X-RAY EMISSION FROM MATERIALS PROCESSING LASERS Open Access

Scintillator dosemeter

In order to determine the effective irradiation time during the experiments, a scintillation dosemeter for ambient dose equivalent, H*(10), from the company Automess⁽¹⁴⁾, was used as radiation monitor. The background dose rate was determined to be 0.052 ± 0.007 μSv/h (standard deviation of the single values). The duration of the irradiation was selected by choosing the time for which the indication of the dosemeter exceeded the background dose rate plus three times its standard deviation.

Experimental setups

Figure 2 shows the measuring setups for two different geometries. Table 2 lists the details of the experiments. The workpiece was fixed on its underside on a vacuum table. For reasons of material availability, the same workpiece surfaces were processed by the laser several times during the irradiations. As a result of material removal, in particular during the first processing, the laser focus probably no longer had its maximum intensity on the workpiece surface during the further processing steps, since the workpiece surface was now somewhat lowered. An additional effect occurs with the Tungsten foil of 0.2 mm thickness, since it was not as flat as the 6 mm metal sheet.

Figure 2.

Pictures of the setup during the first (left) and second (right) setup.

Table 2.

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Details of the experiments.

Parameter	First setup		Second setup
Parameter	Spectrometer 11	Spectrometer 13	Spectrometer 11	Spectrometer 12
Workpiece material	Tungsten		Steel (St37)	Alloy^a
Workpiece thickness	0.2 mm		6 mm
Workpiece condition	Plane parallelism and flatness not specified		Plane parallelism and flatness ~15 μm
Frequency of workpiece processing at the same surface position	One time		Up to seven times
Angle relative to workpiece surface	46°	13°	31°
Distance $x$ of the spectrometer front from the laser focus	17 cm		9.76 cm
Effective irradiation time	2.6 h		3.1 h	2.2 h

Parameter	First setup		Second setup
Parameter	Spectrometer 11	Spectrometer 13	Spectrometer 11	Spectrometer 12
Workpiece material	Tungsten		Steel (St37)	Alloy^a
Workpiece thickness	0.2 mm		6 mm
Workpiece condition	Plane parallelism and flatness not specified		Plane parallelism and flatness ~15 μm
Frequency of workpiece processing at the same surface position	One time		Up to seven times
Angle relative to workpiece surface	46°	13°	31°
Distance $x$ of the spectrometer front from the laser focus	17 cm		9.76 cm
Effective irradiation time	2.6 h		3.1 h	2.2 h

^a92.5% mass fraction tungsten; 3.75% mass fraction iron; 3.75% mass fraction nickel.

Table 2.

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Details of the experiments.

Parameter	First setup		Second setup
Parameter	Spectrometer 11	Spectrometer 13	Spectrometer 11	Spectrometer 12
Workpiece material	Tungsten		Steel (St37)	Alloy^a
Workpiece thickness	0.2 mm		6 mm
Workpiece condition	Plane parallelism and flatness not specified		Plane parallelism and flatness ~15 μm
Frequency of workpiece processing at the same surface position	One time		Up to seven times
Angle relative to workpiece surface	46°	13°	31°
Distance $x$ of the spectrometer front from the laser focus	17 cm		9.76 cm
Effective irradiation time	2.6 h		3.1 h	2.2 h

Parameter	First setup		Second setup
Parameter	Spectrometer 11	Spectrometer 13	Spectrometer 11	Spectrometer 12
Workpiece material	Tungsten		Steel (St37)	Alloy^a
Workpiece thickness	0.2 mm		6 mm
Workpiece condition	Plane parallelism and flatness not specified		Plane parallelism and flatness ~15 μm
Frequency of workpiece processing at the same surface position	One time		Up to seven times
Angle relative to workpiece surface	46°	13°	31°
Distance $x$ of the spectrometer front from the laser focus	17 cm		9.76 cm
Effective irradiation time	2.6 h		3.1 h	2.2 h

^a92.5% mass fraction tungsten; 3.75% mass fraction iron; 3.75% mass fraction nickel.

For measurement of the background dose in the 30 TLD layers (due to the zero effect in the TLDs and due to natural background radiation), an additional spectrometer was not irradiated.

DATA EVALUATION AND RESULTS

Method for the few-channel spectrometer

Following the irradiations, the doses were measured in the 30 TLD layers of each spectrometer and the background dose from the unirradiated spectrometer was subtracted from the doses in the irradiated ones. The dose measurement was calibrated by irradiating separate TLDs to a dose traceable to PTB’s primary standards. This allowed absolute fluence spectra to be determined and absolute dose values in terms of different quantities to be determined therefrom. For evaluation, the doses were related to the effective irradiation time.

In the first 13 TLD layers, doses significantly above background were measured. Only these 13 layers were used for data evaluation, for which a Bayesian method was utilized^{(8, 9)}. The main advantages of this method are that pre-information can be included in the evaluation and that, in addition to the results, also their standard uncertainties and coverage intervals are reported. The uncertainty contributions considered are listed in Appendix 2; details will be given in a separate paper⁽¹⁵⁾.

The following pre-information was included in the parametrization, see equation (1). The first term describes the characteristic fluorescence radiation of the target material. Due to the mechanisms of the laser interaction with matter, it is known that the emitted radiation is Maxwellian distributed for electrons and for photons it is dominated by an exponential decrease as the photon energy increases; this is accounted for in the second term. In addition, there were at least ~10 cm of air between the laser focus and the spectrometer front resulting in a significant absorption of low energy radiation, which is represented by the smooth rise via the ‘+cosine’ term in the second line of equation (1). Finally, a drop off to zero fluence was assumed at some unknown particle energy, which is represented by the smooth drop via the ‘−cosine’ term in the fourth line of equation (1).

Significant contributions due to electrons could be ruled out, as discussed in the next subsection. Therefore, only the photon contribution was considered for the subsequent data evaluation. As outlined above, equation (1) was used to parametrize the photon fluence $Φ {(E)}_{x}$ at the distance $x$ from the laser focus, i.e. the measuring position (Table 2).

Two additional alternatives utilizing different models compared to equation (1) were also used for the data evaluation in order to identify the most appropriate model. The one represented by equation (1) is the most appropriate, further details will be given in a separate paper⁽¹⁵⁾.

An overall validation of the spectrometer using equation (1) is outlined in Appendix 3.

with $a_{fluor}$ the amplitude of the fluorescence radiation, $E_{fluor}$ the energy of the fluorescence radiation: 6.5 keV was chosen for the steel target (rounded mean energy of the K_α and K_β emission lines from iron) and 9 keV for the tungsten and alloy targets (rounded mean energy of the L_α and L_β emission lines from tungsten), $a_{\exp}$ the amplitude of the exponential decay, $s_{\exp}$ the slope of the exponential decay, $m_{rise} = 1 / (E_{rise, end} - E_{rise, start})$ ⁠, $b_{rise} = - m_{rise} \cdot E_{rise, end}$ ⁠, $m_{drop} = - 1 / (E_{drop, end} - E_{drop, start})$ ⁠, $b_{drop} = - m_{drop} \cdot E_{drop, end}$ ⁠, $E_{rise, start}$ the energy where the rise of the spectrum starts, $E_{rise, end}$ the energy where the spectrum turns into the exponential decay, $E_{drop, start}$ the energy where the drop of the spectrum starts and $E_{drop, end}$ the energy where the spectrum drops to zero.

The seven parameters were optimized to match the measured dose values, i.e. to fulfill equation (2) using the program WinBUGS⁽¹⁶⁾. The allowed parameter ranges and their initial start values for the data evaluation are given in Table 3. Due to the absorption in (at least) ~10 cm of air between the laser focus and the spectrometers, only photons with at least 2 keV reach the spectrometers resulting in the parameter range of E_rise,start starting at 2 keV.

{\vec{D}}_{meas} = R \cdot \vec{Φ}

(2)

with the measured doses

{\vec{D}}_{meas} = (\begin{matrix} D_{1} \\ ⋮ \\ D_{N} \end{matrix})

⁠, in N = 30 TLD layers,

Table 3.

Parameters and their allowed ranges and initial start values for the data evaluation.

Parameter	Range; initial value	Explanation
a_fluor/cm⁻²	0…10¹⁵; 1 · 10¹¹	Amplitude of the fluorescence radiation
a_exp/cm⁻²	0…10¹⁵; 3 · 10¹¹	Amplitude of the spectrum’s exponential decay
s_exp/keV⁻¹	−50…50; −0.5	Slope of the spectrum’s exponential decay
E_rise,start/keV	2…10; 2	Energy at which the spectrum rise starts
E_rise,end/keV	E_rise,start + 0…20; 3	Energy at which the spectrum rise is finished
E_drop,start/keV	0…500; 250	Energy at which the spectrum drop starts
E_drop,end/keV	E_drop,start + 0…1000; 500	Energy at which the spectrum ends

Parameter	Range; initial value	Explanation
a_fluor/cm⁻²	0…10¹⁵; 1 · 10¹¹	Amplitude of the fluorescence radiation
a_exp/cm⁻²	0…10¹⁵; 3 · 10¹¹	Amplitude of the spectrum’s exponential decay
s_exp/keV⁻¹	−50…50; −0.5	Slope of the spectrum’s exponential decay
E_rise,start/keV	2…10; 2	Energy at which the spectrum rise starts
E_rise,end/keV	E_rise,start + 0…20; 3	Energy at which the spectrum rise is finished
E_drop,start/keV	0…500; 250	Energy at which the spectrum drop starts
E_drop,end/keV	E_drop,start + 0…1000; 500	Energy at which the spectrum ends

Table 3.

Parameters and their allowed ranges and initial start values for the data evaluation.

Parameter	Range; initial value	Explanation
a_fluor/cm⁻²	0…10¹⁵; 1 · 10¹¹	Amplitude of the fluorescence radiation
a_exp/cm⁻²	0…10¹⁵; 3 · 10¹¹	Amplitude of the spectrum’s exponential decay
s_exp/keV⁻¹	−50…50; −0.5	Slope of the spectrum’s exponential decay
E_rise,start/keV	2…10; 2	Energy at which the spectrum rise starts
E_rise,end/keV	E_rise,start + 0…20; 3	Energy at which the spectrum rise is finished
E_drop,start/keV	0…500; 250	Energy at which the spectrum drop starts
E_drop,end/keV	E_drop,start + 0…1000; 500	Energy at which the spectrum ends

Parameter	Range; initial value	Explanation
a_fluor/cm⁻²	0…10¹⁵; 1 · 10¹¹	Amplitude of the fluorescence radiation
a_exp/cm⁻²	0…10¹⁵; 3 · 10¹¹	Amplitude of the spectrum’s exponential decay
s_exp/keV⁻¹	−50…50; −0.5	Slope of the spectrum’s exponential decay
E_rise,start/keV	2…10; 2	Energy at which the spectrum rise starts
E_rise,end/keV	E_rise,start + 0…20; 3	Energy at which the spectrum rise is finished
E_drop,start/keV	0…500; 250	Energy at which the spectrum drop starts
E_drop,end/keV	E_drop,start + 0…1000; 500	Energy at which the spectrum ends

the fluences $\vec{Φ}$ to be determined, $\vec{Φ} = (\begin{matrix} Φ_{1} \\ ⋮ \\ Φ_{M} \end{matrix})$ ⁠, in M = 60 energy channels and

the calculated responses $R = (\begin{matrix} R_{1, 1} & \dots & R_{1, M} \\ ⋮ & ⋱ & ⋮ \\ R_{N, 1} & \dots & R_{N, M} \end{matrix})$ ⁠.

As the spectrometer positions were different during the experiments (Table 2), the results were related to 10 cm distance from the laser focus. This was performed in two steps: firstly, the quadratic distance law was applied and, secondly, the exponential attenuation law was used to correct for the different air absorptions at the measuring position and at 10 cm distance, see the following equation.

\begin{matrix} Φ {(E)}_{10 cm} & = Φ {(E)}_{x} \cdot {x / 10 cm}^{2} \\ \cdot \exp [- {10 cm - x} \cdot μ_{en} (E) / ρ] \end{matrix}

(3)

with $Φ {(E)}_{10 cm}$ the photon fluence at 10 cm distance from the laser focus, $Φ {(E)}_{x}$ the photon fluence at the distance $x$ from the laser focus, $x$ the distance of the spectrometer front from the laser focus during the irradiation and $μ_{en} (E) / ρ$ the energy absorption coefficient depending on the photon energy⁽¹⁷⁾.

Note that for x larger than 10 cm the correction factor $\exp [- {10 cm - x} \cdot μ_{en} (E) / ρ]$ results in values larger than unity.

Results: contribution of electron radiation

Preliminary evaluations also took the contribution due to electrons into account in equation (1). For this evaluation, an exponential decay was assumed for photons and a Maxwellian distribution for electrons. The results clearly showed that no significant dose contribution due to electrons was present (of the order of 10⁻³ of the dose due to photons) and, consequently, no significant contribution of electron radiation at all.

Results: contribution of photon radiation

Spectra

Figures 3–6 show the spectra for the fluence, Φ, and the radiation protection quantities H′(0.07), H′(3) and H*(10), respectively, together with the 95% coverage intervals as uncertainty bars. These intervals represent the region which covers the actual (correct) values (with a probability of 95%). The position of the (correct) value is the less likely, the closer the position is assumed near the edge of the interval.

Figure 3.

Fluence spectra at the four measuring positions (normalized to the effective irradiation time and 10 cm distance). The uncertainty bars represent the 95% coverage intervals. Note that the ordinate is broken and has a 10 times larger scale after the break.

Figure 4.

H′(0.07) spectra at the four measuring positions (normalized to the effective irradiation time and 10 cm distance). The uncertainty bars represent the 95% coverage intervals. Note that the ordinate is broken and has an eight times larger scale after the break.

Figure 5.

H′(3) spectra at the four measuring positions (normalized to the effective irradiation time and 10 cm distance). The uncertainty bars represent the 95% coverage intervals.

Figure 6.

H*(10) spectra at the four measuring positions (normalized to the effective irradiation time and 10 cm distance). The uncertainty bars represent the 95% coverage intervals.

10.1007/978-3-540-46065-7

Conversion of the fluence to the operational quantities was carried out by multiplication with conversion coefficients for mono-energetic photons: for H′(0.07) and H*(10) taken from ICRU 57⁽¹⁸⁾ and for H′(3) from Behrens⁽¹⁹⁾. The quantities H′(0.07), H′(3) and H*(10) are relevant for monitoring local skin dose, eye lens dose and effective dose, respectively. From the figures it can clearly be seen that significant contributions exist only to up to ~20–25 keV of photon energy.

The spectra are less uncertain the higher the photon’s energy (Figures 3–6) especially below ~5 keV. This is because the higher the photon’s energy, the deeper the radiation penetrates the spectrometer and, consequently, more TLD layers contain information in their dose values resulting in less uncertain spectral fluences. Photons with energies below 5 keV only penetrate the first TLD layer resulting in practically no spectral information. This is one important reasons for the necessity of taking pre-information into account for the data evaluation.

Although the optimized values of the parameters from equation (1) are not as important as the resulting spectra, it shall be noted that the values for E_drop,start and E_drop,end were rather large, i.e. in the order of a few 100 keV. This means that no definite endpoint energy of the spectra was found by the optimization software WinBUGS. This coincides with the assumption that the primary electrons from the plasma are Maxwellian distributed and consequently, the photons follow an exponential decay both with no finite endpoint energy.

Dose rate values

By integrating the spectra over the energy range, the total dose rate values were determined (Table 4). The maximum dose rate occurs for the alloy workpiece as a solid sheet, ~4.1 mSv/h for the quantity Ḣ*(10). The corresponding value for the alloy foil is only one-fourth of that. As stated in subsection ‘Experimental setups’, in contrast to the metal sheet the foil was not as flat as the sheet. In addition, the sheet was processed with the laser up to 7 times at the same position. Because of this, the maximum intensity of the laser focus, especially in the case of the foil, was not always directly on the workpiece surface, with the result that the intensity on the actual workpiece surface was lower than indicated in Table 3. As in the case of the spectra, the uncertainties are larger for lower photon energies. This is because the larger the energy, the deeper the radiation penetrates the spectrometer and, consequently, the more TLD layers contain information from that radiation.

Table 4.

Dose rate values for operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07) mSv/h	$\overset{\cdot}{H}$ ′(3) mSv/h	$\overset{\cdot}{H}$ *(10) mSv/h
Alloy: 31° above the target	(8.3 ± 2.1) · 10³ {±25%}	(76 ± 6) {±8%}	(4.3 ± 0.3) {±7%}
Alloy: 31° above the target	95%-IV: [4.3;12.5] · 10³	95%-IV: [64;89]	95%-IV: [3.8;4.9]
Tungsten: 46° above the target	(4.8 ± 2.6) · 10³ {±54%}	(27.7 ± 2.0) {±7%}	(1.53 ± 0.09) {±6%}
Tungsten: 46° above the target	95%-IV: [2.3;12.5] · 10³	95%-IV: [24.1;32.0]	95%-IV: [1.36;1.72]
St37: 31° above the target	(3.1 ± 0.4) · 10³ {±12%}	(30.5 ± 2.1) {±7%}	(1.21 ± 0.08) {±7%}
St37: 31° above the target	95%-IV: [2.4;3.8] · 10³	95%-IV: [26.8;35.1]	95%-IV: [1.06;1.39]
Tungsten: 13° above the target	(1.6 ± 1.4) · 10³ {±86%}	(16.8 ± 1.8) {±10%}	(1.04 ± 0.07) {±7%}
Tungsten: 13° above the target	95%-IV: [0.4;5.6] · 10³	95%-IV: [13.7;20.6]	95%-IV: [0.90;1.19]

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07) mSv/h	$\overset{\cdot}{H}$ ′(3) mSv/h	$\overset{\cdot}{H}$ *(10) mSv/h
Alloy: 31° above the target	(8.3 ± 2.1) · 10³ {±25%}	(76 ± 6) {±8%}	(4.3 ± 0.3) {±7%}
Alloy: 31° above the target	95%-IV: [4.3;12.5] · 10³	95%-IV: [64;89]	95%-IV: [3.8;4.9]
Tungsten: 46° above the target	(4.8 ± 2.6) · 10³ {±54%}	(27.7 ± 2.0) {±7%}	(1.53 ± 0.09) {±6%}
Tungsten: 46° above the target	95%-IV: [2.3;12.5] · 10³	95%-IV: [24.1;32.0]	95%-IV: [1.36;1.72]
St37: 31° above the target	(3.1 ± 0.4) · 10³ {±12%}	(30.5 ± 2.1) {±7%}	(1.21 ± 0.08) {±7%}
St37: 31° above the target	95%-IV: [2.4;3.8] · 10³	95%-IV: [26.8;35.1]	95%-IV: [1.06;1.39]
Tungsten: 13° above the target	(1.6 ± 1.4) · 10³ {±86%}	(16.8 ± 1.8) {±10%}	(1.04 ± 0.07) {±7%}
Tungsten: 13° above the target	95%-IV: [0.4;5.6] · 10³	95%-IV: [13.7;20.6]	95%-IV: [0.90;1.19]

Table 4.

Dose rate values for operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07) mSv/h	$\overset{\cdot}{H}$ ′(3) mSv/h	$\overset{\cdot}{H}$ *(10) mSv/h
Alloy: 31° above the target	(8.3 ± 2.1) · 10³ {±25%}	(76 ± 6) {±8%}	(4.3 ± 0.3) {±7%}
Alloy: 31° above the target	95%-IV: [4.3;12.5] · 10³	95%-IV: [64;89]	95%-IV: [3.8;4.9]
Tungsten: 46° above the target	(4.8 ± 2.6) · 10³ {±54%}	(27.7 ± 2.0) {±7%}	(1.53 ± 0.09) {±6%}
Tungsten: 46° above the target	95%-IV: [2.3;12.5] · 10³	95%-IV: [24.1;32.0]	95%-IV: [1.36;1.72]
St37: 31° above the target	(3.1 ± 0.4) · 10³ {±12%}	(30.5 ± 2.1) {±7%}	(1.21 ± 0.08) {±7%}
St37: 31° above the target	95%-IV: [2.4;3.8] · 10³	95%-IV: [26.8;35.1]	95%-IV: [1.06;1.39]
Tungsten: 13° above the target	(1.6 ± 1.4) · 10³ {±86%}	(16.8 ± 1.8) {±10%}	(1.04 ± 0.07) {±7%}
Tungsten: 13° above the target	95%-IV: [0.4;5.6] · 10³	95%-IV: [13.7;20.6]	95%-IV: [0.90;1.19]

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07) mSv/h	$\overset{\cdot}{H}$ ′(3) mSv/h	$\overset{\cdot}{H}$ *(10) mSv/h
Alloy: 31° above the target	(8.3 ± 2.1) · 10³ {±25%}	(76 ± 6) {±8%}	(4.3 ± 0.3) {±7%}
Alloy: 31° above the target	95%-IV: [4.3;12.5] · 10³	95%-IV: [64;89]	95%-IV: [3.8;4.9]
Tungsten: 46° above the target	(4.8 ± 2.6) · 10³ {±54%}	(27.7 ± 2.0) {±7%}	(1.53 ± 0.09) {±6%}
Tungsten: 46° above the target	95%-IV: [2.3;12.5] · 10³	95%-IV: [24.1;32.0]	95%-IV: [1.36;1.72]
St37: 31° above the target	(3.1 ± 0.4) · 10³ {±12%}	(30.5 ± 2.1) {±7%}	(1.21 ± 0.08) {±7%}
St37: 31° above the target	95%-IV: [2.4;3.8] · 10³	95%-IV: [26.8;35.1]	95%-IV: [1.06;1.39]
Tungsten: 13° above the target	(1.6 ± 1.4) · 10³ {±86%}	(16.8 ± 1.8) {±10%}	(1.04 ± 0.07) {±7%}
Tungsten: 13° above the target	95%-IV: [0.4;5.6] · 10³	95%-IV: [13.7;20.6]	95%-IV: [0.90;1.19]

Dose contributions from photon energies above 30 keV

The dose contributions from photons with energies above 30 keV were also determined from the spectra (Table 5). The contribution lies below 2·10⁻⁷, 2·10⁻⁵ and 4·10⁻⁴ for the quantities H′(0.07), H′(3) and H*(10) independent of the workpiece material and emittance angle above the target. Again, the uncertainties decrease for deeper reference depths of the quantity.

Table 5.

Dose rate contributions above 30 keV photon energy to the operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07)_{>30 keV}/ $\overset{\cdot}{H}$ ′(0.07)	$\overset{\cdot}{H}$ ′(3)_{>30 keV}/ $\overset{\cdot}{H}$ ′(3)	$\overset{\cdot}{H}$ (10)_{>30 keV}/ $\overset{\cdot}{H}$ (10)
Alloy: 31° above the target	(0.8 ± 0.4) · 10⁻⁷ {±48%}	(0.88 ± 0.18) · 10⁻⁵ {±20%}	(1.4 ± 0.3) · 10⁻⁴ {±21%}
	95%-IV: [0.4;1.9] · 10⁻⁷	95%-IV: [0.61;1.31] · 10⁻⁵	95%-IV: [0.99;2.12] · 10⁻⁴
Tungsten: 46° above the target	(4.1 ± 1.7) · 10⁻⁸ {±42%}	(7.3 ± 1.2) · 10⁻⁶ {±16%}	(1.22 ± 0.20) · 10⁻⁴ {±16%}
	95%-IV: [1.7;8.3] · 10⁻⁸	95%-IV: [5.1;9.8] · 10⁻⁶	95%-IV: [0.85;1.61] · 10⁻⁴
St37: 31° above the target	(1.36 ± 0.29) · 10⁻⁷ {±22%}	(1.38 ± 0.23) · 10⁻⁵ {±16%}	(3.2 ± 0.5) · 10⁻⁴ {±16%}
	95%-IV: [0.89;2.04] · 10⁻⁷	95%-IV: [0.99;1.88] · 10⁻⁵	95%-IV: [2.3;4.3] · 10⁻⁴
Tungsten: 13° above the target	(2 ± 3) · 10⁻⁷ {±164%}	(1.8 ± 0.5) · 10⁻⁵ {±31%}	(2.6 ± 0.8) · 10⁻⁴ {±32%}
	95%-IV: [0;10] · 10⁻⁷	95%-IV: [1.0;3.1] · 10⁻⁵	95%-IV: [1.5;4.7] · 10⁻⁴

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07)_{>30 keV}/ $\overset{\cdot}{H}$ ′(0.07)	$\overset{\cdot}{H}$ ′(3)_{>30 keV}/ $\overset{\cdot}{H}$ ′(3)	$\overset{\cdot}{H}$ (10)_{>30 keV}/ $\overset{\cdot}{H}$ (10)
Alloy: 31° above the target	(0.8 ± 0.4) · 10⁻⁷ {±48%}	(0.88 ± 0.18) · 10⁻⁵ {±20%}	(1.4 ± 0.3) · 10⁻⁴ {±21%}
	95%-IV: [0.4;1.9] · 10⁻⁷	95%-IV: [0.61;1.31] · 10⁻⁵	95%-IV: [0.99;2.12] · 10⁻⁴
Tungsten: 46° above the target	(4.1 ± 1.7) · 10⁻⁸ {±42%}	(7.3 ± 1.2) · 10⁻⁶ {±16%}	(1.22 ± 0.20) · 10⁻⁴ {±16%}
	95%-IV: [1.7;8.3] · 10⁻⁸	95%-IV: [5.1;9.8] · 10⁻⁶	95%-IV: [0.85;1.61] · 10⁻⁴
St37: 31° above the target	(1.36 ± 0.29) · 10⁻⁷ {±22%}	(1.38 ± 0.23) · 10⁻⁵ {±16%}	(3.2 ± 0.5) · 10⁻⁴ {±16%}
	95%-IV: [0.89;2.04] · 10⁻⁷	95%-IV: [0.99;1.88] · 10⁻⁵	95%-IV: [2.3;4.3] · 10⁻⁴
Tungsten: 13° above the target	(2 ± 3) · 10⁻⁷ {±164%}	(1.8 ± 0.5) · 10⁻⁵ {±31%}	(2.6 ± 0.8) · 10⁻⁴ {±32%}
	95%-IV: [0;10] · 10⁻⁷	95%-IV: [1.0;3.1] · 10⁻⁵	95%-IV: [1.5;4.7] · 10⁻⁴

Table 5.

Dose rate contributions above 30 keV photon energy to the operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07)_{>30 keV}/ $\overset{\cdot}{H}$ ′(0.07)	$\overset{\cdot}{H}$ ′(3)_{>30 keV}/ $\overset{\cdot}{H}$ ′(3)	$\overset{\cdot}{H}$ (10)_{>30 keV}/ $\overset{\cdot}{H}$ (10)
Alloy: 31° above the target	(0.8 ± 0.4) · 10⁻⁷ {±48%}	(0.88 ± 0.18) · 10⁻⁵ {±20%}	(1.4 ± 0.3) · 10⁻⁴ {±21%}
	95%-IV: [0.4;1.9] · 10⁻⁷	95%-IV: [0.61;1.31] · 10⁻⁵	95%-IV: [0.99;2.12] · 10⁻⁴
Tungsten: 46° above the target	(4.1 ± 1.7) · 10⁻⁸ {±42%}	(7.3 ± 1.2) · 10⁻⁶ {±16%}	(1.22 ± 0.20) · 10⁻⁴ {±16%}
	95%-IV: [1.7;8.3] · 10⁻⁸	95%-IV: [5.1;9.8] · 10⁻⁶	95%-IV: [0.85;1.61] · 10⁻⁴
St37: 31° above the target	(1.36 ± 0.29) · 10⁻⁷ {±22%}	(1.38 ± 0.23) · 10⁻⁵ {±16%}	(3.2 ± 0.5) · 10⁻⁴ {±16%}
	95%-IV: [0.89;2.04] · 10⁻⁷	95%-IV: [0.99;1.88] · 10⁻⁵	95%-IV: [2.3;4.3] · 10⁻⁴
Tungsten: 13° above the target	(2 ± 3) · 10⁻⁷ {±164%}	(1.8 ± 0.5) · 10⁻⁵ {±31%}	(2.6 ± 0.8) · 10⁻⁴ {±32%}
	95%-IV: [0;10] · 10⁻⁷	95%-IV: [1.0;3.1] · 10⁻⁵	95%-IV: [1.5;4.7] · 10⁻⁴

Workpiece and emittance angle	$\overset{\cdot}{H}$ ′(0.07)_{>30 keV}/ $\overset{\cdot}{H}$ ′(0.07)	$\overset{\cdot}{H}$ ′(3)_{>30 keV}/ $\overset{\cdot}{H}$ ′(3)	$\overset{\cdot}{H}$ (10)_{>30 keV}/ $\overset{\cdot}{H}$ (10)
Alloy: 31° above the target	(0.8 ± 0.4) · 10⁻⁷ {±48%}	(0.88 ± 0.18) · 10⁻⁵ {±20%}	(1.4 ± 0.3) · 10⁻⁴ {±21%}
	95%-IV: [0.4;1.9] · 10⁻⁷	95%-IV: [0.61;1.31] · 10⁻⁵	95%-IV: [0.99;2.12] · 10⁻⁴
Tungsten: 46° above the target	(4.1 ± 1.7) · 10⁻⁸ {±42%}	(7.3 ± 1.2) · 10⁻⁶ {±16%}	(1.22 ± 0.20) · 10⁻⁴ {±16%}
	95%-IV: [1.7;8.3] · 10⁻⁸	95%-IV: [5.1;9.8] · 10⁻⁶	95%-IV: [0.85;1.61] · 10⁻⁴
St37: 31° above the target	(1.36 ± 0.29) · 10⁻⁷ {±22%}	(1.38 ± 0.23) · 10⁻⁵ {±16%}	(3.2 ± 0.5) · 10⁻⁴ {±16%}
	95%-IV: [0.89;2.04] · 10⁻⁷	95%-IV: [0.99;1.88] · 10⁻⁵	95%-IV: [2.3;4.3] · 10⁻⁴
Tungsten: 13° above the target	(2 ± 3) · 10⁻⁷ {±164%}	(1.8 ± 0.5) · 10⁻⁵ {±31%}	(2.6 ± 0.8) · 10⁻⁴ {±32%}
	95%-IV: [0;10] · 10⁻⁷	95%-IV: [1.0;3.1] · 10⁻⁵	95%-IV: [1.5;4.7] · 10⁻⁴

Mean energies

Finally, the mean energies for the four quantities were determined from the spectra using different types of weighting (Table 6). They range from ~4–6 keV (Φ‒ and H′(0.07)‒weighted) to up to 13 keV (H*(10)‒weighted) and show no significant tendency with regards to dependence on the workpiece material and/or emittance angle above the target.

Table 6.

Mean energies of the spectra weighted with fluence and operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\bar{E} {Φ} / keV$	$\bar{E} {H' (0.07)} / keV$	$\bar{E} {H' (3)} / keV$	$\bar{E} {H * (10)} / keV$
Alloy: 31° above the target	(5.1 ± 0.5) {±9%}	(4.4 ± 0.3) {±7%}	(9.62 ± 0.03) {±0.4%}	(12.94 ± 0.06) {±0.5%}
	95%-IV: [4.3;6.0]	95%-IV: [4.1;5.3]	95%-IV: [9.55;9.69]	95%-IV: [12.82;13.07]
Tungsten: 46° above the target	(4.7 ± 0.7) {±15%}	(4.3 ± 0.5) {±12%}	(9.53 ± 0.03) {±0.3%}	(12.89 ± 0.05) {±0.4%}
	95%-IV: [3.2;5.8]	95%-IV: [3.3;5.2]	95%-IV: [9.47;9.59]	95%-IV: [12.79;12.99]
St37: 31° above the target	(5.8 ± 0.2) {±4%}	(5.3 ± 0.2) {±4%}	(8.31 ± 0.06) {±0.8%}	(13.44 ± 0.07) {±0.5%}
	95%-IV: [5.3;6.2]	95%-IV: [5.0;5.7]	95%-IV: [8.20;8.44]	95%-IV: [13.31;13.58]
Tungsten: 13° above the target	(5.4 ± 1.0) {±19%}	(4.7 ± 0.8) {±17%}	(9.71 ± 0.06) {±0.6%}	(13.16 ± 0.10) {±0.7%}
	95%-IV: [3.4;7.4]	95%-IV: [3.4;6.6]	95%-IV: [9.60;9.84]	95%-IV: [12.98;13.36]

Workpiece and emittance angle	$\bar{E} {Φ} / keV$	$\bar{E} {H' (0.07)} / keV$	$\bar{E} {H' (3)} / keV$	$\bar{E} {H * (10)} / keV$
Alloy: 31° above the target	(5.1 ± 0.5) {±9%}	(4.4 ± 0.3) {±7%}	(9.62 ± 0.03) {±0.4%}	(12.94 ± 0.06) {±0.5%}
	95%-IV: [4.3;6.0]	95%-IV: [4.1;5.3]	95%-IV: [9.55;9.69]	95%-IV: [12.82;13.07]
Tungsten: 46° above the target	(4.7 ± 0.7) {±15%}	(4.3 ± 0.5) {±12%}	(9.53 ± 0.03) {±0.3%}	(12.89 ± 0.05) {±0.4%}
	95%-IV: [3.2;5.8]	95%-IV: [3.3;5.2]	95%-IV: [9.47;9.59]	95%-IV: [12.79;12.99]
St37: 31° above the target	(5.8 ± 0.2) {±4%}	(5.3 ± 0.2) {±4%}	(8.31 ± 0.06) {±0.8%}	(13.44 ± 0.07) {±0.5%}
	95%-IV: [5.3;6.2]	95%-IV: [5.0;5.7]	95%-IV: [8.20;8.44]	95%-IV: [13.31;13.58]
Tungsten: 13° above the target	(5.4 ± 1.0) {±19%}	(4.7 ± 0.8) {±17%}	(9.71 ± 0.06) {±0.6%}	(13.16 ± 0.10) {±0.7%}
	95%-IV: [3.4;7.4]	95%-IV: [3.4;6.6]	95%-IV: [9.60;9.84]	95%-IV: [12.98;13.36]

Table 6.

Mean energies of the spectra weighted with fluence and operational quantities (at 10 cm distance from the laser focus), their standard deviations and 95% coverage intervals.

Workpiece and emittance angle	$\bar{E} {Φ} / keV$	$\bar{E} {H' (0.07)} / keV$	$\bar{E} {H' (3)} / keV$	$\bar{E} {H * (10)} / keV$
Alloy: 31° above the target	(5.1 ± 0.5) {±9%}	(4.4 ± 0.3) {±7%}	(9.62 ± 0.03) {±0.4%}	(12.94 ± 0.06) {±0.5%}
	95%-IV: [4.3;6.0]	95%-IV: [4.1;5.3]	95%-IV: [9.55;9.69]	95%-IV: [12.82;13.07]
Tungsten: 46° above the target	(4.7 ± 0.7) {±15%}	(4.3 ± 0.5) {±12%}	(9.53 ± 0.03) {±0.3%}	(12.89 ± 0.05) {±0.4%}
	95%-IV: [3.2;5.8]	95%-IV: [3.3;5.2]	95%-IV: [9.47;9.59]	95%-IV: [12.79;12.99]
St37: 31° above the target	(5.8 ± 0.2) {±4%}	(5.3 ± 0.2) {±4%}	(8.31 ± 0.06) {±0.8%}	(13.44 ± 0.07) {±0.5%}
	95%-IV: [5.3;6.2]	95%-IV: [5.0;5.7]	95%-IV: [8.20;8.44]	95%-IV: [13.31;13.58]
Tungsten: 13° above the target	(5.4 ± 1.0) {±19%}	(4.7 ± 0.8) {±17%}	(9.71 ± 0.06) {±0.6%}	(13.16 ± 0.10) {±0.7%}
	95%-IV: [3.4;7.4]	95%-IV: [3.4;6.6]	95%-IV: [9.60;9.84]	95%-IV: [12.98;13.36]

Workpiece and emittance angle	$\bar{E} {Φ} / keV$	$\bar{E} {H' (0.07)} / keV$	$\bar{E} {H' (3)} / keV$	$\bar{E} {H * (10)} / keV$
Alloy: 31° above the target	(5.1 ± 0.5) {±9%}	(4.4 ± 0.3) {±7%}	(9.62 ± 0.03) {±0.4%}	(12.94 ± 0.06) {±0.5%}
	95%-IV: [4.3;6.0]	95%-IV: [4.1;5.3]	95%-IV: [9.55;9.69]	95%-IV: [12.82;13.07]
Tungsten: 46° above the target	(4.7 ± 0.7) {±15%}	(4.3 ± 0.5) {±12%}	(9.53 ± 0.03) {±0.3%}	(12.89 ± 0.05) {±0.4%}
	95%-IV: [3.2;5.8]	95%-IV: [3.3;5.2]	95%-IV: [9.47;9.59]	95%-IV: [12.79;12.99]
St37: 31° above the target	(5.8 ± 0.2) {±4%}	(5.3 ± 0.2) {±4%}	(8.31 ± 0.06) {±0.8%}	(13.44 ± 0.07) {±0.5%}
	95%-IV: [5.3;6.2]	95%-IV: [5.0;5.7]	95%-IV: [8.20;8.44]	95%-IV: [13.31;13.58]
Tungsten: 13° above the target	(5.4 ± 1.0) {±19%}	(4.7 ± 0.8) {±17%}	(9.71 ± 0.06) {±0.6%}	(13.16 ± 0.10) {±0.7%}
	95%-IV: [3.4;7.4]	95%-IV: [3.4;6.6]	95%-IV: [9.60;9.84]	95%-IV: [12.98;13.36]

CONCLUSIONS

The emission (including its spectral distribution) of laser induced X-rays from materials processing ultra-short pulsed laser system was successfully determined. To achieve this, a TLD-based few-channel spectrometer was mechanically modified to also cover the photon energy region of a few to up to 100 keV. The spectrometer’s response (dose per incident fluence) was newly calculated and the original method of data evaluation (from dose to spectrum) was further developed for this particular application. With this, a reliable method was established to measure pulsed photon spectra in the low energy region up to a 100 keV.

The use of other laser parameters (like focus intensity, wavelength, angle of incidence of the laser beam, etc.), workpieces (both material and surface), and methods used for the materials processing that are different from the ones described in this work will very likely lead to different results for the radiation emission both for photons and electrons.

ACKNOWLEDGEMENTS

The authors are grateful to D. Heisenberg (TRUMPF company) and A. Röttger (PTB) for initiating this work, M. Sailer (TRUMPF company) for operating the laser and to J. Kretzer, C. Fuhg and Q. Zhao (all three from PTB) for contributing to the successful experiments.

FUNDING

This work was supported by the cooperation agreement FV-Nr. 63 010⁽²⁰⁾ between PTB and TRUMPF Laser GmbH, Aichhalder Straße 39, 78 713 Schramberg, Deutschland.

REFERENCES

Mulser

and

Bauer

High Power Laser–Matter Interaction. STMP 238

(

Berlin Heidelberg

Springer

) (

2010

)

10.1016/0030-4018(96)00250-7

Momma

et al. .

Short-pulse laser ablation of solid targets

Opt. Commun.

129

134

(

1996

)

10.1007/978-3-319-17659-8

Gerhard

Viöl

and

Wieneke

: Plasma-enhanced laser materials processing. Plasma Science and Technology—Progress in Physical States and Chemical Reactions, Prof. Tetsu Mieno (Ed.), InTec (

2016

). DOI:

10.5772/61567

, freely available

Nolte

Schrempel

and

Dausinger

, Eds

Ultrashort pulse laser technology—laser sources and applications.

SSOS 195 (Cham: Springer) (

2016

)

10.1103/PhysRevLett.68.1535

Gibbon

and

Bell

A. R.

Collisionless absorption in sharp-edged plasmas

Phys. Rev. Lett.

1535

(

1992

)

Company GFH GmbH

. Deggendorf, Germany. https://gfh-gmbh.de/en/

Behrens

and

Ambrosi

A TLD-based few-channel spectrometer for mixed photon, electron, and ion fields with high fluence rates

Radiat. Prot. Dosim.

101

(

2002

)

10.1093/oxfordjournals.rpd.a006062

10.1088/1748-0221/4/03/P03027

Behrens

Schwoerer

Düsterer

Ambrosi

Pretzler

Karsch

and

Sauerbrey

A thermoluminescence detector-based few-channel spectrometer for simultaneous detection of electrons and photons from relativistic laser-produced plasmas

Rev. Sci. Instrum.

961

(

2003

)

Behrens

Wenig-Kanal-Spektrometer zur Messung von Elektronen- und Photonenspektren in ultrakurz gepulsten Strahlungsfeldern. PTB report PTB-Dos-44 ISBN 978-3-86509-002-7 (

2003

). DOI:

10.7795/110.20171113

Behrens

A spectrometer for pulsed and continuous photon radiation

J. Instrum.

P03027

(

2009

)

10.1016/S0168-583X(86)80027-1

Nelson

W. R.

Hirayama

and

Rogers

D. W. O.

: The EGS4 code system. Report SLAC-265 (Stanford Linear Accelerator Center) (

1985

Namito

Ban

and

Hirayama

: LSCAT: low-energy photon-scattering expansion for the EGS4 code. Report KEK Internal 95-10 (National Laboratory for High Energy Physics, Japan) (

1995

Bielajew

and

Rogers

D. W. O.

PRESTA: the parameter reduced electron-step transport algorithm for electron Monte Carlo transport

Nucl. Instrum. Methods

B18

165

(

1987

)

Automation und Messtechnik GmbH

. Scintillator Probe 6150AD-b/H/E connected to the Dose rate meter 6150 AD 6/H/E. https://www.automess.de/6150AD-b_E.htm

Behrens

and

Reginatto

Bayesian spectrum deconvolution including uncertainties and model selection: application to X-ray emission data using WinBUGS

Radiat. Prot. Dosim.

in preparation.

Lunn

D. J.

Thomas

Best

and

Spiegelhalter

WinBUGS—a Bayesian modelling framework: concepts, structure, and extensibility

Stat. Comput.

325

(

2010

)

10.1023/A:1008929526011

10.1093/jicru/os29.2.Report57

Hubbell

J. H.

and

Seltzer

S. M.

Tables of x-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest. Report NISTIR 5632 (

1995

International Commission on Radiation Units and Measurements (ICRU)

. Conversion coefficients for use in radiological protection against external radiation. ICRU Report 57 (Bethesda, MA: ICRU Publications) (

1998

Behrens

Conversion coefficients for H’(3;Ω) for photons

J. Radiol. Prot.

354

(

2017

)

10.1088/1361-6498/aa51e8

Pullner

and

Behrens

: Röntgenstrahlung an Ultrakurzpuls-Lasermaschinen. Ergebnisbericht der PTB, Geschäftszeichen 1W-63010 (2018-04-04).

Joint Committee for Guides in Metrology (JCGM)

. Evaluation of measurement data—guide to the expression of uncertainty in measurement. Available in the internet (

2008

International Organization for Standardization

X and Gamma Reference Radiation for Calibrating Dosemeters and Doserate Meters and for Determining their Response as a Function of Photon Energy—Part 1: Radiation Characteristics and Production Method. ISO 4037-1

(

Geneva

ISO) (

) (

1996

Deutsches Institut für Normung e.V

Strahlenschutzdosimeter—Allgemeine Regeln DIN 6818-1

(

Berlin

Beuth Verlag

) (

2004

10.1093/oxfordjournals.rpd.a032591

Ankerhold

Behrens

and

Ambrosi

X-ray spectrometry of low energy photons for determining conversion coefficients from air kerma, Ka, to personal dose equivalent, Hp(10), for radiation qualities of the ISO narrow spectrum series

Radiat. Prot. Dosim.

247

(

1999

)

. the spectra are available at PTB’s website, R&D of department 6.3.

Appendix 1 Details of the few-channel spectrometer

Table A1 lists the filter materials and thicknesses used in the spectrometer. The very first filter made of polycarbonate is doped with graphite so that it is light-tight. This prevents laser light from penetrating the PMMA and reaching the TLDs which are sensitive to light. Figure A1 shows the response functions for photons and electrons. The latter were calculated for 11 cm distance between a point source and the spectrometer front. For measurements performed at other distances the responses are converted via the quadratic distance law to the actual distance during the measurement. Doing so the different depths of the 30 TLD layers within the spectrometer are taken into account.

Table A1.

Material and thickness of the layers of the few-channel spectrometer.

Filter material	Thickness (g/cm²)	No. of TLD layer behind filter
Polycarbonate^a	0.0147	1
PMMA^b	0.118	2
PMMA	0.118	3
PMMA	0.118	4
PMMA	0.230	5
PMMA	0.226	6
PMMA	0.490	7
PMMA	0.706	8
PMMA	0.942	9
PMMA	1.18	10
PMMA	0.118	Additional absorber in front of layer 11
Titanium	0.0232	11
Titanium	0.0232	12
Titanium	0.0463	13
Iron	0.0413	14
Iron	0.0413	15
Copper	0.0536	16
Copper	0.0536	17
Copper	0.0893	18
Molybdenum	0.0767	19
Molybdenum	0.0767	20
Molybdenum	0.104	21
Silver	0.110	22
Silver	0.147	23
Silver	0.147	24
Tin	0.183	25
Tin	0.183	26
Tin	0.371	27
Alloy^c	0.356	28
Alloy	0.356	29
Alloy	0.356	30
Teflon	0.0572	In front of and behind TLD layers 11–30
Teflon spacer	0. 227	Beside TLD layers (layer 11–30)
Lithium fluoride^d	0.158	Located within Teflon spacers

Filter material	Thickness (g/cm²)	No. of TLD layer behind filter
Polycarbonate^a	0.0147	1
PMMA^b	0.118	2
PMMA	0.118	3
PMMA	0.118	4
PMMA	0.230	5
PMMA	0.226	6
PMMA	0.490	7
PMMA	0.706	8
PMMA	0.942	9
PMMA	1.18	10
PMMA	0.118	Additional absorber in front of layer 11
Titanium	0.0232	11
Titanium	0.0232	12
Titanium	0.0463	13
Iron	0.0413	14
Iron	0.0413	15
Copper	0.0536	16
Copper	0.0536	17
Copper	0.0893	18
Molybdenum	0.0767	19
Molybdenum	0.0767	20
Molybdenum	0.104	21
Silver	0.110	22
Silver	0.147	23
Silver	0.147	24
Tin	0.183	25
Tin	0.183	26
Tin	0.371	27
Alloy^c	0.356	28
Alloy	0.356	29
Alloy	0.356	30
Teflon	0.0572	In front of and behind TLD layers 11–30
Teflon spacer	0. 227	Beside TLD layers (layer 11–30)
Lithium fluoride^d	0.158	Located within Teflon spacers

^aDoped with graphite.

^bChemical composition: C₅H₈O₂; Polymethyl metacrylate (PMMA).

^cAlloy: 92.5% mass fraction tungsten; 3.75% mass fraction iron; 3.75% mass fraction nickel.

^dTLD700: LiF (enriched ⁷Li) doped with Mg and Ti.

Table A1.

Material and thickness of the layers of the few-channel spectrometer.

Filter material	Thickness (g/cm²)	No. of TLD layer behind filter
Polycarbonate^a	0.0147	1
PMMA^b	0.118	2
PMMA	0.118	3
PMMA	0.118	4
PMMA	0.230	5
PMMA	0.226	6
PMMA	0.490	7
PMMA	0.706	8
PMMA	0.942	9
PMMA	1.18	10
PMMA	0.118	Additional absorber in front of layer 11
Titanium	0.0232	11
Titanium	0.0232	12
Titanium	0.0463	13
Iron	0.0413	14
Iron	0.0413	15
Copper	0.0536	16
Copper	0.0536	17
Copper	0.0893	18
Molybdenum	0.0767	19
Molybdenum	0.0767	20
Molybdenum	0.104	21
Silver	0.110	22
Silver	0.147	23
Silver	0.147	24
Tin	0.183	25
Tin	0.183	26
Tin	0.371	27
Alloy^c	0.356	28
Alloy	0.356	29
Alloy	0.356	30
Teflon	0.0572	In front of and behind TLD layers 11–30
Teflon spacer	0. 227	Beside TLD layers (layer 11–30)
Lithium fluoride^d	0.158	Located within Teflon spacers

Filter material	Thickness (g/cm²)	No. of TLD layer behind filter
Polycarbonate^a	0.0147	1
PMMA^b	0.118	2
PMMA	0.118	3
PMMA	0.118	4
PMMA	0.230	5
PMMA	0.226	6
PMMA	0.490	7
PMMA	0.706	8
PMMA	0.942	9
PMMA	1.18	10
PMMA	0.118	Additional absorber in front of layer 11
Titanium	0.0232	11
Titanium	0.0232	12
Titanium	0.0463	13
Iron	0.0413	14
Iron	0.0413	15
Copper	0.0536	16
Copper	0.0536	17
Copper	0.0893	18
Molybdenum	0.0767	19
Molybdenum	0.0767	20
Molybdenum	0.104	21
Silver	0.110	22
Silver	0.147	23
Silver	0.147	24
Tin	0.183	25
Tin	0.183	26
Tin	0.371	27
Alloy^c	0.356	28
Alloy	0.356	29
Alloy	0.356	30
Teflon	0.0572	In front of and behind TLD layers 11–30
Teflon spacer	0. 227	Beside TLD layers (layer 11–30)
Lithium fluoride^d	0.158	Located within Teflon spacers

^aDoped with graphite.

^bChemical composition: C₅H₈O₂; Polymethyl metacrylate (PMMA).

^cAlloy: 92.5% mass fraction tungsten; 3.75% mass fraction iron; 3.75% mass fraction nickel.

^dTLD700: LiF (enriched ⁷Li) doped with Mg and Ti.

Figure A1.

Response functions (depth dose curves) for mono-energetic photons (left) and electrons (right): dose per incident fluence at the front of the spectrometer vs. TLD layer in the spectrometer, calculated for 11 cm from a point. From one line to the next, the energy differs by a factor of 1.0674. For a few energy channels the mean energy is given. Note that both scales are logarithmic.

Appendix 2 Uncertainty contributions

For the Bayesian data evaluation, the following uncertainty contributions were taken into account during the optimization of the parameters in equation (1):

the statistical contributions to the dose measurement: in the order of ±2% or larger (type A uncertainties);
the uncertainty of the absolute dose calibration: ±3% (type B uncertainty);
the uncertainty contribution due to the distance uncertainty of the spectrometers: ±2.5 and ±5 mm (half width of rectangular distributions) for a distance of 9.76 and 17 cm, respectively, resulting in ~±2 up to 3.5% uncertainty of the dose, depending on the spectrometer’s position and on the position of the TLD layer in the spectrometer (type B uncertainty); and
the uncertainty of the response matrix’ entries, which was estimated from the uncertainty of the interaction coefficients, the modeling of the spectrometer’s setup (geometry and materials) and the simulation process itself: from ±3 up to ±6% from the upper down to the lower energy end of the response matrix, i.e. from 100 down to 2 keV (type B uncertainty).

Only the statistical uncertainties of the doses (a) are uncorrelated from one TLD layer to the other. The other contributions (b) to (d) are correlated in the following ways: the uncertainty of the absolute dose calibration (b) is 100% correlated among all TLD layers; at the uncertainty due to the distance uncertainty (c), however, the uncertainties in the different TLD layers depend on the layers’ position in the spectrometer; the uncertainties of the response matrix entries (d) are certainly correlated for neighboring energy channels but not for very different energies. These different types of correlation were implemented in the Bayesian data evaluation using the WinBUGS program. Further details will be given in a dedicated publication⁽¹⁵⁾.

Unless otherwise stated, all uncertainties contributions stated above are standard uncertainties and were determined according to the GUM⁽²¹⁾.

Appendix 3 Validation of the overall performance of the spectrometer

To check the overall performance of the few-channel spectrometer, i.e. the determination of the spectrum and the dose in terms of different quantities, it was irradiated in four reference radiation X-ray fields at PTB, N-15 (=A-15), H-20 (=C-20), (B-40) and W-80 (=B-80) (nomenclature according to ISO 4037-1⁽²²⁾; and in brackets according to DIN 6818-1⁽²³⁾), to a dose of H*(10) = 10.0 mSv, traceable to PTB’s primary standards, at a distance of 2.5 m from the focus of the X-ray tube. The first two X-ray fields were chosen as their spectral range and mean energy is approximately in the energy range of the spectra measured at the laser facilities. N-15 is a strongly filtered X-ray field with an accelerating voltage of 15 kV, H-20 is weakly filtered with a voltage of 20 kV and B-40 and W-80 are medium filtered with voltages of 40 and 80 kV, respectively. The two latter X-ray fields were chosen to complete the energy range up to nearly 100 keV.

Figures C1– C4 show the fluence spectra of the four radiation qualities resulting from the data evaluation of the few-channel spectrometer compared to the spectra measured with a high purity Germanium (HPGe) spectrometer⁽²⁴⁾. As expected, not all the details of the spectra are reproduced correctly, like the fluorescence radiation where the model for the few-channel spectrometer only uses one energy bin while the HPGe spectrometer resolves, e.g. the α and β lines. However, the energy range, the approximate form of the spectra and their absolute intensity are reproduced quite well. It shall be noted that,

for the spectrum evaluation, no prior information beyond the ones from equation (1) and Table 3 (both in the main text) was used, i.e. no further energy or dose information at all,
as the X-ray fields were produced with a Tungsten anode, also 9 keV (for the L-lines) was chosen, not 59 keV (for the K-lines) as the high voltage was assumed to be unknown, and
apart from the ¹³⁷Cs dose calibration of the TLDs, no normalization was applied to the spectra of the few-channel spectrometer.

The spectra of the HPGe spectrometer were normalized to the irradiated dose of the X-ray fields, H*(10) = 10.0 mSv by conversion to the operational quantities using the conversion coefficients from fluence to air kerma, K_a/Φ, and from air kerma to the operational quantities, h′_K(0.07), h′_K(3) and h*_K(10). The mono-energetic conversion coefficients were taken from the literature^{(18, 19)}.

Tables C1– C3 show the resulting spectrum characteristics from the data evaluation compared to the ones obtained for the spectra measured with the HPGe spectrometer. The ratios of the values from the few-channel spectrometer and the HPGe spectrometer roughly agree with unity within their 95% coverage intervals. Only the dose contribution due to photons above 30 keV is significantly above zero for H-20 (up 2 · 10⁻⁴) which it should not be. Further on, for B-40 and W-80 the ratios of the dose contributions above 30 keV significantly deviate from unity, possibly, as no uncertainties are available for the spectra of the HPGe spectrometer⁽²⁴⁾. Apart from these small deviations, the Bayesian data evaluation for the few-channel spectrometer leads to reliable spectrum characteristics, attributed uncertainties and coverage intervals.

Table C1.

Dose values from the few-channel spectrometer for operational quantities for the two X-ray reference radiation fields, their standard deviations and 95% coverage intervals, and, in each second line, the ratio to the corresponding values from the reference dosimetry with their 95% coverage intervals.

Reference radiation field; quantity	H′(0.07) (mSv)	H′(3) (mSv)	H*(10) (mSv)
N-15
Dose values: few-channel spectrometer	(111 ± 7) {±6%}	(50.1 ± 2.9) {±6%}	(10.2 ± 0.6) {±6%}
	95%-IV: [99;126]	95%-IV: [45.0;56.4]	95%-IV: [9.1;11.4]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.15	1.11 ± 0.13	1.02 ± 0.12
H-20
Dose values: few-channel spectrometer	(75 ± 4) {±6%}	(36.6 ± 1.9) {±5%}	(11.0 ± 0.6) {±5%}
	95%-IV: [67;84]	95%-IV: [33.2;40.6]	95%-IV: [9.9;12.2]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.10 ± 0.13	1.13 ± 0.12	1.10 ± 0.11
B-40
Dose values: few-channel spectrometer	(13.7 ± 0.7) {±5%}	(12.8 ± 0.6) {±5%}	(10.8 ± 0.5) {±5%}
	95%-IV: [12.5;15.1]	95%-IV: [11.7;14.1]	95%-IV: [9.9;11.9]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.12	1.12 ± 0.11	1.08 ± 0.11
W-80
Dose values: few-channel spectrometer	(10.3 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}
	95%-IV: [9.4;11.3]	95%-IV: [9.5;11.4]	95%-IV: [9.5;11.5]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.11 ± 0.11	1.07 ± 0.10	1.04 ± 0.10

Reference radiation field; quantity	H′(0.07) (mSv)	H′(3) (mSv)	H*(10) (mSv)
N-15
Dose values: few-channel spectrometer	(111 ± 7) {±6%}	(50.1 ± 2.9) {±6%}	(10.2 ± 0.6) {±6%}
	95%-IV: [99;126]	95%-IV: [45.0;56.4]	95%-IV: [9.1;11.4]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.15	1.11 ± 0.13	1.02 ± 0.12
H-20
Dose values: few-channel spectrometer	(75 ± 4) {±6%}	(36.6 ± 1.9) {±5%}	(11.0 ± 0.6) {±5%}
	95%-IV: [67;84]	95%-IV: [33.2;40.6]	95%-IV: [9.9;12.2]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.10 ± 0.13	1.13 ± 0.12	1.10 ± 0.11
B-40
Dose values: few-channel spectrometer	(13.7 ± 0.7) {±5%}	(12.8 ± 0.6) {±5%}	(10.8 ± 0.5) {±5%}
	95%-IV: [12.5;15.1]	95%-IV: [11.7;14.1]	95%-IV: [9.9;11.9]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.12	1.12 ± 0.11	1.08 ± 0.11
W-80
Dose values: few-channel spectrometer	(10.3 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}
	95%-IV: [9.4;11.3]	95%-IV: [9.5;11.4]	95%-IV: [9.5;11.5]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.11 ± 0.11	1.07 ± 0.10	1.04 ± 0.10

Table C1.

Reference radiation field; quantity	H′(0.07) (mSv)	H′(3) (mSv)	H*(10) (mSv)
N-15
Dose values: few-channel spectrometer	(111 ± 7) {±6%}	(50.1 ± 2.9) {±6%}	(10.2 ± 0.6) {±6%}
	95%-IV: [99;126]	95%-IV: [45.0;56.4]	95%-IV: [9.1;11.4]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.15	1.11 ± 0.13	1.02 ± 0.12
H-20
Dose values: few-channel spectrometer	(75 ± 4) {±6%}	(36.6 ± 1.9) {±5%}	(11.0 ± 0.6) {±5%}
	95%-IV: [67;84]	95%-IV: [33.2;40.6]	95%-IV: [9.9;12.2]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.10 ± 0.13	1.13 ± 0.12	1.10 ± 0.11
B-40
Dose values: few-channel spectrometer	(13.7 ± 0.7) {±5%}	(12.8 ± 0.6) {±5%}	(10.8 ± 0.5) {±5%}
	95%-IV: [12.5;15.1]	95%-IV: [11.7;14.1]	95%-IV: [9.9;11.9]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.12	1.12 ± 0.11	1.08 ± 0.11
W-80
Dose values: few-channel spectrometer	(10.3 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}
	95%-IV: [9.4;11.3]	95%-IV: [9.5;11.4]	95%-IV: [9.5;11.5]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.11 ± 0.11	1.07 ± 0.10	1.04 ± 0.10

Reference radiation field; quantity	H′(0.07) (mSv)	H′(3) (mSv)	H*(10) (mSv)
N-15
Dose values: few-channel spectrometer	(111 ± 7) {±6%}	(50.1 ± 2.9) {±6%}	(10.2 ± 0.6) {±6%}
	95%-IV: [99;126]	95%-IV: [45.0;56.4]	95%-IV: [9.1;11.4]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.15	1.11 ± 0.13	1.02 ± 0.12
H-20
Dose values: few-channel spectrometer	(75 ± 4) {±6%}	(36.6 ± 1.9) {±5%}	(11.0 ± 0.6) {±5%}
	95%-IV: [67;84]	95%-IV: [33.2;40.6]	95%-IV: [9.9;12.2]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.10 ± 0.13	1.13 ± 0.12	1.10 ± 0.11
B-40
Dose values: few-channel spectrometer	(13.7 ± 0.7) {±5%}	(12.8 ± 0.6) {±5%}	(10.8 ± 0.5) {±5%}
	95%-IV: [12.5;15.1]	95%-IV: [11.7;14.1]	95%-IV: [9.9;11.9]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.16 ± 0.12	1.12 ± 0.11	1.08 ± 0.11
W-80
Dose values: few-channel spectrometer	(10.3 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}	(10.4 ± 0.5) {±5%}
	95%-IV: [9.4;11.3]	95%-IV: [9.5;11.4]	95%-IV: [9.5;11.5]
Dose ratios: few-channel spectrometer/HPGe spectrometer	1.11 ± 0.11	1.07 ± 0.10	1.04 ± 0.10

Table C2.

Dose contributions above 30 keV photon energy of the spectra from the few-channel spectrometer: for N-15 and H-20, the values, standard deviations and 95% coverage intervals are given while for B-40 and W-80, the ratios to the corresponding values from the HPGe spectrometer with their 95% coverage intervals are stated.

Reference radiation field; quantity			H′(0.07)_{>30 keV}/H′(0.07)	H′(3)_{>30 keV}/H′(3)	H(10)_{>30 keV}/H(10)
N-15	Dose contributions above 30 keV		0	0	0
H-20	Dose contributions above 30 keV		(3.7 ± 0.6) · 10⁻⁵ {±17%}	(7.7 ± 1.3) · 10⁻⁵ {±17%}	(2.3 ± 0.4) · 10⁻⁴ {±17%}
			95%-IV: [2.8;5.2] · 10⁻⁵	95%-IV: [5.7;10.7] · 10⁻⁵	95%-IV: [1.8;3.3] · 10⁻⁴
B-40	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	1.10 ± 0.06	1.13 ± 0.06	1.16 ± 0.05
W-80	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	0.91 ± 0.03	0.94 ± 0.02	0.96 ± 0.01

Reference radiation field; quantity			H′(0.07)_{>30 keV}/H′(0.07)	H′(3)_{>30 keV}/H′(3)	H(10)_{>30 keV}/H(10)
N-15	Dose contributions above 30 keV		0	0	0
H-20	Dose contributions above 30 keV		(3.7 ± 0.6) · 10⁻⁵ {±17%}	(7.7 ± 1.3) · 10⁻⁵ {±17%}	(2.3 ± 0.4) · 10⁻⁴ {±17%}
			95%-IV: [2.8;5.2] · 10⁻⁵	95%-IV: [5.7;10.7] · 10⁻⁵	95%-IV: [1.8;3.3] · 10⁻⁴
B-40	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	1.10 ± 0.06	1.13 ± 0.06	1.16 ± 0.05
W-80	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	0.91 ± 0.03	0.94 ± 0.02	0.96 ± 0.01

Table C2.

Reference radiation field; quantity			H′(0.07)_{>30 keV}/H′(0.07)	H′(3)_{>30 keV}/H′(3)	H(10)_{>30 keV}/H(10)
N-15	Dose contributions above 30 keV		0	0	0
H-20	Dose contributions above 30 keV		(3.7 ± 0.6) · 10⁻⁵ {±17%}	(7.7 ± 1.3) · 10⁻⁵ {±17%}	(2.3 ± 0.4) · 10⁻⁴ {±17%}
			95%-IV: [2.8;5.2] · 10⁻⁵	95%-IV: [5.7;10.7] · 10⁻⁵	95%-IV: [1.8;3.3] · 10⁻⁴
B-40	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	1.10 ± 0.06	1.13 ± 0.06	1.16 ± 0.05
W-80	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	0.91 ± 0.03	0.94 ± 0.02	0.96 ± 0.01

Reference radiation field; quantity			H′(0.07)_{>30 keV}/H′(0.07)	H′(3)_{>30 keV}/H′(3)	H(10)_{>30 keV}/H(10)
N-15	Dose contributions above 30 keV		0	0	0
H-20	Dose contributions above 30 keV		(3.7 ± 0.6) · 10⁻⁵ {±17%}	(7.7 ± 1.3) · 10⁻⁵ {±17%}	(2.3 ± 0.4) · 10⁻⁴ {±17%}
			95%-IV: [2.8;5.2] · 10⁻⁵	95%-IV: [5.7;10.7] · 10⁻⁵	95%-IV: [1.8;3.3] · 10⁻⁴
B-40	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	1.10 ± 0.06	1.13 ± 0.06	1.16 ± 0.05
W-80	Ratios of contrib. above 30 keV:	few-chan. spec./HPGe spec.	0.91 ± 0.03	0.94 ± 0.02	0.96 ± 0.01

Table C3.

Ratios of mean energies of the spectra from the few-channel spectrometer and the spectra from the HPGe spectrometer, weighted with fluence and operational quantities. The 95% coverage intervals are given.

Reference radiation field; quantity		$\bar{E} {F}_{few - ch spc} / \bar{E} {F}_{HPGe . spc}$	$\bar{E} {H' (0.07)}_{few - ch spc} / \bar{E} {H' (0.07)}_{HPGe . spc}$	$\bar{E} {H' (3)}_{few - ch spc} / \bar{E} {H' (3)}_{HPGe . spc}$	$\bar{E} {H ⁎ (10)}_{few - ch spc} / \bar{E} {H ⁎ (10)}_{HPGe . spc}$
N-15	Energy ratios: few-channel spec./HPGe spec.	0.98 ± 0.01	0.98 ± 0.02	0.98 ± 0.01	0.99 ± 0.01
H-20	Energy ratios: few-channel spec./HPGe spec.	1.00 ± 0.02	1.01 ± 0.03	0.99 ± 0.01	0.99 ± 0.01
B-40	Energy ratios: few-channel spec./HPGe spec.	0.99 ± 0.01	0.96 ± 0.02	0.97 ± 0.01	0.99 ± 0.01
W-80	Energy ratios: few-channel spec./HPGe spec.	1.01 ± 0.01	0.96 ± 0.03	0.99 ± 0.01	1.00 ± 0.01

Reference radiation field; quantity		$\bar{E} {F}_{few - ch spc} / \bar{E} {F}_{HPGe . spc}$	$\bar{E} {H' (0.07)}_{few - ch spc} / \bar{E} {H' (0.07)}_{HPGe . spc}$	$\bar{E} {H' (3)}_{few - ch spc} / \bar{E} {H' (3)}_{HPGe . spc}$	$\bar{E} {H ⁎ (10)}_{few - ch spc} / \bar{E} {H ⁎ (10)}_{HPGe . spc}$
N-15	Energy ratios: few-channel spec./HPGe spec.	0.98 ± 0.01	0.98 ± 0.02	0.98 ± 0.01	0.99 ± 0.01
H-20	Energy ratios: few-channel spec./HPGe spec.	1.00 ± 0.02	1.01 ± 0.03	0.99 ± 0.01	0.99 ± 0.01
B-40	Energy ratios: few-channel spec./HPGe spec.	0.99 ± 0.01	0.96 ± 0.02	0.97 ± 0.01	0.99 ± 0.01
W-80	Energy ratios: few-channel spec./HPGe spec.	1.01 ± 0.01	0.96 ± 0.03	0.99 ± 0.01	1.00 ± 0.01

Table C3.

Reference radiation field; quantity		$\bar{E} {F}_{few - ch spc} / \bar{E} {F}_{HPGe . spc}$	$\bar{E} {H' (0.07)}_{few - ch spc} / \bar{E} {H' (0.07)}_{HPGe . spc}$	$\bar{E} {H' (3)}_{few - ch spc} / \bar{E} {H' (3)}_{HPGe . spc}$	$\bar{E} {H ⁎ (10)}_{few - ch spc} / \bar{E} {H ⁎ (10)}_{HPGe . spc}$
N-15	Energy ratios: few-channel spec./HPGe spec.	0.98 ± 0.01	0.98 ± 0.02	0.98 ± 0.01	0.99 ± 0.01
H-20	Energy ratios: few-channel spec./HPGe spec.	1.00 ± 0.02	1.01 ± 0.03	0.99 ± 0.01	0.99 ± 0.01
B-40	Energy ratios: few-channel spec./HPGe spec.	0.99 ± 0.01	0.96 ± 0.02	0.97 ± 0.01	0.99 ± 0.01
W-80	Energy ratios: few-channel spec./HPGe spec.	1.01 ± 0.01	0.96 ± 0.03	0.99 ± 0.01	1.00 ± 0.01

Reference radiation field; quantity		$\bar{E} {F}_{few - ch spc} / \bar{E} {F}_{HPGe . spc}$	$\bar{E} {H' (0.07)}_{few - ch spc} / \bar{E} {H' (0.07)}_{HPGe . spc}$	$\bar{E} {H' (3)}_{few - ch spc} / \bar{E} {H' (3)}_{HPGe . spc}$	$\bar{E} {H ⁎ (10)}_{few - ch spc} / \bar{E} {H ⁎ (10)}_{HPGe . spc}$
N-15	Energy ratios: few-channel spec./HPGe spec.	0.98 ± 0.01	0.98 ± 0.02	0.98 ± 0.01	0.99 ± 0.01
H-20	Energy ratios: few-channel spec./HPGe spec.	1.00 ± 0.02	1.01 ± 0.03	0.99 ± 0.01	0.99 ± 0.01
B-40	Energy ratios: few-channel spec./HPGe spec.	0.99 ± 0.01	0.96 ± 0.02	0.97 ± 0.01	0.99 ± 0.01
W-80	Energy ratios: few-channel spec./HPGe spec.	1.01 ± 0.01	0.96 ± 0.03	0.99 ± 0.01	1.00 ± 0.01

Figure C1.

Fluence spectra for the reference radiation quality N-15 (=A-15) from the data evaluation of the spectrometer and, as reference, from a HPGe spectrometer. The uncertainty bars represent the 95% coverage intervals.

Figure C2.

Fluence spectra for the reference radiation quality H-20 (= C-20) from the data evaluation of the spectrometer and, as reference, from a HPGe spectrometer. The uncertainty bars represent the 95% coverage intervals.

Figure C3.

Fluence spectra for the reference radiation quality B-40 from the data evaluation of the spectrometer and, as reference, from a HPGe spectrometer. The uncertainty bars represent the 95% coverage intervals.

Figure C4.

Fluence spectra for the reference radiation quality W-80 (= B-80) from the data evaluation of the spectrometer and, as reference, from a HPGe spectrometer. The uncertainty bars represent the 95% coverage intervals.