Ultrafast electron diffraction and phonon-diffuse scattering (UED(S)) experiments make use of photo-induced changes to electron scattering intensity across 2D detectors to report on a very wide range of dynamic structural phenomena in molecules and materials. Compared to ultrafast spectroscopies, these techniques have very high structural-information content and competitive time-resolution, but sensitivity to relative changes in electron scattering intensity is orders of magnitude lower. Hybrid pixel counting detectors (HPCDs) are a promising technology for improved sensitivity and signal-to-noise in UED(S) experiments, as they offer near-zero readout noise and dark counts with the possibility of new acquisition modalities (e.g. shot-to-shot normalization) due to their high frame rates. However, it is well known that HPCDs suffer from count losses at high electron fluxes even in CW beam applications. How this translates to ultrashort electron pulse exposures has yet to be determined and is critical to understanding the application of this technology to ultrafast electron scattering experiments. Here we show that count losses are exacerbated significantly in ultrafast (pulsed) experiments and that HPCDs require count rates to be kept below $\approx 2$ electrons per pixel per pulse. This count-rate limitation presents a severe constraint on electron bunch charge when interrogating single crystal samples. A model for the electron counting uncertainties in HPCDs across the entire relevant range of average count rates is proposed, from which we derive experimental strategies to optimize data quality in UEDS using direct electron detectors. Finally, we suggest ways HPCDs could be better adapted to ultrashort pulsed beam experiments.
Ultrafast laser-pump, electron (or X-ray) probe experiments have made it possible to directly measure structural and electronic dynamics in molecules and materials in the time-domain 1,2 with sub-50 fs resolution. These nonequilibrium methods provide access to many of the microscopic processes that underlie material properties, including electronphonon [3][4][5] and phonon-phonon coupling 6,7 , lattice, charge and orbital ordering phenomena [8][9][10] . The ability to interrogate photo-induced phase transitions with these techniques has also deepened our understanding of how to optically prepare and control novel states of materials that exhibit properties that are inaccessible under equilibrium conditions [11][12][13] .
Here we focus on ultrafast electron-probe experiments. The default mode of data acquisition in these experiments is time-resolved scattering (Fig. 1), with the scattering signals measured over a range of scattering-angles using a 2D detector. Although time-resolved transmission electron imaging/microscopy is also under active development 14 , we will not discuss the particularities of time-resolved image resolution and sensitivity (detector quantum efficiency), focusing entirely on electron scattering measurements. An essential feature of the raw scattering signals measured is that they can be distributed highly non-uniformly across the detector. For gas-phase samples, polycrystalline materials or textured films, the dynamic range of the raw scattering signals tends to be narrow. For example, in a pattern of polycrystalline monoclinic VO 2 , the dynamic range between low-versus highindex Debye-Scherrer ring intensities measured under typical conditions in an ultrafast electron diffractometer is only of or-der ≈ 10. When probing high-quality single crystal samples, however, scattering is concentrated into Bragg peaks and the dynamic range of the raw scattered intensity tends to be many orders of magnitude larger than that observed from polycrystalline, amorphous or gas-phase samples. For example, under typical experimental conditions peak intensity in the first and second order Bragg reflections of graphite is 10 5 times the intensity of the phonon diffuse scattering features observable between the Bragg peaks 15 (Fig. 1).
The relevant signals in UES are the pump-probe delay-time dependent changes in electron scattering that result from photoexcitation of the sample, measured over as wide a range of scattering vector as possible. Current state of the art measurements are capable of resolving differential scattering signals (i.e. pump-on minus pump-off) at the 1-10% level relative to the unpumped scattering intensity, although signals approaching 0.1% have been reported for high-intensity features (Bragg peaks). To achieve a SNR (signal-to-noise ratio) of 5 for a signal change of 1%, differential scattering intensity measurements with a relative uncertainty (or relative standard error of the mean) of 0.002 are required. If the measurement is shot-noise limited, this requires the feature in question to contain at least 240,000 counts.
It is worthwhile to compare these actually measured signals with those that can be expected under weak-excitation conditions in a system that does not undergo a structural phase transition. For example, if laser-deposited energy results a 10 K increase in specimen temperature (after full thermalization) the (200), (300) and (400) Bragg peaks in graphite would be suppressed by 0.05%, 0.16% and 0.25% respectively (at room temperature) while single phonon diffuse scatter-FIG. 1. Schematic illustration of the experimental setup. Electron bunches (blue particle clouds) are compressed and focused onto the sample in normal incidence and produce a diffraction pattern on the detector, represented by a plane behind the sample. Simultaneously, the sample can be illuminated with a short optical laser pulse (red discs) with an adjustable time-delay. The temporal distance between electron bunches and optical pulses is dictated by the laser amplifier, in our case Γ -1 = 1 ms. The four screens on the far right side illustrate how difference images are calculated for different delay times. Red (blue) regions increase (decrease) in diffracted intensity. Projected onto the screen are simulated diffraction patterns of graphite.
ing from low-frequency acoustic modes increases by approximately 3% and optical modes by only 0.1-0.3%. Measurements of signal changes at the 0.1% level (or even the 0.001% level) are required to access the weak pump-excitation regime in UED(S) experiments. Under shot-noise limits, every 10fold improvement in the resolvable relative signal change (at constant SNR) requires a 100-fold increase in the number of counts contained in the feature measured. Thus, a critical direction for improving the sensitivity of UED(S) measurements has been maximizing electron count rates and the primary argument favouring the development of high bunch charge and high repeti
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