pulsed laser that generates pulses on the nanosecond or picosecond timescale. The
X-ray source can be pulsed in a number of ways. Initially, for experiments involving
crystalline species with lifetimes in the nanosecond to microsecond range, the X-ray
pulses were generated by placing a mechanical chopper in the incident beam [25, 27]
which interrupts the beam so that the X-rays are only “on” in synchronisation with
the laser pulse. When using these short pulses, the X-ray flux that impinges on the
crystal is limited, and in order to overcome this problem, high-intensity synchrotron
radiation is normally required. Even with this higher X-ray intensity, many pumpprobe laser and X-ray cycles are required per data collection frame to build up a
sufficiently strong diffraction image, and many frames are required in order to obtain
a complete X-ray data set. The repeated pumping and probing usually has a
detrimental effect on the crystalline sample, and significant sample heating effects
may also be a problem.
One development to overcome the crystal degradation problem has been devised
and used effectively in the macromolecular crystallographic community, and that is
the pump-multi-probe method based on the Hadamard transformation [28]. In the
conventional pump-probe approach described above, the photoactivation event is
initiated by a laser pulse and then probed at a later time by an X-ray pulse, so that
every laser (pump) pulse is followed by a single probe (X-ray) pulse after a
predetermined time delay (see Fig. 4a). Therefore, to measure n time points,
n pump-probe pairs are required. In contrast, in the Hadamard approach, each
pump pulse is followed by a sequence of probe pulses, and the total signal from
each sequence is recorded in a single measurement (see Fig. 4b). The sensitivity of
the experiment is thus defined by the total number of photons in the complete probe
sequence, with the time resolution defined as the total probe sequence length divided
by the number of pulses. This method no longer limits the time resolution that can be
achieved to the brilliance of the X-ray source by summing the time points across the
probe sequence. It also gives an improved signal-to-noise ratio because of the larger
number of photons recorded during the measurement.
As in standard pump-probe experiments, n pump-probe sequences are required to
measure n time points. The pattern of the probe sequence is represented as rows of a
nxn matrix (S) obtained from the Hadamard sequence. The simplest case is shown in
Fig. 4b where each row of the matrix (and the probe sequence) is obtained by cycling
by one element from the previous row to the left (see Fig. 4c).
For the Hadamard time-resolved experiment, the photoactivation is initiated and
then the complete probe sequence (first row of the S matrix) is recorded as a single
image. This process is repeated on the sample after relaxation but with the probe
sequence now defined by the second row of the S matrix, until all the rows have been
completed. The resulting encoded signals from the n excitations are then collated to
form a vector W of length n. The time-dependent signal, I t , is then obtained by
reversing the probe sequence encoding by multiplying the vector W by the inverse of
the matrix S, so that I t ¼ S
21 W. A time-resolved crystallographic Hadamard
experiment has been dubbed a HATRX experiment.
246
P. R. Raithby
X-ray source can be pulsed in a number of ways. Initially, for experiments involving
crystalline species with lifetimes in the nanosecond to microsecond range, the X-ray
pulses were generated by placing a mechanical chopper in the incident beam [25, 27]
which interrupts the beam so that the X-rays are only “on” in synchronisation with
the laser pulse. When using these short pulses, the X-ray flux that impinges on the
crystal is limited, and in order to overcome this problem, high-intensity synchrotron
radiation is normally required. Even with this higher X-ray intensity, many pumpprobe laser and X-ray cycles are required per data collection frame to build up a
sufficiently strong diffraction image, and many frames are required in order to obtain
a complete X-ray data set. The repeated pumping and probing usually has a
detrimental effect on the crystalline sample, and significant sample heating effects
may also be a problem.
One development to overcome the crystal degradation problem has been devised
and used effectively in the macromolecular crystallographic community, and that is
the pump-multi-probe method based on the Hadamard transformation [28]. In the
conventional pump-probe approach described above, the photoactivation event is
initiated by a laser pulse and then probed at a later time by an X-ray pulse, so that
every laser (pump) pulse is followed by a single probe (X-ray) pulse after a
predetermined time delay (see Fig. 4a). Therefore, to measure n time points,
n pump-probe pairs are required. In contrast, in the Hadamard approach, each
pump pulse is followed by a sequence of probe pulses, and the total signal from
each sequence is recorded in a single measurement (see Fig. 4b). The sensitivity of
the experiment is thus defined by the total number of photons in the complete probe
sequence, with the time resolution defined as the total probe sequence length divided
by the number of pulses. This method no longer limits the time resolution that can be
achieved to the brilliance of the X-ray source by summing the time points across the
probe sequence. It also gives an improved signal-to-noise ratio because of the larger
number of photons recorded during the measurement.
As in standard pump-probe experiments, n pump-probe sequences are required to
measure n time points. The pattern of the probe sequence is represented as rows of a
nxn matrix (S) obtained from the Hadamard sequence. The simplest case is shown in
Fig. 4b where each row of the matrix (and the probe sequence) is obtained by cycling
by one element from the previous row to the left (see Fig. 4c).
For the Hadamard time-resolved experiment, the photoactivation is initiated and
then the complete probe sequence (first row of the S matrix) is recorded as a single
image. This process is repeated on the sample after relaxation but with the probe
sequence now defined by the second row of the S matrix, until all the rows have been
completed. The resulting encoded signals from the n excitations are then collated to
form a vector W of length n. The time-dependent signal, I t , is then obtained by
reversing the probe sequence encoding by multiplying the vector W by the inverse of
the matrix S, so that I t ¼ S
21 W. A time-resolved crystallographic Hadamard
experiment has been dubbed a HATRX experiment.
246
P. R. Raithby