Calculating Statistics

In the same way that it was useful to display images at intermediate stages in the data reduction, it is often useful to be able to calculate and list gross statistics (mean value, standard deviation etc.) for images as they are processed. There are a couple of applications which provide this facility. Proceed as follows.

1. Assuming that KAPPA is loaded (see the recipe in Section ), move to the subdirectory containing the target astronomical images and type:

   stats ngc2336_r_2

   The following information should be displayed:

      Pixel statistics for the NDF structure /acdscratch/sc5/targets/ngc2336_r_2
   
         Title                     : N2366 R
         NDF array analysed        : DATA
   
            Pixel sum              : 1.6012529E9
            Pixel mean             : 1267.44
            Standard deviation     : 279.5582
            Minimum pixel value    : 166
               At pixel            : (1, 547)
               Co-ordinate         : (0.5, 546.5)
            Maximum pixel value    : 50963
               At pixel            : (1023, 146)
               Co-ordinate         : (1022.5, 145.5)
            Total number of pixels : 1263376
            Number of pixels used  : 1263376 (100.0%)
   

2. The statistics can also be written to a log file. Type:

   stats ngc2336_r_2 logfile=ngc2336_r_2.log

   Text file ngc2336_r_2.log will be created containing a copy of the output.

3. stats has a `$\kappa$-sigma clipping' option which allows outlying values, such as star images, to be rejected when computing the statistics. If a clipping level is given, stats will compute statistics using all the available pixels, reject all those pixels whose values lie outside $\kappa$ standard deviations of the mean and then re-evaluate the statistics. An array of up to five clipping levels may be given, which are applied sequentially. For example, to reject values outside two standard deviations type:

   stats ngc2336_r_2 clip=2

   The statistics will again be displayed, but this time the clipping will have been applied before they were computed.

4. Often the information generated by stats will be adequate. However, application histpeak in the ESP package (see SUN/180[12]) gives further details. To load ESP type:

   esp

   then type histpeak and respond to the prompts:

   histpeak
   
   ESP HISTPEAK running.
   
   IN - Image NDF filename /@ngc2336_r_2/ > ngc2336_r_2
   Filename:   /acdscratch/sc5/targets/ngc2336_r_2
   Title:      N2366 R
   Shape:      1124 x 1124  pixels
   Bounds:     x = 1:1124  y = 1:1124
   Image size: 1263376 pixels
   
   USE - Use the whole image or an ARD file /'w'/ >
   
   SFACT - Smoothing width you wish to use /0/ >
   
   DEVICE - Display device code or name /@xwindows/ >
   

   Output similar to the following should be produced:

   HISTPEAK Results: /acdscratch/sc5/targets/ngc2336_r_2
   
   Pixels (used):            1263376     Pixels (bad):                0
   Lowest count:             166.000     Highest count:       50963.000
   Skewness:                  63.680     Kurtosis:             7114.975
   
   Mean:                    1267.440     Median:               1294.776
   
   Histogram modal values:
   Unsmoothed:              1298.000     Smoothed:             1298.000
   Projected:               1296.511     Interpolated:         1298.696
   
   Absolute dev.:             90.361     Variance:               78153.
   Standard. dev.:           279.558     Back. st. dev.:         33.353
   
   Smoothing filter radius:
   Radius request:                 0     Radius actual:               0
   
   Contents of the most occupied histogram bin:
   Unsmoothed:             21104.000     Smoothed:            21104.000
   Interpolated:           12126.075
   

   and a plot similar to Figure  should appear. For the purpose of determining the sky background level it is probably best to use either histpeak or stats with the clipping option. Also note that the histpeak pre-amble contains the dimensions and bounds of the image.

Figure: Example of histogram produced by histpeak