Ionizing x-rays are provided by a commercial x-ray tube with a maximum voltage and power capability of 30 kV and 9 W. The tube is model TFS-5109 manufactured by TruFocus Corp. The tube has a takeoff angle of , a molybdenum target, and a 0.005'' Be window. The tube is powered by a Spellman power supply  SL30P10/FPS/X2130, with a 30 kV capability. The Spellman power supply is especially modified for use with the TruFocus tube. The x-ray tube is housed in a vented brass box for radiation protection, which is connected to a vacuum system containing a fluorescent target chamber and CCD detector, as shown in Fig. 1. X-rays are emitted from the TruFocus tube through a 1/8'' diameter aperture, and exit the brass box in an aluminum-lined 1/4'' diameter aperture. The target chamber vacuum interface lies 12 cm beyond. X-rays enter that chamber through a 1/2'' dia. Be window of thickness 0.005''. A fluorescing target lies 14 cm beyond the Be window so that the distance between the tube's molybdenum target and the fluorescing target is 34 cm. Of this distance, 17.5 cm is air at 1 atm. A 8.8 mm diameter aperture lies between the x-ray tube and the fluorescing target to limit the x-ray beam to only fall on the target. The target itself lies on one face of a vertical, square rotatable bar of solid aluminum (1 inch on a side). The bar can also by withdrawn 2 inches in the vertical direction to expose addition targets. Thus, twelve different target materials may quickly be presented to the x-ray beam without breaking vacuum. Normal operation has the target face oriented with a 45 angle of incidence and emission with respect to the x-ray tube and CCD, respectively. The CCD lies about 60 cm away from the fluorescing target and is baffled with a 1.6 cm diameter aperture so that only the fluorescing target has a line-of-sight to the CCD (conversely, all portions of the CCD view all portions of the fluorescing target). All critical surfaces and apertures are lined with aluminum to minimize excitation of contaminating high energy x-rays. The 12 different targets used for our CCD calibration are aluminum, silicon, phosphorus, potassium chloride, titanium, vanadium, iron cobalt, nickel, copper, zinc, and germanium.
Figure 1: Basic schematic of high energy x-ray source (HEXS).
It is important to have a theoretical description of the physics of x-ray emission so as to understand the x-ray emission rate. Electron bombardment of a material produces both continuous (bremsstrahlung) and line radiation. An analysis of the continuous spectrum starts with Kramer's Rule which states that the locally generated x-ray photon number spectrum by a single electron on a thick target is
where is the incident electron voltage and Z is the target atomic number. In reality, the numerical factor is a slowly varying function of E and Z. For molybdenum (z=42), . More accurate modern analyses including corrections for internal absorption and electron backscatter have been developed. Using the approach by Pella, et al, a theoretical to experimental comparison of the x-ray spectra emerging from the molybdenum x-ray tube and incident on a target material is shown in Fig. 2. The model gives the x-ray spectra in terms of incident photons per CCD per keV per 10 A, and includes all attenuations due to the beryllium windows and air. The solid line is the experimental spectrum taken with a CCD, and the lightly dotted line is the model spectrum, which also includes a simple CCD model. The x-ray tube voltage and current for this particular example are 15 kV and 10 A, respectively. The tall peaks around 2.2 keV are molybdenum L lines, while the peak at 1.7 keV is the silicon escape peak.
Figure 2: X-ray spectrum incident on target assembly.
Once the incident spectrum on a target material is known, it is possible to calculate the outgoing flux of fluorescent K radiation. See Van Grieken for a summary. The physics is straightforward once given the incident x-ray spectrum: for an incident monochromatic x-ray beam of intensity (photons/sec/steradian/eV) on a thick homogeneous target, the outgoing K intensity is
where is the photoelectric absorption cross section, is the fluorescent yield, is the probability for K emission (as opposed to K), j is the ``jump factor'', is the mass absorption coefficient, and are the respective incident and takeoff angles for the photons with respect to the surface, is the incident x-ray energy, and is the emitted K energy. This formula does not include geometry factors and detector efficiency. It remains to integrate this expression over the appropriate energy range of the incident x-ray spectrum to obtain the entire K flux.
HEXS has been tested with twenty different target elements or compounds at all atomic numbers ranging from Z=9 (lithium fluorine) to Z=32 (germanium), except neon, argon, manganese, and gallium. The detected x-ray flux on a CCD from each target is plotted in Fig. 3 (vertical bars), along with the theoretical prediction from the above model (diamonds connected by a line), using no scaling factors. The error bars on the experimental data reflect both low counting statistics for low Z targets and partially detected x-rays for high Z targets. Limitations in the simple CCD model account for the latter effect, which are due to high energy x-rays with large penetration depth. The entire data set is taken with an x-ray tube voltage and current of 15 kV and 80 A, respectively.
Figure 3: Detected x-ray flux from HEXS for different target materials.
Figure 4: Stability of HEXS for silicon K detection over time.
Figure 5: Uniformity of HEXS silicon K detection across CCD.
The x-ray flux from HEXS is remarkably steady, particularly when operated at low power (less than 6 W). Figure 4 shows a cumulative plot of about half the data taken to date of the K flux rate from a silicon target, with a respective constant tube voltage and current of 15 kV and 260 A. The entire data set was taken with the same CCD over a period of nearly 100 days, in six subsets. Each diamond represents the average flux of detected silicon K x-rays taken over 600 exposures of 7.15 seconds duration. The error bar represents standard deviation of all data points. Clearly the standard deviation is smaller within each subset. Thus the calibration accuracy is limited by source stability over periods of an hour or less.
A second characteristic of interest is the uniformity of the x-ray beam across the CCD. Figure 5 shows this variation in a grey scale plot. The data set represents about 65 million silicon K photons collected over the entire CCD during 84,000 seconds. The AXAF ACIS CCDs have a 1024 x 1024 pixel arrangement, but the data is rebinned into a 32 x 32 pixel array to optimize presentation. Quantitatively, the grey scale range from white to darkest corresponds to 0.990, 0.995, 1.000, and 1.005 times the average flux taken over the entire CCD. It is not clear whether this variation is due to either the CCD or the x-ray source. Note that the silicon target is about 70 cm away during this measurement, giving an expected point-source cosine variation of 0.0002, far less than that observed.
The spectra from 12 different targets used in the calibration are presented in Figs. 6 - 17. All these spectra are from the same CCD (I.D. w102c3) and are cumulative spectra from all data taken over a 100 day period. All the spectra include only x-rays detected in one quadrant (which corresponds to a single analogue-to-digital amplifier chain), although the presented flux rate is multiplied by four to easily indicate flux over the entire chip. There are many features worthy of comment, but only a few will be mentioned.
The first six spectra (Figs. 6 - 11) are overlaid with a lightly dotted spectra, which is that from an x-ray monochromator at the PTB laboratory at the BESSY synchrotron source using the same CCD. The synchrotron beam is passed through a double crystal monochromator producing a highly monochromatic x-ray beam with variable energies and high resolution. Due to the purity of the beam, these spectra are the clearest representation of the CCD response. A full presentation of the BESSY analysis will be presented elsewhere.
Figure 6: Aluminum Target.
Figure 7: Silicon Target.
Figure 8: Phosphorus Target.
Figure 9: Potassium Chloride Target.
Figure 10: Titanium Target.
Figure 11: Vanadium Target.
Figure 12: Iron Target.
Figure 13: Cobalt Target.
Figure 14: Nickel Target.
Figure 15: Copper Target.
Figure 16: Zinc Target.
Figure 17: Germanium Target.
Comparing the spectra reveals impurities in the HEXS beam from either scattered x-rays or other atomic processes. One example is seen in the low energy tail of the main photopeak of Fig. 7. Figures 7 and 8 also nicely show the K line lacking in the synchrotron spectra. Another difference at 520 eV in Fig. 11 is due to the L line of vanadium. There is also a large difference above the main peak, seen best in Fig. 8, due to Compton scattering from the target. Lastly, Fig. 10 shows anomalous lines around 3500 eV which are due to diffraction effects from the target (to be discussed later). Note that the large difference seen with the potassium chloride target of Fig. 9 is due the combined spectra from each element of K and Cl. Only the BESSY spectrum from potassium is shown for the reason of clarity. In general, the spectrum from each HEXS target should include a main K, a smaller K, a Si escape peak, and a silicon peak. The low energy rise seen in every spectrum is not due to electronic noise, but is a real feature of the CCD response due to boundaries of the detecting silicon region and the gate structure. The details of the CCD response are described elsewhere.
No comparative BESSY spectra were taken for the targets illustrated in Figs. 12 - 17 due to energy limitations of the reflecting grating monochromator. Many of the lines seen in the high Z target spectra are not due to impurities or the escape peaks, but are from the following diffraction process. Most of the high Z targets are metals which present a polycrystalline matrix at the surface. The target is a flat sample oriented at 45 with respect to the CCD and the molybdenum tube. Thus, when a white light x-ray beam is incident on the target, there will statistically be some crystal grains on exposed surface oriented exactly so the Bragg diffraction condition is meet for some specific energy. If x-rays of this energy are included in the incident white light beam, they will be coherently scattered towards the CCD and superimposed on the spectrum. These extra lines can be useful for obtaining the gain variation with energy. One common impurity line seen is that of iron, due to scattering from the vacuum chamber walls. One interesting line to note is the L line, which grows in prominence with Z, seen best in Fig. 17.