Counting all the counts in each row of the CCD separately for each order of the spectrometer, and plotting intensity as a function of row number a Fig. 3 was produced, where three first orders are shown.
Fig. 3 shows a result of order separation, or, in other words, plots of intensity as a function of CCD row number for the first three orders of the spectrometer.
Figure 3: Intensity as a function of row number for three orders of the spectrometer with a gold target in the X-ray source.
A number of emission lines can be clearly seen in the spectrum, as well as a very clear absorption edge (presumably, oxygen edge). To convert the results into the energy scale one has to set a correspondence between row number and an energy of the incoming beam. This can be done by solving grating equation and identification at least some known emission lines. On Fig. 4 is schematically shown a geometry of the output stage of the spectrometer and a CCD. Input X-ray beam hits reflecting grating at an angle and, after being dispersed, a component of wavelength illuminates a vertical plane of the CCD at the row x. Angle is fixed by the spectrometer geometry and according to the manual .
Figure 4: Geometry of light path between the grating and the CCD in the focal plane.
From Fig. 4 it is clear that
where microns is CCD pixel size, L is a distance from the grating to the focal plane. From standard grating equation we have:
Here m is an order number, d is a grating period (208333 Angstroms). Converting wavelength (in Angstroms) into energy E (in keV) with a formula
and combining (1) and (2), we get an equation that determines an energy of the incoming beam as a function of the row number of the CCD:
Angles and are defined by a geometry of the HIREFS, and if the spectrometer is properly calibrated, according to the manual
Here is reading of the wavelength counter of the spectrometer
in Angstroms, it corresponds to the first order wavelength, hitting CCD
at the row .
To set a precise energy scale we use several emission lines with known energies, namely, carbon , nitrogen , and oxygen lines. Both first and second order oxygen line are used in this calibration procedure. The least square fit to the relation (3) with and L as free parameters at the emission line energies is usually fairly robust. We found that the value of L produced by fitting routine can be used to adjust the distance between the grating and the CCD, if it is out of the focal point. It is the most precise way to measure this distance and focus the instrument.
Equation (3) allows to determine a resolving power of the apparatus for any given energy, corresponding plot is shown at Fig. 5.
Figure 5: Spectrometer resolving power as a function of energy.
Resolving power R here is defined as a relative difference in energy seen by two adjacent rows of a CCD:
. For the interval of interest from 0.2 keV and up to 2 keV R changes roughly from 1000 to 500.