This appendix gives some advice on how you can find out the air mass and zenith distance of your individual observations. It is impossible to give simple instructions which will work in all cases because the procedures adopted by different observatories are different. Ideally, at the conclusion of your observing run you would be given a summary list of all your observations which would include the air mass for each. However, it is much more likely that the air mass or zenith distance will be included in the auxiliary information stored in the data file for each observation. Again, different observatories use different data formats and different keywords17.
Ideally you need to know the average air mass, , of each observation. Alternatively, the zenith distance, , is just as good. The CURSA applications for calibrating instrumental magnitudes (see the recipe in Section 16) can automatically calculate the air mass from the zenith distance. Conversely, if you need to calculate the air mass from the zenith distance yourself then Section 8 gives the requisite formulæ.
If the auxiliary information for your observations contain neither the air mass nor the zenith distance then you will have to calculate the zenith distance from whatever information is available about the celestial coordinates and times of your observations. The zenith distance, , can be calculated from:
The Hour Angle is simply:
where is the Right Ascension of the object observed and is the local sidereal time. Again, the local sidereal time may not be recorded in your observations and it might be necessary to calculate it from whatever information is available about the time of your observations. Most standard textbooks on spherical astronomy give further details of calculating the zenith distance and converting between time systems (see, for example, Spherical Astronomy by Green). Another useful source of information is the explanation and notes for the SLALIB positional-astronomy subroutine library (see SUN/67).
The keywords used to represent these various items of information differ between different
observatories. Table 5 gives some examples. It is based on CCD frames observed with
the Jacobus Kapteyn Telescope (JKT) on La Palma. In this case both the air mass and the
zenith distance are included and hence there is no need to calculate them. The keywords
used at the Anglo-Australian Observatory are available via the World Wide Web (at URL
http://www.aao.gov.au/local/www/tjf/fits.html). The appropriate instrument and observatory
manuals should document the keywords used in a given dataset. In case of difficulty staff at the
observatory where the dataset was acquired should be able to advise.
| ||air mass|
| ||zenith distance (degrees)|
| ||start time of exposure|
| ||end time of exposure|
| ||Right Ascension of the object|
| ||Declination of the object|
| ||equinox of coordinate system|
| ||date of the observation|
Files containing observations come in a number of different formats. The procedures for inspecting them to determine the values of the keywords that they contain differ for different formats. The following notes cover some of the more common formats, though they are not comprehensive. Note that you can convert a data file between any of the formats mentioned below (and others) using the CONVERT package (see SUN/55).
.sdf’. In this case, the file name specified to applications, such as those in KAPPA, must omit the ‘
.sdf’ file type.
If the observations were originally formatted as FITS files (see below) prior to being
converted to the NDF format then all the FITS keywords are preserved in an extension
to the NDF file and usually this extension will contain any information about the air
mass etc. Application
fitslist in KAPPA (see SUN/95) will list the FITS extension
of an NDF. Briefly, if you have not previously started KAPPA type
kappa. Then type
fitslist filename (remembering to omit the file type).
If you know the name of the required keyword then you can use the Unix command
to extract just the required line from the output produced by
fitslist. For example, if
the required keyword was ‘
AIRMASS’ you would type:
grep -i AIRMASS
If you cannot find the required datum in the FITS keywords then it is worth reading the FITS comments to see if they give any useful information.
You can examine the entire contents of an HDS file using
hdstrace (see SUN/102). This
option will be useful if the file is not an NDF which was created from a FITS file. Simply type
hdstrace filename (again remembering to omit the file type).
hdstrace is a flexible utility and
you should refer to SUN/102 for a full description.
fitshead in KAPPA (see SUN/95) will list all the header information, including
the keywords, in a FITS file. Briefly, if you have not previously started KAPPA type
fitshead filename. Alternatively, and perhaps even more simply, the header information
can be displayed using Unix command
more. The resulting display is perfectly readable, though
perhaps not very æsthetic. This technique works best with a window which is eighty characters
A description of the FITS format is beyond the scope of this note. However, briefly, a FITS file
comprises a primary dataset and optionally one or more extensions.
you to access the header information for the primary dataset and all the extensions.
Conversely, often only the primary header information can be conveniently accessed with
hdstrace. See above for details. The air mass, zenith distance and similar information are most likely to be found in the
.pix’, the other ‘
.pixfile contains the ‘bulk data’ for the dataset; the array comprising the two-dimensional image in the case of CCD photometry. The
.imhfile contains all the header information. It is a simple text file and the keywords have a similar format to FITS keywords. It can be listed using standard Unix commands such as
17In this context, a keyword is simply the name of each datum or item of information. For example, the keyword for the
air mass might be ‘
18The original FITS format was proposed by Wells et al. in 1981. However, it has been developed and enhanced over
the years. The FITS standard is now maintained and documented by the FITS Support Office of the Astrophysics Data
Facility at the NASA Goddard Space Flight Center (see URL:
http://fits.gsfc.nasa.gov/fits_home.html). Though FITS
is basically an astronomical format it is sometimes mentioned in books about standard image formats. See, for example,
Graphics File Formats by Kay and Levine.