1 Introduction

When a relativistically intense laser pulse (i.e., I > 1018 W/cm2) irradiates a solid material, a dense plasma is formed near the target surface. During the laser interaction with the plasma, part of the laser energy is coupled to a “hot” suprathermal electron population through processes such as resonance absorption, vacuum heating, and J × B heating [1, 2]. These electrons then propagate into the target as well as along the target surface, and consequently, they generate line emission X-rays (Kα emission) that are characteristic of the target material. Simultaneously, there is bremsstrahlung emission in the X-ray region produced from the stopping of the hot electrons in the target.

Over the past decade, the advent of kilohertz femtosecond laser systems has enabled the generation of these X-ray pulses using low-energy laser pulses (micro to millijoules) at high fluxes and in a much more compact setup as compared to higher energy low repetition rate laser systems. The development of such laser systems has also led to renewed interest in applications utilizing them as high flux sources of electrons [3, 4], ions [5], neutrons [6], and gamma rays [7].

For X-ray applications, the properties of the emitted radiation depend largely on the transport of the energetic electrons into the target material as well as the parameters of the driving pulses. Such X-ray sources typically have dimensions of tens of microns and relatively high laser to X-ray energy conversion efficiencies [8,9,10,11,12,13]. Such ultrafast X-ray sources have found use in phase-contrast imaging of biological specimens and low-density materials [14,15,16,17,18,19,20,21]. For such applications, the spatial resolution of the resulting image depends on the size of the X-ray source and the ultra-short temporal duration of the X-ray generation mechanism allows objects to be imaged dynamically on picosecond timescales or less. The variation in the properties of the radiation source with respect to increasing laser energy is an important parameter to consider as the use of these kilohertz laser systems becomes more widespread. There has also been recent work on the scaling of these sources with laser wavelength [22] as well as with respect to laser pulse contrast [23].

In this paper, we examine the scaling of high-repetition rate, laser-driven X-ray sources at the highest intensities presently available, and the subsequent application of these sources for phase-contrast imaging applications. The effect of increasing pulse energy on the emission spectra, flux, and source sizes of the X-rays produced from different bulk targets (Ni, Cu, Mo, Ag, and Sn) is characterized. Conversion efficiencies from total laser energy to total X-ray emission energy and Kα and Kβ line emissions are determined and compared with the previous work conducted at lower power [8]. For comparison, the targets are also coated with two different thicknesses of Al (203 ± 9 nm and 1000 ± 40 nm) to study the effect of a surface layer of high conductivity metal on fast electron transport across the substrate surface and the effect on the resulting X-ray emission properties. Phase-contrast imaging of a PicoTip® nanospray emitter (New Objective Inc.) and a 3D printed plastic target using uncoated Cu and Mo targets are also presented and discussed.

2 Experimental setup

The experiments were conducted using the Relativistic Lambda-Cubed (λ3) laser facility at the Center for Ultrafast Optical Science at the University of Michigan. Figure 1 shows the experimental setup. λ3 is a 0.5 kHz Ti:Sapphire system (λ = 800 nm) capable of producing laser pulses with 29 fs full-width at half maximum (FWHM) pulse duration, a compressed energy of 18 mJ when operated at full capability, and an amplified spontaneous emission-to-peak intensity contrast of 108. The previous investigations have examined the effect of laser pulse contrast on X-ray emission [23], harmonic emission [24], and electron emission [4], and it was found that extremely high contrast (no prepulse) actually reduced coupling of the laser energy to the plasma.

Fig. 1
figure 1

Schematic of the experimental setup. The fully compressed beam from the deformable mirror irradiates the target at an angle of incidence of 45°. A 2 µm pellicle protects the paraboloid from target debris. Electrons are deflected using a magnet pair. X-ray spectra are recorded using a CdTe detector, while the source size, flux, and phase-contrast images are recorded using a CCD camera

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In the experiments described here, the laser pulse energy can also be easily changed by adjusting the output of the final amplification stage. Wavefront distortions in the compressed laser beam are corrected using a 47 mm-diameter, silver-coated deformable mirror (Xinetics Inc.) with 37 computer-controlled electrostrictive actuators. After correction, the pulses are directed through a 3 mm-thick fused silica window and into the main target chamber where the p-polarized light is focused using an f/1.2 60° off-axis parabolic mirror to a 1.3 µm spot size [7]. Since the paraboloid is highly sensitive to the alignment of the laser beam, the deformable mirror is optimized under the experimental vacuum condition of ~ 10− 4 bar to compensate for vacuum-induced mechanical distortions in the beam. A 2 µm-thick nitrocellulose pellicle is placed between the paraboloid and the target to prevent debris from accumulating on the focusing optic during the high-repetition rate shots. A magnet pair is also placed in front of the target at the position where the X-rays are generated to deflect fast electrons and prevent X-ray fluorescence from the beryllium windows and other chamber components.

Each target is a circular disk 100 mm in diameter with a thickness of 10 ± 2 mm. The targets were polished and mounted on a computer-controlled rotation-translation stage (R/θ/Z) for proper alignment. The radial position was set up, such that the laser-generated “damage track” started on the outer edge of the target and advanced towards the target center (creating an inward spiral pattern). This ensured that a fresh surface was used for each shot and maximized the usable surface area for each target (enabling ~ 105 shots per target). The surface flatness of the target was calibrated using a Mitutoyo 513-405 Anti-magnetic Quick Set Test indicator, so that the surface peak to valley deviation over a full rotation was within ± 4 µm. The axial position of the target was optimized by maximizing the X-ray signal (in single-shot mode) on a silicon X-ray photodiode connected to a digital oscilloscope. The target was irradiated at 45° and the X-ray path was 5° toward target normal from the specular direction. The targets were coated at the Lurie Nanofabrication Facility at the University of Michigan using the technique of electron beam physical vapor deposition.

Upon passing through the beryllium windows and 6 cm of air, the X-ray spectra were recorded using an Amptek CdTe semiconductor diode gamma/X-ray detector. This detector, which served as a photon-counting diagnostic, was calibrated using a 241Am source and was located approximately 1.44 m from the interaction. This distance was needed, since very high X-ray emission resulting from the laser–solid interaction typically resulted in pulse pileup at the detector. Pulse pileup occurs when multiple photons are collected in the detector volume in a time period shorter than the pulse resolution time of the detector which is typically on the order of microseconds. To eliminate the effect of pulse pileup in the X-ray spectra, the detector was also surrounded by lead bricks and a lead casing, with the detector opening covered by a 120 µm-diameter lead pinhole. Measurements of the X-ray source size and flux along with phase-contrast images were conducted using an Andor iKon-M BR-DD CCD camera located 1.7 m from the source. This camera is sensitive to much lower energy X-rays than the CdTe detector. A 600 µm-thick, cleaved GaAs crystal was used to determine the source size using the knife edge technique [20, 21].

3 X-ray emission spectra and energy conversion efficiencies

Figure 2 shows the X-ray spectra generated from each target measured using the CdTe detector. The Ni target was overlaid with a micron-thick layer of SiO2. From the manufacturer’s data, the sensitivity of the detector is fairly constant at approximately 95% from 7 to 60 keV, falling to approximately 44% at 120 keV. The spectra have, therefore, been corrected for the detector efficiency. The number of shots accumulated for each spectrum ranged from 1.1 to 1.5 × 105 with an average 9.2 mJ (8.6–9.4 mJ) on target (average peak intensity 4.1 × 1019 W/cm2). The characteristic emission lines for each target (shown in their respective insets) are clearly superimposed on a bremsstrahlung continuum ranging from 5 to 120 keV. The bump in the spectra near 80 keV is due to Kα emission of lead produced by hard X-rays interacting with the lead shielding around the detector. Reduction of pileup was successful for the most part; however, slight pileup was still observed in the spectra for Mo and Ag at twice the respective Kα energies. Table 1 provides a reference of the properties for each bulk target.

Fig. 2
figure 2

X-ray spectra from a Ni with SiO2, b Cu, c Mo, d Ag, and e Sn. The characteristic line emissions for each target are shown in their respective insets. Slight pulse pileup effects are present in the spectra for Mo and Ag. A bump around 80 keV is present in all the spectra due to hard X-rays from the interaction causing Kα fluorescence in the lead shielding around the detector

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Table 1 Properties of the bulk targets used in the experiments
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The conversion efficiency from laser energy to total X-ray energy (i.e., bremsstrahlung plus line emission) for each target can be measured by integrating the signal from the respective X-ray spectra and dividing by the laser energy per pulse. Characteristic line emission efficiencies are determined in a similar manner using the bremsstrahlung subtracted signal under each emission peak. In Fig. 3, the laser-to-total X-ray emission efficiency is plotted for the 2π sr solid angle in front of the target as a function of target Z. The corresponding comparison at 1.3 mJ from Ref [8] is shown, as well. Hou et al. [8] also obtained data from a Ge target (at 1.3 mJ) which is given here but not included in the current experiment. As shown in Fig. 3, the laser-to-total X-ray emission efficiency increased with Z due to the dependence of bremsstrahlung radiation with Z2 for all targets except for Ag. The conversion efficiency for Ag is unusually high and does not follow this trend as for the other targets. This is discussed further in Sect. 7.

Fig. 3
figure 3

Conversion efficiencies as a function of laser energy and target Z. X’s represent data from Ref. [8] taken at 1.3 mJ

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Table 2 provides a summary of the efficiencies (with respect to 2π sr solid angle) in front of each target, with an average standard deviation of 17% for the various targets. Values from Ref [8] are shown in parentheses. An order of magnitude increase in the total X-ray conversion efficiency was observed for each target at the higher laser energy in addition to an improvement in the Kα emission conversion efficiency. Kβ emission increased for Cu and Ag but remained approximately the same for the other targets. It is noted that the SiO2 coating for the Ni target decreased the ratio of Kβ-to-Kα emission by a factor of two compared with the other non-coated targets. In Ref. [8], the reported values for the X-ray flux of Kα and total X-ray emission were 7.8 × 106 and 4.3 × 107 photons/(2π sr pulse), respectively, for the Mo target. Here, we measured 3.0 × 109 and 5. 5 × 1010 photons/(2π sr pulse) for the Kα and total X-ray emission.

Table 2 Conversion efficiencies from laser to total X-ray emission and laser to characteristic line emissions obtained using 9.2 mJ on target
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Although the conversion efficiencies for both Kα and bremsstrahlung emissions increased significantly for the higher laser energy, the relative line emission efficiencies decreased. As shown in Fig. 4a, b, the ratio of Kα and Kβ to bremsstrahlung emission decreased significantly for the higher laser energy. This is in agreement with Ref [26], which attributed lower ratios to increased depletion of the target M shell under higher energy density conditions. For both laser energies, the relative emissions also decreased as the target Z increased. This behavior is expected as well, since bremsstrahlung emission scales as Z2 and the K-shell ionization cross section by electron impact is reduced for higher Z targets [8, 27].

Fig. 4
figure 4

a Emission of Kα photons relative to bremsstrahlung decreased for the higher laser energy (square markers). b This trend is also observed for the Kα emission at the higher laser energy (diamond markers). In addition, the relative emissions also decreased with increasing target Z for both laser energies. In a/b, circular/triangular markers show the corresponding parameter obtained from Ref. [8] at the lower laser energy

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4 X-ray energy

Figure 5 shows the radiant energy per mm2 on the X-ray CCD camera as a function of the laser pulse energy for the different targets. The energies at 1 mJ, 5.5 mJ, and 11.5 mJ correspond to vacuum peak intensities of 0.3, 1.8, and 3.7 × 1019 W/cm2, respectively. The quantum efficiency of the camera peaks at 90% at 3 keV and falls off exponentially to under 1% for the Kβ emission for Sn at 28.5 keV. Thus, for Mo, Ag, and Sn, the majority of the detected photons throughout the laser energy range are likely due to bremsstrahlung. This hypothesis was tested by measuring the X-ray flux from the Mo target with and without a 30 µm Mo filter in front of the camera. An order of magnitude decrease in the flux was observed with the filter was in place, showing that the measured flux from the high Z targets is due to low-energy bremsstrahlung radiation. The energy conversion efficiency scalings shown in Table 2 also implies that the majority of the photons at 11.5 mJ are due to bremsstrahlung radiation for all the targets. Regardless, an increase in the flux with laser energy is observed for each target with and without the Al coatings, with the increase being greatest between 1 and 5.5 mJ. For the same target, coatings generally decreased the emitted radiation, with an attenuation generally becoming more pronounced at the higher laser energies.

Fig. 5
figure 5

Radiant energy per mm2 increased with laser energy for all targets regardless of the coating material and thickness. At the higher energies, the coating has a more noticeable effect on the flux for most targets. The measured photons for the higher Z targets are likely to originate from bremsstrahlung radiation rather than line emission due to the quantum efficiency of the detector. In addition, an increase in bremsstrahlung radiation is also generated at the higher laser energies (Table 2)

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5 X-ray source size

For the X-ray source size measurements, the average object-to-detector distance was 164 cm with a geometric magnification of M = 31 and ~ 105 shots were taken for each dimension of the X-ray source. A cleaved GaAs crystal was used to determine the source size by spatially integrating the X-ray signal parallel to the crystal edge. The vertical (horizontal) edge provided information on the horizontal (vertical) source size [28]. The lineout across the crystal edge produces an edge spread function that is typically fitted to a Fermi function of the form f(x) = a + b/[1 + e(x−c)/d]. Differentiating this function gives a Gaussian line spread function from which the source size is inferred using the FWHM value. This method works reasonably well provided the edge spread function is flat in the regions on either side of the sharp rise due to the crystal edge. However, for most images, the edge spread function exhibits a non-zero slope in these regions. The non-zero slopes cause an inaccurate fitting of the Fermi function to the spatial profile which tends to overestimate the source size. Furthermore, analysis of the data showed that this procedure can give widely varying values for the source size from the same target under the same irradiation conditions. Consequently, the noisy edge spread function is first smoothed using a Savitzky–Golay filter [29] using a second–order polynomial and an 8% window span. The smoothed edge spread function is then deconvolved with a step function representing the crystal edge. An FWHM value for the source size is then calculated from the resulting (non-Gaussian) line spread function.

Figure 6 shows the source size and the ratio of the horizontal-to-vertical source sizes as a function of the pulse energy (legend follows from Fig. 5). In Fig. 6a–d, the horizontal and vertical source size is observed to increase with increasing pulse energy for the different targets and coatings. The X-ray source also exhibited an ellipticity in the horizontal (i.e., laser polarization) direction. This behavior, as shown in Fig. 6e, f, is minimal at 1 mJ but becomes much more pronounced at the higher energies.

Fig. 6
figure 6

Measured X-ray source size as a function of laser energy. a, b show the horizontal source size for the different targets, while c, d show the vertical source size. Both dimensions of the X-ray source increased with increasing laser energy. e, f show that the ratio of the horizontal-to-vertical source size (i.e., the ellipticity of the source) increases with laser energy. Legend follows from Fig. 5

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6 Phase-contrast imaging

Phase-contrast imaging of a PicoTip® nanospray emitter (Fig. 7a) and a 3D printed plastic target (Fig. 7d) was conducted using the uncoated Cu and Mo targets. In the geometry of in-line phase-contrast imaging, the object is placed between an X-ray source and the detector, such that the near-field diffraction condition (Fresnel) is realized. The spatial resolution that can be achieved using a laser-based plasma X-ray source under the Fresnel condition depends primarily on the spatial coherence of the X-rays emitted and is given by dcoh = λL/2πσ, where λ is the wavelength of the emitted radiation, L is the source-to-object distance, and σ is the X-ray source diameter. Since the X-ray source size resulting from uncoated Cu and Mo is approximately the same at 5.5 mJ, a better spatial resolution is expected using the Mo target due to the shorter wavelength of its line emission. However, the quantum efficiency of the X-ray detection camera drops significantly for the line emission radiation resulting from Mo (~ 5%) and the majority of the detected photons are from bremsstrahlung radiation instead. This results in a poorer phase-contrast image compared with that obtained using the Cu target. Lineouts of the rectangular region in Fig. 7a from the Mo and Cu targets are shown in Fig. 7(b) and 7(c) respectively. Both lineouts are the result of an 8 min exposure with approximately 5.5 mJ on target. An improved contrast enhancement of the hollow core in the nanospray emitter is observed using the Cu target. A 16 min exposure using Mo showed no improvement in the contrast.

Fig. 7
figure 7

a Image of a PicoTip® nanospray emitter taken using a Cu target with a source-to-object distance of 26 cm and a magnification of 6.5. b Lineout of the rectangular region in a using a Mo target. c Lineout of the same region in a using a Cu target. Both b, c were obtained with an 8 min exposure and 5.5 mJ on a Cu target with a source-to-object distance of 49 cm and a magnification of 3.5. Imperfections in the printing process lead to an intensity gradient in the target around the edges. e, f Are lineouts of the rectangular region in d with 2 mJ and 5.5 mJ, respectively, on target

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Lineouts of the rectangular region from the 3D printed plastic target in Fig. 7d are shown in Fig. 7e, f. These lineouts are the result of an 8 min exposure using Cu as the target at 2 mJ and 5.5 mJ, respectively. The target is printed in layers from bottom to top (i.e., it is extruded out of the page). Due to imperfections in the printing process, these layers are not overlaid perfectly; thus, a gradient appears around the edges of the target. This gradient is washed out by the background at 2 mJ, but is clearly observable at 5.5 mJ due to the significant increase in the X-ray flux between 1 mJ and 5.5 mJ (Fig. 5).

7 Discussion

A comparison of the energy conversion efficiencies (c.f. Table 2) between the current experiment and Ref. [8] shows an order of magnitude increase in the total radiation and an improvement in the Kα emission. Kβ emission increased for Cu and Ag only. The K-photon emission depends on the number of fast electrons generated during the interaction, their transport through the target and their collision with bound electrons in the target. When the electron temperature surpasses a few hundred electron volts, thermal ionization of the target M shell occurs, resulting in a reduction in the Kβ yield. Electron temperatures approaching kiloelectron volts are required to completely ionize the L shell which is responsible for Kα emission. Thus, line emission yields can be used to infer the thermal electron temperature in the target. For Cu (Sn), the M shell is depleted when the thermal background electron temperature exceeds 0.7 (2.8) kiloelectron volts [30]. Table 2 shows an increase in the ratio of Kβ-to-Kα emission as a function of target Z from Ref [8] taken at 1.3 mJ. For the current experiment where a pulse energy of 9.2 mJ was used, this ratio is essentially constant for all targets, providing evidence for a much higher thermal electron temperature in the target.

The anomalously high conversion efficiencies for Ag may be a result of several factors. It is possible that surface roughness of the target plays a role in the absorption of laser light. Although each target is polished prior to shots, some materials are easier to polish and result in a smoother, mirror-like finish—however, there is no evidence that the surface of the Ag targets were worse than the others. The unevenness in the surface can enhance laser energy absorption and, consequently, the conversion efficiency [31]. However, such an effect was also noticed for certain targets in Ref [8]. It is also interesting to note that Ag has a low Fermi energy and consequently has the highest thermal conductivity among the targets used. This may affect optical damage thresholds as well as hot electron propagation in the target. While such effects are unlikely to play a significant role during laser–plasma interactions at the intensities and field gradients associated with the main pulse, metals with high conductivity may ionize earlier due to prepulse and, consequently, create a larger plasma volume at the front of the target. The increased plasma volume can subsequently enhance energy absorption.

The decrease in the line emission efficiencies and the ratio of Kβ-to-Kα emission for the Ni with SiO2 coating compared with the other uncoated targets is of particular interest (Table 2). A comparison with an uncoated Ni target is not available from the data set. However, Table 2 shows that both line emission efficiencies from the coated Ni target is lower than the corresponding emissions from Cu, even though one would expect Ni to be higher, since it is a lower Z material. Thus, it is likely that the reduction for Ni is due to the SiO2 coating rather than the target itself. The effect of a high-resistivity coating on the X-ray properties is a subject that warrants further study.

The targets were coated with Al to investigate the effect of a high conductive layer on the propagation of fast electrons across the surface of the substrate material and the resulting X-ray emission properties. The size of the X-ray source depends on contributions from both line and bremsstrahlung emission and the measurements presented in Fig. 6 include both components. Figure 6 shows that the Al coating had mixed results with respect to reducing the source size. For Cu, Ni, and Sn at 1 mJ and 5.5 mJ, the Al coating reduces the source size, but this effect is reversed at 11.5 mJ for these targets. For Mo and Ag, the 1 µm Al also coating reduced the source size but only significantly at 11.5 mJ. Moreover, the 0.2 µm Al coating increased the source size for the Ag target. The coating also increased the ellipticity of the source size for all the targets with the exception of Mo and Sn, with the effect becoming greater at higher laser energies.

From Fig. 5, it can be seen that the radiant energy (i.e., line plus bremsstrahlung emission) decreased for each target as a result of the coating. At the higher laser energies, the measured photons are mainly due to bremsstrahlung, especially for the higher Z targets (Table 2). This suggests that the reduction in the radiant energy is due to a decrease in the overall bremsstrahlung emission as a result of the fast electrons interacting primarily with the low Z coating instead of the substrate material.

The coating also made it difficult to align the wobble of the target. For most coated targets, the wobble was on the order of ± 4 µm. Although this is within the confocal length of the focusing optic (13 µm), a 4 µm difference in the surface flatness of the target may lead to a slight change in the peak intensity on target.

8 Conclusions

We have presented a systematic study of the scaling of high-repetition rate and laser-driven X-ray sources with increasing pulse energy. Although the Kα emission from the different targets increased at the higher pulse energy, measurements of the X-ray spectra show that the contribution to the total X-ray flux is dominated by bremsstrahlung radiation. The decrease in the ratio of Kβ-to-Kα emission with increasing pulse energy is attributed to the existence of higher energy density conditions and electron temperatures during the interaction.

The X-ray flux increased with pulse energy for all the targets, regardless of the Al coating thickness. For each target, the coating decreased the flux with the effect becoming more noticeable at the higher laser energies, suggesting that bremsstrahlung emission can be reduced using a conductive coating on the different substrates. This holds promise for using high-repetition rate, femtosecond laser pulses to conduct coherent phase-contrast imaging as the intensities of these systems increase. The dimensions and ellipticity of the source of X-rays also increased with pulse energy with the ellipticity becoming greater in the laser polarization direction at the higher laser energies. The source size can be controlled through the use of a low Z coating on the substrate material. However, the thickness of the coating and its properties need to be optimized for each metallic target. It is also likely that the prepulse scale length should be optimized for each target material and laser pulse energy.