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Combining Methods

Except for summing the frames together, combining frames may require correcting for variations between the frames due to different exposure times, sky backgrounds, extinctions, and positions. Currently, scaling and shifting corrections are included. The scaling corrections may be done by exposure times or by using statistics in each frame over a selected part of the image. The statistics can reveal (depending on the keyword `exp'_STA) setting, (where `exp' is the exposure type) for each image the mean, median, or the mode. In the following we refer to the value by MMM. Additive shifting is also done by computing the statistics in the frames.

The region of the frames in which the statistics is computed can be specified by the keyword `exp'_SEC. By default the whole frame is used. A scaling correction is used when the flux level or sensitivity is varying. The offset correction is used when the sky brightness is varying independently of the object brightness. If the frames are not scaled then special routines combine the frames more efficiently.

Below follows a simple overview how the weighting, scaling and offset parameters are determined. All obviously depend on the settings of the keywords `exp'_SCA `exp'_OFF, `exp'_WEI, and `exp'_EXP. The overview makes clear that offset corrections will only be applied if the scaling correction is switched off. The same is true for applying an exposure time correction.

  o_i = 0.0 
  w_i = 1.0
  s_i = 1.0

     s_i = M_i                        
        w_i = sqrt(N*s_i)
        s_i = e_i 
           w_i = sqrt(N*s_i) 
        o_i = M_i/s_i
           w_i = sqrt(N*s_i/o_i)

  s_i = s_i/s_mean
  o_i = (o_i - o_mean) * s_mean
  w_i = w_i/w_sum
  key: o_i:    offset for frame i
       o_mean: mean offset over all input frames
       s_i:    scale factor for frame i
       s_mean: mean scale factor over all input frames
       w_i:    weight factor for frame i
       w_sum:  sum over all weight factors of all input frames
       e_i:    exposure time of frame i
       M_i:    MMM of frame i
       N:      number of of frames previously combined

In the combining no checks are done on the reduction status of the input frames and no attempts are made for any calibration correction like for bias or dark. Hence, in more complicated reduction sequences the user should be sure not to combine e.g. flat fields that have been corrected for bias and dark with flats fields that are not corrected.

Except for medianing and summing, the frames are combined by averaging. The average may be weighted by

weight = (N * scale) ** 1/2 (3.10)

where N is the number of frames previously combined (the command records the number of frames combined in the frame descriptor), scale is the scale factor depending on the keyword settings listed above (s_i or s_i/o_i). In most of the applications N = 1, i.e. the input calibration frames are the original ones and not the result of previous combinings.

There are a number of algorithms which may be used as well as applying statistical weights. The algorithms are used to detect and reject deviant pixels, such as cosmic rays. The choice of algorithm depends on the data, the number of frames, and the importance of rejecting cosmic rays. The more complex the algorithm the more time consuming the operation. For every method pixels above and below specified thresholds can be rejected. These thresholds are stored in the keyword `exp'_MET. If used the input frames are combined with pixels above and below the specified threshold values (before scaling) excluded. The sigma frame, if requested, will also have the rejected pixels excluded.

The following list summarizes the algorithms. Further algorithms are available elsewhere in MIDAS (see COMPUTE/..., AVERAGE/...), or may be added in time.

The "avsigclip" algorithm is the best algorithm for rejecting cosmic rays, especially with a small number of frames, but it is also the most time consuming. With many frames (>10-15) it might be advisable to use one of the other algorithms ("maxreject", "median", "minmaxrej") because of their greater speed.

The choice of the most optimal combining algorithm will clearly depend on the nature of the data and on the exposure type. Therefore, for every supported exposure type the CCD context contains a default combining setup. Currently, there are five combining setups stored in the CCD keywords, all starting with a specific two letter prefix: for bias BS_, dark DK_, dome flats FF_, sky flats SK_, and for all other exposure types OT_. At initialization these keywords are filled with sensible defaults. Below we will shortly comment on combining the various calibration frames and list the default keywords settings.

next up previous contents
Next: Combining Bias Frames Up: Preparing Your Calibration Frames Previous: Input and Output
Petra Nass