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Abstract
Performing experiments at free-electron lasers (FELs) requires an exhaustive knowledge of the pulse temporal and spectral profile, as well as the focal spot shape and size. Operating FELs in the extreme ultraviolet (EUV) and soft X-ray (SXR) spectral regions calls for designing ad-hoc optical layouts to transport and characterize the EUV/SXR beam, as well as tailoring its spatial dimensions at the focal plane down to sizes in the few micrometers range. At the FERMI FEL (Trieste, Italy) this task is carried out by the Photon Analysis Delivery and Reduction System (PADReS). In particular, to meet the different experimental requests on the focal spot shape and size, a proper tuning of the optical systems is required, and this should be monitored by means of dedicated techniques. Here, we present and compare two reconstruction methods for spot characterization: single-shot imprints captured via ablation on a poly(methyl methacrylate) sample (PMMA) and pulse profiles retrieved by means of a Hartmann wavefront sensor (WFS). By recording complementary datasets at and nearby the focal plane, we exploit the tomography of the pulse profile along the beam propagation axis, as well as a qualitative and quantitative comparison between these two reconstruction methods.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
FERMI is the seeded free-electron laser (FEL) located at the Elettra Sincrotrone Trieste user-facility (Italy). It is designed to deliver high-brightness, quasi transform-limited, and fully coherent pulses, with wavelengths covering the extreme ultraviolet (EUV) and the soft X-rays (SXR) spectral domains, as well as pulse temporal length in the sub-100 femtoseconds (fs) range [1]. The use of APPLE-like undulators in the machine design represents a unique asset, since it allows the full control of the EUV/SXR pulses polarization state, too [2]. Specifically, lasing at EUV wavelengths (between 10 nm and 100 nm) occurs by seeding the electron bunches directly with ultra-violet (UV) optical pulses, resulting in the generation of well-defined high-harmonics of the fundamental seeding frequency via the high-gain harmonic-generation (HGHG) process. Since the seeding optical layout delivers a broad selection of UV wavelengths (between 240 nm and 260 nm), FERMI holds cutting-edge performances in terms of EUV photon energies tunability. Indeed, it recently enabled the extension, in the time-domain, of spectroscopies strictly demanding for chemical selectivity as X-rays absorption (XAS), linear and circular magnetic dichroism (XMLD/XMCD), and resonant inelastic scattering (RIXS) [3–6]. On the other hand, lasing at SXR wavelengths (between 4 nm and 10 nm) occurs via double cascade-seeding the same electron bunch, exploiting the EUV pulses delivered in the first radiating chain as a secondary seeding source [7,8]. To transport these EUV/SXR pulses from their source-points towards the different beamline branches, it is mandatory to operate an optical layout that i) limits the radiation losses along the transport, i.e., to transmit an appreciable intensity to be focused in the experimental end-stations, ii) avoids the introduction of additional temporal dispersion, i.e., to preserve the pulse temporal length, iii) characterizes in real time, shot-by-shot, the intensity and spectral profile, as well as iv) tailors the focal spot towards customized shapes and sizes, in the range of few micrometers (μm). The Photon Analysis Delivery and Reduction System (PADReS) is the optical layout at FERMI designed to satisfy all these requirements [9].
To ensure predefined focal spot shapes and size at the experimental end-stations, the pulse spatial profile is routinely characterized by means of a Hartmann wavefront sensor (WFS) located downstream of the focal plane [10]. Reconstructing the focal spot properties from the propagating wavefront is a suitable ad-hoc metrological method able to reveal in real time the exact characteristics of the pulses delivered in the experimental end-stations. The WFS can operate up to fluences (in the focus) of ≈ 1 J/cm2 due to radiation hardness. Quite often, focal spot areas characterized by low intensity and beam tails are not disclosed in a satisfactory way. A good, but time consuming, characterization method of the FEL focal spot properties is represented by the analysis of the (single-shot) imprint profiles created by the beam via non-thermal ablation [11–13]. Whereas the WFS reconstructs the focal spot from the propagating wavefront downstream to the focus, ablation imprints can be created directly at the interaction area of an experiment, thus serving as a direct probe in real space. Moreover, by chemically treating the imprint, its sensitivity can be extended over three orders of magnitude [13]. This method is suitable to detect beam features marked by extremely low local photon densities, like the seventh side maxima in the spot of a Fresnel zone plate. which cannot be resolved by means of the WFS due to its limited resolution [13]. The single-shot imprints have been largely exploited in the last decade, particularly operating self-amplified spontaneous emission (SASE) FELs [11–18]. The SASE pulses are characterized by intrinsic wavefront distortions that reflect both i) the SASE process itself, ii) the lack of a resonant cavity and iii) potential imperfections in the optical transport and the focusing devices. These turn to be a quite evident example of non-Gaussian pulses. Within this framework, single-shot imprints have been widely used to reveal the shape and the size of non-Gaussian pulses, developing a robust quantitative method to characterize their effective transverse area at the focal plane, since the use of FWHM is not anymore suitable for non-Gaussian distributions. Additionally, SASE FELs are also characterized by a not negligible pointing jitter, which can be properly revealed and measured by means of the single-shot imprints.
To date, it is still unclear where the exact qualitative limitations of both reconstruction methods are, and how quantitative comparable they are. To address this point, we performed an experiment at the FERMI FEL at the DiProI end-station using different fluences and focal settings to determine the beam properties using two complementary reconstruction methods. In particular, our datasets include imprints captured via single-shot ablation on a poly(methyl methacrylate) sample (PMMA) and pulse profiles reconstruction by means of the WFS. By tuning several dynamical parameters, as the FEL fluence, the amount of aberration affecting the pulse wavefront, and the longitudinal position of the PMMA, we were able to exploit the tomography of the (spatial) transverse pulse profile, as well as to present a qualitative and quantitative comparison between these reconstruction methods. We are confident that these results represent a step further towards the complete characterization of the spatial properties of FEL pulses delivered by seeded sources like FERMI [11–18]. Additionally, we think that our approach bears potential to extend the knowledge of the pulses delivered by SASE FELs, particularly in the EUV/SXR spectral range where commercial WFS devices, based on the Hartmann grid design, can easily operate.
2. Experimental layout
The EUV pulses generated in the FERMI undulators are first steered towards the PRESTO spectrometer by means of two grazing incidence mirrors (see Fig. 1). PRESTO is endowed with a set of gratings working at 2.5 degrees grazing incidence angle along the horizontal plane and engineered to send (≈ 98%) its specular reflection (zero-order) towards the different beamline branches. The diffracted radiation (1st or 2nd orders) acts as a feedback signal to monitor, shot-by-shot, the beam spectral features [19,20]. Downstream of PRESTO, the beam freely propagates up to a third grazing incidence plane mirror, which further deviates (along the vertical plane) the radiation towards the last (refocusing) optical device, i.e., a Kirkpatrick-Baez (KB) Active Optics System (KAOS) [21]. KAOS aims at refocusing the beam in the experimental end-station and consists of a couple of (horizontal and vertical) slits and two mirrors. The slits spatially filter the beam from any spurious tail surrounding the main spot and select the desired working area of the two mirrors installed downstream. The first mirror refocuses the radiation along the vertical plane, while the second one acts on the horizontal plane. These mirrors are placed at focal distances of 1750 mm and 1200 mm (see Fig. 2), respectively. KAOS can adjust the focal spot size in the hundreds to few μm range, according to the user’s requests [22–24]. Ultimate performance corresponds to a focal spot size of ≈ 1.8 μm (horizontal) x ≈ 2.4 μm (vertical), measured at a wavelength of 4.14 nm [25]. Such a tunability is feasible since each mirror substrate has an intrinsic harmonic response to externally driven mechanical stress. Forces can be applied thanks to a double motor scheme hosting i) a couple of step-motors used for coarse-grain bending the mirrors, plus ii) a couple of fine-tuning piezo actuators used for optimizing the substrate curvature. The goal is to bend the mirrors from a quasi-flat profile towards an elliptical one down to a figure-error of less than ≈ 80 nm, i.e., the amount of residual curvature lacking to match the ideal mirror curved profile [26]. The optimization consists of i) focusing the beam by acting exclusively on the step-motors while looking at the spot size on a scintillator, and ii) minimizing the optical aberration affecting the pulse wavefront. This last step takes advantage of the WFS as a diagnostic tool, as it retrieves the pulse wavefront and allows to minimize up to the third order aberrations, i.e., astigmatism, coma [25,26]. The WFS measures in real time the spatial phase carried by the pulse, and decomposes it into its fundamental eigenmodes, i.e., the Zernike polynomials, each of them carrying a different aberration component [27]. These defects can be minimized by acting exclusively on the fine-tuning piezos. During our experiment, the WFS was placed at 2130 mm downstream the focal plane. The WFS is a commercial device (from Imagine Optique), composed by a two-dimensional Hartmann grid made of 72 × 72 pinholes, separated by 180 μm (spatial sampling) and an area of 13 × 13 mm2. The detector mounted right after the Hartmann grid is an X-ray CCD (PIXIS XO 1024B from Princeton Instrument) designed to operate between ≈ 30 eV and ≈ 20 keV and characterized by a minimum readout time of ≈ 600 ms. The intrinsic WFS resolution is ≈ λ/50 (rms) and the instrument is optimized to operate in the spectral domain between ≈ 4 nm and ≈ 60 nm, so covering the lasing domain of FERMI [10]. Acquiring data by means of the WFS can be exclusively performed in single-shot mode, and to do this a fast-shutter is installed before the DiProi end-station and synchronized with the machine main trigger signal. As previously mentioned, to safety operate the WFS it is mandatory to reduce the fluence in the range of ≈ 1 J/cm2, to avoid any permanent damage on the X-ray CCD. This task can be easily accomplished using the filters and the gas attenuator along PADReS [28].
Fig. 1. Sketch of the PADReS optical layout designed to transport the EUV beam from the source-point towards the DiProI beamline branch.
Fig. 2. Sketch of the KAOS optical device designed to refocus the EUV/SXR beam in the DiProI end-station. The KB mirrors are installed at 1750 mm (vertical mirror) and 1200 mm (horizontal mirror), respectively. The WFS is placed downstream the focal plane at 2130 mm.
3. Sample preparation, characterization, and ex-situ measurements
We prepared PMMA films of ≈ 1 µm thickness (950k molecular weight, spin-coated from an 8% solution in anisole at 3000 rpm) on silicon substrates as targets for irradiation. The experiment was performed at a wavelength of λ=27.7 nm (photon energy of 44.7 eV). The DiProI experimental end-station was equipped with a three-axis piezo-driven manipulator able to raster scan the sample to guarantee that each imprint is captured at a new and pre-defined position [29]. To ensure that a single pulse is responsible for each imprint, we performed the measurement in a single-shot mode by means of a fast-shutter synchronized with the main machine trigger signal. With the third axis, the sample was moved along the beam trajectory to access positions upstream and downstream of the focal plane. Furthermore, the PMMA sample could be removed to illuminate the WFS. After single-shot ablation, the PMMA films were investigated in detail ex situ and subsequently treated with a 1 to 1 mixture of isopropanol (IPA) and methyl isobutyl ketone (MIBK) as described in [13]. After chemical treatment, they were analyzed by means of an Atomic Force Microscopy (AFM), using an MFP3D (Oxford Instruments/Asylum Research) instrument. Imprints images were acquired in AC mode using standard silicon cantilevers (NSG30, NT-MDT, nominal radius of curvature <10 nm, nominal spring constant = 40 N/m). We acquired 90 μm x 90 μm topographic maps with 256 (out of focus data) and 512 (focal plane data) pixels resolution at a scan rate between 0.3 and 0.7 Hz, precisely positioning the cantilever on the chosen spot with the help of the optical microscope integrated into the AFM setup.
4. Results and discussion
4.1 Quantitative analysis of PMMA imprints
To compare the imprints and the data captured by means of the WFS, the quantitative knowledge of the intensity pulse profiles is required. It has to be retrieved from the imprint depth array at each position in x and y, d(x,y). To do this, we employ the Beer-Lambert law. In absence of thermal ablation processes taking place in the sample, the impinging intensity distribution can be calculated as a function of the ratio of the local intensity, I0(x,y), to the development threshold, Ith [13]:
If high fluences are used, the analysis is much more complicated, and we must deal with imprints generated by non-linear ablation processes. This problem has been already addressed in the last decade in the first pioneering studies on the non-Gaussian focal spots of SASE FELs pulses, leading to the development of the so-called peak-to-threshold approach [11–13]. Our procedure implements the peak-to-threshold approach step-by-step and can be summarized as follows [11–13]:
- i) The imprint depth array, d(x,y), is measured on the chemically developed PMMA sample using an AFM. The non-ablated region is defined as a depth of zero. In our notation the depth is positive.
- iii) Quantitative intensity pulse profiles are retrieved exclusively for the dataset captured at the fluence of ≈ 1 J/cm2. This limitation is set by the WFS radiation hardness. As previously mentioned, it cannot operate at much larger fluences due to potential irreversible damages.
4.2 PMMA imprints at the focal plane
In this section we present and discuss the features of the imprints captured at focal plane (z=0 mm), as a function of both the FEL fluence and the amount of aberration affecting the pulse wavefront. The FEL was initially tuned at two different fluences (high or low) preserving the pulse wavefront into an aberration-free state. Afterward, the wavefront was set into an aberrated state, keeping the FEL fluence at the low state. We would like to stress that the aberration-free and the aberrated states can be experimentally defined by monitoring the WFS signal, removing the sample from the focal plane. In this way it is possible to i) identify the fine-tuning piezos values required to find the best KB mirrors curvature and the degraded one, and to ii) get a feedback for the focal spot area values (FWHM) to calculate the corresponding fluences. Additionally, the choice of capturing the imprints as a function of the aberration keeping the FEL fluence at the low state is strongly driven by the aim to compare the imprints and the WFS signals. As previously underlined, this can be done only using fluences in the range of ≈ 1 J/cm2, to safely operate the WFS.
Figure 3 presents the imprints captured at focal plane (z=0 mm). The pulse wavefront is initially set into an aberration-free state, corresponding to a quasi-perfect focal spot. The aberration-free state is identified by means of the WFS and corresponds to a condition where the weight of each Zernike polynomial is practically equal to zero. As previously discussed, this state can be implemented by exclusively acting on the fine-tuning piezos to tailor the KB mirrors curvature close to perfect. A maximum depth of ≈ 780 nm is achieved by exposing the PMMA to a single pulse carrying a fluence of ≈ 30 J/cm2 (see Fig. 3(a)). The limits of the colormap scale of Fig. 3(a) are set on purpose between 0 nm and 500 nm, to visualize the diffraction pattern surrounding the main focal spot (that would be suppressed on a scale reaching the maximum depth).
Fig. 3. Imprints captured in the aberration-free state at a) high (≈ 30 J/cm2) and b) low (≈ 1 J/cm2) fluences. The aberrated state is achieved by degrading on purpose the KB mirrors curvature and is collected at c) low fluence (expected to be less than ≈ 1 J/cm2 due to the aberration affecting the pulse wavefront).
However, we have to emphasize that the peak-to-threshold ratio under these conditions is, even for the chemically developed imprints, much higher than the one reported by Rösner et al. [13] based on the attenuation lengths found by Chalupský et al. [11,12]. This means in essence that thermal melting has occurred, and that the depth cannot be a quantitative measure of the (peak) beam intensity at high fluence values. On the other hand, the high fluence values provide a good picture of even faint beam tails as shown in Fig. 3(a). To get to a fully quantitative regime, we reduced the maximum fluence to ≈ 1 J/cm2 (see Fig. 3(b)) by inserting filters and gas in the attenuator along PADReS, preserving the beam profile into the aberration-free state and consequently the quasi-perfect focal spot [29]. Although the fluence is reduced by a factor ≈ 30, it is still possible to obtain a maximum depth of ≈ 320 nm, corresponding to a peak-to-threshold ratio, p, ≈ 207. This value is well below the maximum ratio of 345 to stay below the thermal ablation threshold, found by Rösner et al. [13]. The maximum depth of the low fluence indicates a threshold fluence for the development of 4.8 mJ/cm2, close to the values found by Rösner et al. [13]. After that, we set the pulse wavefront into an aberrated state by exclusively acting on the fine-tuning piezos to degrade (on purpose) the KB curvature profiles. In this specific case, the wavefront is contaminated by a large amount of astigmatism, coma, and third-order aberrations, leading to an extremely not uniform focal shape (see Fig. 3(c)). The intensity is spread over a larger and irregular area, and the maximum depth is reduced to a maximum of 127 nm. This corresponds to a peak-to-threshold ratio of 8.3, i.e. the maximum (local) fluence is only 4% of the one found for the aberration-free case.
4.3 Quantitative comparison of WFS and PMMA imprints
Figure 4(a) and (b) reports the profiles retrieved from the imprint and the WFS, respectively. These data are captured in the aberration-free state, and at a first look, the two reconstruction methods offer an appreciable qualitative matching. To get a more precise quantitative comparison, Fig. 4(c) presents the differential map between these two signals, revealing their quantitative mismatch. In the aberration-free state the matching is close to perfect. The ≈ 10% difference that we observe is found along the vertical plane, where the WFS signal is stronger than the retrieved pulse profile. The horizontal mismatch arises from a slightly non-orthogonality of the x- and y- direction, suggesting a minimal misalignment of the KB mirror roll, that the WFS might not be sensitive enough to resolve.
Fig. 4. Aberration-free state profiles retrieved from a) the imprint and b) the WFS, in addition to their c) differential map. Aberrated state profiles retrieved from d) the imprint and e) the WFS, in addition to their f) differential map.
Figure 4(d) and (e) shows the profiles retrieved from the imprint and the WFS, respectively. These are both captured in the aberrated state. Despite of the two reconstruction methods still showing a qualitative matching, the differential map (see Fig. 4(f)) points out that (nearby the main focal spot) the retrieved pulse profile is by ≈ 30% stronger than the WFS signal along both the horizontal and the vertical planes. If we take the maximum intensity as reference, this strongly indicates that the method to develop the imprints is certainly more sensitive in the regions marked by low flux density than the use of the WFS.
A detailed analysis of the previous data is highlighted in Fig. 5. Figure 5(a) presents the contour plot of the profile retrieved from the imprint captured in the aberration-free state. The red domain marks the cross-section area at FWHM. It has a slightly larger size along the horizontal plane, and a measure of ≈ 14.6 μm2 calculated by means of the ellipse area equation. The intensity distribution is mainly localized at the peak, while the surrounding diffraction features contribute only to a minimal amount of the overall intensity (in the few % range). Its shape offers a direct feedback on the goodness of the fine focusing operations. Figure 5(b) highlights the horizontal (blue dots) and vertical (red dots) profiles of the differential map (see Fig. 4(c)), captured at the pulse peak. The horizontal and vertical spot sizes retrieved from the imprints and the WFS are found by fitting the profiles shown in Fig. 5(c) and (d). The blue and red dots refer to the horizontal and vertical data, respectively, while the black lines are the results of the fit function $f(x )= {a_1} + {a_2}sin{c^2}({{a_3}\pi x/\lambda } )+ {a_4}exp({ - {x^2}/2a_5^2} )$. The fitting parameters return sizes (FWHM) equal to 4.86 ± 0.02 μm (horizontal) and 3.84 ± 0.01 μm (vertical). The same function is used to fit the WFS profiles (see Fig. 5(d)) and gives sizes equal to 4.98 ± 0.05 μm (horizontal) and 4.84 ± 0.05 μm (vertical). The sinc term accounts for the expected diffraction pattern, while the Gaussian one models the main focal spot. It is mandatory to stress that appreciable results can be achieved only including both the sinc and the Gaussian in the fit function. Our first conclusion is that these two methods return qualitatively consistent results in the aberration-free state at z = 0 mm, while from a quantitative point of view we confirm what we already observed in Fig. 4(c), i.e., the WFS has the intrinsic trend to (slightly) overestimate the vertical spot size by ≈ 1 μm.
Fig. 5. a) Contour plot of the profile retrieved from the imprint. The red domain marks the cross-section area at FWHM. b) Horizontal (blue dots) and vertical (red dots) profiles at the peak of the differential map. Horizontal (blue) and vertical (red) profiles retrieved from c) the imprint, and d) the WFS (both evaluated at the peak signal).
Figure 6(a) highlights the contour plot of the retrieved profile in the aberrated state. The red domain marks the cross-section area at FWHM. It measures ≈ 23.3 μm2, larger (as expected) than the aberration-free state one. The insertion of a large amount of astigmatism, coma and third order aberrations leads to an irregularly spread intensity, proving that in the aberrated state is not possible to achieve the highest accessible power density. In addition to the main cross-section area we cannot overlook the existence of secondary domains (orange areas) corresponding to scattering radiation carrying an intensity between 20% and 50% of the pulse peak intensity. Figure 6(b) reports the horizontal (blue dots) and vertical (red dots) profiles of the differential map (see Fig. 4(f)) captured at the pulse peak. Figure 6(c) and (d) reports the horizontal (blue dots) and vertical (red dots) profiles of the retrieved pulse and the WFS, respectively. Oppositely to the aberration-free state, this profile overcomes the WFS along both the horizontal and vertical planes. We exclude that this behavior is the result of physical processes involving the formation of the liquid phase. Indeed, at this (very low) fluence value the ablation process is clearly nonthermal and so the solid to liquid transition is obviously absent. Rather, it can be ascribed to the extreme sensitivity of the ablation imprints technique to resolve not only the main focal spot shape and size, but the entire diffraction pattern surrounding it [11–13].
Fig. 6. a) Contour plot of the profile retrieved from the imprint. The red domain marks the cross-section area at FWHM. The orange areas correspond to sample regions illuminated with at least 20% of the peak pulse intensity. b) Horizontal (blue dots) and vertical (red dots) profiles at the peak of differential map. Horizontal (blue) and vertical (red) profiles retrieved from c) the imprint, and d) the WFS (both evaluated at the peak signal).
An additional observation regards the periodicity of the fringes resulting from the diffraction introduced by the KB mirrors. In the aberration-free state it is easy to observe that the profiles retrieved from the imprints and the WFS (see Fig. 5(c) and (d)) exhibit fringes which are (in first approximation) symmetrical on both sides. The symmetric diffraction is a fingerprint of an almost perfect curvature achieved by the KB mirrors. Moreover, in the aberrated state (see Fig. 6(c) and (d)) the fringes are marked by a variable periodicity. This effect can be explained in terms of the not negligible amount of astigmatism, coma or third-order aberration introduced by acting on the fine-tuning piezos to degrade the KB mirrors curvature. The KB mirrors are so bent in a configuration such that their curvatures are not anymore comparable to the ideal ones, i.e., the figure error is not negligible, and gives birth to the asymmetric diffraction at the edges of each mirror [22–26].
4.4 Tomography of the focal region
Afterwards, we extended our experimental approach over the entire focal region (see Fig. 7-8) to realize the pulse profile topography. Such an experimental approach helps us to disclose if and how the results of the two reconstruction methods deviate while moving the sample along the beam propagation axis by several mm (≈ 5 mm) downstream and upstream of the focal plane. As done previously, the topographies are performed by exclusively collecting datasets at the low fluence value (≈ 1 J/cm2), where is still possible to safely operate the WFS. Figure 7(a) compares the aberration-free topographies built by means of the profiles retrieved from the imprints (upper line) and the WFS (bottom line). These are both realized by merging the snapshots captured in the interval between z=-3 mm and z=+3 mm (in steps of 1 mm), plus the ones acquired at z=-5 mm and z=+5 mm. Positive values refer to the upstream propagation axis and vice versa, while the red domains mark the cross-section areas at FWHM.
Fig. 7. Topographies built merging the profiles retrieved from the imprints (upper line) and the WFS (lower line), captured in the a) aberration-free state and in the b) aberrated state.
At a first look, both reconstruction methods retrieve profiles which appear qualitatively consistent, particularly in the propagation axis interval enclosed nearby the focal plane (between z=-3 mm and z=+2 mm). Instead, at the topographies’ edges (z=±5 mm) it is quite evident that the imprints and the WFS data start to deviate more distinctively from each other. This mismatch can be easily explained in terms of the WFS resolution. Its working principle can be easily explained as follows. The Hartmann grid samples the incoming wavefront and defines a two-dimensional reference array. Any potential change in the wavefront surface, introduced by astigmatism, coma and third-order aberration, is seen by the WFS as a shift from the reference point along both the horizontal and vertical planes, i.e., as a couple of horizontal and vertical slopes. The WFS software transform the slopes into a finite sum of Zernike (or Legendre) polynomial orders and returns the feedback for tuning the KB mirrors. The wavefront is a surface whose curvature changes along the beam propagation axis and reaches its maximum at the focal plane. The slopes sampling reaches its maximum at z=0 mm, i.e., the WFS is expected to be more sensitive at the focal plane. Moreover, moving away from the focal plane the wavefront diverges, while its curvature decreases, and this leads to a weaker slopes sampling. At larger distances (as z=±5 mm) this effect becomes even more pronounced and correspond to a not negligible drop in terms of reconstruction efficiency.
At a deeper quantitative look, by applying the same fit function used for the data captured at z=0 mm, we extracted the results presented in Tab. 1. It includes the horizontal and vertical spot sizes (FWHM) of the profiles retrieved from the imprints and the WFS, as well as their areas evaluated by means of the standard ellipse area equation. As previously observed, at the focal plane the WFS has the trend to slightly overestimates the vertical spot size by ≈ +1 μm, which reflects into an cross-section area larger by a factor ≈ 20%. Downstream of it (z<0 mm) the imprints return areas with progressively larger elliptical shape, squeezed along the horizontal axis. Upstream to the focal plane (z>0 mm) the spot shapes become progressively elliptical along the opposite plane (horizontal), as expected. The WFS has the intrinsic trend to return focal spot shapes marked by approximately circular areas. At z=±1 mm both areas are only a few μm2 larger than the one at the focal plane, while at z=±2 mm these are practically doubled. This slightly anomalous drop is explained in terms of the mentioned WFS resolution, i.e., the slopes sampling decreases moving towards the edges of the focal region. At z=±5 mm, it is even more pronounced.
Table 1. Sizes and cross-section areas (FWHM) of the aberration-free focal spots between z=-3mm and z=+2mm.
Figure 7(b) compares the aberrated topographies. As in the previous case, both reconstruction methods return qualitatively consistent results in the range between z=-3 mm and z=+2 mm. In this specific case, the imprints clearly exhibit their strength to resolve the entire diffraction pattern surrounding the main focal spot, where the WFS is practically blind. From a quantitative point of view, in this case, it is extremely difficult to get an estimation for the cross-section areas, being them characterized by the appearance of irregular secondary domains lying in the proximity of the main one and carrying at least 20% of the impinging peak amplitude. Additionally, at the topographies’ edges (at z=±5 mm) it is quite evident that the results start to largely deviate as in the aberration-free state.
5. Conclusions
The analysis of these datasets proves that the investigation of ablation imprints is an extremely powerful technique to resolve the main focal spot shape and size, as well as the entire diffraction pattern surrounding it. This is a consequence of its intrinsic low damage threshold if compared to the usual fluences operating at the FELs. However, extreme caution has to be taken to remain in the linear regime: for a quantitative picture, one has to take a fluence series to ensure this linearly. The main focal spot properties can be, however, also retrieved by the WFS, although it is practically blind to resolve the diffraction features of the higher order diffraction fringes. In particular, our results prove that in the aberration-free state both reconstruction methods give consistent qualitative results. This conclusion is not only true at the focal plane but for at least few mm along the beam propagation axis. Moreover, such experimental approach allows us to compare these two methods quantitatively, revealing that at the focal plane the WFS has the intrinsic trend to overestimate the spot size slightly along the vertical plane in the range of ≈ +1 μm (or less). When moving the sample along z it was possible to reveal the qualitative similarities and the quantitative differences between the imprints and the WFS methods. In the aberrated case, it is difficult to estimate the focal spot areas due to the extremely irregular shapes, although we can still observe a consistent qualitative agreement in a range of a few mm around the focal plane. In both cases (imprints and WFS) at the edges of the focal region both reconstruction methods return qualitatively different results. These largely appear at ≈ ± 5 mm and, in first approximation, can be explained in terms of WFS resolution and a non-planar wavefront.
Moreover, it is important to underline that the imprint approach suffers from a main intrinsic limitation, that is its extremely time-consuming ex-situ operations required to post-process the PMMA samples via chemical development plus the AFM analysis required to measure the imprints depth arrays. Consequently, it is not the right choice to be offered to a FEL users’ experiment and the related activities for its setup. On the contrary, the WFS approach is an extremely powerful tool thanks to its unique capability to reconstruct in real time the focal spot properties and represents the optimal choice for fine tuning optimization during standard users’ activities.
Nonetheless, the PMMA approach finds its proper place in the framework of dedicated studies for the characterization of the EUV/SXR pulse properties, as well as in experiments strictly dependent on the knowledge of the focal spot areas. A good strategy here is to use the WFS to set up the correct spot properties, and to use the imprints method to verify and control these properties ad-hoc within few hours. Further potential for good beam characterization will be dependent on the capability to improve the intrinsic efficiency of the WFS device, a careful calibration to conditions outside the working range, and their operating spectral range. We are confident that our results and methodologies represent a step further in the study of the FELs pulses properties and can pave the way towards the setting of new metrological standards for ultrafast X-ray science.
Funding
Horizon 2020 Framework Programme (654360 NFFA-Europe).
Acknowledgments
The authors thank the entire FERMI team, as well as the European Union’s Horizon 2020 research and innovation program.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
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