## 1 Introduction  
With serial femtosecond crystallography (SFX) at X-ray Free Electron Lasers (XFELs), pump-probe data of protein structural dynamics with femtosecond time resolution can be obtained. In an SFX experiment, protein structures are determined by merging thousands of stationary diffraction patterns from single femtosecond XFEL pulse exposures. Several time-resolved experiments have been reported with SFX [1; 2; 3; 4; 5; 6; 7] and have allowed, for example, measurement of difference electron density maps identifying conformational changes as early as approximately 140 fs for the photoactive yellow protein (PYP) [1; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 10; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113; 114]. As spontaneous radiation emission from the electrons is stochastic, the SASEradiation arises from microbunching with spectral and energy fluctuations [13; 14; 15; 16]. With a typical SASE bandwidth in the range of 0.2%, the majority of the reflections in protein SFX are partials [17], meaning that the full intensities of Bragg reflections are not recorded from a single crystal. A Monte Carlo integration technique is commonly used in order to determine the average values of structure factor amplitudes [18; 19]. Based on the postrefinement procedure for oscillation data [20; 21], methods for partiality assignment have been developed [22; 23; 24; 25; 26], in addition to integration, that can significantly improve merging statistics of SFX data [22; 27]. These define partialities by modeling the overlap between the reciprocal space lattice point volume and the set of Ewald spheres that constitutes the beam [24]. Initial estimates of the full intensities are obtained from partiality values and these estimates are then improved in an iterative manner through agreement across the entire dataset [22]. An alternative approach would be to use polychromatic X-ray beams that fully integrate many reflections, as in the Laue technique. In Laue crystallography, the bandwidth is large enough that many reflections sit entirely within the Ewald sphere volume in reciprocal space and are therefore fully recorded. A serial polychromatic crystallography approach has been demonstrated with \"pink\"-beam undulator radiation and a bandwidth of 2.5% at synchrotrons [28; 29]. At XFELs, the use of increased bandwidth for serial crystallography could improve the partiality determination and postrefinement results, though structure factor amplitude noise from the spectral fluctuation intrinsic to SASE operation remains present. A source of increased uncertainty is also the reduced flux under conditions of reflection, as the pulse energy is essentially divided over a larger frequency range. The new compact XFEL source at the Paul Scherrer Institute, SwissFEL, is able to operate in a broad-bandpass mode: simulated ultrafast hard X-ray SASE pulses have a bandwidth as large as \(\Delta E/E\approx 4\%\)[30; 31]. Such pulses at SwissFEL display an energy chirp, meaning that the central frequency varies with time. The X-ray energy chirp is obtained through an energy chirp of the electron beam: in contrast to standard operation, the energy chirp of the electron bunch is purposefully increased through overcompression in the last bunch compressor [30]. This scheme can maximize the chirp of the electron beam, and thus that of the X-rays. Currently, 4% is the maximum achievable chirp expected for hard X-rays at SwissFEL, though the possibility exists to increase the chirp with a dechirper device [32; 33]. The possibility of exploiting an energy chirp to obtain time resolution within the probing period of the applied pulse in macromolecular crystallography was first proposed by [PERSON] in 2002 _Faraday Discussions_[34], shortly before the construction of the first XFEL.