Rebin to Reference 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:

Scan, detector, line, and scan-direction buttons will appear under the label "Rebin Separately to Reference These Parts of Prime AAR..." 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, no buttons will appear for some AARs. Again, the tags used to build the buttons on the gui are only from the prime AAR and not from the reference AAR.

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.

The feeder will first take unique portions of the prime AAR according to what buttons have been pushed.  It will then make a decision about which part of the reference scale to feed the routine.  If the reference has a tag present like the one that is selected for the prime data, then the reference data with those matching the prime tag values are feed.  However, if the reference does not have that tag present, then that tag is not used as a criteria for rejecting reference data.  That is, no match is required in this case, and any reference data can be feed.
 

An Example: Suppose the prime AAR has one scan for each of the 10 detector ranges and has one value for each of the line and scan-direction tags.  First, only the detector button will appear on the gui window.  Now, if the reference AAR also has 10 different detector values as well, and the detector button is pushed down, then the prime AAR's individual detector scans will be rebinned using the corresponding reference detector's x-values.  Hence, there will be ten spectra - one for each detector.  On the other hand, if the detector button is not selected, then only one spectrum results because no consideration is given to the detector tag values.  In another case, if the reference AAR has no tags, then there are two possibilities again, assuming that both prime and reference spectra cover a similar wavelength range.  One, if the detector button is selected, then the individual detector arrays of the prime AAR will be rebinned using the corresponding wavelength ranges from the reference AAR.  If the detector button is not selected, then there will be only one spectrum because the whole prime AAR data will be rebinned using the corresponding reference AAR's wavelength range.

• Defining the x-scale:

The reference AAR provides the x scale for the output and the routine.  When possible, the rebinned result should have y-values at each of the reference wavelengths, but not all of these reference wavelengths are necessarily used.  The following check is applied in the beginning to limit the reference x-scale if it covers wider wavelength range than the prime array selected to be rebinned.  Suppose xarr is the array of prime AAR wavelength values, and refarr is the array of reference AAR wavelength values.  Then, the x-values used in rebinning include only those reference wavelengths that lies between the first xarr - delta and the last xarr + delta, where delta is defined as the difference between the first and the second xarr elements.

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 obtained as described above.

Next, the "chk_multix" routine is performed.  This checks if any array of x values from the prime AAR contains multiple points at the same wavelength value from the reference AAR.  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 wavelength array of the reference AAR.

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 of xarr within the range, refarr(0) to xmid(0) are used if there are no xarr points to the left of the refarr(0).  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.