X-ray multi-probe data acquisition: A novel technique for laser pump x-ray transient absorption spectroscopy

Laser pump X-ray Transient Absorption (XTA) spectroscopy combines advanced laser technologies with the high flux and stability of modern synchrotron facilities. The insight of hard x-ray spectroscopy in the context of pump–probe measurements yields information about excited state structural dynamics that is inaccessible with laser spectroscopy techniques alone.

Most synchrotron-based time resolved spectroscopic techniques in the 1980s and 1990s neglected the intrinsic temporal structure of the synchrotron radiation, yielding a time resolution limited by other aspects of the experimental apparatus or data acquisition (DAQ) technique.^1–5 Around the year 2000, at least two groups began developing XTA techniques with a time resolution limited only by the width of the synchronized x-ray probe pulse (or group of pulses). The first published work from such a technique came from Chen at the Advanced Photon Source (APS), who measured the excited state X-ray Absorption Near Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) of NiTPP-L₂ molecules (NiTPP: nickel tetraphenylporphyrin and L: piperidine)^6,7 and others.^8,9 Early and significant advances in XTA instrumentation were also achieved at the Advanced Light Source¹⁰ (ALS). These developments were reported in 2003 by Saes et al.^11,12 who studied the metal to ligand charge transfer state (MLCT) of [Ru^II(bpy)₃]²⁺ (bpy: 2,2′-bipyridine). The early significant works in XTA science and instrumentation have been thoroughly reported and reviewed.^10,12–21

While initial reports from the ALS focused on transmission mode XTA, work at the APS focused on fluorescence detected²² XTA. In the following years, the latter detection scheme became dominant because many interesting samples either have low solubility or cannot be produced in large enough quantities for transmission mode measurements. Early fluorescence based XTA studies utilized energy resolving germanium¹⁴ detectors (and others²³), while transmission measurements utilized large area silicon avalanche photodiodes (Si-APDs). Between 2007 and 2011, large area Si-APDs^20,24–29 became commonly used in fluorescence detected XTA as well, and they are now employed in many XTA facilities.^{25–27,30–32} The advantage of Si-APD detectors is straightforward: their fast rise and fall times allow the fluorescence signals from adjacent x-ray probe pulses (separated by ∼100 ns) to be easily distinguished. Furthermore, Si-APD detectors have a large dynamic range. A typical synchrotron insertion device source delivers 10¹³ photons/s monochromatic beam (ΔE/E∼0.1%) incident on the sample. For a dilute sample system (1 mM), the number of signal photons received by each detector is generally less than eight photons per x-ray pulse, which is well within the linear operating region of these detectors.

Early XTA experimental setups utilized high energy (∼mJ) laser pump pulses to excite a large fraction of the molecules in a large x-ray probe beam. These schemes employed ∼1 kHz laser systems [Fig. 1(a)] and only utilized a small fraction of x-ray pulses to probe the excited state [dark purple pulses in Fig. 1(a)]. This left the vast majority of the x-ray flux unused [light purple pulses in Fig. 1(a)]. Micrometer scale x-ray focusing and the commercialization of high power, high repetition rate lasers motivated the development of XTA techniques with MHz repetition rates. Figure 1(b) shows how these setups utilize almost all of the x-ray probe pulses and enable a near complete utilization of x-ray flux to calculate the probe spectrum. In 2011, Maech et al.²⁸ and Lima et al.²⁹ reported XTA setups that exemplify the high repetition rate XTA technique. These works brought the previously investigated^33–35 high repetition rate XTA concept to its logical conclusion. Other MHz repetition rate setups have been developed since.^30,31 High repetition rate XTA schemes feature exceptional performance for short pump–probe time delays. However, the relatively short time window between laser pulses places an upper limit on the timescale of observable phenomena.

X-ray Multi-Probe (XMP) DAQ [Fig. 1(c)] represents a distinct approach that can effectively utilize synchrotron x-ray flux in XTA measurements. XMP DAQ maintains the ∼kHz laser repetition rate but acquires data from every x-ray pulse after laser excitation, enabling the acquisition of time resolved x-ray absorption spectra at thousands of pump–probe time delays simultaneously. Each spectrum Sⁱ(E) occurs at a time delay from the laser (Δtⁱ), given by

where Δt⁰ is the time delay of the x-ray pulse closest to the laser, T_X is the x-ray pulse spacing, and i is an integer. The value of T_X depends on the synchrotron storage ring filling pattern. For example, the values are 1.8 µs, 153 ns, and 11.4 ns in the APS’s hybrid bunch mode, 24 bunch mode, and 324 bunch mode, respectively.

In contrast to XMP DAQ, traditional XTA DAQ techniques gather time resolved spectra at different time delays in separate measurements. Such a measurement technique is affected by drifts in the experimental apparatus over time, such as fluctuations in the sample jet (position and width), pump laser position and intensity, x-ray beam position, and sample concentration changes and degradation. Gathering all pump–probe time delays in a single measurement eliminates the impact of these drifts from the kinetic data. Therefore, XMP DAQ presents distinct advantages for measuring spectral kinetics over a long (∼100 µs) time window, which would otherwise require a large number of individual measurements. Traditional XTA techniques also acquire a separate ground state spectrum for each measured time delay. Therefore, a sizable fraction of the total measured counts are dedicated to measuring the ground state spectrum. XMP DAQ uses the same ground state spectrum (⁠$S̄GS$⁠) to calculate the XTA spectrum [$ΔSE,Δti=SiE−S̄GSE$] for thousands of laser time delays, which represents an important increase in DAQ efficiency. These features enable XMP DAQ to construct low noise, two-dimensional XTA datasets [ΔS(E, Δtⁱ)] with a high degree of consistency between the various spectra.

The two-dimensional XMP-DAQ dataset [ΔS(E, Δtⁱ)] contains spectro-kinetic information over a time window up to 240 µs. The data acquired in this range of time delays enable the observation of complex photochemical reactions, such as the photocatalytic generation of solar fuel, and other diffusion limited photo-redox chemistry. While the set of spectra at long (1–100 µs) time delays enables the study of “slow,” solution-based photochemical processes, the ∼70 ps time resolution enables the observation of the initially created charge separated state and the subsequent processes of electron and hole trapping. Thus, the range of time delays acquired by XMP DAQ enables the complete picture of a photochemical reaction to be efficiently observed.

Presently, we report two distinct yet related XMP DAQ techniques: Current Integration (CI) DAQ and Photon Counting (PC) DAQ. CI DAQ is well-suited to the high single pulse x-ray flux (>10⁶ photons/pulse) and long pulse separation (>100 ns) in the APS 24 bunch mode and hybrid bunch mode. XMP with CI-DAQ has proven to be a powerful tool for the study of in situ photochemical reactions. In contrast, a small x-ray probe pulse spacing (∼10 ns) has rarely been used for time resolved measurements because of challenges in temporally resolving the signal from individual x-ray pulses. However, a significant fraction of synchrotron resources world-wide operate with a <20 ns x-ray pulse spacing. Also, the upgraded APS storage ring will operate in 324 bunch mode (11.4 ns x-ray pulse spacing) approximately 50% of the time. Therefore, PC XMP DAQ was developed to meet the challenges and leverage the opportunities of XTA studies with densely spaced x-ray pulses. In particular, while the short pulse spacing creates challenges from a DAQ point of view, it also enables the acquisition of a higher number of excited state spectra in a given time window. We demonstrate the PC XMP DAQ by measuring the two-dimensional XTA spectrum of a dilute osmium polypyridyl complex solution in the APS 324 bunch mode.

Although many XTA sample environments have been implemented at the beamline 11-ID-D of the APS, fluorescence mode measurements on dilute (0.1–5 mM) solutions are the most used and optimized. A simplified schematic of the liquid-based sample environment is shown in Fig. 2. During experiments, the sample is drawn from a reservoir and conveyed to the experimental chamber via polytetrafluoroethylene (PTFE) and stainless-steel tubing. The sample emerges into the experimental chamber as a vertical and freely falling liquid jet, which intersects with the laser and x-ray beams at a ∼90° angle. The jet is collected at the bottom of the chamber and flows back to the sample reservoir closing the loop. Solvent saturated inert gas (typically N₂) is bubbled in the sample reservoir, both degassing the sample and maintaining an inert atmosphere. The sample reservoir, experimental chamber, and pump system are sealed, except for a long thin ventilation tube used to release the positive pressure from the gas bubbling.

The x-ray fluorescence from the liquid jet is measured with two large area APD detectors positioned at 90° from the plane defined by the vertical jet and x-ray beam. Elastic scattering from the jet is attenuated by a combination of Soller slits and a Z − 1 filter³⁶ (Fig. 2). A third APD detector is positioned upstream of the experimental chamber and collects air scattering from the beam as a measure of the incoming x-ray flux.

Rough spatial alignment of the pump and probe beams is achieved by optimizing the laser and x-ray flux through a stationary 500 µm aluminum pinhole placed at the sample position. The alignment is fine-tuned by removing the pinhole and varying the position of the laser spot on the sample jet to optimize the differential x-ray fluorescence signal induced by the laser.

The synchronized, high-energy optical pump pulses used in XTA spectroscopy are produced in two stages shown in Fig. 3. The first stage occurs in the laser oscillator, which produces a train of optical seed pulse (88 MHz) phase locked to the x-ray pulse train. The second stage selects (3–10 kHz) a synchronized seed pulse from the train and amplifies its energy to a level suitable for sample excitation.

The laser oscillator (Coherent Micra-5, Titanium Sapphire, 88 MHz, 800 nm, 50 fs pulse width, 5 nJ pulse energy) produces phase locked seed pulses with the help of a commercial synchronization unit (Coherent Synchrolock-AP 55 fs timing jitter). The unit monitors the seed pulse repetition rate with a photodiode, compares it to the ¼ sub harmonic (∼88 MHz) of the synchrotron bucket clock, and feeds an error signal back to the oscillator. The oscillator repetition rate is determined by the cavity length, and the error signal dynamically tunes the cavity end-mirror with piezoelectric actuators to achieve the lock. Once a lock is achieved, the time delay (Δt) between the x-ray pulse train and the laser pulse train can be continuously varied by introducing a constant phase shift (Δφ_Delay = [2πΔt]88 MHz) into the 88 MHz synchronization signal. φ_Delay is varied with the Colby Instruments Programmable Delay Line (PDL) outlined in pink in Fig. 3.

One out of ∼10⁴ synchronized seed pulses is used to pump a regenerative amplifier (Coherent Legend Elite Duo, 800 nm, 1 mJ pulse energy). The amplifier is typically operated at 10 kHz, but can also run at 3 kHz for use in conjunction with an optical parametric amplifier (producing pump pulses with a variable wavelength). The trigger for the regenerative amplifier is obtained by dividing the APS orbit clock frequency (271.544 kHz) by exactly 27 with a Stanford Research Systems (SRS) DG535 delay generator. The phase of the amplifier trigger signal (φ_RA) is varied with a Highland V851 digital delay generator (outlined in pink in Fig. 3). φ_RA must be chosen to properly trap the desired seed pulse in the amplifier cavity. The synchronization of the amplified pulse is fundamentally derived from the seed laser, making it largely insensitive to jitter in the amplifier trigger. The resulting temporal cross correlation of the pump and probe is dominated by the width of the synchrotron x-ray pulse (∼79 ps in APS 24 bunch mode and ∼52 ps in APS 324 bunch mode). The time delay between the pump and the probe is adjusted by varying the combination of φ_Delay and φ_RA with the laser control computer.

Temporal overlap of the laser and the x-ray pulses is achieved using a pair of PIN photodiodes (∼100 ps rise time, Teledyne Judson Technologies J22-18I-R40U-1.7) and a fast oscilloscope (Agilent DSA 91304A 13 GHz 40 GSa/s). One photodiode (triggering diode) collects scattered light from laser pulses and generates a trigger signal for the oscilloscope acquisition. The other diode (sample diode) is placed at the sample jet location, where the x-ray and laser spatially overlap, and is used to measure the timing of both the x-ray and laser pulses relative to the oscilloscope trigger. The φ_Delay and φ_RA are varied until the signal traces from laser and x-ray overlap on the oscilloscope screen. This is defined as initial delay time zero. This method can establish time zero with a precision around 10 ps and an accuracy of about 30 ps. The more accurate time zero is then extracted from the fitting of the XTA kinetics rising edge on real samples.

Photon Counting (PC) XMP DAQ and Current Integration (CI) XMP DAQ require different methods to calculate the XTA spectra from the APD detector signals. Details specific to CI XMP and PC XMP are reported in Secs. IV B and IV C, respectively. This section describes the aspects that are common both DAQ techniques.

Efficient and fast detection of x-ray fluorescence photons is accomplished with home-built large area (100 mm²) Avalanche PhotoDiode (APD) detectors. The detectors utilize a silicon sensor (Excelitas CF30703-200T) and are typically biased between 350 and 550 V for a gain of 20–200. The Excelitas sensor has an absorption layer thickness of around 200 µm, enabling a detection efficiency above 50% for x-ray photons up to ∼13 keV. Absorption of x-ray photons in the APD sensor produces a fast and small voltage pulse whose amplitude is proportional to the number of absorbed photons. Single photon voltage pulses are around 10⁻⁵–10⁻⁴ V without amplification. The sensor output is amplified with a low noise, broadband preamplifier (Femto HSA-X-1-40, 1.7 dB noise figure, 10 kHz–1.2 GHz bandwidth, 40 dB gain), and then filtered with a 200 MHz low pass filter. Details of our detector circuit and performance will be reported in a separate article.

The amplified detector voltage signals are measured by a high-performance analog to digital converter (as shown in Fig. 3, Acqiris U5303A-SR1; https://acqiris.com/wp-content/uploads/2019/12/Acqiris_U5303A_Datasheet.pdf). When the Acqiris receives a transistor-transistor logic (TTL) trigger, it measures the analog detector voltage profile at 1 ns intervals (with 12 bits of accuracy) and stores the data in a digital “single trigger waveform.” The waveform length is limited by the time window between laser pulses (∼100 µs) and the 800 ns trigger re-arm time of the Acqiris. Waveforms up to 240 µs long with 2.4 × 10⁵ voltage measurements are possible. Each Acqiris card can digitize two detector signals, and two cards are utilized to acquire data from the three detectors shown in Fig. 2.

The temporal relationship between the laser pump pulses, x-ray probe pulses, and the acquisition trigger is presented in Figs. 4(a)–4(c) [note that Figs. 4(e)–4(g) are described in Secs. IV B and IV C]. The acquisition trigger [Fig. 4(c)] and laser timing [Fig. 4(b)] are both derived from the synchrotron (as shown in Fig. 3), and are thus synchronized with the x-ray pulses [Fig. 4(a)]. The x-ray pulses are labeled with an index i, which indicates their time delay from the laser (Δtⁱ) according to Eq. (1). The mutual synchronization between the pump, probe, and acquisition is represented by the purple and red dotted lines, which extend vertically as shown in Fig. 4. Figure 4(d) shows a schematic single trigger waveform containing the detector voltage profile measured by the Acqiris. The number of voltage peaks in Fig. 4(d) is fewer than the number of x-ray probe pulses in Fig. 4(a), indicating that not all x-ray pulses result in detected signal photons. The synchronization of the acquisition trigger implies that each fluorescence photon [voltage peak in Fig. 4(d)] can be traced to the ith x-ray probe pulse and a time delay Δtⁱ from the pump laser [for example, the voltage pulse on the left of Fig. 4(d) at time delay Δt⁰ from the laser]. The synchronization scheme described here is common in pump–probe measurements and enables the acquisition of XAS spectra with a time resolution limited by the x-ray probe pulse width, rather than the fluorescence detector or digitizer.

The relative delay between the laser and the acquisition trigger [Figs. 4(b) and 4(c), respectively] is controlled with an additional Highland V851 digital delay generator (Fig. 3). This flexibility is necessary to independently tune the timing of the regenerative amplifier and the acquisition. The acquisition is synchronized to obtain the signal photons from x-ray pulses at times before the laser (used to calculate the ground state spectrum) and after the laser (used to calculate the excited state spectra).

Acquiring waveforms at the typical trigger rate (∼10 kHz) generates a staggering 10 gigabits-per-second of data. To keep up with this data rate, the single-trigger waveforms are reduced by Acqiris’s on-board field programmable gate array (FPGA) during the measurement integration time. When the measurement integration is complete, the reduced data (from the three detectors in Fig. 2) are transferred via PCIe connection from the Acqiris cards to a computer. Home built software (QAVRG, http://qavrg.sourceforge.net) extracts the XTA signal from the reduced data at all pump–probe time delays (for the current x-ray probe energy). Extracting the data from the Acqiris card, calculating the XTA signal, and moving the monochromator yield around 0.8 s of overhead time for each probe energy measurement. The typical 4 s integration time is chosen to minimize the amount of overhead time while ensuring that the XTA spectra can be measured repeatedly many times. Acqiris’s FPGA processor reduces single trigger waveforms in real time according to an algorithm described in the FPGA firmware (specified by the user). Different FPGA firmwares are utilized for CI DAQ and PC DAQ. Both are described in detail in Secs. IV B and IV C.

For sample concentrations around 1 mM, XTA experiments in APS 24 bunch mode (∼10⁶ photons/pulse incident) detect an average of 0.5–8 fluorescence photons per probe pulse at each time delay. The number of photons detected at Δtⁱ is proportional to the amplitude of the average detector response at Δtⁱ. CI DAQ averages the single trigger waveforms acquired during the integration time (4 × 10⁴ waveforms with 4 s integration time) using the commercial “AVG” FPGA firmware in the Acqiris digitizer. A schematic averaged waveform is shown in Fig. 4(e). Each peak in Fig. 4(e) represents averaged number of detected photons generated by the ith probe pulse, at time Δtⁱ from the laser. When the integration time is complete, the averaged waveform from each detector is transferred from the Acqiris cards to the analysis computer, where the amplitude of each peak is extracted. Extracting the amplitudes of all individual peaks in the averaged waveform in a self-consistent way is accomplished with a fitting procedure implemented in the QAVRG software.

Each segment is fit with a combination of empirically determined curves. The first empirical curve is a dark measurement $Dτ$⁠, which is an average waveform acquired with the x-ray shutters closed. The second empirical fitting curve is measured with the x-ray shutter open and is called the “reference measurement” $Rτ$⁠. Both $Dτ$ and $Rτ$ are measured with large integration time (200 s) to minimize the random noise. $Dτ$ accounts for systematic noise in the acquisition, while $Rτ$ represents the expected detector peak shape. Each segment of the waveform has a unique reference and dark measurement denoted by $Riτ$ and $Diτ$⁠, respectively [Fig. 5(a)]. At probe energy E, an averaged waveform V_Raw(E, τ) is measured, and each segment of the waveform $VRawiE,τ$ is fit with a function of the form

where $AiE$ and Δ_B are the values extracted from the fit and represent the relative detector peak amplitude and waveform baseline shift, respectively. For a sample detector waveform, $AiE$ is proportional to the x-ray absorption at pump–probe time delay Δtⁱ at probe energy E. The model in Eq. (2) allows the accurate extraction of the peak amplitude $AiE$ subtracting dark noise [$Diτ$] and a shifting voltage baseline (Δ_B). The linear least-squares fitting procedure to extract $AiE$ is parallelized for minimal overhead time. An example of raw data and the fit for one segment are shown in Fig. 5(b). An identical procedure is used to extract air scattering intensity $Ni(E)$ from the normalization detector waveform, generating a highly accurate measurement of the incident flux at each time delay. Thus, in CI DAQ, the x-ray absorption spectrum at delay Δtⁱ is calculated as

The amplitude of each individual x-ray pulse of two sample detectors, $AiE$⁠, is normalized by that of the same ith x-ray pulse given by the normalization detector, $Ni(E)$⁠. Such a normalization scheme (called pulse-to-pulse) is important because the intensity of the x-ray pulses can vary by ∼14% in 24 bunch mode and ∼40% in 324 bunch mode.

By convention, $SCIiE|i<0$ are measurements of the x-ray absorption spectrum before the laser pulse and correspond to the ground state spectrum. The averaged ground state spectrum is calculated as

where −m is the index of the first peak in the averaged waveform. The XTA spectrum in CI DAQ at time delay Δt_i from the laser is thus

The same ground state spectrum is used to calculate $ΔSCIiE$ for every time delay. Fitting the average waveform with Eq. (2) requires that the (normalized, baseline subtracted) shape of the average detector response is highly linear (independent of the amplitude). Avalanche photodiode detectors excel in this respect, and we have had great success with the Excelitas CF30703-200T sensors.

The APS 324 bunch mode has a similar total flux to the APS 24 bunch mode but 13.5× higher x-ray pulse frequency. Thus, compared to the 24 bunch mode, there are 13.5× more time delays in the acquisition window (100 µs), with each time delay receiving 13.5× fewer detected photons (<0.6 photons/pulse for a 1 mM sample). PC DAQ utilizes the Acqiris peak detection (PKD) FPGA firmware, which is well suited for these conditions. The PKD algorithm first locates the voltage peaks in the single trigger waveform [Fig. 4(d)] and produces an analogous binary waveform [Fig. 4(f), 1 = detected photon, 0 = no photon] in real time. While CI DAQ requires fitting the full time-domain detector response, the PKD firmware is only sensitive to the binary presence or absence of a peak, and is significantly less sensitive to partial temporal overlap between detector responses from adjacent x-ray pulses. This makes the PKD firmware uniquely advantageous for XTA measurements at synchrotrons with a relatively small (∼10 ns) x-ray pulse spacing. One binary waveform is generated for each acquisition trigger, and the waveforms gathered during the experimental integration time (∼4 s in typical measurements) are summed to produce a time resolved histogram [Fig. 4(g)]. Similar to the averaged waveform, the time resolved histogram reflects the temporal structure and synchronization of the x-ray probe pulses, and it enables a laser time delay to be assigned to each peak.

For the PKD firmware to record a count, a voltage peak in the single trigger waveform must meet several necessary conditions. These conditions are specified in terms of three user-defined algorithm input parameters: Δ_offset, Δ_rise, and Δ_fall. The first condition stipulates that the peak voltage must exceed the parameter Δ_offset. Next, the algorithm must detect a rising edge and falling edge. A rising (falling) edge is identified when the difference between consecutive voltage samples is greater (less) than Δ_rise (−|Δ_fall|). The falling edge must occur less than nine samples after the rising edge, and not before. This imposes a limitation on the width of the detector response, which must be less than about 9 ns. Δ_offset is typically set high enough to eliminate the dark counts coming from the noise floor of the detector (limited by the pre-amplifier).

To improve the consistency of the photon count histogram, we found it necessary to lock the sampling rate of the Acqiris digitizer to the synchrotron bucket clock. This ensures that there are exactly ten samples for each x-ray pulse in the 324 bunch mode. Locking the sampling rate of the Acqiris card is accomplished by multiplying the 351.933 MHz synchrotron bucket clock by 5 (Wenzel Associates, 352 MHz 5× multiplier, IFM-1R-352-5-13-13), and feeding this clock signal (1759.665 MHz) to the Acqiris card, as shown in Fig. 3.

The time resolved absorption spectrum $SPCiE$ is proportional to λⁱ(E), the average number of fluorescence photons detected after each trigger at time delay Δtⁱ from the laser. At low count rates (λⁱ ≪ 1), λⁱ can be estimated to be $λPCi$⁠,

where $ΛPCi$ is the sum of the counts in the histogram peak at Δtⁱ and N is the number of triggers in the acquisition. However, when λⁱ becomes large, $λPCi$ becomes non-linear and saturates at a value of 1 (only one fluorescence count can be recorded at Δtⁱ for each trigger). Limiting the incident flux to ensure linearity in the detection would lead to excessively long integration times. Therefore, we employ a theoretical correction from Poisson statistics, which relates the count rate extracted from the histogram (⁠$λPCi$⁠) to the true count rate,

Equation (7) is valid whenever Poisson statistics are valid and enables PC XMP DAQ to reliably operate at high count rates (tested up to λⁱ = 0.5). Detailed studies of the linearity of PC DAQ and detector optimization will be reported separately.

Given λⁱ calculated according to Eq. (7) and the corresponding calibrated counts in the normalization detector ϕⁱ, the time resolved absorption spectrum is given by

In contrast to Eq. (4), a small nonlinearity in the calibrated counts λⁱ and ϕⁱ introduces some subtlety into calculating the averaged ground state spectra $S̄PC,GSE$⁠, described below.

About 8000 photon peaks in each time resolved histogram (10 kHz laser, 324 bunch mode) are generated by x-ray pulses with 324 distinct fluxes, corresponding to the 324 electron bunches in the storage ring. The histogram peak Δtⁱ has the same flux as peaks with indices in the set {j|j ≡ i mod 324}. When calculating the averaged ground state in analogy to Eq. (4), only spectra generated with identical probe flux are included in the sum

where J is the number of elements in the set {j|j ≡ i mod 324, j < 0} (typically ∼8). Equation (9) implies that there are 324 ground state spectra in each dataset (one for each distinct flux). Differences between ground state spectra generated by different pulses arise from deficiencies in the Poisson correction to the non-linearity [Eq. (7)]. However, spectra generated by pulses from the same electron bunch differ only by shot noise. Thus, when calculating the laser induced difference spectra $ΔSPCiE$⁠, it is necessary to compare spectra by the same electron bunch. Thus,

With $ΔSPCiE$ calculated according to Eqs. (7)–(10), the residual nonlinearity of PC DAQ has a negligible impact. While systematic distortions in $ΔSPCiE$ exist, this small effect (<1%) is generally much less than the signal to noise obtained in the measurement of $ΔSPCiE$⁠.

The XTA spectrum of the Os (II) L_III edge was obtained using PC XMP DAQ in the APS 324 bunch mode. Osmium(II) tris(2,2′-bipyridine) in methanol (0.7 mM) was measured with 400 nm excitation and Δt⁰ = 50 ps. The sample was excited with pump pulses about 30 mJ/cm², producing a molecular photoexcited fraction around 55%. Figure 6(a) shows the two-dimensional data ΔS_PC(E, Δtⁱ) simultaneously collected at time delays Δtⁱ given by Eq. (1), with T_X = 11.363 ns. Overall, the observed spectral kinetics reflect the electronic structure and decay of the lowest energy metal to ligand charge transfer triplet (MLCT³) of osmium(II) tris(2,2′-bipyridine). The positive feature at ∼10.868 keV corresponds to the creation of a t_2g hole upon photoexcitation, while the adjacent pair of negative and positive features (at ∼10.873 and ∼10.876 keV, respectively) describe an increased binding energy of the 2p-5d(e_g) “white line” transition in the MLCT³ state. All observed features are expected based on previous studies.³⁷ Figure 6(b) is generated by varying Δt⁰ (at 10.865 keV) and stitching together the resulting differential kinetics from each pulse. The constructed decay curve reveals an ∼40 ns MLCT³ lifetime, in reasonable agreement with previous studies.³⁷ The smooth nature of the decay curve indicates that our calibration procedure was a success. Figure 6(c) shows the measured XTA signal (10.865 keV) for three consecutive x-ray pulses (⁠$i=−1,0,+1$⁠) as Δt⁰ is scanned from −100 to 100 ps. The amplitude of the difference signal in the i = 0 pulse rises abruptly around Δt⁰ = 0, while the $i=−1,+1$ spectra evolve smoothly in this delay range. These data demonstrate that despite the 11.36 ns x-ray pulse spacing, the measured XTA signal in adjacent pulses is completely independent and establishes the efficacy of the PC XMP technique in the 324 bunch mode. The width of the rising edge in Fig. 6(c) is related to the 52 ps temporal cross correlation of the pump and probe and reflects the x-ray pulse width in the 324 bunch mode. Thus, this method demonstrates the expected increase in time resolution (52 ps) compared to the 24 bunch mode (78 ps) and hybrid mode (117 ps).

A comparison between the performance of CI DAQ and PC DAQ is shown in Fig. 7. We measured the static XAS spectra of 1.5 mM [Cu^I(dmp)₂](BarF) in acetonitrile [dmp: 2,9-dimethyl-1,10-phenanthroline; BarF: tetrakis(3,5-bis(trifluoromethylphenyl))borate], with PC DAQ and CI DAQ in the APS 24 bunch mode. The spectra were simultaneously acquired using two sample detectors and two normalization detectors. The detectors were setup symmetrically about the sample jet to ensure that they received the same number of fluorescence photons. The incident flux was varied using aluminum beamline filters, and the spectra obtained with three different levels of flux are displayed in Fig. 7. With an incident flux producing around 0.5 detected fluorescence photons per x-ray pulse, the signal to noise values of the two DAQ schemes are about the same. However, in this case, the PC DAQ spectrum exhibits clear distortions associated with multiphoton non-linearity. These distortions can be corrected with the method discussed in Sec. V. At lower count rates (〈n〉 = 0.094), the spectral shapes of the two DAQ techniques agree nearly perfectly, while the PC DAQ spectrum shows less noise. A further decrease in the count rate to 〈n〉 = 0.0036 shows a relatively large increase in the noise of the spectrum generated by CI DAQ. This noise occurs because at very low count rates, the quality of the fit obtained in CI DAQ is degraded by the noise in the averaged waveform. Thus, in the 24 bunch mode, CI DAQ is typically employed to leverage the large flux per bunch. In the 324 bunch mode, we expect 13.5 times fewer detected photons per pulse, and PC DAQ performs the best under these circumstances. Switching between the two techniques can be done easily through the QAVRG software.

X-ray Multi-Probe (XMP) DAQ is a technique that measures the x-ray transient absorption (XTA) spectrum at thousands of laser time delays simultaneously. We have developed two XMP DAQ schemes. The appropriate technique can be selected based on the temporal separation of the x-ray pulses and the average expected number of detected fluorescence photons. Current Integration (CI) XMP DAQ is well suited for detecting multiple x-ray probe photons per probe pulse, with a relatively large separation between the pulses (>20 ns). Photon Counting (PC) XMP DAQ is optimized for a count rate less than 1, with relatively closely spaced pulses (<20 ns). XTA with XMP DAQ generates a highly consistent two-dimensional dataset ΔS(E, Δtⁱ), which enables global fitting techniques based on the singular value decomposition. Photoexcitation can easily produce mixtures of species, and such analysis allows one to extract the spectra and kinetics of the individual species from ΔS(E, Δtⁱ). Quantitative XAS simulations can then help identify photoinitiated species. This scheme represents a promising route to map out photoinitiated reaction mechanisms and a new avenue to understand the rich and complex phenomena in the fields of photochemistry and photocatalysis.

PC XMP DAQ can be readily applied at synchrotron sources with operational modes of more than 10 ns x-ray pulse spacing. We expect that advances in fluorescence detector technology and the development of custom FPGA firmware will enable the deployment of PC XMP DAQ at synchrotrons with an arbitrary pulse spacing. While XMP DAQ was developed for laser pump XTA measurements, it can be applied to measure small XAS changes in response to other types of synchronized sample perturbations, such as electric or magnetic pulse field, temperature change, shock wave, and chemical parameter variation.

This work was supported by the Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. The authors acknowledge the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 for the use of the A. M. March and L. X. Chen U.S. also acknowledge Department of Energy, Office of Science, Basic Energy Science, Chemical Sciences, Geosciences and Biosciences Division under Contract No. DE-AC02-06CH11357.

The data that support the findings of this study are available from the corresponding author upon reasonable request.