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LETTERS to NATURE Observation of Speckle by Diffraction with Coherent

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LETTERS to NATURE Observation of Speckle by Diffraction with Coherent LETTERS TO NATURE shows the scattering geometry. The nominal size of the wiggler Observation of speckle by 4 source is 0.4 mm in the horizontal and 0.1 mm in the vertical . A wavelength of 0.155 nm was selected by a specially designed diffraction with coherent X -rays 5 double crystal silicon (Ill) monochromator • A coherent beam of X-rays was obtained by placing either a 2.5-j.Lm or 5 iJ.m M. Sutton*, S. G. J. Mochriet, T. Greytakt, nominal diameter pinhole 28 m from the source. The collimated S. E. Nagler*, L. E. Berman§, G. A. Heldll beam was then diffracted by the sample, which was located & G. B. Stephensonll 40 mm behind the pinhole. A second, analysing pinhole was placed 1 m from the sample and the scattered intensity profile * Department of Physics, Centre for the Physics of Materials, measured by counting the photons that passed through this McGill University, Montreal, Quebec, Canada H3A 2T8 pinhole as it was scanned in and perpendicular to the scattering t Department of Physics, Massachusetts Institute of Technology, plane (the 28 and a directions, respectively). Cambridge, Massachusetts 02139, USA To verify that our X-ray source provided the required trans­ t Department of Physics, University of Florida, Gainesville, verse coherence, we measured the Fraunhofer diffraction pattern Florida 32611, USA § National Synchrotron Light Source, Brookhaven National Laboratory, of the collimating pinhole by removing the sample and bringing Upton, New York 11973, USA the detector angle, 20, to near zero. Figure 2 shows the diffraction II IBM Research Division, Thomas J. Watson Research Center, patterns in the 20 direction for the 2.5- and 5-j.Lm pinholes. Yorktown Heights, New York 10598, USA Diffraction profiles in the a direction are similar. The solid lines are the fits to Fraunhofer diffraction patterns of circular aper­ REFLECTED light from a coherent light source such as a laser tures3 convolved with the acceptance of the analysing pinhole. shows a graininess known as speckle. In general, a speckle pattern The fitted aperture diameters of 2.9 and 4.5 iJ.m agree well with is produced whenever randomly distributed regions of a material the pinhole sizes measured by electron microscopy. The introduce different phase shifts into the scattering of coherent observed shape of the central peak and the positions of the incident light. If the arrangement of the regions evolves with time, subsidiary minima and maxima of the measured patterns agree the speckle pattern will also change. Observation of the intensity well with the theoretical curve, indicating that the transverse fluctuations at a single point in the speckle pattern provides a coherence length of the source is at least 5 iJ.m in both the direct measure of the time correlation function of the horizontal and vertical. 1 2 inhomogeneity. This leads to a technique • , alternatively called In conventional diffuse X-ray scattering with incoherent light, light-beating spectroscopy, dynamic light scattering or intensity the angular width of a peak is -A/ g where g is the average fluctuation spectroscopy, which has been widely used with visible domain size. Such a diffuse peak results from the incoherent light to study processes such as critical fluctuations near phase sum of the scattering from different domains. With coherent transitions in fluids and the diffusion of particles in liquids. But light, the coherent sum of the scattering from a random array it is not possible to study processes involving length scales less of domains results in a speckle pattern modulating the diffuse 6 than about 200 nm, or those in opaque materials, using visible peak . The angular extent of each 'speckle' is comparable to the light. If intensity fluctuation spectroscopy could be carried out width of the central peak in the Fraunhofer diffraction pattern using coherent X-rays, however, one could probe the dynamics of of the collimating pinhole, as this corresponds to a change of processes involving atomic length scales in a wide range of A in the largest path-length difference. This width is -A/ L, materials. Here we show that by using a high-brilliance X-ray where Lis the beam diameter. If, instead of diffuse scattering, source it should be possible to perform this type of measurement we consider Bragg diffraction from a highly ordered sample using radiation of wavelength -0.15 nm. Specifically, we have (g"' L ), the complete peak is the size of a single speckle. We observed a speckle pattern in the diffraction of coherent X-rays confirmed this by measuring the ( 11 I) peak of a perfect silicon from randomly arranged antiphase domains in a single crystal of crystal which simply reproduced the Fraunhofer diffraction pat­ the binary alloy Cu3 Au. tern of the collimating pinhole. Because of the limited intensity To obtain a speckle pattern, the incident beam must be of our coherent beam, the optimum condition to observe a sufficiently coherent. With visible light this is typically achieved speckle pattern is obtained with a diffuse peak not too much with a laser source, but it is possible to use an incoherent source, broader than A/ L. such as a mercury arc lamp2 or, as in our case, an X-ray wiggler, We chose to measure the diffuse (001) peak from an ordered provided that it is suitably collimated and monochromatic. The single crystal of Cu3 Au. The structure of such a crystal consists coherent intensity so obtained depends directly on the brilliance of a random arrangement of antiphase domains, which arise of the source. To resolve speckle, the difference in the path because of the four equivalent ways in which the Cu3Au unit 7 lengths of rays scattered by different parts of the sample must can occupy the underlying crystal lattice • Neighbouring not be much greater than the longitudinal coherence length of domains differ only by a phase shift in the periodic occupation the incident beam. This is equal to A2 /2SA, where A is the of lattice sites by this unit. By an appropriate heat treatment, wavelength and SA is the distribution of wavelengths. In addi­ the crystal was prepared with an average domain size of a few tion, the incident beam size must not be much greater than the transverse coherence length3, given by ARsf2d" where R, is the distance from the source and d, is the source size. For a typical X-ray wavelength, A= 0.15 nm, a silicon (111) monochromator detector 4 gives SA/ A= 1.4 x 10- , which results in a longitudinal coherence length of -0.5 iJ.m. For a 0.3-mm-diameter synchrotron source at R, =30m, the transverse coherence length is -7 iJ.m. Thus an X-ray wiggler source with a brilliance of 10 15 photons s- 1 mrad-2 mm-2 per 0.1% bandwidth, when collimated 0 monochromatic through a 5 iJ.m pinhole, is expected to deliver a usable coherent ~ X-rays beam of -3 x 105 photons s-• . As we shall demonstrate, it is collimating possible to obtain sufficient coherent intensity with current pinhole wiggler X-ray sources to perform scattering measurements from certain types of samples. FIG. 1 Schematic representation of the scattering geometry. The angle 211 The experiments were performed using the X25 wiggler beam­ is shown; a (not shown) is the corresponding angle in the direction normal line at the national synchrotron light source (NSLS). Figure 1 to the scattering plane (normal to the page). 608 NATURE · VOL 352 · 15 AUGUST 1991 LETTERS TO NATURE 5 is 2L sin 0, where Lz is the penetration depth normal to the 10 7 a surface. For Cu3 Au, L 7 = 0.6 f.lm. en Figure 3 shows a photograph of the speckle pattern observed 0 from this Cu3 Au crystal. It was obtained by placing film (Kodak '<:t DEF) at the analyser position. A 2.5-t-Lm collimating pinhole 3 was used. The diffuse peak is seen to be made up of small g_ 10 intense spots. The angular extent of each spot is comparable to en that of the central peak of the Fraunhofer diffraction pattern of ....c the pinhole (A/ L =50 f.lrad). A more quantitative measurement ::J H is presented in Fig. 4, which shows the scattering patterns 0 () 1 obtained using 2.5-, 5- and 50-f.lm collimating pinholes with 50-, 10 25- and 100-f.lm analysing pinholes, respectively. For the first en b two cases, the observed angular sizes of the intense spots are 0 -50 and 25 f.lrad, respectively, again in good agreement with (") 4 A/ L. The measurement using the 50-f.lm collimating pinhole is ..... 10 Q.l included for comparison. It is equivalent to a conventional 0. incoherent X-ray measurement, because 50 f.lm is larger than ....en 3 the coherence length of the source. c 10 The observed structure in the (001) peak cannot be explained ::J .... by a topographic imaging effect, where each of the intense spots 0 H () arises by independent diffraction from a small region of the 2 illuminated area. This is ruled out because diffraction from a 10 -0.2 -0.1 0.0 0.1 0.2 region much smaller than L would spread over an angular region much larger than A/ L. As the observed size of the intense spots 2e (mradl is comparable to A/ L, they must arise by diffraction from the FIG. 2 Fraunhofer diffraction from a, 2.5-f.lm and b, 5-f.lm nominal diameter full illuminated volume. pinholes. Error bars due to counting statistics are smaller than the symbol size.
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