Order definition: Method Hough

The method described above is recommended because it is quick and usually efficient. However an alternative method is available which enables you to process images of lower quality than required by DEFINE/ECHELLE and generally returns more accurate results. The price to be paid however is a higher demand for CPU time. The algorithm accepts frame which can be mildly contaminated by particle hits, bad columns, order gaps due to absorption lines, as found in FLAT or STD. If the frame is of very low quality for the order definition, as it may be the case for a science frame, an initial cleaning is required.

The algorithm assumes that:

• the interorder background is roughly constant over the frame.
• the slope of the orders is in the range ]0.,0.5[

The method is enabled by the parameter:

SET/ECHELLE DEFMTD=HOUGH

The command can run in a fully automatic mode if all three parameters NBORDI, WIDTHI, THRESI are set to zero. To enforce the detection of a given number of orders, set the value of NBORDI. If the frame has a low contrast or if some areas of the interorder background are brighter than faint orders in the image, it may be useful to set WIDTHI. Given hwthe half width of the orders and io the mean interorder distance, the optimal value of WIDTHI is in the range ]hw,io - hw[. The threshold THRESI is normally estimated for each order independently. However the value can be enforced by giving a non null value to THRESI.

See also the help file of the commands DEFINE/HOUGH and HOUGH/ECHELLE for more details about the possibilities of this method.

If the image is overscanned, that is includes unsensitive areas in its lower and upper parts, it is better to avoid this areas by use of the command SCAN/ECHELLE.

The best way to use this command is to start with null value for all three parameters NBORDI, WIDTHI, THRESI. For example:

INIT/ECHELLE
SET/ECHELLE DEFMTD=HOUGH ORDREF= ... (order reference frame)
SCAN/ECHELLE ORDREF CURSOR
DEFINE/HOUGH

The successive steps are the following:

• The image ORDREF is smoothed by FILTER/MEDIAN, a background value is estimated as the minimum of the smoothed frame in its central part and this value is subtracted from the frame. The result is stored in middummi.bdf. The frame middummi is displayed. this image must show a uniformly black background and a good contrast of the orders against the background. If this step does not provide a satisfying result, use another order reference image or clean it using general MIDAS commands. For a background estimate without previous order definition, consider the echelle command BACKGROUND/SMOOTH.

• The Hough transform of the middummi is computed and stored in middummh. A description of this step and of the cluster detection can be found in Ballester, 1991, Finding Echelle Orders by Hough Transform, Proceedings of the 3^rd ESO/ST-ECF Data Analysis Workshop, pp. 23-28. The image middummh.bdf must show clear accumulation peaks, roughly aligned along the columns and with a characteristic ``butterfly'' shape. The number of peaks is equal to the number of orders. This step is usually straightforward. It may happen however that bright straight lines in the Hough transform are generated by uncorrectly removed particle hits.

• The cluster detection is performed on middummh. The slope of detected orders must be rather constant, as well as the FWHM of the first bright orders. The FWHM measured on the first order is taken as reference. The displayed values provide an initial guess for WIDTHI. A visual check of the cluster detection is available by the low level command:

  HOUGH/ECHELLE middummi P5=NMV

  The result of the cluster detection is a table middummr.tbl containing slope, intercept, fwhm and peak value of the detected orders. To enforce the behaviour of cluster detection, set the parameter WIDTHI to a value big enough to remove correctly the detected features.

• The orders are followed individually and a threshold is estimated for each order. The threshold must vary continuously with the order number, and the detected positions must be in sufficient number for each order. The table order.tbl is created by this command. The measured positions can be visualised on the display window by the commands:

  LOAD middummi scale=... cuts=...
  SELECT/TABLE order all
  LOAD/TAB order :X :Y :ORDER
  or
  LOAD/TAB order :X :Y

  Descriptors START and STEP of middummi must be equal to 1.,1. This step can be controlled by the parameter THRESI.

• A bivariate polynomial is fitted to the table and outliers are discarded by a kappa-sigma algorithm. The algorithm should not discard more than say, 10 percent of the positions and the resulting fit must be better than 0.3 pixels. The iterative regression and the kappa-sigma clipping are controlled by the low level command REGRESSION/ECHELLE.