We demonstrate delayed-frame X-ray Photon Correlation Spectroscopy with 120 microsecond time resolution, limited only by sample scattering rates, with a prototype Pixel-array detector capable of taking two image frames separated by 153 ns or less. Although the overall frame rate is currently limited to about 4 frame pairs per second, we easily measured millisecond correlation functions. This technology, coupled to the use of brighter synchrotrons such as Petra III or the NSLS-II should enable X-ray Photon Correlation Spectroscopy on microsecond time scales on a wider variety of materials.
© 2016 Optical Society of America
Visible Photon Correlation Spectroscopy (PCS) and X-ray Photon Correlation Spectroscopy (XPCS) are widely used techniques to study equilibrium and non-equilibrium thermodynamic fluctuations in condensed matter systems. These techniques are based on the obervation of speckle patterns that are generated when a coherent light source is scattered from a disordered sample and measured with high spatial resolution detectors . A speckle pattern from a fully coherent source has spatial variations as large as the spatial average. When the state of disorder of a sample changes in time, it produces a time-dependent speckle pattern which can be analyzed to reveal transport properties of the sample.
PCS blossomed with the invention of the laser, while its x-ray extension, XPCS, required the development of bright x-ray sources such as third generation synchrotron sources [1–3]. Both these techniques require a coherent source of light, but due to the limited coherent flux of synchrotron sources, significant progress in XPCS has also required advances in parallel speckle detection enabled by high spatial resolution and high gain and fidelity area detectors. Charge Coupled Device (CCD) detectors with direct detection of x-rays in the sensor have largely been used for this effort to date. This technology is capable of taking Megapixel frames with a frame rate of approximately 100 Hz [4,5]. One can also read a small area of the detector with higher frame rate, but at the expense of the number of pixels collected.
More recently, the development of Pixel Array Detectors (PAD) composed of a thick sensor coupled by bump-bonding to a complementary metal-oxide semiconductor (CMOS) application specific integrated circuit (ASIC) has increased the detection efficiency of area detectors because of the thick sensor, as well as improved the speed from the highly parallel CMOS readout technology. Commercial PADs with 0.5 mm thick Si or high atomic number sensors are now capable of frame rates above 2 kHz . We note that a research version of the commercial Eiger detector demonstrated a 20 kHz frame rate with a Mpixel detector with 4-bit counters .
Brighter sources of X-rays such as X-ray Free Electron Lasers (FEL) are now available, but their repetition rates at the moment are about 100 Hz, which compares with state of the art repetition rate of CCDs. One attractive technique to extend the time resolution in XPCS has been proposed for use at FELs. The idea is to build a split-and-delay line capable of delivering two coherent x-ray laser beams on a sample delayed from each other by an arbitrary time delay (see Fig. 1) .
In a practical instrument, this time delay is limited to a few nanoseconds due to the limitations in path length difference of a few meters. If the two delayed x-ray pulses scatter from a sample that is static on time scales set by the delay time, a speckle pattern with maximum visibility will be observed. As the delay time is increased to match the characteristic time constant of the fluctuations in the system, the speckle visibility will be reduced and one can learn from analyzing these measurements key transport properties of these condensed matter systems.
Success in this approach has recently been demonstrated using visible light . In this experimental method, two short laser pulses are delivered on a sample using an electrooptic light modulator controlled by a programmable delay generator. The pulses produce two speckle patterns that are recorded on a slow CCD camera. The time correlation function is determined from the delay time dependence of the spatial visibility of the summed speckle patterns on the camera. On the other hand, success using this approach with x-rays has been slow presumably because of the difficulty in using highly variable x-ray pulses from a XFEL in a time domain technique requiring very high wavefront and mechanical stability.
In this context, it is important to note that considerably brighter synchrotron sources are also on the horizon. The current plans for the Advanced Photon Source (APS) Upgrade calls for a Multibend Achromat Lattice delivering at least two orders of magnitude improvement in coherent flux. With such increase over today’s coherent flux, one should be able to perform sub-microsecond XPCS measurements on a wide variety of materials. Thus to push XPCS at synchrotrons to access faster time scales, one needs to develop area detectors capable of much finer time resolution.
One step in that direction is an area detector that Voxtel Inc. and the APS have recently built as part of a Small Business Innovative Research program . Each detector pixel has two gates that can be triggered with fine time resolution. The detector can thus take two images with some given integration time and separated by a set time delay . Since there are two different time scales involved in this detector, we define the frame pair period as the time delay between frame pairs (slower) and the gate delay to refer to the time delay between pairs of frames.
If these images are generated by a time-varying speckle pattern, one will be able to find the correlation function of these frames and thus sample the XPCS correlation functions by varying the time delay between these frames. Although the overall frame rate is capped at 135 frame pairs per second for this particular generation of the detector, time delays of nano or microseconds can be used with this technology .
This paper shows the first XPCS measurement that uses this novel detector technology to perform two pulse XPCS at a synchrotron. The potential of this approach is that the synchrotron beam is intrinsically more stable than free electron laser beams and complex X-ray delay lines are not needed. The detector is also capable of isolating a single APS bunch in 24-bunch mode, thus with brighter sources or pink beam, one may be able to perform XPCS with 153 ns sampling resolution or less in the future.
2. Experimental method
The experiment was performed at beamline 8-ID-I of the APS with two phased inline undulators each with a 33 mm period and set to 7.38 keV. The coherent flux was 6.2 × 109 ph/s in a 20 μm by 20 μm coherence defining slit. This slit opening is comparable to the transverse coherence lengths of the source at the sample position, and thus sets up coherent illumination of the sample. The pinhole SAXS camera included this coherence slit, followed by two guard slits adjusted to reduce the background scattering from the main beam and windows. A 3 mm diameter beamstop prevented the direct beam from hitting the detector. The energy was selected by a water-cooled double-crystal Ge (111) monochromator. The speckle size on the detector plane located a distance Rd = 5 m from the sample is
Test samples of silica nanoparticle colloids in water with a 150 nm diameter and polystyrene nanoparticles in glycerol with a 142 nm diameter were used in this demonstration. The silica colloid had a 5.25% volume fraction. The sample preparation for the polystryrene colloid in glycerol was discussed earlier . Both samples were dilute solutions, so we expect the correlation function to be controlled by simple diffusion. The viscosity of glycerol was controlled by changing the sample temperature. The maximum count rate at low wavevectors was about 3000 cts/s/pixel on the silica colloid in water as shown in Fig. 2.
The prototype Voxtel detector has 48×48 130 micron square pixels. The detector was developed for pump/probe experiments where two rapid frames can be collected within an arbitrary time-delay . For example, one measurement can be performed just before a laser beam excites a sample, one shortly after. Its minumum gate width is 10 ns, and it can isolate the 24-bunch pattern of the APS where bunches are separated by 153 ns . We used an internal shaping time below 100 ns. Typically however, for pump-probe experiments at synchrotrons, the results are accumulated over many pump-probe cycles before being readout. We used this two-frame capability to collect two independent speckle patterns but saved each pair of gated images to disk at the overall frame rate.
Each pixel is single photon counting. Ross et al describe its response as a function of intensity . A dead time correction can be applied when the count rate per pixel approaches a few MHz. Each pixel has two 15 bit counters, and the product of the maximum count rate and exposure time didn’t saturate the counters. The lower X-ray energy limit is around 2 keV. It is set by an oxide layer on the sensor. The 520 μm thick silicon sensor has a quantum efficiency of 50% at 18.3 keV. This detector has an energy resolution of 660 eV in the range of 7–12 keV.
The pixel area subtends (130/42)2 ≈ 10 speckle areas, thus we expect the speckle contrast to be reduced by a factor 10 from the beamline usual contrast (See Ref.  and references within). With the beamline CCD camera with 20 μm pixels, the contrast is typically around 35 %, so we expect a contrast of about 3.5 % with the Voxtel detector. We measured a speckle contrast of about 4% (see Fig. 3), which enabled us to collect adequate data on delay times much faster than one ms with typically about 5000 frame pairs. The experimental set up was not fully optimized in this demonstration experiment. The contrast and coherent flux could be increased in the future by focusing the x-ray beam on the sample.
The detector is designed to record 135 frame pairs per second continuously, but the frame pair frequency at the time of the experiment was limited to about 4 frame pairs per second due to programming and hardware limitations. We used the non-accumulating mode of the detector that is required for two-pulse XPCS . In pump-probe mode, two delayed frames are accumulated over many gate cycles. This mode would completely destroy the speckle contrast. The correlation function signal to noise improves with the total number of frames taken, thus improving the frame rate to its design value would greatly improve the data quality. We developed an EPICS IOC to control the camera. Python scripts enabled us to trigger the camera with EPICS channel access and save the frame pairs in HDF5 format. SPEC macros enabled us to use this python script and scan the camera timing.
Two independent trigger signals were generated with a custom built timing system phase-locked to the ring RF clock . The timing system provides an overall time delay to synchronize the detector to the x-ray bunch pattern, as well as can generate two gate signals with arbitrary widths and delay. A commercial Avalanche Photodiode Detector (APD) (Oxford Inc.) was used to adjust the timing signals sent to the detector vis-a-vis the RF clock signals. The APD detector has a few nanosecond response time. It was centered in the direct beam and located about one meter upstream of the Voxtel detector enabling timing synchronization to within a few nanoseconds. It was only used once to synchronize the detector gates to the x-ray bunches.
The timing system is also synchronized to the camera internal integration cycle through a trigger signal supplied by the camera. The camera requires a 50 microseconds settling time before it can start integration. The first gate signal was thus started 50 microseconds from the ring revolution frequency signal in order to overlap the two gates with the camera internal integration period. Figure 1 shows a simplified timing diagram for an arbitrary gate delay ΔT. The experiment timing scheme was chosen by taking the width of both pulses to be the same while the gate delay was set to their width. The widths were then doubled for the second point, quadrupled for the third point, and so on. This sampled the time delay logarithmically, while increasing the collection time as the delay time increased. This mimics in hardware the software multitau correlator algorithm .
The correlation function is written asFig. 1, with t2 > t1. We note that for exposure and delay times comparable to the bunch period, <I(q, t1)> and <I(q, t2)> could differ by several percent due to bunch charge variations. On the time scale sampled in this experiment, both intensity averages are identical. The correlations were then averaged azimuthally at fixed wavevectors over 7 bins. Pixels with equivalent wavevectors were averaged in these bins over 360° from 1.9 to 5.6 × 10−3Å−1, in fixed width regions of 6 × 10−4Å−1.
The 5000 frame pairs gave us two independent sequences to record standard time correlation functions at the low overall frame pair rate of the detector. The correlation function for the low or high channel was then calculated fromEq. (2). We modified the existing 8-ID multi-tau software  to include the two gate analysis described by Eq. (2). This software is a hybrid software from existing software on 8-ID, performing multitau time-correlation functions on traditional single frames taken for example by the first counter, and adding a data point before the frame pair period with the small delay computed from the correlation function of pairs of frames for a given gate delay. The multitau computation provides one with a good baseline, as well as takes care of slow time constants. The two independent gate sequences should yield identical correlation functions. For faster time constants, the data is collected with varying time delays between the two channels.
Figure 2 shows the measured scattered intensity from a time average of the high or low counter, plotted versus the magnitude of the wavevector. Evidently, the two gates respond identically to scattered intensities. The high and low counter data differ by less than a factor 4×10−4 over the whole range of wavevector displayed. Similar data was collected with the polystyrene samples in glycerol.
Figure 3 shows a typical correlation function for the wavevector q = 2.47 × 10−3Å−1. The solid line is a least squares fit to a simple exponential withFig. 3 is 1.04. This baseline increased at lower count rates (or higher wavevector), thus it is related to systematic errors originating from poor counting statistics. The contrast is 4.2%, which is consistent with earlier discussion about the speckle and pixel areas. The relaxation rate in Fig. 3 is 3.2 Hz. The two data sets shown are for sequential XPCS (+) in Eq. (3) and the new two-frame technique (o) in Eq. (2). They overlap quite well with the largest gate width set to 1.024 s. We note that the minimum gate width for both gates is 1 ms, while the time delay between pairs of frame is 0.27 s. This fast sampling is a factor 270 faster than the frame rate.
Figure 4 shows the relaxation rate versus q2 at −7.5 and 25 °C for latex particles in glycerol with radius r = 71 nm. The relaxation rate Γ is expected to follow simple Brownian diffusion, thus15]. The expected ratio of the viscosity of glycerol at −7.5 and 25 °C is about 26. We observe a ratio of relaxation rates at the two temperatures of 12. It is likely that the difference comes from some water contamination in the colloidal mixture as the sample is fabricated from a commercial solution of polystyrene spheres in water, mixed with glycerol, then dried in a vacuum furnace . Nevertheless, the data in Fig. 4 is well characterized by Eq. (5).
Figure 5 shows the measured time correlation for the Silica colloid for one wavevector q = 1.8925 × 10−3 Å−1. The minimum sampling time was 120 μs, and 5000 pairs of frames were collected per time delays. The error bars displayed are the error on the averaged <g2> over Np equivalent pixels in a band of equivalent wavevectors. The solid and dashed lines are given by g2(τ) = βexp(−2Γτ) + g2(∞), where g2(∞) = 1.011, the speckle contrast β = 0.042, and the relaxation rate Γ = Dq2 ≈ 1.2 kHz. The two curves show the range of the time decay of the correlation function in the band of wavevector used in the circular average. The exponentials thus have a time constant τc = 1/(2Γ) ≈ 0.43 ms.
The error bars of g2 can be computed from the following equation taken from Ref. :16]. For our experimental condition, <I> = 2300 cts/s/pixel, τ = Δt, and Np = 122. For the shortest exposure, we find σg2 = 0.0047, while the error computed from the average is 0.00574. Thus Equation (7) can be used to guide the experiment. The data differ from theory in part due to the poor counting statistics. The two shortest delay times though are several standard deviations below the expected g2 due to diffusion in water. We speculate that g2 is reduced due to charging or other non-equilibrium effects of the particles in the intense beam.
It is interesting to compare the performance of a prototype detector like the Voxtel with a single channel correlator based on a photon-counting APD. Our prototype is specified to measure 622 kpixels/s, while an APD and hardware correlator can sample at 6.5 MHz (in 24-bunch mode of the APS). Both an APD and our prototype will saturate as the count rate approaches the repetition rate of the APS, so dead time corrections become important at count rates of order 1 MHz.
A new generation of PAD detectors now offers two counters per pixels for setting different energy threshold to detect fluorescence from scattering for example. This is the case for the Pixirad and Medipix 3 detectors [6, 17]. If these two counters can be triggered by external signals as discussed in this paper, then one could get megapixel arrays with this technique. For example, a Pixirad-1 detector with 512×476 pixels can save 160 frames/s or 39 Mpixels/s while our prototype saved 13.8 kpixel/s. This is an increase of nearly a factor 3000. These new PAD detectors also have pixel areas about a factor 4 smaller than our prototype, thus one would expect the contrast to improve by a factor 4 from these measurements. The improvement in contrast would improve the signal to noise of the measurement.
We note that if a third counter could be added to the prototype’s ASIC, it might be advantageous to use this new counter to sum the product of the two frames, enabling the correlation function to be read directly from the detector. Another use of a third counter could be to measure three consecutive frames with a uniform sampling period. In this case, the correlation function could be computed twice with delay τ, and once for the delay 2τ.
Since our detector can acquire frames with short exposures, one could have analyzed the data using X-ray speckle visibility spectroscopy (XSVS) . In XSVS, one measures the spatial contrast of equivalent speckles in individual frames as a function of exposure time. The treatment requires a detailed understanding of the detector resolution, noise and spatial uniformity. Nevertheless, it can measure dynamics several times faster than standard XPCS for a given exposure . The technique developped in this paper is performed in time, in the same manner as serial XPCS, and uses the same formalism. It is easier to interpret than XSVS in systems with unknown intermediate scattering functions . A XSVS analysis was not performed on the data as it is beyond the scope of this paper.
The two-frame XPCS technique introduced in this paper can also normalize the bunch-to-bunch current variations of the APS. Every two minutes or so in top-up operation, a bunch charge increases by about 10 %. For a given filled bunch, this is done about once per hour, so the single bunch intensity will vary by 10% over an hour. The next filled bunch will also have similar but uncorrelated bunch intensity variation. With a single channel correlator, one must normalize the scattered signal to the time correlation of a monitor channel measured with another APD. We expect that our two-frame XPCS technique can normalize these variations when the gate width and gate delay is set to multiples of the 24-bunch mode period.
We note that the technique presented in this paper requires the sample to be stationary over elapsed times much larger than the gate delay spanned. For example, it took approximately 9 hours to complete the measurements that resulted in Fig. 3. There may be serious limitations to this approach in system out of thermodynamic equilibrium, with the exception perhaps of systems under periodic excitation by an external field.
We have demonstrated a novel method to measure time-correlation functions in XPCS with a detector able to record two frames separated by a delay much smaller than the frame period. We measured the time correlation function of speckle patterns from latex particles in glycerol with time delays 300 times shorter than the frame rate. Relaxation rates as high as 10 Hz were measured for this colloid.
We expect that the next generation of PAD with two counters can be programmed to take two rapid frames as shown in this experiment . This would allow much faster relaxation rates to be measured. The high instantaneous count and frame rate of our prototype detector could also be used in pump-and-probe speckle contrast studies, where a disordered sample is excited to a transient state by a laser or electric field.
We are greatful to Benjamin Pausma for interfacing the camera controls in Python. We wish to thank Adam Lee from Voxtel Inc. for his help is reconfiguring the detector firmware for XPCS experiments. This research was performed on beamline 8-ID-I of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The detector development by Voxtel Inc. was supported by the U.S. Department of Energy (DOE) Small Business Innovative Research program contract DE-SC0004235.
References and links
1. M. Sutton, S. Mochrie, T. Greytak, S. Nagler, L. Berman, G. Held, and G. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352, 608 (1991). [CrossRef]
2. S. Brauer, G. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. Mochrie, G. Grübel, J. Als-Nielsen, and D. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995). [CrossRef] [PubMed]
3. S. Dierker, R. Pindak, R. Fleming, I. Robinson, and L. Berman, “X-ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75, 449–452 (1995). [CrossRef] [PubMed]
5. T. Madden, P. Fernandez, P. Jemian, S. Narayanan, A. R. Sandy, M. Sikorski, M. Sprung, and J. Weizeorick, “Firmware lower-level discrimination and compression applied to streaming x-ray photon correlation spectroscopy area-detector data,” Rev. Sci. Instrum. 82, 075109 (2011). [CrossRef] [PubMed]
6. D. Pennicard, S. Lange, S. Smoljanin, H. Hirsemann, H. Graafsma, M. Epple, M. Zuvic, M.-O. Lampert, T. Fritzsch, and M. Rothermund, in 11th International Conference on Synchrotron Radiation Instrumentation (SRI 2012), vol. 425, J. Susini and P. Dumas, eds. (2013), vol. 425, p. 062010.
7. I. Johnson, A. Bergamaschi, J. Buitenhuis, R. Dinapoli, D. Greiffenberg, B. Henrich, T. Ikonen, G. Meier, A. Menzel, A. Mozzanica, V. Radicci, D. K. Satapathy, B. Schmitt, and X. Shi, “Capturing dynamics with Eiger, a fast-framing X-ray detector,” J. Synchrotron Rad. 19, 1001–1005 (2012). [CrossRef]
8. W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard x-ray delay line for x-ray photon correlation spectroscopy and jitter-free pump-probe experiments at x-ray free-electron laser sources,” J. Synchrotron. Rad. 18, 481–491 (2011). [CrossRef]
9. S. Lee, W. Jo, H. S. Wi, C. Gutt, and G. W. Lee, “Resolving high-speed colloidal dynamics beyond detector response time via two pulse speckle contrast correlation,” Opt. Expr. 22, 21567–21576 (2014). [CrossRef]
10. S. Ross, M. Haji-Sheikh, A. Huntington, D. Kline, A. Lee, Y. Li, J. Rhee, M. Tarpley, D. Walko, G. Westberg, G. Williams, H. Zou, and E. Landahl, “X-ray characterization of a multichannel smart-pixel array detector,” Accepted for publication in Journal of Synchrotron Radiation on September 26 2015.
11. L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84, 785 (2000). [CrossRef] [PubMed]
12. E. M. Dufresne, T. S. Nurushev, S. Dierker, and R. Clarke, “Concentration fluctuations in the binary mixture hexane-nitrobenzene with static and dynamic x-ray scattering,” Phys. Rev. E 65, 061507 (2002). [CrossRef]
13. D. Kline and S. Ross, in the Proceedings of PCaPAC 2010, Eighth International Workshop on Personal Computers and Particle Accelerators, C. Finlay, ed. (JACoW, the Joint Accelerator Conferences Website, CERN, Geneva, Switzerland, 2010), pp. 27–29.
14. L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214–3221 (1999). [CrossRef]
15. M. L. F. Nascimentoa and C. Aparicio, “Data classification with the Vogel-Fulcher-Tammann-Hesse viscosity equation using correspondence analysis,” Physica B 398, 71–77 (2007). [CrossRef]
16. T. Thurn-Albrecht, G. Meier, P. Müller-Buschbaum, A. Patkowski, W. Steffen, G. Grübel, D. Abernathy, O. Diat, M. Winter, M. Koch, and M. Reetz, “Structure and dynamics of surfactant-stabilized aggregates of palladium nanoparticles under dilute and semidilute conditions:static and dynamic x-ray scattering,” Phys. Rev. E 59, 642–649 (1999). [CrossRef]
17. R. Bellazzini, G. Spandre, A. Brez, M. Minuti, M. Pinchera, and P. Mozzo, “Chromatic x-ray imaging with a fine pitch CdTe sensor coupled to a large area photon counting pixel asic,” J. Instrum. 8, C02028 (2013). [CrossRef]
18. C. DeCaro, V. N. Karunaratne, S. Bera, L. B. Lurio, A. R. Sandy, S. Narayanan, M. Sutton, J. Winans, K. Duffin, J. Lehutad, and N. Karonis, “X-ray speckle visibility spectroscopy in the single-photon limit,” J. Synchrotron Rad. 20, 332–338 (2013). [CrossRef]