant of the image (a one ADU intensity star is of magnitude 24.93).
Some files are created in the working directory (ASCII format - edit with a word processing):
STAR.LST file: characteristics of detected stars in the images. Each line contains the following information:
POLX.POL & POLY.POL files: contains the coefficients of the polynoms (degree 2) 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. At last, lines 22 & 23 contain the equatorial coordinates (in decimal degrees) of the center of the image.
ERROR_X.LST & ERROR_Y.LST files: they contain 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 files : the lists of common stars between detected in the input image and the catalogue (respectively in cartesian coordinates and equatorial coordinates).
CATALOG.FIT : an image of the catalogue field.
Now that you can have the precise equatorial coordinates of any stars within the image. This is done with the COMPUTE command. To use this command, first define a small rectangle around the star you want to measure, then, type from the console (no parameters):
Iris COMPUTE command execute automatically the PSF command (see contextual menu), this give X,Y coordinates of the star, then compute astrometric equatorial coordinates and approximate V magnitude. Select an other star, re-execute COMPUTE command, and so on.
The command REC2SKY compute 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):
REC2SKY 166.747 255.477
There is a symmetric command to REC2SKY, namely SKY2REC. It will 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 degree 1 polynomials (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.
SKY2REC 7h06m12.47s 50d34'31.9"
Use of the COMPUTE, REC2SKY and SKY2REC commands.
At this point it is of course possible to use the Sigma rejection in the Astrometry/Photometry dialog box for a more precise reduction (not really necessary in this example):
Result of the astrometric reduction then Sigma rejection=3. Iris eliminate 332-320=12 bad stars before the final astrometric calculation.
Of course you can use the GSC for the reference catalogue. In this situation we have 170 GSC stars (L2 list) in the field of NGC 2320. Compare to the 464 stars given by MicroCat. The later give more stars and finaly a more precise result!
The Display sky map... option of the menu Data base display the sky map extracted from the used catalogue:
Parameters of this dialog box are very similars to Astrometry/Photometry dialog box (AD & DEC are the equatorial coordinate of the field center). Note the question about the image size in pixels (this fields are automaticalled filled if an image is in memory).
The Display sky map command will then 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.
Example of image produced by Display sky map command and the MicroCat catalogue. The synthetic image is very realistic (compare to the real image N2320.FIT).
Field of NGC 2320 produced by Display sky map command and the GSC catalogue.
Field of NGC 2320 produced by Display sky map command and the USNO-A catalogue. The result is very difficult to interpret!
The power of the MicroCat compilation. Simulation of a field around M45. The image size is 256x256 pixels. The pixel size is 9x9 microns. Left, the focal length of the virtual instrument is of 5 mm and the limit magnitude is 6 (note the presence of Hyades). Center, the focal length is of 50 mm and the limit magnitude is 8. Right, the focal length is of 500 mm and the limit magnitude is 16.
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 counts.