Rebin and Define Scale :

• Masked data:

If there are any masked data, they will be ignored during the rebinning but retained in the output AAR.  If the user wishes, these can be unmasked or deleted afterwards from the main GUI window.

• Rebinning data separately or together:

The rebinning can be performed across scans, detectors, lines, and scan-directions under the user's control. Scan, detector, line, and scan-direction buttons will appear under the label "Rebin Across...." in the top left corner of the gui window.  Buttons will appear for only those tags found in the prime AAR which have two or more values.  Thus for some AARs, no buttons will appear.

Depending on the AOT type, some of the scan, detector, line, and scan-direction buttons will be preselected for the user's convenience.  The user may override these selections.  When any of these buttons is selected, then the rebinning will be performed across the data ignoring the corresponding tags. When the buttons are not selected, data will be rebinned separately.

An Example: Suppose the selected data has three scans for each of ten detectors and only one value for the lines and scan-directions tags. Then only the scan and detector buttons will appear and the user has four different ways to rebin this data.  First, if both buttons are not turned on, then thirty rebinned spectra will appear corresponding to each scan from each detector.  Second, if only the scan button is selected, then the scans corresponding to each detector are rebinned together such that ten spectra (one for each detector) are produced. Third, if only the detector button is pressed, then for each scan, all the detector data will be rebinned together; hence, only three spectra results corresponding to each scan. Finally, when the both button are turned on, then only one spectrum appears because all the scan and detector data are rebinned together.

• Defining the x-scale:

This can be done in four different ways:
 
• Start/End/No. of Steps (log grid option available) :  equidistant with a given start and end wavelength and a given number of steps
• Start/Step Width/No. of Steps:  equidistant with a given start wavelength, a step width (in microns) and a number of steps
• Start/Resolution/No. of Steps:  consistent with a given resolution, a start wavelength and a number of steps
• Start/Resolution/End:  consistent with a given resolution and a start and end wavelength

Resolution is defined as lambda/delta-lambda.

One or two lists of the wavelengths found in the input data are shown under the define scale option so that the user may easily select (by clicking) a new starting or stopping wavelength for the grid.

epsilon is used to eliminate multiple x-values as discussed below.

• Plotting:

Finally, on the gui_rebin, a user has the advantage of viewing the data before and after rebin.  These two displays also come with all the flexibilities such as Set Plotstyle, Replot, Unzoom, Hard Copy, Freeze Ranges and etc.  In the end, the user has the choice to quit without saving rebin or to exit which delivers the result to the main gui.
 
• The Algorithm:

First, the reference x-array is created as defined by the user with one of the options stated above.

Next, the "chk_multix" routine is performed.  This checks if any array of x values contains multiple points at the same value.  Here, the "same" value means value +- epsilon.  If so, this routine computes the mean of the corresponding y values and stdev values at the mean of the duplicated points in the x-array and modifies the x-array, y-array, and stdev-array accordingly.  In addition, this routine remembers the number of multiple points used for each of the modified y-array elements.  This information will be used later, when rebinning the data, as the weight of each flux value.  This is intended as a pre-binning operation to simplify interpolation and rebinning of a spectrum.

Finally, the rebin is performed conserving flux via approximate trapezoidal integration method.  This is outlined as follows.
 

Let xarr and yarr be the wavelength and flux array of the prime AAR, and refarr the user-defined wavelength array.

1.  The middle point array is generated from the user-defined wavelength scale according to
 

xmid(i) = (refarr(i+1) + refarr(i)) / 2.
 
2.  Using all the xarr values ranging from the xmid(i-1) to xmid(i) and the corresponding yarr values, this routine computes the new flux at refarr(i) as the total integral via the simple trapezoidal rule. That is,
 
Sum of ( (yarr(k) + yarr(k-1)) * (xarr(k) - xarr(k-1)) * w_av(k) / 2 )
----------------------------------------------------------------------
              Sum of ( w_av(k) * (xarr(k) - xarr(k-1)) )

where w_av is (weight(k-1) + weight(k)) / 2


for all k such that xmid(i-1) <= xarr(k) <= xmid(i).  Because of the boundary, the first k in this range will not be applied to this formula.  The weight(k) is the product of the chk_multix routine explained above; it is a number equal to or greater than one, and it shows how many data points were used in calculating this modified yarr(k).

3.  For the edges at the xmid(i-1) and xmid(i), there are two cases.  First, if a data point coincidentally exists at either of these points, then its corresponding flux is used to compute the integration.  If not (which is the usual case), then the fluxes at these points are linearly interpolated from the two nearest points to each side of them.

4.  For the first element, refarr(0), all the points at xarr within the range, refarr(0) to xmid(0) are used.  Note that "(0)" designates the first element in the array.

5.  If there are no points inside a bin, the value for that bin is found by linearly interpolating between the nearest two data point on either side of the bin: call these: (x_lo, y_lo), (x_hi, y_hi):

 
                                xarr(i) - x_lo
yarr(i) = y_lo + (y_hi - y_lo)  --------------
                                 x_hi  - x_lo


6.  New "STDEV" values are computed as the errors in the mean. Specifically:

 
             sum ( (yarr(k) - yc)^2 )
STDEV= SQRT ( ------------------------ )
                     n * (n-1)

where yc = computed flux for the bin
and n = number of data points found in the bin + 2 (for bin edges)
 

Please refer to sap_rebin for more details.