- Email: [email protected]
Beam parameters of FLASH beamline BL1 from Hartmann wavefront measurements
Nuclear Instruments and Methods in Physics Research A 635 (2011) S108–S112
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam parameters of FLASH beamline BL1 from Hartmann wavefront measurements a,n ¨ Bernhard Floter , Pavle Juranic´ b, Peter Großmann a, Svea Kapitzki b, Barbara Keitel b, a b a ¨ ¨ , Bernd Schafer , Kai Tiedtke b Klaus Mann , Elke Plonjes a b
Laser-Laboratorium G¨ ottingen, Hans-Adolf-Krebs-Weg 1, D-37077 G¨ ottingen, Germany Deutsches Elektronen-Synchrotron, Notkestraße 85, D-22603 Hamburg, Germany
a r t i c l e i n f o
a b s t r a c t
Available online 13 October 2010
We report on online measurements of beam parameters in the soft X-ray and extreme ultraviolet (EUV) spectral range at the free-electron laser FLASH. A compact, self-supporting Hartmann sensor operating in the wavelength range from 6 to 30 nm was used to determine the wavefront quality of individual freeelectron laser (FEL) pulses. Beam characterization and alignment of beamline BL1 was performed with l13.5 nm/90 accuracy for wavefront rms (wrms). A spot size of 159 mm (second moment) and other beam parameters are computed using a spherical reference wavefront generated by a 5 mm pinhole. Beam parameters are also computed relative to a reference wavefront created by a laser-driven plasma source of low coherence, proving the feasibility of such a calibration and reaching l13.5 nm/7.5 wrms accuracy. The sensor was used for alignment of the toroidal focusing mirror of beamline BL1, resulting in a reduction of wrms by 25%, and to investigate wavefront distortions induced by thin solid filters. & 2010 Elsevier B.V. All rights reserved.
Keywords: Wavefront Free-electron laser Hartmann sensor EUV
1. Introduction Hartmann–Shack and Hartmann sensors are routinely used for real-time wavefront detection and laser beam characterization in the near infrared, visible and ultraviolet spectral region. Both the wavefront (directional distribution) and the beam profile (intensity distribution) of a radiation field can be recorded for a single pulse, enabling evaluation of paraxial beam parameters such as beam diameter d, divergence y, beam propagation factor M2, Rayleigh length zR, waist position z0 and waist diameter d0 for coherent radiation [1]. Solving the Fresnel–Kirchhoff integral allows also numerical propagation of the beam and thereby prediction of intensity distribution in any plane [2]. The Free-electron LAser in Hamburg (FLASH), operating in the extreme ultraviolet (EUV) spectral region, is based on the self-amplified spontaneous emission (SASE) process, which builds up laser emission from spontaneous undulator radiation. The photon beam characteristics relevant for user experiments can differ from pulse to pulse, leading to a strong requirement for single-pulse photon diagnostics and on-line characterization of the beam propagation parameters [3,4]. Recently, we reported on a compact EUV Hartmann wavefront sensor that was jointly developed by Laser¨ Laboratorium Gottingen (LLG) and DESY for photon diagnostics, beamline alignment and monitoring of FEL radiation at FLASH [5].
n
Corresponding author. ¨ E-mail address: bernhard.fl[email protected] (B. Floter).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.10.016
The validity of beam parameters, computed in the framework of second moments, was confirmed using data from beamline BL2. In this paper, we present results from measurements at beamline BL1, including determination of beam parameters relevant for many user experiments as well as alignment of the toroidal focusing mirror. One of the major challenges using the Hartmann technique is to create a known reference wavefront. Two approaches are taken here: using a laboratory-scale laser-driven plasma source and spatial filtering at FLASH. Great effort is currently undertaken to design optical elements that preserve coherence and wavefront properties of FEL pulses. The gas attenuator, developed at FLASH [3], and thin solid filters are standard techniques for intensity attenuation at FELs. Both techniques were investigated at FLASH, and it was reported that in general the gas attenuator induces less wavefront aberrations [4]. Solid filters provide other features such as very high attenuation levels and spectral characteristics that may outweigh this disadvantage in certain applications. In this context the Hartmann sensor has proven to be a useful tool for pulse resolved beamline monitoring. 2. Hartmann sensor and reference wavefront generation The setup for the Hartmann sensor is based on the ideas Hartmann [6] presented in 1900. The essential parts are the Hartmann plate, a pinhole array consisting of a 7 mm thick tantalum foil with laser drilled holes (pitch 320 mm, diameter 65 mm), which divides the incoming beam into an array of smaller beams, and a 12bit camera with a
B. Fl¨ oter et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) S108–S112
S109
The wavefront quality is given in terms of wavefront peak-tovalley wpv and wavefront root-mean-square wrms values. Tilt and the best-fitting sphere are subtracted prior to computation of these values. The selection of area of interest (AOI) for wavefront and beam profile evaluation is based on clipping of noise at a level of 1% of the full dynamic range of the camera. The largest circle inscribed into this AOI defines the evaluation radius a. Two techniques, spatial filtering at FLASH and a lab-scale EUV plasma source were used to create near-spherical reference wavefronts. For the latter, a Nd:YAG laser (1064 nm, 1 Hz, 800 mJ, 7 ns) is focused down to about 60 mm into a Krypton (Kr) gas jet (backing pressure 15 bar) centered in a vacuum chamber, producing a 250 mm 150 mm plasma (FWHM) (Fig. 1a). For blocking of outof-band radiation from the plasma a 200 nm titanium filter is used, resulting in broadband radiation (Kr XXV–Kr XXXVI) in the spectral range l ¼2.5–6.5 nm as seen from the measured spectrum in Fig. 1b. The EUV spectrometer (1–7 nm) used for the spectral investigation of the plasma source consists of a 100 mm entrance slit, an aberration corrected flat-field grating (2400 lines/mm) and a back-side illuminated CCD camera. The plasma was monitored with a pinhole camera, consisting of a CCD chip with an EUV-to-VIS quantum converter and a pinhole (diameter 50 mm) coated with a titanium foil (thickness 200 nm). A more detailed description of the EUV source is given in Ref. [13]. The Hartmann sensor described above was placed at a distance of 1213 mm from the plasma. The reference spot patterns shown in Fig. 2a were recorded, averaging over 100 frames, each containing 50 pulses. The directional characteristic of the plasma source, emitting into 4p steradian, results in a homogeneous intensity profile.
charge-coupled device (CCD) chip at the distance l¼97 mm behind the plate, which monitors the position and intensity of the beams from each subaperture. The CCD chip (1279 1023, 6.45 mm pixel size) is coated with Gd2O2S:Tb (grain size 1–2 mm, central emission wavelength 545 nm) for EUV-to-VIS conversion. The Hartmann sensor is described in greater detail in Ref. [5]. The displacement of a spot centroid Dx divided by l yields the local wavefront gradient inside one subaperture relative to a known reference wavefront. The wavefront is reconstructed from local gradients in a modal approach according to Refs. [7–9], using 37 Zernike polynomials in the ordering referred to in Ref. [10]. Summation over pixel data inside the individual subapertures samples the intensity distribution or beam profile I(x,y). The Hartmann data, consisting of sampled intensity and wavefront gradients, allows for computation of the first and second order moments of spatial (x,y) and angular (u,v) coordinates over the intensity distribution [1]. For paraxial coherent beams this information is sufficient to compute the following beam parameters: beam width d, divergence y, beam propagation factor M2, waist diameter d0, Rayleigh length zR and waist position z0 as shown in Refs. [1,11]. Influences from partial coherence are neglected in this evaluation. For our purposes, this is justified by the high degree of spatial coherence reported for the FLASH beam [12]. The computation of second moment beam parameters from the Hartmann data for EUV FEL radiation and general agreement with caustic scan techniques was reported in Ref. [5]. Once intensity and phase of a beam are known from the Hartmann measurement, the Fresnel–Kirchhoff propagation yields intensity distribution at different positions z [2].
Krypton Z = 36
Intensity /a.u.
15000
Kr XXV - XXXVI
10000
5000
0 2
3
4 5 Wavelength / nm
6
Fig. 1. Laboratory-scale EUV source: a Nd:YAG laser is focused into a Kr gas jet in a vacuum chamber, creating a plasma emitting in the EUV spectral range. A pinhole camera image is shown in (a). The radiation of the plasma is filtered by a 200 nm titanium foil, producing the spectrum shown in (b).
Fig. 2. Reference spot patterns taken at the EUV laser-driven plasma source (a) and at FLASH with a 5 mm pinhole at l ¼ 13.5 nm (b); the center pinhole on the Hartmann plate is omitted for alignment purposes.
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The FLASH-reference wavefront was created using a 5 mm pinhole [14] placed 175 mm upstream of the focal plane at beamline BL1 and 3270 mm in front of the Hartmann sensor. Focusing is produced by the beamline toroidal mirror that has a focal length of 10 m and is coated with high-density amorphous carbon, deposited by magnetron-sputtering [3]. A single FEL pulse with a typical pulse energy of 8 mJ [15] provided sufficient intensity for the CCD even after the pinhole. Throughout all measurements presented in this paper, FLASH operated at a fundamental wavelength of l ¼ 13.5 nm. For improved signal-to-noise ratio, 103 pulses were averaged to create the reference shown in Fig. 2b. Measuring the plasma source reference against the FLASH reference yields a maximal wavefront deviation of 11.4 nm or wpv ¼ l13.5 nm/1.2 and a root-mean-square of wrms ¼ l13.5 nm/7.5 on a circular AOI with the evaluation radius a¼2.84 mm. The plasma source reference turns out to be not quite uniform over the evaluation area, which might be due to the employed titanium filter. Using the 5 mm pinhole, a series of single FEL pulses was recorded against the FLASH reference, yielding an average relative single-pulse repeatability of the wavefront sensor of l/15 (wpv) or l/90 (wrms) at l ¼13.5 nm (a ¼3.04 mm). Comparative wavefront measurements were performed, leaving the sensor position unchanged and using a 137 nm Al filter. Based on the FLASH reference we find wpv ¼48 nm and wrms ¼ 9.4 nm and for the laser-driven plasma source wpv ¼ 49.3 nm and wrms ¼9.3 nm (a ¼1.81 mm), thus differing by 1.3 nm (3%) and 0.1 nm (1%) only, respectively
3. Beamline commissioning and beam characterization at BL1 The sensor was placed about 3695 mm downstream of the expected focal plane to adapt the beam size to the detector area, further using a 137 nm Al filter and a 10 mm aperture, 43 m upstream of the toroidal mirror. SASE pulse generation is a stochastic process and leads to fluctuations both in intensity and phase. These fluctuations can be observed in the wavefront as
shown in Fig. 3 for four single pulses (a¼2.72 mm). For wpv and wrms, we find a standard deviation of approximately 10%, calculated over 75 pulses. Therefore, any optics testing or alignment task at FLASH requires a certain number of averaged pulses (see Fig. 4a, b), whereas single pulse resolution is needed for characterization of the FEL beam itself. Prior to the actual measurements, the employed Al filters (thickness 200 and 137 nm) were checked for aberrations by comparing the transmitted wavefronts (Fig. 4). As seen from Fig. 4(a) and (b), showing two subsequent recordings of the wavefront behind the same 137 nm filter averaged over 16 single pulses, the FEL fluctuations are efficiently averaged out. Apparently, use of the 200 nm Al filter (Fig. 4c) leads to slight changes in the shape of the wavefront, although both wrms and wpv values are similar. In the following, the 137 nm Al filter is used, which attenuates the single pulse energy from 8 to about 0.18 mJ [17]. Before measuring the beam parameters, the focusing mirror was aligned by successively moving the mirror with respect to pitch and yaw angles around the pre-aligned position. The goal of alignment procedure with a wavefront sensor is to maximize the Strehl value, which is, according to the Mare´chal formula, equivalent to minimizing wrms [2,18]. The wavefronts (a¼ 2.23 mm) used for alignment of the BL1 toroidal mirror are shown in Fig. 5, plotted against pitch and yaw angles. A 5 mm circular aperture was placed in the FEL beam path 43 m upstream of the toroidal mirror. Four averaged camera frames, each containing a single FEL pulse, were used for centroid determination to reduce effects from shot-to-shot noise of the FEL beam. First the yaw angle was aligned such that the astigmatism is oriented along the coordinate axes. Afterwards, the pitch was adjusted, finally leading to a reduction of the wrms value by 25% from 7.2 to 5.4 nm and of wpv by 16% from 40.9 to 34.4 nm. The starting and end points of the alignment process are marked red in Fig. 5. The alignment process of the ellipsoidal mirror at BL2, which follows the same principles, is described in detail in Ref. [5]. After alignment, the second moments are measured for the full FEL beam, using a 10 mm aperture 43 m upstream of the toroidal mirror. For each of the 75 single pulses, the beam parameters are
Fig. 3. Wavefronts for single FLASH pulses on a circular AOI with 5.44 mm diameter and a 137 nm Al filter, corresponding to the data compiled in Table 1.
Fig. 4. Wavefronts measured for a 137 nm Al (a,b) and a 200 nm Al filter (c) at l ¼13.5 nm, averaged over 16 single pulses (circular AOI, 4.87 mm diameter, 37 Zernike polynomials).
B. Fl¨ oter et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) S108–S112
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propagation factor M2 of the 75 single pulses is 7.5 whereas M2 is 6.8 for the average pulse (integrated on-chip) at BL1. From the FLASH divergence of about 90 710 mrad FWHM reported in Ref. [3] and the distance source-toroidal mirror (focal length f¼ 10 m) of 68 m, a beam diameter of d ¼10.4 mm on the mirror is calculated presuming a Gaussian beam. Estimating the divergence behind the mirror as y ¼d/f and neglecting beam clipping effects on the mirror, the diffraction limited waist diameter follows 4l/py ¼17 mm. Our measurement is in good agreement with this estimation, the diffraction limit follows d0/M2 ¼21 mm (see Table 1).
4. Conclusion
Fig. 5. Wavefronts measured during the alignment process of the BL1 toroidal mirror, plotted against pitch and yaw angles (circular AOI, 4.47 mm diameter). Starting point of the alignment process is pitch 39 mrad, yaw 0 mrad with wrms ¼ 7.2 nm and end point is both pitch and yaw 0 mrad with wrms ¼5.4 nm.
Table 1 Second moment beam parameters from Hartmann measurements at BL1 at 13.5 nm using a 137 nm Al filter and a 10 mm aperture, 43 m upstream of the toroidal mirror (averaged over 75 single pulses). The row d0 indicates the diameters in the plane z0, both in the x and y direction, and the diameter according to (A3), d0,i, gives the waist diameters in the planes located at z0,x and z0,y. Beam parameters wpv (nm) wrms (nm) Beam propagation parameter M2 Waist position z0 (mm) Rayleigh length zR (mm) Waist diameter d0 (mm) 2nd moment (FWHM) Divergence y (mrad) Waist position z0,i (mm) Rayleigh length zR,i (mm) Waist diameter d0,i (mm) 2nd moment (FWHM) Divergence yi (mrad)
x
y
8.8
6.8
174 (103)
143 (84)
3656 132 144 (85)
3824 96 108 (64)
1.09
1.13
Global 58.4 8.5 7.5 3743 144 159 (94) 1.11
computed (a ¼2.72) assuming a simple astigmatic beam, according to Refs. [1,11] and Eqs. (A1)–(A5). The parameter averages are compiled in Table 1, where the index i ¼x, y indicates the parameters for the two lateral dimensions. Other parameters are given with respect to the beam diameter definition qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ¼ 23=2 /x2 Sþ /y2 S ð1Þ for a near-circular beam [16] (Appendix A), defined as a beam with ellipticity e 40.87 [16]. For most planes, this is fulfilled at FLASH BL1 and BL2. From these measurements the beam waist diameter d0 ¼ 159 mm (94 mm FWHM) was determined. For ease of comparison, the full-width at half-maximum (FWHM) value is given for a Gaussian beam with the same second moment beam diameter as computed for the actual FEL pulses. The beamline is designed for a focal spot diameter of 100 mm FWHM [3]. The axial waist position z0 varies by s ¼29 mm shot-to-shot, which corresponds to a 1 m source point deviation when assuming the thin lens formula. The average beam quality for a single pulse does not reach the beam quality of the average FEL pulse. The average beam
In this paper we present beam characterization measurements for the FLASH beamline BL1 using a compact EUV Hartmann wavefront sensor. The capabilities of this device and the validity of the obtained beam parameters in the EUV range were reported in Ref. [5] based on data measured at beamline BL2. Characteristic beam parameters such as waist size and Rayleigh length are computed from the Hartmann data using the 2nd moment method. On average, we find a focal spot size of 159 mm (2nd moment) or 94 mm (FWHM) and a Rayleigh length of 144 mm for single pulses at beamline BL1. Further, an axial fluctuation of the waist position of 29 mm (pulse-to-pulse, standard deviation) is observed, corresponding to a deviation of the source point of about 1 m. The detected wavefront fluctuations (wrms and wpv) are about 10% pulse-to-pulse. Therefore, averaging over several pulses (depending on the actual application) is required for optics testing and alignment. Here, we presented the alignment procedure for the toroidal mirror, resulting in a reduction of wrms by 25%, and testing of thin solid attenuation filters regarding induced wavefront distortions. These filters can deteriorate the wavefront considerably, whereas no measurable effect is observed for the gas attenuator, as reported earlier. Furthermore, two different techniques to generate near-spherical reference wavefronts for the Hartmann sensor are compared in this paper. In addition to a pinhole-based reference obtained at FLASH with a relative accuracy of l13.5 nm/90 (wrms), a laboratory-scale laserproduced EUV plasma can be used for calibration, facilitating the use of EUV Hartmann sensors at free-electron laser beamlines. The accuracy achieved of about l13.5 nm/7.5 is sufficient for many applications.
Acknowledgements This work is partly supported by ‘‘IRUVX-PP’’, EU co-funded project under FP7 (Grant Agreement 211285). Support of the FLASH user facility, in particular the funding of wavefront sensors through the BMBF Programme FSP301-FLASH, is greatly acknowledged. We also acknowledge the support from Deutsche Forschungsgemeinschaft within SFB755 ‘‘Nanoscale Photonic Imaging’’.
Appendix A Beam diameter definition (1) follows the hyperbolic propagation law sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðzz0 Þ2 d ¼ d0 1 þ ðA1Þ z2R where z denotes the optical axis, d0 the waist diameter, z0 the waist position and zR the Rayleigh length. These beam parameters, expressed in terms of the corresponding parameters for x and y
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References
for a simple astigmatic beam, read z0 ¼
2 2 z0,x yx þ z0,y yy 2 2 yx þ yy
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi u 2 2 2u td2 þ d2 þ yx yy ðz z Þ2 d0 ¼ 0,x 0,y 0,x 0,y 2 y2x þ y2y
y¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2x þ y2y
zR ¼
2 d0
y
ðA2Þ
ðA3Þ
ðA4Þ
ðA5Þ
where the index i¼x, y denotes the transversal coordinates. Eqs. (A2)–(A5) can be verified by inserting the hyperbolic propagation law for the beam diameter in x and y directions (A1 with specified parameters for x and y) into Eq. (1) and using d2x ¼16/x2S as well as lim(d/z)¼ y for z-N.
¨ [1] B. Schafer, et al., Appl. Opt. 41 (15) (2002). [2] M. Born, E. Wolf, Principles of Optics, 6th ed., Cambridge University Press, Cambridge, 1985. [3] K. Tiedtke, et al., New J. Phys. 11 (2009) 023029. [4] M. Kuhlmann et al., in: Proceedings of FEL 2006, Berlin, 2006. ¨ [5] B. Floter, et al., New J. Phys. 12 (2010) 083015. [6] J. Hartmann, Z. Instr. 20 (1900) 47–58. [7] R. Cubalchini, J. opt. Soc. Am. 69 (1979) 972–977. [8] R.J. Noll, J. Opt. Soc. Am. 68 (1978) 139–140. [9] ISO 15367, Lasers and laser-related equipment—Test methods for determination of the shape of a laser beam wavefront, 2005. [10] J. Wyant, Education and training in optics and photonics (ETOP), 2003, EMF2. ¨ [11] B. Schafer, et al., Rev. Sci. Instr. 77 (2006) 053103. [12] A. Singer, et al., Phys. Rev. Lett. 101 (2008) 254801. [13] C. Peth, et al., J. Phys. D 41 (2008) 105202. [14] P. Merce re, et al., Opt. Lett. 28 (17) (2003). [15] K. Tiedtke, et al., J. Appl. Phys. 103 (2008) 094511. [16] ISO 11146, Lasers and laser-related equipment—Test methods for laser beam width, divergence angle and beam propagation ratios, 2005. [17] B.L. Henke, et al., Atom. Data Nucl. Data Tables 54 (2) (1993) 181. [18] A. Mare´chal, Rev. Opt. 26 (1947) 257.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam parameters of FLASH beamline BL1 from Hartmann wavefront measurements a,n ¨ Bernhard Floter , Pavle Juranic´ b, Peter Großmann a, Svea Kapitzki b, Barbara Keitel b, a b a ¨ ¨ , Bernd Schafer , Kai Tiedtke b Klaus Mann , Elke Plonjes a b
Laser-Laboratorium G¨ ottingen, Hans-Adolf-Krebs-Weg 1, D-37077 G¨ ottingen, Germany Deutsches Elektronen-Synchrotron, Notkestraße 85, D-22603 Hamburg, Germany
a r t i c l e i n f o
a b s t r a c t
Available online 13 October 2010
We report on online measurements of beam parameters in the soft X-ray and extreme ultraviolet (EUV) spectral range at the free-electron laser FLASH. A compact, self-supporting Hartmann sensor operating in the wavelength range from 6 to 30 nm was used to determine the wavefront quality of individual freeelectron laser (FEL) pulses. Beam characterization and alignment of beamline BL1 was performed with l13.5 nm/90 accuracy for wavefront rms (wrms). A spot size of 159 mm (second moment) and other beam parameters are computed using a spherical reference wavefront generated by a 5 mm pinhole. Beam parameters are also computed relative to a reference wavefront created by a laser-driven plasma source of low coherence, proving the feasibility of such a calibration and reaching l13.5 nm/7.5 wrms accuracy. The sensor was used for alignment of the toroidal focusing mirror of beamline BL1, resulting in a reduction of wrms by 25%, and to investigate wavefront distortions induced by thin solid filters. & 2010 Elsevier B.V. All rights reserved.
Keywords: Wavefront Free-electron laser Hartmann sensor EUV
1. Introduction Hartmann–Shack and Hartmann sensors are routinely used for real-time wavefront detection and laser beam characterization in the near infrared, visible and ultraviolet spectral region. Both the wavefront (directional distribution) and the beam profile (intensity distribution) of a radiation field can be recorded for a single pulse, enabling evaluation of paraxial beam parameters such as beam diameter d, divergence y, beam propagation factor M2, Rayleigh length zR, waist position z0 and waist diameter d0 for coherent radiation [1]. Solving the Fresnel–Kirchhoff integral allows also numerical propagation of the beam and thereby prediction of intensity distribution in any plane [2]. The Free-electron LAser in Hamburg (FLASH), operating in the extreme ultraviolet (EUV) spectral region, is based on the self-amplified spontaneous emission (SASE) process, which builds up laser emission from spontaneous undulator radiation. The photon beam characteristics relevant for user experiments can differ from pulse to pulse, leading to a strong requirement for single-pulse photon diagnostics and on-line characterization of the beam propagation parameters [3,4]. Recently, we reported on a compact EUV Hartmann wavefront sensor that was jointly developed by Laser¨ Laboratorium Gottingen (LLG) and DESY for photon diagnostics, beamline alignment and monitoring of FEL radiation at FLASH [5].
n
Corresponding author. ¨ E-mail address: bernhard.fl[email protected] (B. Floter).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.10.016
The validity of beam parameters, computed in the framework of second moments, was confirmed using data from beamline BL2. In this paper, we present results from measurements at beamline BL1, including determination of beam parameters relevant for many user experiments as well as alignment of the toroidal focusing mirror. One of the major challenges using the Hartmann technique is to create a known reference wavefront. Two approaches are taken here: using a laboratory-scale laser-driven plasma source and spatial filtering at FLASH. Great effort is currently undertaken to design optical elements that preserve coherence and wavefront properties of FEL pulses. The gas attenuator, developed at FLASH [3], and thin solid filters are standard techniques for intensity attenuation at FELs. Both techniques were investigated at FLASH, and it was reported that in general the gas attenuator induces less wavefront aberrations [4]. Solid filters provide other features such as very high attenuation levels and spectral characteristics that may outweigh this disadvantage in certain applications. In this context the Hartmann sensor has proven to be a useful tool for pulse resolved beamline monitoring. 2. Hartmann sensor and reference wavefront generation The setup for the Hartmann sensor is based on the ideas Hartmann [6] presented in 1900. The essential parts are the Hartmann plate, a pinhole array consisting of a 7 mm thick tantalum foil with laser drilled holes (pitch 320 mm, diameter 65 mm), which divides the incoming beam into an array of smaller beams, and a 12bit camera with a
B. Fl¨ oter et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) S108–S112
S109
The wavefront quality is given in terms of wavefront peak-tovalley wpv and wavefront root-mean-square wrms values. Tilt and the best-fitting sphere are subtracted prior to computation of these values. The selection of area of interest (AOI) for wavefront and beam profile evaluation is based on clipping of noise at a level of 1% of the full dynamic range of the camera. The largest circle inscribed into this AOI defines the evaluation radius a. Two techniques, spatial filtering at FLASH and a lab-scale EUV plasma source were used to create near-spherical reference wavefronts. For the latter, a Nd:YAG laser (1064 nm, 1 Hz, 800 mJ, 7 ns) is focused down to about 60 mm into a Krypton (Kr) gas jet (backing pressure 15 bar) centered in a vacuum chamber, producing a 250 mm 150 mm plasma (FWHM) (Fig. 1a). For blocking of outof-band radiation from the plasma a 200 nm titanium filter is used, resulting in broadband radiation (Kr XXV–Kr XXXVI) in the spectral range l ¼2.5–6.5 nm as seen from the measured spectrum in Fig. 1b. The EUV spectrometer (1–7 nm) used for the spectral investigation of the plasma source consists of a 100 mm entrance slit, an aberration corrected flat-field grating (2400 lines/mm) and a back-side illuminated CCD camera. The plasma was monitored with a pinhole camera, consisting of a CCD chip with an EUV-to-VIS quantum converter and a pinhole (diameter 50 mm) coated with a titanium foil (thickness 200 nm). A more detailed description of the EUV source is given in Ref. [13]. The Hartmann sensor described above was placed at a distance of 1213 mm from the plasma. The reference spot patterns shown in Fig. 2a were recorded, averaging over 100 frames, each containing 50 pulses. The directional characteristic of the plasma source, emitting into 4p steradian, results in a homogeneous intensity profile.
charge-coupled device (CCD) chip at the distance l¼97 mm behind the plate, which monitors the position and intensity of the beams from each subaperture. The CCD chip (1279 1023, 6.45 mm pixel size) is coated with Gd2O2S:Tb (grain size 1–2 mm, central emission wavelength 545 nm) for EUV-to-VIS conversion. The Hartmann sensor is described in greater detail in Ref. [5]. The displacement of a spot centroid Dx divided by l yields the local wavefront gradient inside one subaperture relative to a known reference wavefront. The wavefront is reconstructed from local gradients in a modal approach according to Refs. [7–9], using 37 Zernike polynomials in the ordering referred to in Ref. [10]. Summation over pixel data inside the individual subapertures samples the intensity distribution or beam profile I(x,y). The Hartmann data, consisting of sampled intensity and wavefront gradients, allows for computation of the first and second order moments of spatial (x,y) and angular (u,v) coordinates over the intensity distribution [1]. For paraxial coherent beams this information is sufficient to compute the following beam parameters: beam width d, divergence y, beam propagation factor M2, waist diameter d0, Rayleigh length zR and waist position z0 as shown in Refs. [1,11]. Influences from partial coherence are neglected in this evaluation. For our purposes, this is justified by the high degree of spatial coherence reported for the FLASH beam [12]. The computation of second moment beam parameters from the Hartmann data for EUV FEL radiation and general agreement with caustic scan techniques was reported in Ref. [5]. Once intensity and phase of a beam are known from the Hartmann measurement, the Fresnel–Kirchhoff propagation yields intensity distribution at different positions z [2].
Krypton Z = 36
Intensity /a.u.
15000
Kr XXV - XXXVI
10000
5000
0 2
3
4 5 Wavelength / nm
6
Fig. 1. Laboratory-scale EUV source: a Nd:YAG laser is focused into a Kr gas jet in a vacuum chamber, creating a plasma emitting in the EUV spectral range. A pinhole camera image is shown in (a). The radiation of the plasma is filtered by a 200 nm titanium foil, producing the spectrum shown in (b).
Fig. 2. Reference spot patterns taken at the EUV laser-driven plasma source (a) and at FLASH with a 5 mm pinhole at l ¼ 13.5 nm (b); the center pinhole on the Hartmann plate is omitted for alignment purposes.
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The FLASH-reference wavefront was created using a 5 mm pinhole [14] placed 175 mm upstream of the focal plane at beamline BL1 and 3270 mm in front of the Hartmann sensor. Focusing is produced by the beamline toroidal mirror that has a focal length of 10 m and is coated with high-density amorphous carbon, deposited by magnetron-sputtering [3]. A single FEL pulse with a typical pulse energy of 8 mJ [15] provided sufficient intensity for the CCD even after the pinhole. Throughout all measurements presented in this paper, FLASH operated at a fundamental wavelength of l ¼ 13.5 nm. For improved signal-to-noise ratio, 103 pulses were averaged to create the reference shown in Fig. 2b. Measuring the plasma source reference against the FLASH reference yields a maximal wavefront deviation of 11.4 nm or wpv ¼ l13.5 nm/1.2 and a root-mean-square of wrms ¼ l13.5 nm/7.5 on a circular AOI with the evaluation radius a¼2.84 mm. The plasma source reference turns out to be not quite uniform over the evaluation area, which might be due to the employed titanium filter. Using the 5 mm pinhole, a series of single FEL pulses was recorded against the FLASH reference, yielding an average relative single-pulse repeatability of the wavefront sensor of l/15 (wpv) or l/90 (wrms) at l ¼13.5 nm (a ¼3.04 mm). Comparative wavefront measurements were performed, leaving the sensor position unchanged and using a 137 nm Al filter. Based on the FLASH reference we find wpv ¼48 nm and wrms ¼ 9.4 nm and for the laser-driven plasma source wpv ¼ 49.3 nm and wrms ¼9.3 nm (a ¼1.81 mm), thus differing by 1.3 nm (3%) and 0.1 nm (1%) only, respectively
3. Beamline commissioning and beam characterization at BL1 The sensor was placed about 3695 mm downstream of the expected focal plane to adapt the beam size to the detector area, further using a 137 nm Al filter and a 10 mm aperture, 43 m upstream of the toroidal mirror. SASE pulse generation is a stochastic process and leads to fluctuations both in intensity and phase. These fluctuations can be observed in the wavefront as
shown in Fig. 3 for four single pulses (a¼2.72 mm). For wpv and wrms, we find a standard deviation of approximately 10%, calculated over 75 pulses. Therefore, any optics testing or alignment task at FLASH requires a certain number of averaged pulses (see Fig. 4a, b), whereas single pulse resolution is needed for characterization of the FEL beam itself. Prior to the actual measurements, the employed Al filters (thickness 200 and 137 nm) were checked for aberrations by comparing the transmitted wavefronts (Fig. 4). As seen from Fig. 4(a) and (b), showing two subsequent recordings of the wavefront behind the same 137 nm filter averaged over 16 single pulses, the FEL fluctuations are efficiently averaged out. Apparently, use of the 200 nm Al filter (Fig. 4c) leads to slight changes in the shape of the wavefront, although both wrms and wpv values are similar. In the following, the 137 nm Al filter is used, which attenuates the single pulse energy from 8 to about 0.18 mJ [17]. Before measuring the beam parameters, the focusing mirror was aligned by successively moving the mirror with respect to pitch and yaw angles around the pre-aligned position. The goal of alignment procedure with a wavefront sensor is to maximize the Strehl value, which is, according to the Mare´chal formula, equivalent to minimizing wrms [2,18]. The wavefronts (a¼ 2.23 mm) used for alignment of the BL1 toroidal mirror are shown in Fig. 5, plotted against pitch and yaw angles. A 5 mm circular aperture was placed in the FEL beam path 43 m upstream of the toroidal mirror. Four averaged camera frames, each containing a single FEL pulse, were used for centroid determination to reduce effects from shot-to-shot noise of the FEL beam. First the yaw angle was aligned such that the astigmatism is oriented along the coordinate axes. Afterwards, the pitch was adjusted, finally leading to a reduction of the wrms value by 25% from 7.2 to 5.4 nm and of wpv by 16% from 40.9 to 34.4 nm. The starting and end points of the alignment process are marked red in Fig. 5. The alignment process of the ellipsoidal mirror at BL2, which follows the same principles, is described in detail in Ref. [5]. After alignment, the second moments are measured for the full FEL beam, using a 10 mm aperture 43 m upstream of the toroidal mirror. For each of the 75 single pulses, the beam parameters are
Fig. 3. Wavefronts for single FLASH pulses on a circular AOI with 5.44 mm diameter and a 137 nm Al filter, corresponding to the data compiled in Table 1.
Fig. 4. Wavefronts measured for a 137 nm Al (a,b) and a 200 nm Al filter (c) at l ¼13.5 nm, averaged over 16 single pulses (circular AOI, 4.87 mm diameter, 37 Zernike polynomials).
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propagation factor M2 of the 75 single pulses is 7.5 whereas M2 is 6.8 for the average pulse (integrated on-chip) at BL1. From the FLASH divergence of about 90 710 mrad FWHM reported in Ref. [3] and the distance source-toroidal mirror (focal length f¼ 10 m) of 68 m, a beam diameter of d ¼10.4 mm on the mirror is calculated presuming a Gaussian beam. Estimating the divergence behind the mirror as y ¼d/f and neglecting beam clipping effects on the mirror, the diffraction limited waist diameter follows 4l/py ¼17 mm. Our measurement is in good agreement with this estimation, the diffraction limit follows d0/M2 ¼21 mm (see Table 1).
4. Conclusion
Fig. 5. Wavefronts measured during the alignment process of the BL1 toroidal mirror, plotted against pitch and yaw angles (circular AOI, 4.47 mm diameter). Starting point of the alignment process is pitch 39 mrad, yaw 0 mrad with wrms ¼ 7.2 nm and end point is both pitch and yaw 0 mrad with wrms ¼5.4 nm.
Table 1 Second moment beam parameters from Hartmann measurements at BL1 at 13.5 nm using a 137 nm Al filter and a 10 mm aperture, 43 m upstream of the toroidal mirror (averaged over 75 single pulses). The row d0 indicates the diameters in the plane z0, both in the x and y direction, and the diameter according to (A3), d0,i, gives the waist diameters in the planes located at z0,x and z0,y. Beam parameters wpv (nm) wrms (nm) Beam propagation parameter M2 Waist position z0 (mm) Rayleigh length zR (mm) Waist diameter d0 (mm) 2nd moment (FWHM) Divergence y (mrad) Waist position z0,i (mm) Rayleigh length zR,i (mm) Waist diameter d0,i (mm) 2nd moment (FWHM) Divergence yi (mrad)
x
y
8.8
6.8
174 (103)
143 (84)
3656 132 144 (85)
3824 96 108 (64)
1.09
1.13
Global 58.4 8.5 7.5 3743 144 159 (94) 1.11
computed (a ¼2.72) assuming a simple astigmatic beam, according to Refs. [1,11] and Eqs. (A1)–(A5). The parameter averages are compiled in Table 1, where the index i ¼x, y indicates the parameters for the two lateral dimensions. Other parameters are given with respect to the beam diameter definition qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ¼ 23=2 /x2 Sþ /y2 S ð1Þ for a near-circular beam [16] (Appendix A), defined as a beam with ellipticity e 40.87 [16]. For most planes, this is fulfilled at FLASH BL1 and BL2. From these measurements the beam waist diameter d0 ¼ 159 mm (94 mm FWHM) was determined. For ease of comparison, the full-width at half-maximum (FWHM) value is given for a Gaussian beam with the same second moment beam diameter as computed for the actual FEL pulses. The beamline is designed for a focal spot diameter of 100 mm FWHM [3]. The axial waist position z0 varies by s ¼29 mm shot-to-shot, which corresponds to a 1 m source point deviation when assuming the thin lens formula. The average beam quality for a single pulse does not reach the beam quality of the average FEL pulse. The average beam
In this paper we present beam characterization measurements for the FLASH beamline BL1 using a compact EUV Hartmann wavefront sensor. The capabilities of this device and the validity of the obtained beam parameters in the EUV range were reported in Ref. [5] based on data measured at beamline BL2. Characteristic beam parameters such as waist size and Rayleigh length are computed from the Hartmann data using the 2nd moment method. On average, we find a focal spot size of 159 mm (2nd moment) or 94 mm (FWHM) and a Rayleigh length of 144 mm for single pulses at beamline BL1. Further, an axial fluctuation of the waist position of 29 mm (pulse-to-pulse, standard deviation) is observed, corresponding to a deviation of the source point of about 1 m. The detected wavefront fluctuations (wrms and wpv) are about 10% pulse-to-pulse. Therefore, averaging over several pulses (depending on the actual application) is required for optics testing and alignment. Here, we presented the alignment procedure for the toroidal mirror, resulting in a reduction of wrms by 25%, and testing of thin solid attenuation filters regarding induced wavefront distortions. These filters can deteriorate the wavefront considerably, whereas no measurable effect is observed for the gas attenuator, as reported earlier. Furthermore, two different techniques to generate near-spherical reference wavefronts for the Hartmann sensor are compared in this paper. In addition to a pinhole-based reference obtained at FLASH with a relative accuracy of l13.5 nm/90 (wrms), a laboratory-scale laserproduced EUV plasma can be used for calibration, facilitating the use of EUV Hartmann sensors at free-electron laser beamlines. The accuracy achieved of about l13.5 nm/7.5 is sufficient for many applications.
Acknowledgements This work is partly supported by ‘‘IRUVX-PP’’, EU co-funded project under FP7 (Grant Agreement 211285). Support of the FLASH user facility, in particular the funding of wavefront sensors through the BMBF Programme FSP301-FLASH, is greatly acknowledged. We also acknowledge the support from Deutsche Forschungsgemeinschaft within SFB755 ‘‘Nanoscale Photonic Imaging’’.
Appendix A Beam diameter definition (1) follows the hyperbolic propagation law sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðzz0 Þ2 d ¼ d0 1 þ ðA1Þ z2R where z denotes the optical axis, d0 the waist diameter, z0 the waist position and zR the Rayleigh length. These beam parameters, expressed in terms of the corresponding parameters for x and y
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References
for a simple astigmatic beam, read z0 ¼
2 2 z0,x yx þ z0,y yy 2 2 yx þ yy
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi u 2 2 2u td2 þ d2 þ yx yy ðz z Þ2 d0 ¼ 0,x 0,y 0,x 0,y 2 y2x þ y2y
y¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2x þ y2y
zR ¼
2 d0
y
ðA2Þ
ðA3Þ
ðA4Þ
ðA5Þ
where the index i¼x, y denotes the transversal coordinates. Eqs. (A2)–(A5) can be verified by inserting the hyperbolic propagation law for the beam diameter in x and y directions (A1 with specified parameters for x and y) into Eq. (1) and using d2x ¼16/x2S as well as lim(d/z)¼ y for z-N.
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