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X-ray wavefront characterization of a Fresnel zone plate using a two-dimensional grating interferometer Hongchang Wang,1,* Sebastien Berujon,1,2 Ian Pape,1 Simon Rutishauser,3 Christian David,3 and Kawal Sawhney1 1
Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, UK 2 European Synchrotron Radiation Facility, BP-220, Grenoble F-38043, France 3
Paul Scherrer Institut, Villigen PSI 5232, Switzerland *Corresponding author:
[email protected] Received August 24, 2012; revised November 27, 2012; accepted February 8, 2013; posted February 8, 2013 (Doc. ID 173627); published March 6, 2013 The x-ray wavefront downstream of a Fresnel zone plate (FZP) was characterized using a two-dimensional grating interferometer. Transverse wavefront slope maps, measured using a raster phase-stepping scan, allowed accurate phase reconstruction of the x-ray beam. Wavefront measurements revealed that the wavefront error is very sensitive to the input beam entering the FZP. A small stack of one-dimensional compound refractive lenses was used to introduce astigmatism in the probing x-ray beam to investigate the contribution of the incoming beam in contrast to the optical aberrations. Experimental data were shown to be consistent with theoretical calculations. © 2013 Optical Society of America OCIS codes: 050.2770, 340.7450, 120.3940, 120.4640.
Fresnel zone plates (FZPs) are diffractive focusing x-ray optics that are attracting increasing interest due to their ease of use and good performance: a zone-doubled FZP was able to resolve line features separated by 15 nm [1]. For general users to take full advantage of an FZP, the effective performance of these devices needs to be quantified with high accuracy, and if possible with only moderate effort. This creates the need for a reliable and fast method to routinely characterize and optimize the performance of FZPs on synchrotron x-ray beamlines. Several techniques have been developed to characterize the imperfections of FZPs at the submicrometer scale. For instance, the knife-edge technique is a valuable tool for focus size characterization, but it does not permit an in-depth and workable evaluation of the performance of the focusing optic. This technique can also be difficult to implement for optics with extremely short focal lengths. To solve several experimental problems, researchers usually measure the wavefront away from the focal position, as this allows easier and better quantitative characterization and subsequent corrections of optical imperfections. The ptychographic coherent diffractive imaging method has recently been used to perform wavefront characterization [2]. However, for successful reconstructions, this technique requires highly coherent x-ray beams, and can be time consuming, as several hundred images are required per reconstruction. The use of x-ray grating interferometers (GIs) for atwavelength metrology is now spreading. This technique was shown to be successful for accurate measurement of wavefronts downstream of refractive x-ray lenses, mirrors, and monochromators, using one-dimensional (1D) GI [3–5]. An important limitation of this 1D GI is that measurements can only be recorded in one transverse direction at a time, often leading to reconstruction artifacts. Recently, a two-dimensional (2D) x-ray GI has been demonstrated, which is able to simultaneously recover the differential phase in both horizontal and vertical directions [6–8]. In this Letter, we employ a 2D GI to characterize the diffracted x-ray wavefront of a beam after passing 0146-9592/13/060827-03$15.00/0
through an FZP and investigate the corresponding aberrations. The wavefront phase gradient in two orthogonal directions was retrieved simultaneously from a single GI scan. Furthermore, in order to investigate the accuracy of the measurements and the contribution of the incoming beam, a small stack of 1D compound refractive lenses (CRLs) was used to generate variable astigmatism in the probing wavefront. Experiments were performed at the Diamond Light Source beamline B16 with x rays produced by a bending magnet (BM) on a 3 GeV storage ring [5,7]. An x-ray energy of 8.2 keV was selected using a Si(111) double crystal monochromator. As presented in the schematic in Fig. 1, the FZP, the order sorting aperture (OSA), and the 2D GI were mounted on three different motorized towers of an optics test bench. Upstream of the FZP, a slit was used to select different sections of the incoming beam. The FZP under investigation had an aperture of 200 μm, and its outermost zone width was 100 nm. The FZP was made from Au with a zone height of ∼1 μm on a silicon nitride membrane [9]. At 8.2 keV, the FZP focal length, f Z , was 132.4 mm with efficiency greater than 10%. The FZP was mounted at a distance of L0 L1 46 m downstream from the BM source. No central stop was used for the zone plate, but an OSA with a diameter of 10 μm was placed in the focal plane to select only photons from the first diffraction order of the FZP.
Fig. 1. (Color online) Optical layout of the experiment used for in situ characterization of an FZP using a 2D GI. © 2013 Optical Society of America
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The stack of 1D CRLs containing six lenses was mounted on a stage located at a distance L1 2 m upstream from the FZP. CRLs were made from beryllium with a radius of curvature of 0.5 mm at the apex of the lens; the theoretical focal length f c of the CRL stack is 8.3 m. Linear translation motors permitted the removal of the stack of CRLs from the x-ray beam. The introduction of the CRLs into the beam moved the combined CRL–FZP focus by 2.5 mm upstream, as predicted by the standard lens equation as applied to the two sequential optics. The 2D grating shearing interferometer consists of a checkerboard-pattern phase grating G1 , with a periodicity p1 3.576 μm, and an absorption grating G2 with a pitch p2 2.000 μm. Gratings were fabricated using deep reactive ion etching in silicon. The accuracy of grating periodicity can be controlled to within 1 nm [10]. Hence, the effect on the wavefront from grating defects was minimal and was neglected in subsequent measurements. The grating G1 was placed at a distance L3 556 mm downstream from the focal plane of the FZP, and the intergrating distance of G1 to G2 was set to L4 36.4 mm, corresponding to the third fractional Talbot order. Interferograms at the end of the system were recorded with an x-ray 2D CCD detector with a pixel size of S p 6.4 μm. 2D phase-stepping raster scans of 8 × 8 steps were performed over one grating period in both transverse beam directions. Figure 2 shows images (a), (b), and (c) corresponding to three acquisitions taken at different lateral positions of the grating. Fig. 2(d) displays the recorded intensity, at the point marked by a cross, as a function of the lateral G2 position. The maximum intensity was ∼2000 counts, and the visibility of the moiré fringe was greater than 50% [4]. Hence, the limit encountered within interferometers set by the lowest exploitable photon statistics was not encountered in that case [11]. A Fourier-based method allows independent analysis of the signal in each pixel. Using this algorithm, the two orthogonal fringe phases φx x; y and φy x; y of the 2D moiré pattern recorded in each pixel [Fig. 2(d)] can be retrieved [8]. Fringe phases are proportional to the wavefront differential phase ϕx x; y and ϕy x; y, and therefore related to the wavefront phase profile Φx; y through [6,8]
p2 ϕx x; y ≡ ∂Φx;y λL φx x; y ∂x 4
p2 ϕy x; y ≡ ∂Φx;y λL φy x; y ∂y 4
;
transverse phase gradients have been calculated, the total 2D wavefront phase Φx; y is reconstructed by solving a Poisson equation using a pseudo-inversion matrix algorithm. An average wavefront radius of curvature R was derived by fitting the reconstructed wavefront with an ellipsoid. To deal with the zeroth-order, a mask was used in the data processing to select only pixels of interest identified by two intensity thresholds [7]. Since no reference beam was removed from the data, the wavefront error downstream is not solely related to manufacturing defects of the FZP, but is also a function of imperfections in the incoming beam. [2] In order to isolate the effects of the upstream beam, the x-ray wavefront of the FZP was measured without the CRL stack inserted into the beam and at two incoming beam positions by moving the upstream slit and FZP. The offset between the two parts of the beam used was 0.5 and 1.5 mm for the horizontal and vertical directions, respectively. As displayed in Figs. 3(a) and 3(b), the reconstructed wavefronts showed spherical shape. The measured horizontal wavefront curvatures Rh were 556.2 and 556.3 mm for the two slit positions. In the vertical direction, the measured wavefront curvatures Rv were both 556.8 mm. These calculated wavefront curvatures are in good agreement with distances L3 556 mm physically measured between the phase grating G1 and the FZP focal position. However, after removing the ideal ellipsoidal wavefront, one can see from Figs. 3(c) and 3(d) that the wavefront errors are different from each other. The standard deviations of the wavefront error were 2.8 × 10−2 nm and 3.8 × 10−2 nm for slit positions I and II, respectively. This important discrepancy tends to show that the distortion of the measured wavefront is due to the incoming beam entering the optics rather than the FZP defects. In an attempt to generate the defect of the incoming beam and confirm the previous deductions, wavefront changes in the incoming beam were introduced by rotating the CRLs around the optical axis by an angle varying
1
where λ is the x-ray wavelength. The measured differential phase shifts represent the deviation in the propagation direction of the local wavefront. Once the two
Fig. 2. (Color online) Three images (a), (b), and (c) from the raster scan, corresponding to acquisitions taken at different grating G2 positions. The recorded intensity at the marked point is plotted in (d).
Fig. 3. (Color online) Wavefront reconstructions (top) and corresponding wavefront error (bottom) at two incoming beam positions, I (a), (c) and II (b), (d) without 1D CRLs in the beam.
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not sufficient to detect the outermost feature of an FZP due to limited spatial resolution, it demonstrates the capability to perform the in situ wavefront characterization. In principle, it should be able to examine the defects or deformations of an FZP by testing the wavefront at different incoming beam positions. The fine characterization of an FZP also showed that the performance of the optic is not only limited by the manufacturing but also by the incoming beam defects. Great care should be taken to disentangle these issues so that the focusing performance can finally be improved either by optimizing the manufacture parameters, or changing the mounting structure, or by correcting the aberration of the incoming beam. In parallel, the 2D GI could be used as an online setup permitting focusing optimization, for example, by assisting in the alignment an FZP or compensating for the stigmatism of an incoming beam. Fig. 4. (Color online) Wavefront (top) reconstructions and corresponding wavefront error (bottom) with 1D CRLs at 0° (a), (c) and 90° (b), (d).
from θ 0° to 90°. The slit position was same with case I in Fig. 3. As shown in Fig. 4(a), when the orientation of the CRL stack was θ 0°, the vertical wavefront curvature was of 556.9 mm, equivalently to the setup without the CRL stack. However, the horizontal radius of curvature changes by 2.5 mm, which corresponds to the astigmatism introduced into the beam. For the θ 90° case, shown in Fig. 4(b), the vertical wavefront curvature was 559.3 mm, as a stronger focusing occurs in the vertical direction, and mm in the horizontal direction. This discrepancy of 2.5 mm is consistent with the predicted change in the focal position of 2.4 mm. The large spatial period features of the wavefront errors for the two cases, displayed in Figs. 4(c) and 4(d), are largely independent of the orientation of the CRLs, and hence permit us to conclude that the majority of the wavefront errors downstream from the FZP are not caused by the CRLs. In addition, some of the wavefront errors are similar to those observed without CRLs in the beam in Fig. 3(c), giving further evidence that these effects are mainly due to defects of the beam upstream from the FZP. In this instance, the spatial resolution was limited by the detector resolution rather than the shear distance of the first grating: S P ∕M 1.5 μm, where M is the magnification ratio M L4 ∕L3 4.3. This limitation can be reduced by using a detector with smaller pixels or by increasing the magnification ratio, though at the cost of an angular sensitivity decrease. Although the 2D GI is
This work was carried out with the support of Diamond Light Source Ltd. UK. The authors are also grateful to Yong Chu and Hanfei Yan from NSLS II for providing the CRLs and Joan Vila-Comamala for fabricating the FZP used in this experiment. The authors also thank Andrew Malandain for his technical assistance and Simon Alcock for correcting the manuscript. References 1. J. Vila-Comamala, S. Gorelick, E. Färm, C. M. Kewish, A. Diaz, R. Barrett, V. A. Guzenko, M. Ritala, and C. David, Opt. Express 19, 175 (2011). 2. J. Vila-Comamala, A. Diaz, M. Guizar-Sicairos, A. Mantion, C. M. Kewish, A. Menzel, O. Bunk, and C. David, Opt. Express 19, 21333 (2011). 3. T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005). 4. A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, J. Synchrotron Radiat. 17, 299 (2010). 5. H. Wang, K. Sawhney, S. Berujon, E. Ziegler, S. Rutishauser, and C. David, Opt. Express 19, 16550 (2011). 6. S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, Appl. Phys. Lett. 99, 221104 (2011). 7. S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, Opt. Lett. 37, 1622 (2012). 8. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010). 9. S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, J. Synchrotron Radiat. 18, 442 (2011). 10. S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013). 11. W. Yashiro, Y. Takeda, and A. Momose, J. Opt. Soc. Am. A 25, 2025 (2008).
