Dynamic optical spectroscopy and pyrometry of static targets under optical and x-ray laser heating at the European XFEL

The study of warm dense matter (WDM) and high pressure-temperature states of condensed matter is vital to understanding complex physical systems that exist in nature, such as planetary interiors,^1,2 and in technologies, such as internal confinement fusion.³ The description of WDM is also a challenge for theory because strong correlations and quantum effects have to be treated consistently beyond perturbative methods by using, e.g., ab initio simulations.^4–6 

Laboratory experiments are, therefore, central to characterizing WDM behavior. The creation of high pressure (millions of atmospheres) and temperature (thousands of degrees Kelvin or higher) conditions are required to study these fundamental systems.^7–16 Traditionally, these are created through intense irradiation,^17–21 dynamic shock compression,^22–25 or a combination of static compression with these techniques, often using a diamond anvil pressure cell (DAC).^7–16,26 However, these techniques are often constrained by short experimental lifetimes due to loss of high-density conditions. Damage to samples can also occur over longer periods through sample contamination from chemical reactions with surrounding material (e.g., diamond anvils) or cumulative thermal or mechanical damage. This can then lead to discrepancies between various experimental results.^9,14,27–29 At the boundary between traditionally fast and slow measurements, a variety of experiments are possible which address common challenges of WDM experiments; however, novel measurement techniques and diagnostics are often needed for such regimes.^11,13,30

X-ray Free Electron Lasers (XFELs) present a new frontier for intermediate timescale extreme conditions studies. Excited states following femtosecond pulsed irradiation can persist for beyond microsecond timescales on XFELs, for example, due to volumetric heating of massive objects.³¹ Meanwhile, pulse repetition rates in the MHz range, such as that currently available at the European X-ray Free Electron Laser (EuXFEL),^32,33 offer opportunities for serial probing and excitation on similar, microsecond timescales.

Controlling samples subjected to WDM extremes over such experimental lifetimes as well as defining the pressure-density conditions reached is made possible using DACs to contain and pressurize samples of interest.³¹ This configuration is ideal to study WDM as it is possible to use pulsed x-ray heating to heat targets to tens of thousands of Kelvin.^{29,31,34–37} In this scenario, hard x-ray energies greater than 10 keV have long absorption lengths (⁠ $∼$millimeters) for light elements (i.e., carbon), allowing penetration of millimeter thick diamonds, while absorption lengths in the micrometer range for high atomic number elements enable localized energy deposition within micrometer thick samples. XFELs are ideally suited to this type of experiment because they are able to produce short (femtosecond pulse length), high-power (⁠ $∼ 10 12$ photons per pulse), hard x-ray (⁠ $>10$ keV) pulses. These pulses also provide a fast and high power probe to observe the sample conditions^29,37–39 and are often available in a pair or train. This, therefore, naturally leads to the ability to perform serial pump–probe experiments.^17,40

A number of diagnostics can be employed to measure the conditions in such experiments, including temperature, many using the pulsed x-ray source itself. If the pump is also an x-ray pulse, the pump and probe are automatically spatially aligned, which is ideal for sampling the heated volume. X-ray diffraction (XRD)¹⁸ can determine sample conditions through measurements of sample volume and phase transformations, but is complicated by the difficulty in discriminating between the effects of pressure and temperature changes. Likewise, x-ray Thomson scattering, often used in conjunction with x-ray heating, can estimate electron temperature via detailed balance in the collective scattering regime inspecting the height of the up- and down-shifted plasmons,⁴¹ with temperature uncertainties often on the order of a few eV,^41–46 but requires high quality information on the source and instrument function.⁴⁶ Such x-ray snapshots of temperature can be further limited when observing continuously changing sample conditions, e.g., due to insufficient time sampling.²⁹ 

An ideal temperature diagnostic will continuously determine sample temperature through a period of interest with high time resolution and small uncertainty independent of assumptions and the detailed sample conditions. Pyrometry provides such a method, inferring sample temperature from optical emission released from heated samples. As opposed to active x-ray probing, pyrometry is passive so can inherently provide a continuous record of temperature. Pyrometric measurements have long been used to estimate the temperature reached in static compression (i.e., laser-heated diamond anvil cell, LHDAC),^7–16,47 shock compression,^22–25 and fast radiative (i.e., isochoric) heating studies,^48,49 though while proposed³⁵ its application to XFEL heating has not been demonstrated. Pyrometry determines temperatures reached¹² usually by the sole assumption that emission follows the behavior of a gray-body radiator, as defined by Planck’s law.^22,50

Streaked optical pyrometry (SOP) provides one method to measure in situ sample temperatures with high time resolution in the picosecond to microsecond range. Streak camera images record emission over a pre-determined time window denoted the streak window. Changes in emission brightness as a function of time are recorded on the image as changes in intensity along the time axis.^51,52 The spatial, spectral, and temporal shape of optical emission from any heated sample is difficult to obtain simultaneously,²² thus the orthogonal axis of the streak image will resolve the emission either spatially or spectrally (i.e., a linear position vs time broadband intensity map, or a wavelength vs time spectrogram from a particular position). Each approach has advantages that depend on the sample properties, temperature range, target design, spatial scale of the event, and other factors. For example, the presence of optical windows in targets, such as those used when observing statically compressed samples or a shocked interface, adds complications such as the requirement that any optical emission pass through layers of other material, potentially affecting the final collected emission.^53,54 In many cases, the use of spectrally (as opposed to spatially) resolved detection is advantageous as it is less sensitive to emissivity, target transmission, other complex optical properties of targets, temperature inhomogeneity, or time dependence of these factors, within certain limits.^55,56 The measured spectral shape also allows an independent verification that emission adheres to the predictions of the Planck model and thus provides a final test of whether the measured temperature can be valid, by resolving obvious distortions in thermal emission or nonthermal contributions to signal. For these reasons, spectrally resolved temperature determination is generally considered more reliable in complex sample environments, such as those using tight focused radiative heating similar to the x-ray and optical heating employed in this study (e.g., in traditional laser heated DAC experiments).

The detection limit of SOP is predicated on the temperature, sweep window, number of events (shots) integrated, size of heated and observed areas, event duration, sample optical characteristics, spectral range detected, and spectrometer dispersion, and varies significantly depending on these factors for different applications. Lower detection limits for SOP fall in the range of 400–4000 K in typical single shot applications^{11,48,51,57,58} and is observed to be 1500–3000 K for the system described here. Fundamentally, this is limited by the rapid reduction in emission with decreasing temperature (i.e., the Stefan–Boltzmann law). While there is no upper limit on detectable temperature, spectral form becomes insensitive to the temperature where the Planck distribution peaks well below the observed wavelength band (i.e., Wien’s law), which occurs, e.g., in the electron volt range for visible diagnostics; in such cases, absolute emission intensity would be a reliable—and possibly superior—indicator of temperature in certain circumstances.⁵¹ 

Here, we report the design and performance of an SOP diagnostic implemented at the High Energy Density (HED) instrument of the EuXFEL. The system measures optical signals in the visible spectral range, in spectral-temporal space and can be deployed in a range of sample environments and extreme conditions scenarios. A selection of common applications are evaluated here. The diagnostic was specifically designed and tested to work in conjunction with DAC static compression techniques. The equipment for the system was provided to the HED instrument by the HIBEF user consortium, and the design and implementation was performed in collaboration between EuXFEL, Deutsches Elektronen-Synchrotron (DESY), and University of Edinburgh. Basic design parameters are discussed in Sec. II, the experimental procedure in Sec. III, samples in Sec. IV, and results in Sec. V. The system was developed at DESY, with first experiments using laser heating only (Sec. V A). It was moved to EuXFEL for the first online measurements with x-rays only, in association with the first User Community Assisted Commissioning Experiment, Proposal No. 2292^38,39,59 (Secs. V B–V F). Laser heating and x-ray heating together were subsequently performed in further commissioning work in Proposal No. 2731 (Secs. V G and V H). Numerical modeling of experiments and comparison to the measurements are included in Sec. VI, while a discussion of the findings and conclusions for future work using the diagnostic are given in Sec. VII.

European XFEL offers three self-amplified spontaneous emission (SASE1, SASE2, SASE3) sections that produce x-ray photons at wavelengths varying from 0.1 to 1.6 nm. The HED experimental hutch is located at the end of the SASE2, which produces photons in the hard x-ray regime between 0.1 and 0.25 nm.⁶⁰ X-ray pulses are grouped into trains of up to 2700 pulses, with a train repetition rate of 10 Hz and intra-train pulse repetition rate of fractions of 4.5 MHz, giving pulse separation of 221.5 ns (or 443, 886, etc.). Pulse intensity monitors are placed upstream and downstream of the experimental vacuum chamber (Interaction Chamber 2, IC2) in order to measure beam intensity and pulse-to-pulse fluctuations in intensity.³⁹ Energy on target was $∼30%$ of the measured upstream beam intensity on the absolutely-calibrated x-ray intensity gas monitor (XGM) in the SASE2 beamline (SASE XGM),^39,61,62 and could be further reduced through user selected attenuation of the beam. Downstream energy intensity monitors are placed in the beamstop after the experimental chamber (Fig. 1). The XFEL heating (XH) due to individual pulses and pulse trains are examined here. The XFEL beam is focused onto the target using several sets of on-axis chromatic compound refractive lenses (CRLs), with spot sizes in the range of 5–20  $μ$m (FWHM) on target used in the described experiments (Table I).

Single or double-sided pulsed or continuous optical heating (LH) of targets is made possible using a near-infrared (NIR) laser (Model SP-100P-A_EP_Z, 1070 nm, 1.2 eV) which was integrated with the SOP optical system [Figs. 1(b) and 2(c)]. The NIR laser has a repetition rate of up to 1 MHz, standard pulse lengths ranging from 20 to 420 ns, and a collimated beam diameter of 10 mm. Focusing creates a spot size on the sample of $11×14μ m$ (FWHM). Some laser waveforms possible are shown in Fig. 3. The maximum pulse energy is 1 mJ (depending on the waveform and repetition rate), and peak power of 10 kW. Incident laser power is attenuated from 100% to 0% by a combination of polarizing beam splitting cubes and rotating quartz waveplates in the laser beam path [Fig. 1(b)]. The upstream and downstream laser powers are controlled separately.

The SOP experiments at the HED instrument are designed to take place in IC2. Figures 1 and 2 show the optical configuration used during these experiments. Further details about the experimental setup of IC2 can be found in Refs. 39 and 63–66.

Optical access to the sample is possible from both upstream and downstream sides, relative to the XFEL beampath (see Sec. II A). The near-sample optics consist of turning mirrors at 45 degrees relative to the XFEL beam, and objectives (AdlOptica geoHEAT-60-NIR) with 60 mm focal length focusing through the mirrors onto the sample plane. The mirror-objective system can be retracted when not in use in order to completely clear the x-ray beampath. The optical beampaths are guided through the chamber window to the custom-built exterior optical table [Fig. 1(b)] where the rest of the optical components are placed.

The upstream turning mirror was initially a dielectric coated glass mirror (Semrock MGP01-650-1300) with a 300  $μ$m diameter hole drilled in the center to allow the x-ray beam to pass through. The downstream turning mirror was a custom-made glassy carbon plate coated with Ag. Both the upstream and downstream mirrors were later replaced by 1 mm thick Ag-coated silica glass mirrors (from AHF) with holes drilled for x-ray direct beam transmission. The hole diameter is 1 mm downstream and 300  $μ$m upstream.

The downstream and upstream optical paths each include microscopic imaging of samples (with recording), illumination of the sample, and heating with the NIR laser. Optical emission for pyrometry is acquired from the upstream side of the sample, by passing light through to the spectrometer and steak camera system. Online microscopy is achieved using long focal length lenses (f = 750 mm upstream, f = 1000 mm downstream) to image onto Basler CCD cameras, to provide sample viewing and alignment at high image magnification. Illumination from both sides of the sample is achieved by inserting pellicle beamsplitters in front of the viewport chamber window on the optical paths to deliver a red LED light source to the sample. Alignments are made using direct imaging of the NIR laser at low laser power and localized effects of x-ray irradiation, including target fluorescence or damage imprinting.

The optical path of the pyrometric signal includes an optional spatial filter consisting of a 50  $μ$m diameter pinhole and two 60 mm focal length lenses (⁠ $∼1:1$ magnification) designed to exclude non-sample emissions and other background light (such as x-ray fluorescence from diamonds above and below the focal plane in DAC targets). The light is focused onto the spectrograph entrance slit by a f = 150 mm lens for an effective magnification of $∼2.5$⁠. The numerical aperture is $∼0.16$ at the imaging objective and spatial filter segments, and less at the spectrometer. Additional details on the optical configuration of the SOP can be found in Refs. 11, 47, and 67.

In order to acquire time- and spectrally-resolved information on the emitted light, an optical spectrometer (IsoPlane 160, Princeton Instruments) is coupled to the front slit of the streak camera. The vertical slit of the spectrograph restricts input emission in the spectral direction. The spectrometer has a 203 mm focal length and f/3.88 aperture ratio.

The streak camera is a Hamamatsu with S-20 photocathode (model C13410-01A) with spectral response in the region of 200–850 nm and a horizontal slit which restricts the input emission in the time axis direction, affecting the time resolution and point spread function (PSF). The microchannel plate (MCP) intensifier gain of the streak camera can be varied from 0 to 60. The gain corresponds to varying the voltage on the MCP electrodes; higher gain increases the signal and also the noise. The sweep windows for the streak camera range between 0.5 ns and 1 ms. The streak tube is coupled to an ORCA-Flash 4.0 V2 Digital CMOS camera with 1344 (wavelength) $×$ 1016 (time) pixels in the working area and 6.5  $μ$m pixel size; sometimes, this is binned $2×2$⁠, i.e., 672  $×$ 508 pixels to improve data handling. The readout speed of the camera is $>100$ frames/s. Two different collection modes, enclosing trigger and sequential mode, are used. In sequential mode, exposure to the CMOS only occurs during a single sweep regardless of how many events are incident, meaning that the visible signal from the interaction of each NIR or XFEL pulse is recorded on the final spectrogram, separated in the time domain by their intrinsic pulse separation (see Sec. II A). In most cases, the experimental data is taken using this mode. For data collected in the enclosing trigger mode, the spectrogram shows emission that has been integrated over many sweeps at a repetition rate of up to 1 kHz, with varying total integration time. Thereby, increasing integration time increases the number of exposures that are accumulated per spectrogram image, each sweep acquiring a (presumably identical) repeating event (i.e., heating cycle). This mode is compatible with accumulation over EuXFEL pulse trains repeating at 10 Hz. Figure 4 shows schematically how the two different collection schemes differ.

The wavelength axis of spectrograms is calibrated to the emission from a Ne calibration lamp resulting in a 451–955 nm observable wavelength range in this experiment. The optical response of the SOP system is a combination of the quantum efficiency of the S20 photo-cathode, the reflectivity of the turning mirrors, and the accumulated behavior of other optics (Fig. 5, see Sec. II G). The transmission function $F(λ)$ is experimentally measured by imaging a W calibration lamp with a known gray-body Planck distribution and comparing the intensity, as a function of wavelength and time, to the theoretical Planck distribution for the temperature at which the lamp is operating. Figure 5(a) shows that between 575 and 775 nm, the experimentally measured transmission closely agrees with the spectra predicted from the two main optical elements discussed above. Most spectral dips and oscillations in this transmission function were later eliminated by replacement of the dielectric turning mirror with the Ag-coated mirror,⁶⁸ also enabling a somewhat broader spectral band for detection [Fig. 5(b)].

The combination of horizontal and vertical slits in the streak spectrometer, located at the imaging planes of the sample, also function as vertical and horizontal spatial filters, respectively, and ensure good time and spectral resolution for spatially extended emission sources. Here, we report both slitted and slitless operation, the latter case being required during early EuXFEL experiments where x-ray beam pointing drift and instability precluded reliable alignment to the slits, with the small emitting area on the samples, imaged to the detector, functioning as a point source in the time and space directions, with sufficient (but reduced) temporal and spectral resolution.

An example of the streak camera acquisition of optical light emitted from the W calibration lamp, designed to be a thermal gray-body source at a set temperature, is illustrated in Fig. 6. The horizontal axis represents time (here a 5  $μ$s sweep window), and the vertical axis contains spectral information covering 451–955 nm. Poor optical sensitivity in the intensity measurement at the edges of the spectrogram are observed, so we restrict the wavelength range when fitting temperatures to 575–775 nm. All reference lamp calibrations were obtained with slits and spatial filtering in place, in order to probe the precise optical path from the sample in the respective transmission function.

From spectral features present in the calibration spectrograms, datasets with distinct event timings, and data on spectrally distinct light sources (i.e., laser or LED), some warping of streak images is observed, dependent on the streak window; that is, shear distortions with respect to the wavelength and time axes are identified. We compensate for this warping by applying a shear distortion to both wavelength and time axes unique to each sweep window. The magnitude of the shear, per pixel, in each direction, dependent on the streak window used, is given in Table II.

Collected spectrograms are also expected to exhibit “pincushion” flat-field sensitivity variation in both axes, on the order of 10% sensitivity. This is corrected for by calibrating the experimental emission data locally (in time and wavelength) to a spectrogram of a calibration lamp at a set temperature (e.g., Fig. 6), using identical sweep window and gain settings.

Non-thermal luminescence due to x-ray exposure is often observed in targets containing dielectric materials, including YAG:Ce scintillator crystals used as fluorescent screens for beam alignments, and diamond anvil cell targets often comprising multiple layers of dielectrics (Fig. 7). On shorter sweeps, in the 5–50  $μ$s range, this often manifests in SOP images as short pulses of emission, coinciding in time with irradiation from the XFEL pulses, and can be attributed to x-ray fluorescence. Fluorescence emission pulses are thus discriminable from thermal emission as they are usually symmetric in time (unlike heat pulses³¹), appear at lower power (where direct heating is small), and only where transparent dielectrics are present in the beam (which also have low emissivity). X-ray fluorescence also increases quasi-linearly with x-ray fluence (Sec. V D). Since fluorescence appears in the streak images as a symmetric peak in time, in most cases we treat it as instantaneous, with an apparent width due only to the PSF of the combined optical-detector system. That is, the width is not dependent on time since true emission duration is much smaller than the time resolution of the utilized streak windows, and instead the width represents the physical size and distribution of emission arriving on the photo-cathode of the streak camera. Femtosecond-excited fluorescence and decay would normally exhibit asymmetric behavior. Indeed, some minor deviations from symmetric emission are observed but are generally not well resolved in experiments to date. The fluorescence could be examined in more detail using faster sweeps but this was not attempted here. Fluorescence peak profiles are thus well modeled with a Lorentzian function. Peaks can be fit to determine peak location, amplitude, and full width at half maximum (FWHM)—which is also the FWHM of the PSF. Fluorescence can also be forward modeled if these parameters are known.

Figure 7 shows how fluorescence emission, collected when operating in the slitless configuration, can be commonly observed from DAC targets when irradiated by x-ray pulses (here a single pulse). Emission intensity is pronounced when using type Ia diamond anvils, and may vary with respect to the pressure medium. In contrast, no fluorescence emission is observed from Type IIa diamonds with an H₂O pressure medium. Other experiments targeting an interface of the diamond with a metal have confirmed significant fluorescence from Type I diamonds and total absence of fluorescence from Type II diamonds, limiting the emission to the diamond itself. For almost all of the targets, fluorescence emission follows a similar Lorentzian-like distribution in the time domain. This confirms the timescale of fluorescence emission is instantaneous in comparison to the streak window and so indicates the PSF of the optical system. However, in the case of an NaCl sample, a time delay and asymmetry of the emission peak is observed with the corresponding Lorentzian fit shifted significantly to later times. The results suggest that the fluorescence lifetime of NaCl is longer than other materials, and so can be detected here.

The spectral shape of fluorescence emission from select DAC samples (HIBEF24, HIBEF30, and D1, see Sec. IV) is compared to thermal emission from the calibration lamp in Fig. 8(a). The raw emission spectral shape is determined by summing the emission from large numbers of pulses over many spectrograms and within spectrograms, where there is no thermal emission and only fluorescence emission is present at the time of the fluorescence pulse. Strong peaks in fluorescence emission at $∼450$ and $∼800$ nm, not seen in emission from the calibration lamp and located in lower-sensitivity spectral ranges of the SOP, are characteristic of the XFEL induced fluorescence. Spectral shape is fitted to five super-imposed Gaussian distributions which approximate the distribution shape for fluorescence forward modeling (see Secs. V D–V F). Similarly, after accounting for the transmission function of our optical system, we see that the strong peaks in fluorescence are magnified, while there is minimal emission between 600 and 750 nm, where we observe a strong thermal signal [Fig. 8(b)]. In comparison, Fig. 8(c) shows the spectral shape of the fluorescence emission measured for both Type Ia and IIa diamonds under synchrotron x-ray irradiation at 18 keV. The spectrum for the Type Ia diamond was measured from an upstream diamond anvil of a DAC, with the x-ray beam targeting the Re gasket to exclude emission from the sample and downstream diamond. The Type IIa spectrum was measured from a free-standing diamond.

The time resolution of temperature measurements is set by the choice of time bin width. The measured PSF establishes the minimum usable time resolution for a certain configuration, below which it is not possible to measure dynamic processes. For example, noisy (e.g. low temperature) data require a larger time resolution, whereas high temperature data with strong signal can be analyzed with a small time resolution, but not smaller than the PSF since this is the intrinsic response time of the detector.

The PSF of the streak images is highly dependent on the optical configuration used, including entrance slit widths. During initial commissioning at EuXFEL, when all spatial filtering and slits were present, the PSF was 15 pixels when the SOP image was binned $2×2$⁠, i.e., 30 pixels for $1×1$ binning, which is 140 ns for a 5  $μ$s streak window. When the spatial filter and slits were removed, the PSF widened to 25 pixels FWHM, i.e., 50 pixels for $1×1$ binning, and 242 ns for a 5  $μ$s streak window. There was also a shift in the peak locations (by $∼2$ pixels earlier). Improvements after the experiments reported here further reduced the PSF with spatial filtering and slits to 7 pixels FWHM in $1×1$ (un-binned) images (i.e., 34 ns for a 5  $μ$s streak window), using an optical configuration similar to experiment 3 (Tables I and III).

Sweep rate, and the associated streak window, of the SOP spectrograms were initially set to factory calibrations.⁶⁹ We confirmed streak window lengths by measuring the distance between neighboring pulses of fluorescence emission. XFEL pulses that are incident on target are separated by 443 ns in this study; therefore, we expect that the associated fluorescence emission is also separated by 443 ns across all wavelengths. By comparing the measured pulse separation of XFEL pulses in pixels to the known pulse separation in seconds, the full length of the streak window is calculated. Durations of the 5, 10, 20, and 50  $μ$s streak windows are determined to be 4.73, 9.27, 18.57, and 45.64  $μ$s, respectively (Table II). For streak windows longer than this, we are unable to determine duration as there is insufficient resolution between neighboring peaks in emission to determine pulse separation. For a 5  $μ$s streak window, we determine that the factory calibration is acceptable, while for longer windows, the discrepancy between our measured values and the factory calibration is such that measured values are recommended. Further measurements are required to determine the absolute timings of the other streak windows. A linear sweep rate approximation is found to be accurate enough for most analyses (including all those presented here), however, non-linear corrections are required in certain scenarios, for example, in modeling fluorescence at smaller PSF where the precise location of the fluorescence peak becomes important.

Fluorescence peak position can also provide absolute information on x-ray timing within the streak window. Thus, where it was possible, the fluorescence of a particular target was used to determine the global timings of streak images collected for that target, i.e., time zero is set to be the time at which the first pulse in any given train reaches the target. If insufficient or indistinct fluorescence emission was present for data on a particular target, then experimental timings were estimated from the timing of separate YAG:Ce screen fluorescence or from the onset of optical emission. Relative timings of the optical laser were estimated using emission observations, and local photo-diodes which observed both radiation sources.

During image processing, the background is first removed by subtracting a dark image from the data and is further corrected by subtracting the averaged emission intensity in the spectral “dead” zone (850–955 nm).

Each spectrogram is binned with respect to the time axis, therefore reducing the time axis to discrete time steps at which we determine temperatures. The size of each bin is the time resolution, $t R$⁠, of a run and will vary based on the type and quality of emission. The time of each bin is calculated to be the time at the center, with $t=0$ denoting the time at which the sample is first irradiated. Generally, a $t R$ comparable to the FWHM of the PSF optimizes the time resolution.

A moving average of the intensity of optical emission with respect to wavelength was also computed in order to visually better compare noisy data with the Planck fit. The spectral intensity distribution is determined by a 50 pixel (or 37.5 nm) wide moving average, regardless of sample or streak window.

As discussed above, certain samples may exhibit x-ray fluorescence during XFEL experiments which can overlap with any thermal signal present. In the examples discussed here, fluorescent emission is clearly discriminated from thermal emission. It only occurs during XFEL pulses, often as distinct peaks (or as a continuum where pulses overlap in longer sweep windows), whereas thermal emission often persists after pulses due to the longer relaxation time of thermal processes. Fluorescence is particularly strong in the blue where thermal emission is usually insignificant. Spectra containing high fluorescence also exhibit clearly non-Planckian trends. Here, we explore removal of fluorescence emission to improve temperature analysis by building an empirical model of the fluorescence spectral and temporal shape and fluence dependence, for any given sample. This is based on data where no thermal emission is observed (at low XFEL power), which then establishes fluorescent background for thermal emission data (at higher XFEL power) (Sec. V D). We find that when the fluorescent background is weak compared to thermal signal it has a negligible influence on the assessed temperatures. Additionally, fluorescent emission tends to be temporally localized so that purely thermal emission can be detected at other times (e.g., between or after pulses).

A number of criteria were used for automatic data reliability assessment in temperature measurements. These criteria were based on a careful review of data accuracy and noise performance and exclude spurious data but do not guarantee measurement quality. Data are excluded if

1. There is significant (⁠ $>30%$⁠) signal at or below zero intensity (after background subtraction), within a time bin. This implies insufficient optical emission to determine sample temperature. It should be noted that in high noise datasets the standard deviation of intensity in a binned spectrum can exceed the average intensity even after this exclusion is applied, but there is sufficient signal above zero for reliable fitting.⁷⁵ 

2. Least-squares fitting returns temperatures below $∼1500$ K.^{11,13,48,51,57,58}

3. The emissivity determined from fitting the data to Eq. (1) (⁠ $ϵ f i t$⁠) is 1000 times smaller or 100 times larger than the emissivity determined from fitting the emission spectrum from the calibration lamp (⁠ $ϵ c a l$⁠), i.e., $100⋅ ϵ c a l< ϵ f i t<0.001⋅ ϵ c a l$⁠. This criterion accounts for physical limits on emissivity variation and the possibilities for different size emitting areas observed.

4. The magnitude of temperature uncertainty (Sec. II H) obtained from least squares fitting exceeds 50% of the absolute temperature.

Temperature is ideally uniform over the heated area which the measurement is restricted to using the slits and spatial filter. The wavelength dependent emission as a function of time can be used to infer local temperatures reached and the subsequent rate of temperature change unambiguously.¹¹ However, temperature gradients are expected to be present in the observed surface areas even when using these filters due to (a) imaged beam sizes similar to or smaller than spatial filtering elements, (b) Gaussian (or similar) beam spot profiles, (c) misalignment and beam drift, (d) thermal conduction in targets, (e) overlapping exposures in x-ray pulse trains, and (f) interplay of optical and x-ray beams of different sizes. Spatial filtering elements (slits and spatial filter) were removed in some earlier experiments to address XFEL beam drift, but this should not affect the observed temperature distribution significantly as the optical pathway and observed area is only weakly affected by this. We consider that the observed temperature in SOP represents the maximum achieved on the observed sample surface, considering the strong scaling of emission intensity with temperature in the visible range and findings in comparable offline systems (e.g., the optical laser heated DAC).⁵⁵ Our experiments combining large-spot optical radiation and small-spot x rays bears out this expectation, with local hotspots tending to dominate apparent temperatures (see Sec. V).

We use two independent ways to calculate the error on the temperature that is determined through least squares fitting: (a) from the in-built error from the curve_fit function in the SciPy python package⁷² that is used for fitting and (b) from the curvature of $χ 2$ in temperature-emissivity space.

The built-in Python error estimate, which is based on the minimization of the goodness-of-fit parameter $χ 2$ and calculated from the square-root of the diagonal of the covariance matrix, is consistently the smaller of the two.

The second derivative of $χ 2$ [Eq. (4)] about the minimum determines $σ T$⁠. Assuming a quadratic relationship between $χ 2$ and the temperature of the form $χ 2=α⋅ T 2+β⋅T+δ$ implies that $σ T= 1 / α$⁠.⁷⁶ Considering that fit parameters are strongly correlated, we compute the second derivative in $χ 2$⁠, with respect to temperature, using the minimum magnitude of $χ 2$ at each temperature, i.e., with emissivity allowed to vary. This is intended to represent a conservative error estimate. The minimum on the contour map slightly differs from the temperature determined from the curve_fit fitting routine but only by up to several degrees; the difference is too small to observe in our plots.

Figure 9 shows the $χ 2$ contour map from least squares fitting of the calibration lamp at 2500 K, calibrated to emission from the same lamp at 2900 K. The standard deviation, $σ$⁠, in a parameter is defined as the magnitude at which a parameter needs to change from the fitted value, i.e., $σ T=|T− T f i t|$⁠, in order to increase $χ 2$ by 1, i.e., $χ 2(T)− χ min 2=1$⁠. Figure 9 shows the variation in the goodness-of-fit parameter, $χ 2$⁠, as a function of temperature and relative emissivity about the minimum, with the $1σ$ contour shown in black; the inset shows the quadratic fit of $χ 2$ versus temperature. Both the error determined with this method and that determined from the fitting routine are shown as temperature error bars for comparison (black and red bar, respectively). We observe that the uncertainty that we obtain using this method regularly exceeds the other estimate.

The uncertainty in a single temperature measurement, from a single bin, is expected to be dependent on both the experimental settings, i.e., streak window or MCP gain, and fitting parameters, i.e., time resolution $t R$⁠. To investigate how the fitted temperature and its associated uncertainty is affected by changing parameters, a series of calibration spectrograms were taken, with the lamp temperature set to 2500 or 2900 K, the MCP gain varied from 30 to 60, and using streak windows between 1 and 200  $μ$s. SOP spectrograms of the calibration lamp were collected in gated enclosing trigger mode with either 1, 10, or 100 integrated sweeps. Because each image will measure the same, known temperature at all times, we can examine how measurement accuracy and precision depend on time resolution (bin width), sweep window, gain, and integrated sweeps and, finally, compare uncertainty obtained from individual spectrum fits as discussed above to the statistical error in fitted temperature across the image (i.e., standard deviation of fitted temperatures at many times), which represents the true measurement error (Fig. 10).

Figure 10(a) shows how the fitted lamp temperature at 2900 K, collected from single sweeps with 60 MCP gain and a 5  $μ$s streak window, varies across the time axis with changing time resolution. The scatter in fitted temperature increases as the binning time is reduced from 483 to 96 ns. Figures 10(b) and 10(c) show how the average temperature across the spectrogram and its statistical error (standard deviation, given by the error bars), varies as a function of binning time from multiple calibration runs at both 2500 K, with MCP gain at 60, and 2900 K, with MCP gain at 50. The range of PSF values (PSF_range, Sec. II E) is shown for comparison. At both lamp temperatures, we see that by increasing the time bin size we decrease the statistical error in the temperature measurement. Figure 10(d) demonstrates how varying the MCP gain affects average temperature, for time resolution fixed at 198 ns in a 5  $μ$s streak window. Generally, changing the gain has very little effect on the average fitted temperature and the associated statistical error as they remain consistent at all gain values. However, increasing the number of integrated images substantially reduces the statistical error. Therefore, in the single shot mode, which is used in the majority of experimental runs, we can increase the MCP gain in order to improve emission detection without largely affecting the validity of the temperature measurement, which implies that additional noise associated with higher gain modes has no effect on measurements.

In all cases above, the streak window has been fixed at 5  $μ$s as it is the most common streak window used in the experiments discussed here. However, observing emission over a longer time window (i.e., up to 200  $μ$s) is often needed to for longer events, such as irradiation by long XFEL pulse trains. With the lamp temperature fixed at 2900 K, MCP gain at 50, and a fixed time bin of 20 pixels, we are able to determine the effects that increasing streak window from 1  $μ$s to 200  $μ$s has on both fitted lamp temperature and its statistical error [Fig. 10(e)]. The reduction in error as the streak window is increased mirrors the effect of increasing the time resolution [Figs. 10(b) and 10(c)], as by fixing the time bin and increasing the streak window, we are essentially increasing the time resolution. Therefore, at longer streak windows it is possible to bin images by a smaller number of pixels and still maintain sufficient emission per bin in order to measure sample temperature precisely.

It is expected that the statistical error in fitted temperature across the image should be equal to the uncertainty of single fits at a given time. By comparing the individual single fit error either from the least squares python fitting routine or the $χ 2$ map to the statistical error in each image, we evaluate the two practical estimates for temperature uncertainty. Figures 10(f) and 10(g) show results when the lamp is set to 2500 and 2900 K, respectively. The line at which the single fit error is exactly equal to the statistical error (1:1) is shown for reference. Generally, we see that the least squares fitting underestimates the error by a factor of $∼0.5$ while the $χ 2$ map error can overestimate the error by up to five times the statistical error. We, therefore, take the least squares fitting error as the standard estimate for the uncertainty of a single temperature measurement in our analysis; where only a single error bar is shown in a plot, it refers to this estimate.

Regardless of collection parameters, we see that the average of fitted temperatures in a given image are consistent with the known lamp temperature [Figs. 10(b)–10(e)], i.e., the mean temperatures match the known temperature within the statistical error better than 68% of the time, consistent with these error bars having 1-sigma precision. Single fits’ least squares errors show generally greater deviations from the known temperature [Fig. 10(a)], consistent with our assessment that these are close to 0.5-sigma equivalent precision, in which case, the single fits are in agreement with the known temperature within 1-sigma error $∼68$% of the time. Thus the measurements exhibit good accuracy for this controlled example.

Irradiation of samples was performed during SOP observation using a nanosecond NIR optical laser pulse at 1070 nm (LH) and a femtosecond XFEL pulse train, with one, two, or multiple pulses, at 17.8 keV (XH) (see Sec. II A). Samples were free-standing or confined at high pressure in a DAC (Table III). The streak window was set to cover both sample heating and cooling. Figures 11(a) and 11(b) illustrate the differences between the two different pump scenarios. For LH, a rise in temperature as the sample is irradiated is expected, after which the sample should start to cool. Peak temperatures are expected to be observed after the peak in laser power. For XH, each XFEL pulse incident on the sample will cause its temperature to rapidly increase upon exposure, after which the sample will cool. Subsequent XFEL pulses may lead to further increase in temperature if arriving before cooling is complete. An XFEL pulse train with high repetition rate results in a stepwise, saw-tooth like temperature change with time.^31,36 When LH and XH are combined, the process is considerably more complex, as discussed below. In addition to time variation in temperature, spatial variation (and its time dependence) can be important. Integration of a single sweep of a single heating and cooling event (sequential mode), or integration of many sweeps over repeating, ideally identical events (enclosing trigger mode), is employed in different experiments, with the latter improving the signal to noise ratio.⁶⁷ 

The SOP system was first tested with the NIR pulsed laser heating system, at the Deutsches Elektronen-Synchrotron, Germany (experiment 1) before being moved to the HED instrument hutch at the European XFEL. Results are reported for a free standing sample of 5  $μ$m thick Pt foil employing LH at a repetition rate of 1 kHz (see Sec. V A) with the laser waveform WF_0 (Fig. 3). The streak camera was configured to operate using the enclosing trigger mode over a integration time of 1 s (collecting 1000 heating cycles) with the streak window set to 1  $μ$s. Sample temperature analysis is limited to 525–800 nm (Fig. 5).

Once installed at the HED instrument, we performed MHz repetition rate (1.13–2.26 MHz)³² pulsed x-ray heating (experiment 2)^{33,39,59,61,64} on samples free-standing in vacuum or statically confined in a DAC (Table III). Beam energy was set to 17.8 keV, with a Gaussian profile with a 10–20  $μ$m FWHM and a pulse length of 20 fs. The number of pulses per train varied from 1 to 20 with a pulse separation of 443 or 886 ns. The maximum energy on target per pulse was $∼240$  $μ$J with a peak fluence of $∼100$ J cm $− 2$⁠. Unless otherwise stated, the wavelength range for fitting in this experiment was restricted to 575–775 nm and a $2×2$ binned spectrogram image size, i.e. 672 $×$ 508 pixels, was used. Due to the limited intensity of emission that we observed at the beginning of the experiment, the slits and pinhole in the optical path were removed mid-experiment, increasing signal.

Further LH experiments were performed at the HED instrument, during a series of laser-heating commissioning runs in combination with XFEL radiation (experiment 3).⁶³ The goal was to understand how to heat samples optically and probe noninvasively with x-rays. These experiments focused on assessing any combined effects of heating with the NIR laser and XFEL, when both lasers are incident on the sample during collection of optical emission. The x-ray pulse train comprised of 10–30 pulses spaced by 443 ns, an x-ray energy of 17.8 keV, an average energy per pulse on target of 126  $μ$J at 100% transmission, a focal spot size of $4.5×5$  $μ$m², and a pulse length of 20 fs. Due to improvements in the beam alignment the NIR laser spot, the XFEL spot and the full spatial filtering system (which was in place during this experiment) were all well aligned. The full spectrogram image size was used, i.e., 1344 $×$ 1016 pixels, and streak windows were set to 5  $μ$s. The optical laser was focused on the upstream surface of the sample, aligned to the same location as the XFEL, and sometimes also on the opposing downstream surface of the sample (double-sided heating).

For experiment 1, the target (DESY1) comprised a 5  $μ$m thick piece of Pt foil suspended in air.

For experiment 2, we report on data from a free standing foil target and samples enclosed and pressurized by a symmetric piston-cylinder type DACs (Fig. 12). For SS2, a 7.0(3)  $μ$m thick Ta foil, from GoodFellow, was mounted on a 100(20)  $μ$m thick Kapton tape substrate and suspended in vaccuum. DAC HIBEF3 was prepared with 200  $μ$m culet type IIa diamonds, and a 2  $μ$m piece of Au foil was loaded inside the chamber with H₂O and compressed to 30.3 GPa. DAC D1 was prepared with 300  $μ$m culet type Ia diamonds and loaded with a 3  $μ$m thick insulating layer of pressed MgO powder and 5  $μ$m Ta foil before gas loading with Ne and compressing to 12.0 GPa. DAC HIBEF30 was prepared with 300  $μ$m culet diamonds, with type IIa downstream and type Ia upstream, then loaded with three 20  $μ$m thick disks of polycrystalline San Carlos Olivine and a 5  $μ$m Pt foil then filled with Ne gas and compressed to 35 GPa. Some samples also contained a ruby (Al $2$O $3$⁠:Cr) grain for use as a pressure marker.⁷⁷ Additional DAC samples where only the pressure medium was targeted are listed in Table III.

For experiment 3, two symmetric piston cylinder DACs were used. XFEL1 was prepared with 300  $μ$m culet type Ia diamonds and XFEL2 was prepared with 200  $μ$m culet type Ia diamonds. A 4  $μ$m thick piece of Pt foil was placed with an insulating layer of KCl on either side in both cells and compressed to 31 (XFEL1) and 30 GPa (XFEL2).

Sample position was moved, where possible, between runs so that each heating cycle was performed on a fresh unheated sample location.

Figure 13 shows the collected spectrogram and the resulting temperature measurement from experiment 1 (Pt foil in air), based on accumulation of 1000 heating cycles. A peak temperature of $3701±71$ K was observed, closely corresponding to the peak in laser power whereas emission intensity peaks later in time. Good agreement of emission spectra with the expected Planck distribution is observed over the full spectral range. We expect that the sample cools to ambient conditions between kHz cycles and that each cycle reaches similar temperatures; the close agreement of the spectra with a Planck distribution supports this. The differences between the different fit error estimations are shown in Fig. 13(b).

Target SS2 (Ta foil in vacuum) underwent irradiation by a single XFEL pulse at 50% x-ray transmission, which corresponded to a pulse energy of $∼44$  $μ$J on target. Using two different time resolutions, 135 and 193 ns, we determine peak temperatures of $∼6500$ K (Fig. 14). Emission was observed for $∼1$  $μ$s after exposure [Fig. 14(a)]. A large uncertainty (⁠ $σ T>10%$⁠) correlates with a weak and noisy emission in this case.⁶² That is, despite reaching higher temperature than both the calibration lamp and laser-heated foil in preceding example, the signal is lower due to only single-shot collection, smaller emitting area, as well as use of spatial filtering. Validity of the temperature estimation is confirmed by the damage imprinting observed during post-experiment analysis [Fig. 14(d)]. The observed hole and drip features formed suggest that there was sufficient heating to melt a large area of the target consistent with high peak temperatures measured well in excess of the melting point. The short emission timescale can be explained by rapid target quenching (Sec. VI).

HIBEF3 (Au foil in H₂O pressure medium) underwent irradiation by a single train of five XFEL pulses at 100% x-ray transmission and 2.26 MHz repetition rate (experiment 2) with an average pulse energy on target of $152±81$  $μ$J. Two different time resolutions, 96 and 135 ns, were used to evaluate the temperature from the SOP (Fig. 15). This cell was loaded with type IIa diamond anvils, and no additional background from fluorescence is observed (see Sec. II D). In Fig. 15(a), it can clearly be seen that as each XFEL pulse interacts with the target there is an increase in emission intensity on the SOP spectrogram, followed by a drop in intensity between pulses, as expected when the Au foil cools. We observe a peak temperature of $∼5500$ K and minimum measurable temperatures of around $∼2500$ K. Figure 15(c) highlights how the wavelength dependence of emission intensity changes with both time and temperature.

The temperatures achieved indicate that the Au sample was partly melted during the experiment, as temperatures exceed the known melting point of Au at 30 GPa (T_melt $∼2300$ K).⁷ We can see from the temperature profile that subsequent pulses do not stepwise heat the sample as expected,³¹ with peak temperatures averaging about 4500 K at the time of pulses 2–5. This could be due to the specific energies of each pulse in the train, disruption of the Au upon melting,²⁹ or increase in the opacity of H₂O under high pressure and temperature^23,78 leading to limitations on apparent temperature.¹¹ It is also notable that peak emission intensity increases with time, despite no clear increase in peak temperature, which can be attributed to increased emitting area (i.e., due to lateral heat conduction) or emissivity (i.e., due to optical changes in pressure medium). Similar effects are detected in other targets. Compared to the freestanding foil, there is a more gradual decay of the emission intensity after heating, likely a result of better confinement and insulation of the sample during quenching.

The preceding examples lacked discernible fluorescence, and emission was interpreted as purely thermal radiation. We now discuss targets having significant x-ray fluorescence background (Sec. II D). For example, Figs. 16(a) and 16(b) compare SOP records for irradiation by two XFEL pulses, with an average energy on target per pulse of $∼135$  $μ$J, where a difference in the observed optical emission between the similar samples and different diamond types (Type Ia in VP002 and Type IIa in HIBEF3) can be seen. In both cases, we are observing emission from a Au sample in H₂O pressure medium, at 37.0 and 30.3 GPa, respectively.

While the SOP spectrogram from the sample in DAC VP002 shows emission across all wavelengths below 850 nm, there is very little or no emission detected for sample of HIBEF3. As the only difference between VP002 and HIBEF3 is the diamond type, we conclude that Fig. 16(a) shows the fluorescence signal from the diamonds in VP002. In terms of the spectral response, we see that in the regions where $λ<575$ nm and $λ∼800$ nm, there are peaks in the emission intensity, which characterize fluorescence emission from a variety of targets (Fig. 8). The optical emission from the sample in VP002 demonstrates a symmetrical shape with respect to time, which as discussed represents the PSF of the SOP.

The weak emission from the sample in HIBEF3 at low XFEL pulse energy [Fig. 16(b)] shows only emission from the second pulse and with a very different temporal and spectral shape than that observed from VP002 — suggestive of thermal emission from cumulative heating. That emission here is purely thermal in nature is further clarified by increasing the XFEL energy on this sample [Fig. 16(c)], i.e., to $245±53$  $μ$J/pulse. The emission is asymmetric with respect to the time axis, with a tail in emission intensity after each XFEL pulse incident on the target, likewise the emission peaks at around $∼700$ nm in the wavelength axis, similar to the spectral shape of the calibration lamp (Fig. 8). Finally, a cumulative increase in emission intensity showing stronger emission from the second pulse is clearly resolved, following expectations of stepwise heating. The peak temperature, after the sample in HIBEF3 has interacted with the two XFEL pulses, is measured to be $5282±650$ K.

While fluorescence is often of some use, such as for alignment⁷ and determining experimental timings (Sec. II E), it can potentially interfere with pyrometric temperature measurements. This is because the measured spectrogram can become a combination of thermal and fluorescence emission at higher powers. Here, we explore how, when there is a large fluorescence signal, e.g., when using type Ia diamond anvils, the fluorescence component can be removed before temperature measurement. We, thus, examine whether and how the fluorescence signal would distort the spectral shape and temperature being measured.

To remove the fluorescence signal, we have developed a method to create a synthetic SOP image that simulates the fluorescence emission for a particular sample configuration. By measuring the optical emission from the same target at low XFEL beam transmission, with the same optical configuration and sample containment, and varying numbers of XFEL pulses, we can survey the fluorescence emission shape in both wavelength and time before the onset of any thermal emission. The streak window used in each run is kept constant throughout and all runs are recorded in sequential (single sweep) mode in order to correlate observed fluorescence with the power of each individual XFEL pulse.

The time evolution of fluorescence emission under pulsed XFEL heating is determined by multi-parameter least squares fitting^70–72 of a superposition of Lorentzian distributions (one Lorentz distribution is used for every pulse in the XFEL pulse train) to the wavelength-averaged spectrogram emission intensity in the UV region [451 $<λ<$545 nm; Figs. 17(c) and 17(d)]. No pincushion effect was accounted for prior to fitting. Peak separation in each fit is fixed and corresponds to the time between XFEL pulses in a train (here 443 ns). At low XFEL transmission there is minimal or no thermal emission so we observe a good fit between the Lorentzian curves and emission intensity with time [Fig. 17(c)]. Whereas at higher XFEL beam intensity and number of pulses there is only good agreement between the Lorentzian distribution and emission intensity at the start of the record (time $<0.75$  $μ$s) where only a few pulses have irradiated the sample, typical of a signal dominated by fluorescence [Fig. 17(d)]. That is, optical emission from later pulses (time $>0.75$  $μ$s) do not exhibit a good fit to the expected Lorentz shape and are seen to reach peak intensity later than expected from the pulse separation and have a longer decay time, indicating thermal emission contribution. This gives us a qualitative measure to distinguish between different emission types. After the Lorentz fits from multiple runs have been manually filtered, to only include fluorescence pulses, we can determine the average FWHM, or PSF, and amplitude of fluorescence emission in the time axis. The relationship between emission intensity and XFEL pulse energy, as measured by the beamstop photodiode “PD_3” [Figs. 1(b) and 17(e)],^{20,39,61,62,79} is determined to be a power-law fit [Intensity $=0.072⋅ PD _ 3 0.83$ for D1, Fig. 17(f)]. We can, therefore, determine the expected fluorescent emission intensity from the photodiode signal for any run using this sample. Spectral shape is determined through a least squares fitting of time-averaged emission intensity from the accumulated spectral shape from multiple fluorescence-only runs to five superimposed Lorentzian distributions [Figs. 8 and 17(b)]. We expect the results of the above fitting routines to depend highly on sample configuration, window thickness, materials present in the beam, etc., and so should be analyzed independently for each sample.

A synthetic fluorescence-only SOP image is then created using the average FWHM emission duration, amplitude of emission with respect to photodiode intensity and spectral shape of emission [Fig. 17(g)]. Subtraction of the synthetic fluorescence emission from the raw SOP image yields a modified SOP image which is used for temperature determination [Fig. 17(h)].

An example of a target with considerable fluorescence emission is DAC D1 (5  $μ$m Ta foil in MgO/Ne medium at 12 GPa in a DAC with Type Ia diamonds). After removal of fluorescence emission (Fig. 17, see Sec. V D), sample temperature is determined for four pulse XFEL irradiation at 100% x-ray transmission (⁠ $216±26$  $μ$J/pulse) (Fig. 18).

Here, we can see that emission from the first pulse is entirely due to fluorescence; prior to fluorescence removal, peak temperatures of 4000–6000 K were suggested, however, after correction the temperature is too low to detect (⁠ $≲2500$ K). The second pulse shows comparable levels of fluorescence and thermal emission; however, the apparent peak temperature rises from $∼4000$ to $∼5000$ K upon fluorescence correction. Hence, the effect of fluorescence on apparent temperature is not straightforward. Subsequent pulses (3 and 4) show much higher thermal emission than fluorescence, with the correction having a negligible effect. Finally, there is a long tail of thermal emission after the pulses which is not affected by fluorescence background and is unaffected by correction. As in the prior example of a DAC under XFEL irradiation (Sec. V C), peak temperatures reached after each pulse remain relatively constant later in the pulse train, while emission intensity rises.

With large numbers of pulses available at high repetition rates at modern XFEL sources (e.g., 2700 pulses at 4.5 MHz at European XFEL), there is much potential in using SOP in dynamic experiments on longer timescales. However, as the streak window length is increased, the spacing, in pixels, between successive XFEL pulses is reduced. This leads to poor definition between the optical emission of neighboring peaks and the expected saw-tooth like shape of emission intensity with time is smoothed out. In addition, it may be more difficult to discriminate and model fluorescence background. This means at longer streak windows, we cannot easily identify emission from individual XFEL pulses in the pulse train.

An example of this scenario is given here for an oxide mineral sample (olivine) with low absorbance and slow thermal transport dynamics at 35 GPa in a DAC (HIBEF 30), undergoing cumulative heating over 20 XFEL pulses at 2.26 MHz with a streak window of 20  $μ$s (Fig. 19). Fluorescence emission is evident from additional datasets collected at lower power, which shows characteristic strong emission in the blue.

To determine the expected fluorescence emission in this case, we surveyed the optical emission from a short streak window, e.g., 5  $μ$s, at varying XFEL pulse energies and converted it to the longer streak window during modeling, e.g., 20  $μ$s. The spectral shape and time dependence of the expected fluorescence spectrum is determined the same way as described above. To adapt from a 5  $μ$s window to a 20  $μ$s window, we assume the spectral and temporal shape [Fig. 19(b)], PSF (Sec. II E), and amplitude of emission intensity dependence on photodiode values is independent of the streak window but the spacing, in pixels, between XFEL pulses is reduced. The resultant fluorescence emission in the time domain [Figs. 19(a) and 19(d)] shows a continuous distribution throughout irradiation.

After removal of the fluorescence emission, the thermal-only signal is observed [Fig. 19(e)] and can be used to measure sample temperature [Fig. 19(f)]. By comparing the SOP spectrogram measured before [Fig. 19(a)] and after [Fig. 19(e)], the fluorescence emission is removed we can clearly see that the emission on the thermal-only image is only significantly changed during the first 5  $μ$s. This suggests that the emission in the first 5  $μ$s is dominated by fluorescence and that at later times thermal emission is dominant. Thus, only temperature measurement obtained early in the record differs significantly before and after fluorescence emission is removed while there is minimal change in temperature at later times — and none at all after the XFEL pulse train is completed [Fig. 19(f)]. A stepwise heating dynamic is clearly observed in both the temperature and emission records after correction.

As the magnitude of the fluorescence correction to temperature was particularly noticeable here, we also examined how uncertainty in the fluorescence correction might impact the results. To do this, we assumed a uniform increase or decrease of fluorescence intensity across all pulses in the pulse train. An increase or decrease within the uncertainty of the fit to image intensity vs photodiode intensity [e.g., Fig. 17(f)] produced negligible changes in the assessed temperature. Only when intensity errors exceed $∼20%$ do systematic errors become comparable to the standard error on the temperature. Fluorescence modeling error is less than this critical level for the experiments examined here.

Installation of the laser-heating system at the HED hutch allowed LH of samples in conjunction with x-ray irradiation. We first discuss results for pulsed LH of DAC samples without any x-rays (Fig. 20). Optical emission collected from Pt foil in a DAC with KCl pressure medium at 31 GPa (XFEL1) under pulsed LH with 1000 heating cycles (1 s exposure at 1 kHz streak repetition rate) using the enclosing trigger mode is shown. A peak temperature of $7800±400$ K is observed at the peak of emission at 0.12  $μ$s after the start of the laser pulse. The timing of the laser pulse is estimated from the onset of optical emission. Upon repeating this LH run multiple times, we observe that there is a large scatter in the measured temperature (Fig. 21), which can be attributed to changes in the sample coupling, which may be due to repeated melting. In all runs there is an unusual broadening of emission in time, such that emission appears well before the start of the laser pulse with relatively high apparent temperatures. This is possibly due to a bleeding effect occurring due to the large number of sweeps collected in the single image;⁶⁷ more study is required to understand this issue. However, it does not appear to play a role in single-shot collections.

Figure 22 shows an example of LH combined with x-ray irradiation of Pt foil in a DAC with KCl pressure medium at 30 GPa (XFEL2). The sample was irradiated by a single NIR laser pulse and 30 XFEL pulses at 12% x-ray transmission. The relative timing of the laser and XFEL is estimated from photodiode traces where both x-ray and optical laser were detected [e.g., Fig. 22(b)], as well as from peak positions in SOP data. Here, the first XFEL pulse is delayed by $−510$ ns from the start of the optical laser pulse. Instead of extending the streak window to encompass the whole event, i.e., all 30 XFEL pulses, the streak window only recorded the first few pulses. Good alignment of the NIR laser with the x-ray beam is confirmed by clear in-situ detection of laser heating by simultaneous x-ray diffraction.

With the x-ray transmission set at a level where no optical emission is observed from the x-rays alone, it is desired that only the laser pulse will heat the sample while the XFEL pulses will only probe the induced states. From the intensity profile, we observe a steady decrease in emission with time suggesting only laser-heating is occurring. From the temperature profile, however, we observe oscillations in the temperature after the laser pulse—not unlike the behavior shown above for x-ray heated targets, and at higher x-ray power on this target (see below). While subtle, the timing of these excursions, and their rather large amplitude, is consistent with significant XH.

At higher XFEL transmission, combined XH and LH clearly occurs in the target. Figure 23 shows an example of laser heating with x-ray pulse exposures at 50% x-ray transmission, on DAC XFEL2. The XFEL pulse train consists of 10 pulses and the delay of the first XFEL pulse from the start of the optical laser pulse was $+60$ ns.

Several noteworthy features are seen in the data. High temperatures are rapidly achieved by the transient optical pulse at the beginning of the experiment, as well as high emission intensity. This heat pulse decays with time after the laser shuts off. The contribution from x-ray heating becomes clearly visible after about 1  $μ$s. In comparison to lower power data on this sample, XH roughly maintains the temperature, while emission intensity drops off considerably. The large difference in emission amplitude in the LH stage compared to the XH stage, at a similar temperature, is likely due to the difference in hotspot size. That is, if the LH spot diameter is larger by a factor of $∼3$ (Sec. II A), the emission intensity should be greater by a factor of 9, which is similar to what we observed. Thus, in this experiment the transition between emission from the larger optical laser heating spot and emission from a smaller hotspot associated with the x-ray beam is observed. Also, rather than sustain the high initial temperature achieved by the optical laser, x-ray heating seems to achieve lower temperatures. This could be due to the conditions adopting a limiting x-ray train heating temperature for this sample,³¹ which is lower than that achievable by the optical laser—i.e. where x-ray pulse heating and inter-pulse cooling reach a balance at long timescales.

Finally, there is no detectable fluorescent emission despite using type Ia diamond in this experiment, with emission in both types of heating (LH and XH) equally well described as thermal only. This indicates that the spatial filtering system reduces the contribution of fluorescent emission from diamonds in the SOP spectrum.

Given that temperature measurements are deployed here in new experimental scenarios where they have been previously untested, we applied numerical finite element analysis (FEA) to representative cases. Examples of modeling for more traditional experiments (with optical laser radiation only) are discussed elsewhere.^11,13,67,75 That is, while the observations presented here are consistent with qualitative expectations for the heating and cooling behavior of samples under XFEL, optical, or combined radiation sources (Fig. 11), we further compare the observations quantitatively with the expected behavior,^13,31 first as predictions, and in cases where the prediction fails, by optimizing parameters to improve agreement between the model and the data. The objective is to provide greater insight into the heating behavior underlying the measurements, including the role of time-dependent temperature gradients, the correlation of emission intensity and temperature, and interactions between multiple radiation sources.

In our models, we assume the model geometry is fixed (see Fig. 24) and employ an isobaric approximation for thermal analysis, i.e., that the heating and cooling can be treated as if it occurred at constant pressure.³¹ This is suitable for making comparisons with the presented datasets. Temperature changes in the sample after initial heating are due to heat diffusion through the target; radiative heat losses from the sample (by way of thermal emission) have a negligible effect on the results (confirmed by running models with and without radiative losses). Inclusion of latent heat effects^39,80 had a minor effect on the models, but as this did not significantly affect first-order comparisons with the data, it was left out in the models reported here. Temperature dependencies of parameters were included where available, whereas pressure changes with temperature were expected to have only a minor effect and were not included.

The models account for the incident energy per pulse as measured in the beamline, with a factor accounting for transmission to the sample, which is nominally $∼30%$ of the upstream pulse energy monitor (SASE XGM)⁶¹ as determined in separate analysis of damage imprinting on freestanding foils.^39,62 In this way, the distribution of conditions achieved are predicted from the known beam properties, geometry of samples, and sample properties at relevant pressures and temperatures (Table IV).