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We have implemented a modified Young’s double slit experiment using pinholes with tunable separation distance coupled with compound refractive lens for hard X-ray spatial coherence characterization. Varying distance between the apertures provides a high sensitivity to the determination of spatial coherence across a wide range of experimental parameters. The use of refractive lenses as a Fourier transformer ensures far field registration conditions and allows the realization of a very compact experimental setup in comparison with the classical Young technique and its derivatives. The tunable double aperture interferometer was experimentally tested at the ESRF ID06 beamline in the energy range from 8 to 25 keV. The spatial coherence and the source size were measured by evaluating the visibility of the interference fringes at various separation distances between the apertures and this value agrees very well with the data obtained by other techniques. The proposed scheme can be used for comprehensive characterization of the coherence properties of the source on low emittance synchrotrons in the hard X-ray region.
© 2016 Optical Society of America
1. Introduction
In recent years, continuous development of synchrotron sources, such as 3rd generation synchrotrons and free electron lasers, has resulted in a dramatic increase of coherence properties of a photon beam especially in the hard X-ray region. The availability of such highly coherent and brilliant X-ray beams has triggered the development of a number of new experimental methods based on coherence and expanded the application area of existing techniques such as phase contrast imaging, X-ray photon correlation spectroscopy, coherent diffraction imaging and interferometry [1–8]. The knowledge of the spatial coherence properties of the beams at X-ray sources is crucial for the scientific community and is very essential for the improvement of existing and development of new methods and instrumentation. There are number of approaches to the measurements of coherence such as fitting of a known diffraction pattern from the boron fiber or slits, direct imaging of the source with lenses, dynamical diffraction, the Talbot effect and shearing interferometer, dynamical near-field speckles formed by scattering from colloidal particles [9–14]. The single shot based coherence properties of hard x-ray pulses from the LCLS and SACLA sources were measured by analysing coherent diffraction patterns from colloidal nano-particles [15–17]. One classical way to characterize the coherence is the Young’s double slit experiment where interference of two coherent beams created by two narrow slits occurs. This is a direct and straightforward technique to measure the spatial coherence and is widely used in the soft X-ray region [18,19]. Although this is a quite challenging technological task in hard X-ray domain, this interference has been demonstrated and visibility of fringes as a function of slit separation was measured [20–22]. An extended Young’s interference experiment using a stream of bimodal gold particles was used to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses at SACLA [23].
A significant decrease of the synchrotron source size to a few microns makes its determination and the spatial coherence measurement more difficult. It is necessary to probe the different coherence length which requires in turn a set of pinholes with different split distances, and this obviously complicate the measurements. In addition, reducing the wavelength substantially increases the far field observation distance. In this letter we propose very compact experimental setup consisting of two apertures with variable separation distance and a compound refractive lens allowing to fulfil the required far field conditions.
In order to address the question of the sensitivity of the double slit interferometer let us perform some estimates for the interference fringe pattern created by the source at third generation synchrotrons. A far field intensity distribution downstream of the interferometer might be expressed as [24]:
where D is the distance between slits, s is the source size applying the van Cittert–Zernike theorem, d is the slit size, L is the interference pattern observation distance, LS is the distance from the source to the interferometer, Ib is a background intensity, x is the vertical coordinate at the detector plane. The quality of the fringes can be estimated using the fringe visibility parameter: V = (Imax - Imin)/(Imax + Imin)*100%, where Imax and Imin are irradiances corresponding to the maximum and adjacent minimum on the interference pattern, respectively.Let us consider the record vertical source size at the ESRF storage ring, which is in the order of 10 μm [25]. Using the Eq. (1) we calculated the far field interference fringe patterns for double slits located at 50 m from the source and which were illuminated by 12 keV X-rays. The fringe visibility for the 100 μm and 400 μm slit separations is 93% and 24% correspondingly. To pinpoint the argument, we estimated the visibility of the interference fringes for the source size of 12 μm. It was found that considering the 100 μm slit separation the visibility for these two sources differs only by 3%. While for 400 μm slit separation the difference in the visibility is 20%. Clearly the sensitivity of the interferometer for the measurements of the source size or spatial coherence length is much higher for the large gap between the slits. On the other hand the slit splitting distance should not exceed the spatial coherence length: lcoh = λLs / s, which for the discussed above parameters is in the order of 500 μm.
Let us now assess the requirements to satisfy the criteria for measuring the Fraunhofer diffraction pattern. The far field observation distance defined as z >> D2/λ for the slit separation of 400 μm should be much larger than 1600 m. Knowing that the real or effective source size is in the order of 40 μm due to the instability of the optical elements, then the spatial coherence length or reasonable gap between the slits approaching 100 μm that reduces the observation distance by a factor of 16, however it is still too far. It is worth noting that the longest beamline at the ESRF is around 150 m. But in classical optics the Fraunhofer diffraction pattern can be observed at distances much closer than implied by mentioned above relation if lenses are used. It is well known attribute of a convergent lens, in the case of a plane wave illumination, at the back focal plane of the lens the Fourier transform occurs and this image is considered as a far field image [26]. This opportunity is widely applicable in the visible optics and, particular, in the interferometry. The X-ray compound refractive lens is a normal conventional lens and all the properties of the lens can be applied to it [27,28]. We would like to stress that refractive lenses have been already used to perform Fourier transform for high resolution X-ray diffraction [29,30].
2. Interferometer manufacturing
To manufacture the tunable double slit system, the high quality disk apertures for use in a scanning electron microscope (SEM) were chosen. These apertures were manufactured to tight tolerances with precision drilled holes. The discs were produced from a platinum and the apertures were made with a size of the hole d = 11 μm. The diameter of the round substrate was 2 mm. The minimum thickness of the aperture is above 25 µm, whereby the attenuation of X-rays below 25 keV is above 99%, which means the transparency of the material can be excluded from the consideration. Using the Leica EM TXP target surfacing system the aperture substrates were cut from the side at distances about 80 – 90 μm from the center of the hole. The SEM image of the cutout aperture is shown in Fig. 1(a).
Fig. 1 (a) SEM image of the cutout platinum aperture. (b), (c) Schematic view of possible apertures arrangements.
The apertures were located at the separate translation stages allowing their straightforward alignment in the X-ray beam. As the source is much smaller vertically, the apertures were arranged so that the upper aperture was moved relative to the lower one in the vertical direction. In order to provide the possibility to change the distances between the holes in the apertures, they were installed with the overlapping of its cut off parts, as shown in the Fig. 1(b). To avoid the primary beam passage between the holes, the minimum overlapping of the apertures was limited by 10 μm. The maximum overlapping was in the order of 80 - 90 μm, so that the split distances between holes varied in the range 90 - 160 μm. To achieve greater values of split distances, one pinhole has to move relative to the other one along the edge of the cut. In order to maintain the vertical displacement of holes, the system of 2 pinholes was rotated in the necessary direction around the imaginary center between holes as shown in the Fig. 1(c). Such an arrangement easily permits to achieve the separation distances up to few hundred microns and therefore allows to measure the coherence length ranging from 50 till 500 μm which corresponds to the source size between 100 and 10 μm.
The distance between the apertures along the beam was about 2 mm which is negligible compared with the distances from the interferometer to the source and the detector, so we can assume that the apertures are located at the same plane.
3. Experiment
The experimental tests of tunable double apertures were carried out at the Micro Optics Test Bench (MOTB) at the ID06 ESRF beamline. The beam was produced by an in-vacuum undulator and desired X-ray energies in the range from 8 keV to 25 keV were selected by a cryogenically cooled Si (111) double crystal fixed exit monochromator. To reduce the influence of the third undulator harmonic, the second crystal of the monochromator was slightly detuned from the Bragg position. The detuning angle was around 10 µrad (2 arc. sec.) to provide the remaining fundamental harmonic flux of about 80%. Interference patterns were recorded with a high resolution CCD camera equipped the fluorescence screen and optical objective providing a spatial resolution about 1.3 μm (0.65 μm effective pixel size). Thetypical exposure time varied between 20 s and 60 s depending on the aperture separation and the current of the storage ring during a 7/8 + 1 beam bunch mode (~200 mA current). To verify the measurements of the source by the Young double aperture apparatus we have measured the source size using other techniques such interference pattern produced by the B-fiber [9] and source imaging by refractive lenses [10]. The determined vertical source size during the experiment was 40 µm which is in a good agreement with the measurements carried out at this beamline earlier.
In the primary step, we placed the interferometer in the first experimental hutch at the distance of Ls = 56 m from the source as shown in Fig. 2(a). To register the interference pattern, X-ray CCD was located at the distance L = 15.2 m from the interferometer in the second experimental hutch. We would like to stress that it is the largest available distance at ID06 for this type of experiments. The recorded interference pattern and the intensity variation obtained for the line through the center of the pattern are shown in Figs. 2(b) and 2(c), respectively. The interferogram was measured at 11 keV photon energy and for 90 μm slits separation. The period of the interference pattern was 18 µm, which is in a good agreement with the calculated one using the Eq. (1). However, the fringe contrast, measured at the center of the interference pattern, is in the order of 40%, that is significantly lower than expected for the source size of 40 µm which should be about 55%. Obviously the discrepancy between the predicted and the experimentally measured values of the visibility is caused by the fact that the far field conditions are not satisfied.
Fig. 2 (a) The sketch of the Young double slit interferometer setup. (b) The 90 degree rotated registered interference pattern for 90 µm separation of pinholes. (c) The intensity variation obtained for the line though the centre of the fringe pattern
In the second step, we combined our tunable double aperture interferometer with the refractive lens as a Fourier transformer. The compound refractive lens (CRL) was comprised of 6 Beryllium parabolic lenses with 200 µm radius of parabola apex giving the focal length F = 4.15 m at 9.2 keV illumination energy. The CRL was mounted on the stage with all necessary rotation and translation movements at the distance 55 m from the source [see Fig. 3(a)]. The interferometer was located at the distance L0 = 20 cm in front of the lens, that was the shortest practically feasible distance to accommodate the tunable slits apparatus. To record the interference pattern, the X-ray CCD camera was placed at the distance L1 = 4.4 m from the lenses, where the lens forms an image of the source. We would like to stress the fact that 20 cm distance between interferometer and lens does not affect the quality of the interference pattern. It is easy to estimate that the developed diffraction pattern at the lens position will be broadened only by several microns (λL0 /d < 3μm) that compared with 900 μm lens effective aperture is negligible.
Fig. 3 (a) The experimental setup for the lens coupled tunable Young double pinhole system. (b, c) Interference patterns rotated by 90 degree recorded with the aperture separation of 90 μm with and without CRL. (d, e) Intensity distribution across the interference patterns shown in (b) and (c) respectively.
The recorded far field interference pattern and the intensity variation obtained for the line through the center of the pattern are presented in the Figs. 3(b) and 3(d) respectively. The period of the interference pattern was 6.5 µm, which is in agreement with theoretical calculations. The interference fringe contrast, measured at the center of the pattern, increased to 57% for the 90 µm pinhole separation which corresponds to the value for the approximate source size of about 40 µm.
To emphasize the validity of our technique, we recorded the interference pattern at the same distance without the lens, which is presented in Fig. 3(c). It is obvious that distance of 4.6 m is not large enough to observe the overlapping of two diffraction cones from individual pinholes giving a very poor visibility in the order of 5% [Fig. 3(e)].
In the final step, we recorded the interference patterns from the apertures with the separation distances varying between 90 and 130 μm. Experimentally determined values of the fringe visibility (dots) for different apertures separation distances are presented in Fig. 4. The error bars represent the standard deviation of the fringe contrast calculated from errors for Poisson statistics [31]. The fringe visibility reduces as a function of slit separation. The numerical evaluation was carried out by fitting of the well-known χ2 functional. The best agreement was obtained for the source size of 39.7 ± 1.3 µm (best fit, χ2 = 0.2). This value is in full agreement with the result of the measurements of the source performed by refractive lenses earlier (40 µm).
Fig. 4 Measured fringe visibility (dots) as a function of the slits separation. Error bar represent the standard deviation of the fringe contrast. The solid line is a theoretical fit for the source size of 39.7 μm.
4. Conclusion
In conclusion, we have demonstrated operation of the double slit interferometer using pinholes with tunable separation distance coupled with compound refractive lens for hard X-ray spatial coherence characterization. Varying distance between the apertures provides a high sensitivity to the determination of the coherent properties of the source on low emittance synchrotrons in the hard X-ray region. The effective vertical source size of 39.7 ± 1.3 µm was determined, which is in excellent agreement with independent results given by other well established techniques.
The use of refractive lenses as a Fourier transformer makes possible to meet the far field registration conditions and greatly simplifies the scheme allowing the realization of a very compact experimental setup in comparison with the classical Young technique and its derivatives. It should be noted that some compact setups to characterize the coherence at free-electron lasers were reported recently [19,20], where X-ray focusing optics is used to shorten the transverse coherence length and interferometer devices are placed at the focus position.
Finally, we would like to stress the fact that it is also possible to use our device to reveal the coherence propagation through a single optical component or the whole experimental setups at present high energy synchrotrons. In view of the future upgrade of the accelerator based sources our system will be particularly useful for the optimization of the parameters of electron beam optics including the emittance, since the length scale over which the coherence length will be measured is very large. We also foresee that the tunable pinholes interferometer could become a viable tool for single-pulse coherence characterization measurements at free-electron lasers.
Acknowledgments
The authors are very grateful to C. Detlefs and P. Wattecamps for their help and support during the experiments at ID 06 beamline. The authors thank O. Konovalov for the helpful discussions. The work was supported by the Ministry of Science and Education of Russian Federation grants Nº 14.Y26.31.0002.
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