The challenges of bio-imaging

The advent of synchrotron radiation X-rays has revolutionized the imaging of biological structures, at the level of organisms, tissues, cells, sub-cellular structures, protein complexes and individual biomolecules. Typically 40% of the allocated beam time at a 3rd generation synchrotron source is used for the bio-imaging techniques phase-contrast tomography, coherent-diffraction imaging and protein crystallography. The growing popularity of phase-contrast methods stems from the much enhanced hard-X-ray contrast for biomaterial compared with absorption- based techniques, e.g., a factor 500 at a photon energy of 10 keV. Coherent diffraction imaging makes use of transverse coherence, obtained at the synchrotron by spatial filtering, to realize a spatial resolution beyond that available from focusing optics. Synchrotron-based protein crystallography is responsible for more than 80% of the structures in the Protein Data Bank, but this represents a mere 6% of all the proteins which have been sequenced to date. A major bottleneck in structural biology today is the necessity of isolating, purifying and crystallizing sufficiently large (>10 μm3) samples for a synchrotron-based experiment. Bio-imaging techniques based on electron microscopy and electron diffraction (see Infobox) are also growing in popularity; a shor t penetration depth limits their application to samples thinner than 1 μm.

By far the major factor limiting the resolution of current X-ray and electron bio-imaging techinques is radiation damage to the sensitive biological material. An undulator beamline at a 3rd generation synchrotron delivers the maximum allowable dose to a protein crystal (1010 photons/ μm2) in approximately a second – higher statistic requires introducing fresh crystals. For imaging non-reproducible objects, the difficulty is more fundamental: at a resolution of better than 1 nm, the required imaging dose exceeds the maximum allowable dose by more than 5 orders of magnitude!

The SwissFEL provides solutions to all of these problems: The fine focus (100 x 100 nm2) and enormous peak brilliance will allow the use of tiny samples: nano-crystals, 2d-crystals and perhaps even single biomolecules (see Fig. III.1). The inherent 100% transverse coherence eliminates the filtering requirement in diffractive imaging. And, in the low-charge / high electron-bunch-compression operation mode, the extremely shor t duration of the SwissFEL X-ray pulses will eliminate the problem of radiation damage by allowing data collection to be performed before the sample undergoes destructive Coulomb explosion. Finally, the 100–400 Hz repetition rate of the SwissFEL is ideally suited to the frame rate of modern 2d-pixel detectors (see Infobox).


Transverse coherence of the SwissFEL beam

The mutual coherence function of an electromagnetic wave is defined as [14]:
\Gamma_{12}(\tau) = \langle \bar{E}(\bar{r_1}, t) \cdot \bar{E}(\bar{r_2},t + \tau) \rangle
where it is assumed that the electric field is a stationary random function and that r1 and r2 lie in the same plane, transverse to the propagation direction. The “degree of coherence”, or the “first-order correlation function”, is then:
\gamma_{12}(\tau) =
\frac{\Gamma_{12}(\tau)}{\sqrt{\Gamma_{11}(0)\Gamma_{22}(0)}}
To assess the spatial (or transverse) coherence, we assume sufficient monochromaticity that the timedelay from the path difference r1–r2 is less than the longitudinal coherence time τlong = λ2/2c∆λ, and we set r1 = r0, on the beam axis. A quality indicator is then the transverse coherence factor γ12(0). Of particular interest to the experimenter is the coherence area, which is a measure of the usable beam area for coherent experiments:
A_{coh} = \int \gamma_{02}(0) dA_2
Numerical simulations for the SwissFEL [15] have shown that at the undulator exit, A_{coh} \approx 5 \times \pi r_0^2 , where r0 is the electron-beam radius. This implies a high degree of transverse coherence over the entire focus spot. The transverse SwissFEL beam shape is approximately Gaussian I(r) \propto \exp(-r^2/2r_0^2) with a transverse phase-space product r0θ = λn /4π, where simulations [15, 16] yield an effective Hermite mode number n≈1.5. Propagation of a Gaussian mode proceeds as shown in Figure III.i1, with
r(z) = r_0 \sqrt{ 1+ (\frac{z}{z_{Ray}})^2}
where the “Rayleigh length” is z_{Ray} = 4 \pi n r_0^2/\lambda. For the (rms) SwissFEL electron beam radius of 22 μm; at a wavelength of 0.1 nm, this yields a θ = 0.9 μrad divergence angle.

Longitudinal coherence and XFEL seeding

In contrast to the excellent transverse coherence, the longitudinal coherence of an XFEL operating in a SASE (self-amplifying spontaneous emission) mode is quite poor. Referring to the first-order correlation function, defined at left, the longitudinal coherence time is given by [1, 16]:
\sum\tau_{long} = \int|\gamma_{00}(\tau)|^2 d\tau =
\frac{\lambda^2}{2 c \triangle \lambda}


A wish of many experimenters is to have Fouriertransform- limited pulses, with a minimum longitudinal phase-space product relating the pulse duration, &#f916;τ = τlong, and the frequency bandwidth:
\triangle \tau \triangle v = \tau_{long} \triangle v =
\frac{1}{2}


The SASE process typically yields a relative bandwidth ΔlSASE / l = 10-3, implying coherence times of 0.17 and 1.7 fs, at 0.1nm and 1nm wavelengths, respectively. The bandwidth can be reduced by the use of a monochromator, typically yielding \triangle \lambda_{mono} / \lambda = 10^{-4}. More attractive from the point of view of pulse-to-pulse stability is the option to “seed“ the XFEL beam (see, for example, [17]). This is done by introducing narrowband radiation along the path of the electrons, causing them to micro-bunch and radiate at a pre-determined wavelength. A simulation comparing SASE pulses with those from seeding is shown in Figure III.i2 [15].