Studies of hard x-rays are very important in both intense short pulse laser plasma interaction and conventional inertial confinement fusion (ICF) research. In ICF experiment, hot electrons generated in many nonlinear processes, such as stimulated Raman scattering, play a negative role because they preheat the nuclear fuel and lead to less effective compression of the fuel. The hard x-rays induced by the hot electrons have been studied for many years and proved to be very useful in understanding some nonlinear processes in ICF. On the other hand, intense short pulse laser easily produces much more abundant energetic electrons with energy up to GeV. The energetic electrons can produce intense hard x-ray pulse via many processes, such as line emission,^[1] bremsstrahlung,^[2] betatron radiation,^[3] and Thomson scattering. Quantitative spectroscopic characterization of the hard x-ray source is essential for these fundamental and applied researches.

Rather than being used as an imaging component, single photon counting charge coupled device (CCD) has become more and more popular in hard x-ray spectroscopic application in the past twenty years. High sensitivity and good energy resolution of the x-ray CCD camera make possible very low x-ray flux imaging and spectroscopy in many applications,^[4–14] such as astronomy,^[4] laser plasma physics,^[5–10] medical imaging,^[11,12] and nuclear physics.^[13,14] Commercial CCDs specially designed for hard x-ray spectroscopic applications have been available for some years. PI-LCX:1300 CCD camera from Princeton Instruments is one, a very popular one. Characterization of its response to x-rays is important in order to obtain a high accuracy quantitative result in relevant experimental research. Many calibrations and characterizations were carried out for a variety of other CCDs^[15–20] by using different x-ray sources. The very preliminary characterization of PI-LCX:1300 CCD camera^[21] was also reported.

In the present study, two identical type PI-LCX:1300 CCD cameras are calibrated with quasi-monochromatic x-rays from radioactive sources and a conventional x-ray tube. Taking a similar event reconstruction method reported^[5,18,22,23] in the literature, which we name the “threshold method”, a computer code of multi-pixel analysis and event-distinguishing capability is obtained. The energy resolution, the fraction of multi-pixel events as a function of x-ray energy, detection efficiency, and consistence of the two CCD cameras are obtained. The measured detection efficiencies are compared with a Monte Carlo calculation (with XOP^[24] software) and the data from manual. We find that PI-LCX 1300 CCDs may be used for x-rays up to 60 keV with a good energy resolution E/ΔE = 82, when the multi-pixel event analysis is carried. The calibrated PI-LCX:1300 CCD is used in Copper K-shell line emission experiments with a high power femtosecond laser. The K_α conversion efficiency is obtained with high accuracy. The high precision measurement of x-ray yields is critical in drawing physical conclusion in these laser plasma experiments.

Monochromatic x-rays are appropriate to calibrate CCD response because photon pileup can be easily distinguished from the known x-ray energy. Two PI-LCX:1300 CCDs (CCD I and CCD II) were calibrated with six radioactive sources and a conventional x-ray tube. Generally, the radioactive sources are quasi-monochromatic x-ray sources because they have multi separate emission lines. The parameters of employed radioactive sources are listed in Table 1. All these radioactive sources are from German Physikalisch Technische Bundesanstalt (PTB). The radioactivity data and their uncertainties listed in Table 1 are from the product datasheet.

Table 1.

Table 1.

Table 1. Radioactive sources employed in the calibration experiment. . Nuclides Half life Energy/keV Probability/% Radioactivity/104 s−1 55Fe 2.7a 5.89, 6.49 24.9, 3.4 7.33±0.22 109Cd 464d 3.1, 21.99, 22.16, 24.9 10.34, 29, 54.7, 15.14 6.05±0.14 133Ba 10.5a 4.53 14.5 8.56±0.09 152Eu 13.6a 5.64 12.7 4.08±0.06 241Am 432.2a 13.76, 13.95, 17.54, 21.01, 59.54 1.08, 11.93, 18.61 4.82, 35.9 5.35±0.06

Table 1. Radioactive sources employed in the calibration experiment. .

The energies of x-rays emitted from the nuclides vary from 3.1 keV to 59.54 keV, which covers the nominal working range of the CCD from 2 keV to 30 keV. The ²⁴¹Am (sealed) has a thick window which is almost transparent to 59.54-keV photons but blocks low energy photons. A magnet was installed between the radioactive source and the CCD camera to turn away possible β rays. Exposure time was set to be 60 s or 90 s due to relatively weak radioactivity. A conventional x-ray tube working at 15 kV/20 mA with a copper target provided a “pure” K_α line emission at 8.04 keV by filtering out the copper K_β line and the bremsstrahlung with a combination of a 200-μm copper foil and a 150-μm nickel foil. By using the x-ray tube, it was possible to directly compare CCD I with CCD II in their response to photons at exact 8.04 keV, which were produced in our laser plasma experiment. In calibration experiment, the photon flux was always regulated to make pileup effect negligible. The CCDs worked at −40 °C to minimize the CCD thermal noise.

PI-LCX:1300 CCD is a front-illuminated CCD (FI CCD). For FI CCDs, x-rays irradiate the front side of pixel where collecting electrodes are located. The majority of detected x-rays are absorbed at the locations close to the electrodes, leading to relatively small final charge clouds. The array of CCD is 1340×1300. A 50-μm silicon absorption layer provides good detection efficiency for 2-keV to 30-keV x-rays. With 20 μm×20 μm pixels, it also provides high spatial resolution. A thin beryllium window seals the CCD chip for deep cooling and reduces background by filtering out low energy photons. The CCD intrinsic noise is related to the energy resolution of the CCD. Energy resolution of single photon counting CCD camera for the Fano-limit^[25] case is expressed as

(1)

Table 2.

Table 2.

Table 2. Dependences of CCD background (after “DC background” subtraction) on exposure time with 100-kHz readout rate. For gain 1, 1 ADU represents 5.02 electrons, for gain 2, 1 ADU refers to 2.57 electrons. . Exposure time 1 ms 10 ms 50 ms 100 ms 5 s 5 s 60 s Gain 1 1 1 1 1 2 2 σsubtraction/e 10.5 85 10.5 8.5 15.1 19.8 46.0

Table 2. Dependences of CCD background (after “DC background” subtraction) on exposure time with 100-kHz readout rate. For gain 1, 1 ADU represents 5.02 electrons, for gain 2, 1 ADU refers to 2.57 electrons. .

It is clear that when the exposure time is less than 100 ms, the σ_subtraction is almost constant while for longer exposure time (5 s and 60 s), the σ_subtraction increases with exposure time. This is not surprising because the thermal noise is small compared with the constant readout noise when exposure time is short enough. The thermal noise can be estimated from a formula . The σ_thermal is less than 1.6 electrons for the 100 e/pixel/s dark current when the exposure time is less than 100 ms, while the readout noise is 5.4 electrons (root mean square value) (RMS value) according to the manual. For longer exposure time (5 s and 60 s), the σ_thermal is larger than the σ_readout, therefore the σ_subtraction increases with exposure time increasing.

All CCDs for x-ray spectroscopic application work in a so-called single photon counting mode. In this mode, incoming x-ray flux is adjusted to make “pileup” negligible (here “pileup” means that more than one photon is absorbed by a pixel). Because the number of electron-hole pairs produced by absorption of an x-ray photon in CCD depletion layer is proportional to the x-ray energy, the energy of incoming x-ray can be obtained by measuring the number of free electrons. In such a way, the energy spectrum of incoming x-ray can be reconstructed without extra dispersive device. Since collected electron clouds are not infinitely small, the electrons belong to a charge cloud may be split into neighbor pixels during collection. This kind of electron splitting leads to so-called multi-pixel event. For multi-pixel events, the number of all electrons for one event is proportional to the incoming x-ray energy. Many studies^[25–31] have been performed to understand the detailed processes of production, drift, diffusion, recombination and collection of excited electron clouds. The experiment^[32–34] with mesh method verified the relationship between the transverse position of x-ray interaction with the pixel and the type of multi-pixel event. The simulations^[35,36] successfully reproduced the measured fraction of each kind of multi-pixel event as a function of x-ray energy.

To construct spectra from raw CCD data, we use a “threshold method”. In this method, a threshold is picked up to determine the count of each pixel caused by incoming x-rays or by CCD noise. The distinguishing test is not absolutely correct for each pixel because the counts induced by x-rays may be smaller than that induced by the noise, especially for the multi-pixel event whose pixels may have a small count due to the small splitting of electron clouds. However, the “threshold method” is still practicable because the percentage of error can be controlled under a certain level by choosing an appropriate threshold due to the statistical property of the CCD background. As discussed in Section 3, the background can be approximated well by a Gaussian distribution with rather small standard deviation (σ). For the Gaussian distribution, the probabilities of pixel with the count larger than the threshold are only 1.3 × 10⁻³, 3.2 × 10⁻⁵, and 3 × 10⁻⁸, when the thresholds are set to 3σ, 4σ, and 5σ respectively. The slight increase of the threshold can lead to the dramatic decrease of the probability of fake signals (i.e., the misjudgment of a noise as a signal) at the expense of some increase of fake noise (i.e., the misjudgment of a signal as a noise). A fake signal may lead to a bigger event and the up-shift of the x-ray energy, while a fake noise may lead to a smaller event and the down-shift of x-ray energy. A low energy tail in the reconstructed spectrum due to the down-shift of x-ray energy is quite obvious when the threshold is set to be 5σ. Generally, a threshold between 3σ and 5σ is appropriate choice, depending on particular data analysis purpose.

Figure 1 presents a portion of a raw CCD data obtained with ²⁴¹Am source, showing each kind of multi-pixel event. As shown in Fig. 1, only pixels of direct connection at edges, rather than connection at corners, belong to one event. This classification has been verified and adopted in previous study.^[37] The calibration data show that there are four types of multi-pixel events (1–4 pixel event) when x-ray photon energy is less than 22 keV. However, for 59-keV x-ray photons, 5-pixel and 6-pixel events exist in addition to 1–4 pixel events, though the fractions of 5-pixel and 6-pixel events are still small (five percent, see Table 3).

Fig. 1.

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	Fig. 1. (color online) A portion of raw CCD data obtained with 241Am source showing each kind of multi-pixel event.

Table 3.

Table 3.

Table 3. Fractions of multi-pixel events for different energy x-rays. . Pixel number of events CCD I CCD II 5.89 keV (55Fe) 8.04 keV (Cu) 13.7 & 13.9 keV (241Am) 22.16 keV (109Cd) 59.54 keV (241Am) 8.04 keV (Cu) 1 55 % 50 % 37% 23% 5% 40 % 2 36 % 39 % 38% 42% 33% 38 % 3 5 % 5 % 12% 12% 23% 9 % 4 4 % 6 % 13% 23% 35% 13 % 5 and 6 5%

Table 3. Fractions of multi-pixel events for different energy x-rays. .

Figure 2 shows the histograms of raw CCD data and the data after the multi-pixel analysis and event-distinguishing with threshold method. The data are obtained with a Cu laser plasma filtered by a 100-μm Cu foil and a sealed ²⁴¹Am source. For Cu laser plasma, the threshold is set to be 3σ. The number of pixels of the above threshold counts induced by x-rays is about twenty-one thousands, giving an exposure rate of 0.9%. In Fig. 2(a), the large plateau from 1 keV to 7 keV is obviously not real because of the very low transmittance of a 100-μm Cu foil for x-rays below 7 keV. This plateau is present due to the distribution of the electron clouds among adjacent pixels. The reconstructed spectrum in Fig. 2(b) correctly shows two emission lines only and the plateau disappears completely. The energy resolution at 8.04 keV for 1 pixel event is 170 eV, which is in excellent agreement with 174 eV calculated from formula (1) for an exposure time of 5 s. If all pixel events are used, the energy resolution at 8.04 keV drops to 240 eV. On the other hand, even though the detection efficiency for 59.5-keV x-rays from ²⁴¹Am is very low, the 59.5-keV line becomes clearly visible in the reconstructed spectrum as shown in Fig. 2(d). In contrast, the 59.5-keV line is not visible at all in the histogram of raw data in Fig. 2(c).

Fig. 2.

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	Fig. 2. (color online) Histograms of the CCD counts before ((a) and (c)) and after ((b) and (d)) the multi-pixel analyzing and event-distinguishing treatment for Cu laser plasmas and 241Am sources.

Using the “threshold method” discussed in Section 4, fractions of all kinds of events are calculated from the raw CCD data. The fractions at five discrete x-ray photon energy points for CCD I and fraction at 8.04 keV for CCD II are listed in Table 3. All data in Table 3 are obtained with 3σ threshold. In addition, pileup probabilities for all cases are less than 0.3%. The data in Table 3 show that each multi-pixel event occurs with different probabilities for x-rays of different energies. Generally, the fraction of small pixel event is larger for smaller energy x-rays. When x-ray photon energy increases from 5.9 keV to 59.5 keV, the fraction of single pixel event monotonously decreases from 55% to 5%, but the fraction of 4-pixel event monotonously increases from 4% to 35%.

Occurrence of multi-pixel event is due to limited size of collected electron cloud. The location where the x-ray is absorbed in the silicon layer in the direction parallel to pixel surface directly determines the type of multi-pixel event.^[34] The location near the pixel center results in single pixel event, the location near the pixel edge results in 2-pixel events, and the location near the pixel corner results in 3 and 4 pixel events.

Different collected electron cloud size leads to different fraction of multi-pixel event. Higher energy x-rays produce larger primary electron clouds and are averagely absorbed at deeper position in silicon layer. Using the formula Φ_{electroncloud} = 73 × (E_photon/2.3 keV)^1.75 nm, the sizes of primary electron clouds are obtained to be 0.4 μm, 1.7 μm, 3.8 μm, and 22 μm for the x-rays of 6 keV, 14 keV, 22 keV, and 60 keV, respectively. Considering longer drift distance to collection electrode for electron clouds produced by higher energy x-rays, the size of final collected electron clouds becomes even bigger for higher energy x-rays. Because 22-μm size of primary electron clouds for 60-keV x-rays is already slightly larger than the 20-μm pixel size, the 5% single pixel event for 60-keV photons is a reasonable number. For 5.9-keV x-rays, according to their experimental data of 4% 4-pixel events, the calculated diameter of electron clouds is 5.6 μm by assuming a spherical electron cloud. This result suggests that the diffusion during the drift of electron clouds to the electrode makes the final collected electron cloud much larger than 0.4-μm electron cloud. Like the previous work,^[36,38] complete quantitatively explanation to data in Table 3 needs detailed simulations, which will be carried out in the future.

Detection efficiency (ε_d) is one of most important parameters of single photon counting CCD spectrometer. The detection efficiency is defined as ε_d ≡ N_d/N_i, where N_d is the detected x-ray photon number, N_i is the number of x-ray photon impinging on the CCD beryllium window of the area equal to the area of CCD chip. For the experiment setup, N_i = A ⋅ P ⋅ t ⋅ (Ω/4π)⋅tr_s ⋅ tr_f ⋅ tr_air, where A is the activity of radioactive source; P is the characteristic photon emission probability; t is the exposure time; Ω is the solid angle for the CCD chip; tr_air, tr_f, tr_s are the transmittances of photons through the given length of air, the protective foil of radioactive source, and the radioactive source itself, respectively. Each measurement is repeated six times. The N_d is calculated by the “threshold method” described in Section 4 for each raw datum. All types of multi-pixel events are included in the counting of detected photons. Detection efficiencies at six discrete energy points for CCD I are plotted in Fig. 3, where the error bars represent the statistic errors of six measurements. The detection efficiency curve from the data sheet of the manual is also included in Fig. 3. Theoretical detection efficiency curve is calculated with the XOP software (ver. 2.4). In the XOP calculation, the percentage of deposited x-ray energy within the 50-μm silicon layer behind a 250-μm beryllium filter is treated as the theoretical ε_d. The calculated detection efficiency curve is also plotted in Fig. 3.

Fig. 3.

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	Fig. 3. (color online) Comparison between the calibrated detection efficiencies from the XOP calculation and data from the manual. The anomalously high detection efficiency of the 155Ba at 4.54 keV is due to the strong noise excited by high energy γ rays.

Figure 3 clearly shows that the ε_d depends strongly on x-ray energy. A maximum of ε_d curve is located at 5.2 keV. When x-ray energy increases from 2 keV to 5.2 keV, the ε_d jumps from 1.5% up to 75%. When x-ray energy increases from 5.2 keV to 30 keV, the ε_d drops relatively slowly from 75% down to 1.5%. Explanation to this dependence is very simple. If x-ray energy is too small, very few x-rays can penetrate the beryllium window and be captured by the silicon layer. Contrariwise, if x-ray energy is too big, most x-rays penetrate beryllium window, but only very few of them deposit their energy in the silicon layer, and most of them will just penetrate the silicon layer.

While the other five data from the calibration are in good agreement with the XOP calculations and the data from the manual, there is an exception for the data of ¹³³Ba at 4.54 keV. The calibrated efficiency at this energy point is much higher than the XOP calculation. This disagreement can be explained as follows. While the ¹³³Ba radioactive source emits the characteristic 4.54-keV photons, it also emits a large number of high energy γ rays. The luminescence excited by the high energy γ rays and the scattering of the high energy photons introduce a lot of low energy photons, which mix with the characteristic photons. These inherent noises cannot be accurately calculated and subtracted, which makes the measured ε_d significantly larger. A similar problem happens in the cases of ¹⁵²Eu at 5.64 keV and ¹⁰⁹Cd at 3.1 keV, which are not included in Fig. 3.

All calibrated data, together with the XOP calculation results, are collected in Table 4. For ⁵⁵Fe, which is free from noises induced by high energy γ photons, the measured ε_d at 5.89 keV is(74.5±1.8)%. The 2.4% (1.8/74.5) relative error is almost consistent with the 2.6% relative error calculated from the relative errors of the A, t, and Ω. Considering the experimental error, the calibrated ε_d and XOP calculation are in very good agreement for all five energy points between 5 keV to 25 keV. On the other hand, the calibrated ε_d at 4.54 keV for ¹³³Ba is 35% larger than the XOP results, which is due to the reason discussed in the previous paragraph. At 59.5 keV, the calibrated efficiency ((8.8±4.4)× 10⁻⁴) and XOP calculation results (2.4×10⁻³) are inconsistent, though the reconstructed spectrum in Fig. 2(d) shows clearly distinguished peak. This inconsistency needs further investigating in the future.

Table 4.

Table 4.

Table 4. Summary of detection efficiencies. The error bars in the third and the sixth columns are the standard deviations of six measurements at each energy points. . Nuclides X-ray energy/keV Detection efficiency from calibration for CCD I/% Detection efficiency from XOP calculation/% Detection efficiency from data sheet/% Detection efficiency from calibration for CCD II/% 133Ba 4.53 95.0±4.1 70.4 70.8 55Fe 5.89 74.5±1.8 71.7 72.8 78.5±2.6 241Am 13.9 14.3±0.9 13.5 14.5 241Am 17.5 6.81±0.54 7.01 6.8 109Cd 22.1 3.48±0.19 3.57 3.9 109Cd 24.9 2.75±0.32 2.53 2.85

Table 4. Summary of detection efficiencies. The error bars in the third and the sixth columns are the standard deviations of six measurements at each energy points. .

The comparison between two CCDs shows an important result which attention should be paid to in usage of the CCDs. The detection efficiencies at 5.89 keV for two CCDs as shown in Table 4 differ by 5.6%. However, the difference in fraction of single pixel event between them is much larger. As shown in Table 3, the difference at 8.04 keV reaches up to 25%. According to the previous discussion, we suggest that the silicon layer of CCD II is thicker than that of CCD I, because thicker silicon layer leads to larger detection efficiency, in the meanwhile, smaller fraction of single pixel event. These results justify the necessity of including all multi-pixel events to reduce the error in comparing their results.

In this work, the detailed calibration of the PI LCX 1300 single photon counting CCD camera is carried out. The multi-pixel analyzing and event-distinguishing method is built and applied successfully to processing the calibration data. The calibrated detection efficiencies of high precision (relative error<2.5% at 5.89 keV) are obtained. The calibrated ε_d and XOP calculation are in very good agreement for x-ray of energy larger than 5.9 keV within the experimental errors. Due to strong dependences of single pixel event on x-ray energy and on particular CCD camera, it is important to take all sorts of multi pixel events into account in the measurement of the hard x-ray yields. Based on the calibration results, the calculated detection efficiency with XOP at other uncalibrated energy points can be confidently used for x-ray energies between 5.9 keV and 30 keV. However, more calibrations are necessary in the future for x-ray energies between 1.5 keV to 4.65 keV.

Compared with crystal hard x-ray spectrometer, which is also commonly used in laser plasma experiment, the single photon counting CCD spectrometer has advantages in measurement range, detection efficiency, accuracy of detection, and alignment. The drawback of single photon counting CCD spectrometer is its lower energy resolution, and the typical energy resolution of crystal spectrometer can easily reach better than one thousand. A weeping magnetic field in front of CCD is also necessary in order to bend away the hot electrons usually present in the intense short pulse laser plasma experiment.