the Creative Commons Attribution 4.0 License.

Special issue: Sensors and Measurement Science International SMSI 2020

**Regular research article**
18 Feb 2021

**Regular research article** | 18 Feb 2021

# Measurements at laser materials processing machines: spectrum deconvolution including uncertainties and model selection

Rolf Behrens Björn Pullner and Marcel Reginatto

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**Rolf Behrens et al.**Rolf Behrens Björn Pullner and Marcel Reginatto

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^{1}Department Radiation Protection Dosimetry, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany^{2}Department Neutron Radiation, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany

^{1}Department Radiation Protection Dosimetry, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany^{2}Department Neutron Radiation, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany

**Correspondence**: Rolf Behrens (rolf.behrens@ptb.de)

**Correspondence**: Rolf Behrens (rolf.behrens@ptb.de)

Received: 07 Sep 2020 – Revised: 09 Jan 2021 – Accepted: 12 Jan 2021 – Published: 18 Feb 2021

Laser materials processing of workpieces using ultra-short pulsed lasers can lead to unwanted X-ray emission. Their dose rate and spectral distribution have been precisely determined. The measurements were carried out using a thermoluminescence detector (TLD)-based spectrometer in which 30 TLD planes are arranged one behind the other, the first 10 layers made of polymethyl methacrylate, while the remaining 20 layers are interspaced by absorbers with, from the front to the back, increasing atomic charge and thickness. The penetration depth of the radiation into the spectrometer depends on its energy, so that the energy-resolved spectrum of the radiation can be calculated from the TLD dose values by means of mathematical methods (Bayesian deconvolution). The evaluation process also takes into account both the uncertainties of all input quantities and the possibility of adopting different models for the spectrum form. This allowed the resulting spectra to be associated with their realistic uncertainty.

The measurements are traceable to the Système international d'unités (SI), i.e. the International System of Units. The results not only provide manufacturers and users of ultra-short pulsed lasers with important information on the design of the machines with regard to radiation protection, but were also included in the recently concluded legislative procedure in the field of radiation protection in Germany.

Ultra-short pulsed lasers have been developed in the last decades for both
research and various applications (Mulser and Bauer, 2010). In some of these
applications, the main purpose is the production of ionizing radiation, with
laser intensities at the focus of the order of up to
10^{22} W/cm^{2}. Much lower intensities have been in use for
materials processing without the production of ionizing radiation (Momma
et al., 1996). However, in the last few years, larger intensities of up to
the order of 10^{14} W/cm^{2} have been in use for materials processing, resulting in an unwanted production of ionizing radiation
(Gerhard et al., 2016; Nolte et al., 2016). The objective of this research
is twofold, the validation of the spectrometer in the presence of photons in the low-energy range and the measurement of X-rays emitted in an industrial laser materials processing environment in terms of absolute spectra and
operational dose equivalent with the focus on radiation protection. At the present time, this objective is more important from a research point of
view as current industrial laser materials processing machines are equipped
under normal conditions with a housing that is very effective for shielding
the low-energy radiation emerging from the machines. The results are relevant to developers of the machines also operating them without housing,
to legislative bodies, and as a basis for future investigations of radiation
from laser machines with even higher intensities.

For the measurements, a thermoluminescence detector (TLD)-based few-channel spectrometer was used (see Fig. 1) (Behrens and Ambrosi, 2002; Behrens, 2009). The penetration depth of the X-ray radiation in the spectrometer depends on the energy, so that the energy-resolved and absolute spectrum of the radiation, including the uncertainties of the spectrum, can be determined from the dose values in the TLD layers by means of mathematical methods (Bayesian deconvolution).

The experimental setup is shown in Fig. 2; the main laser parameters were a
wavelength of 1030 nm, an average power of 78 W, a pulse energy of
195 µJ, a pulse length (full width at half maximum) of 924 fs, a
repetition rate of 400 kHz, and a focus diameter of 16 µm at a focus intensity of 2.1×10^{14} W/cm^{2}; further
experimental parameters are listed in Table 1. A Bayesian data evaluation was
performed using the WinBUGS software (Lunn et al., 2010) which, besides the
photon spectrum, also supplies the corresponding uncertainties and coverage
intervals. The following prior information for the photon spectra was
included in the data evaluation: (i) a smooth rise with increasing energy due
to the fact that there was at least about 10 cm of air absorption between
the laser focus and the spectrometer front; (ii) an exponential decrease at
higher energies (due to well-known laser–plasma interaction mechanisms); and (iii) a peak in the spectrum at the energy of the characteristic fluorescence radiation of the workpiece material. The method of analysis is
outlined in detail in Appendix A as well as in the literature
(Behrens et al., 2019; Behrens and Reginatto, 2019).

To ensure that the evaluation method is reliable, the spectrometer was irradiated in four known reference radiation fields of different photon energies. Figure 3 shows the spectra from the corresponding data evaluation compared to the results measured with a high-purity germanium spectrometer (Ankerhold et al., 1999; Ankerhold, 2000). The radiation fields are specified in an ISO standard (ISO, 2019).

The 95 % coverage intervals were determined from the probability distribution for each energy channel, which is calculated as part of the Bayesian data evaluation. Thus, they incorporate the information about the measurement used for the data evaluation, i.e. the prior information described in Sect. 2.

Apart from a slight shift in the spectra's maximum, these are quite well reproduced with the few-channel spectrometer as compared to the spectra obtained using the germanium spectrometer. The shift is mainly present when significant characteristic lines from the X-ray anode material are contained in the spectrum – indicating the limits of the few-channel spectrometer's energy resolution. Furthermore, the absolute magnitude of the spectra is in good agreement, demonstrating the capability for an absolute dose determination.

Figure 4 shows the absolute photon fluence spectra per materials processing time together with their 95 % coverage intervals for the four measurements normalized to a distance of 10 cm from the workpiece. The mean energies vary from about 4 to 6 keV. The photons significantly contributing to the dose extend to about 25 keV.

The fluence spectra were converted to dose equivalent using the corresponding conversion coefficients (ICRU, 1998; Behrens, 2017). The resulting dose rate depends on the processed material and its nature, varying from 1600 to 8300, from 17 to 76 mSv/h, and from 1 to 4 mSv/h, for the quantities ${\dot{H}}^{\prime}$(0,07), ${\dot{H}}^{\prime}$(3), and ${\dot{H}}^{*}$(10), respectively. Such high dose rates would exceed legal dose limits within a few minutes to 1 h (for the local skin dose estimated by ${\dot{H}}^{\prime}$(0,07) and the eye-lens dose estimated by ${\dot{H}}^{\prime}$(3)) or a few hours (for the effective dose of the whole body estimated by ${\dot{H}}^{*}$(10)). Fortunately, in the normal case, the laser processing is performed in a laser protection housing, which is sufficient to absorb the photons. If, however, the laser intensity in materials processing rises in the future, the laser protection housing may no longer be sufficient to shield the photons.

The measurements performed, traceable to the Système international d'unités (SI), not only provide manufacturers and users of ultra-short pulsed lasers with important radiation protection information for the design of machines, but have also provided important input for recent legislative procedures in the field of radiation
protection in Germany (StrlSchG, 2017; StrlSchV, 2018). Meanwhile, machines
with even higher laser intensities are already under development. Therefore,
the measuring method presented here will become even more relevant in the
future – especially for cases in which laser intensities reach more than
10^{14} W/cm^{2}. Then, significantly higher energies and
larger dose rates would be expected, resulting possibly in significant doses
outside of the machine's housings and leading to radiation protection
issues.

Equation (A1) represents a mathematical description of the experiment and thus the basic formula to be solved to obtain the fluence spectrum from the measured data:

with measured doses ${\mathit{D}}_{\mathrm{meas}}=\left(\begin{array}{c}{D}_{\mathrm{meas},\phantom{\rule{0.125em}{0ex}}\mathrm{1}}\\ \mathrm{\vdots}\\ {D}_{\mathrm{meas},\phantom{\rule{0.125em}{0ex}}N}\end{array}\right)$, calculated responses $\mathbf{R}=\left(\begin{array}{ccc}{R}_{\mathrm{1},\phantom{\rule{0.125em}{0ex}}\mathrm{1}}& \mathrm{\cdots}& {R}_{\mathrm{1},\phantom{\rule{0.125em}{0ex}}M}\\ \mathrm{\vdots}& \mathrm{\ddots}& \mathrm{\vdots}\\ {R}_{N,\phantom{\rule{0.125em}{0ex}}\mathrm{1}}& \mathrm{\cdots}& {R}_{N,\phantom{\rule{0.125em}{0ex}}M}\end{array}\right)$, and fluences $\mathbf{\Phi}=\left(\begin{array}{c}{\mathrm{\Phi}}_{\mathrm{1}}\\ \mathrm{\vdots}\\ {\mathrm{\Phi}}_{M}\end{array}\right)$. The use of the symbol ≈ is meant to
indicate that a strict equality is not achievable in practice due to
uncertainties associated with the measurement. The analysis of the data was
carried out using *N*=13 TLD layers. (The spectrometer consists of 30 TLD
layers; however, significant doses above a few µGy were measured only
in the first 13 layers, which, thus, provided the data points for the
evaluation.) The fluence was binned into *M*=60 energy channels (with logarithmically increasing mean energy, as the energy resolution gets worse
as the energy increases; 60 channels were chosen to cover the range from 2
to 100 keV photon energy and to obtain the desired energy resolution of
about 5 keV at the upper limit).

The data, *D*_{meas}, and the response matrix, **R**, are
known: **R** was calculated using Monte Carlo radiation transport simulation package EGS4 (Nelson et al., 1985; Namito et al., 1995;
Bielajew and Rogers, 1987), while the fluences, Φ(*E*), are determined from the Bayesian analysis.

*a*_{fluor} is the amplitude of the fluorescence radiation, *E*_{fluor} the energy of the fluorescence radiation,
*a*_{exp} the amplitude of the exponential decay,
*s*_{exp} the slope of the exponential decay,
${m}_{\mathrm{rise}}=\mathrm{1}/\left({E}_{\mathrm{rise},\phantom{\rule{0.125em}{0ex}}\mathrm{end}}-{E}_{\mathrm{rise},\phantom{\rule{0.125em}{0ex}}\mathrm{start}}\right)$,
${b}_{\mathrm{rise}}=-{m}_{\mathrm{rise}}\cdot {E}_{\mathrm{rise},\phantom{\rule{0.125em}{0ex}}\mathrm{end}}$, ${m}_{\mathrm{drop}}=-\mathrm{1}/\left({E}_{\mathrm{drop},\phantom{\rule{0.125em}{0ex}}\mathrm{end}}-{E}_{\mathrm{drop},\phantom{\rule{0.125em}{0ex}}\mathrm{start}}\right)$,
${b}_{\mathrm{drop}}=-{m}_{\mathrm{drop}}\cdot {E}_{\mathrm{drop},\phantom{\rule{0.125em}{0ex}}\mathrm{end}}$, *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. In total, these are 12
parameters, of which 4 depend on other parameters (*m*_{rise}, *b*_{rise}, *m*_{drop}, and *b*_{drop}), while
*E*_{fluor} is a constant (6.5 keV was chosen for targets made of
steel, corresponding to the rounded mean energy of the K_{α} and
K_{β} emission lines from iron and 9 keV for targets made of tungsten or the alloy containing more than 90 % tungsten, corresponding
to the rounded mean energy of the *L*_{α} and *L*_{β} emission
lines from tungsten). The remaining seven free parameters were determined
from the data using a program written with the Bayesian software WinBUGS
(Lunn et al., 2010). Appropriate initial values and ranges within which the
optimization process was allowed to vary the parameters were chosen for the
evaluation carried out by WinBUGS.

The WinBUGS code is available at https://www.mrc-bsu.cam.ac.uk/software/bugs/the-bugs-project-winbugs/ (WinBUGS, 2021).

The data are not available as they contain details from the laser machine's internal design and are therefore the property of the laser machine's owner, i.e. TRUMPF Laser GmbH.

RB contributed to the research plan, carried out the measurements, performed the data evaluation, and wrote the manuscript. BP contributed to the research plan and mainly performed the measurements. MR contributed to the data evaluation and the manuscript.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Sensors and Measurement Science International SMSI 2020”. It is a result of the Sensor and Measurement Science International, Nuremberg, Germany, 22–25 June 2020.

This research has been supported by TRUMPF Laser GmbH, Aichhalder Straße 39, 78713 Schramberg, Germany (grant no. 1W-63010 (2018-04-04)).

This open-access publication was funded

by the Physikalisch-Technische Bundesanstalt.

This paper was edited by Thomas Fröhlich and reviewed by two anonymous referees.

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- Abstract
- Background, motivation, and objective
- Measurements and data evaluation
- Validation of the data evaluation
- Results
- Conclusions
- Appendix A: Details of the Bayesian spectrum deconvolution
- Code availability
- Data availability
- Author contributions
- Competing interests
- Special issue statement
- Financial support
- Review statement
- References

- Abstract
- Background, motivation, and objective
- Measurements and data evaluation
- Validation of the data evaluation
- Results
- Conclusions
- Appendix A: Details of the Bayesian spectrum deconvolution
- Code availability
- Data availability
- Author contributions
- Competing interests
- Special issue statement
- Financial support
- Review statement
- References