12
P. R. Willmott
h
Tr
pinhole
ν
coherence
transverse
(spatial)
longitudinal
(temporal)
coherence
Fig. 1.8 Coherent radiation. The coherent fraction of a broadband, spatially extended, source can be
selected as follows. Firstly, a pinhole selects a small, spatially constrained fraction of the radiation
thereby acting as a secondary, quasi-pointlike, source. This secondary source has an improved
transverse (or spatial) coherence, as the emittance, which is the product of the radiation’s divergence
and source size, is now much smaller. Next, a filter (which is normally a monochromator) selects
a narrow BW which is much narrower than the original source. Now, the radiation is spatially and
longitudinally (or temporally) coherent. Note that both the emittance and relative spectral BW are
included in the definition of brilliance. Reproduced from [3] with permission (Copyright 2019, John
Wiley and Sons)
know which factors determine a given value. For example, is the brilliance high
because there are more photons on the sample, or because the emittance is small?
No X-ray source has an infinitely narrow bandwidth. Consequently, the different
frequency components within the beam will sooner or later drift out of phase with
one another. The time for the phase between two waves differing in frequency by
an amount but which are initially in phase to differ by π radians (i.e. from fully
constructive to fully destructive) is simply 1/2ν. This is known as the so-called
longitudinal coherence time,
(l)
c . During this time, the waves have travelled in
vacuum a distance l
(l)
c = c
(l)
c /2, known as the longitudinal (or temporal) coherence
length [see Fig. 1.9a], given by
l
(l)
c =
λ
2
2λ
.
(1.14)
The longitudinal coherence after a monochromator is usually determined by the rocking curve of the crystal or grating used in the monochromator, which defines λ//λ.
For a perfect crystal with insignificant mosaicity, λ is limited by the so-called Dar-
P. R. Willmott
h
Tr
pinhole
ν
coherence
transverse
(spatial)
longitudinal
(temporal)
coherence
Fig. 1.8 Coherent radiation. The coherent fraction of a broadband, spatially extended, source can be
selected as follows. Firstly, a pinhole selects a small, spatially constrained fraction of the radiation
thereby acting as a secondary, quasi-pointlike, source. This secondary source has an improved
transverse (or spatial) coherence, as the emittance, which is the product of the radiation’s divergence
and source size, is now much smaller. Next, a filter (which is normally a monochromator) selects
a narrow BW which is much narrower than the original source. Now, the radiation is spatially and
longitudinally (or temporally) coherent. Note that both the emittance and relative spectral BW are
included in the definition of brilliance. Reproduced from [3] with permission (Copyright 2019, John
Wiley and Sons)
know which factors determine a given value. For example, is the brilliance high
because there are more photons on the sample, or because the emittance is small?
No X-ray source has an infinitely narrow bandwidth. Consequently, the different
frequency components within the beam will sooner or later drift out of phase with
one another. The time for the phase between two waves differing in frequency by
an amount but which are initially in phase to differ by π radians (i.e. from fully
constructive to fully destructive) is simply 1/2ν. This is known as the so-called
longitudinal coherence time,
(l)
c . During this time, the waves have travelled in
vacuum a distance l
(l)
c = c
(l)
c /2, known as the longitudinal (or temporal) coherence
length [see Fig. 1.9a], given by
l
(l)
c =
λ
2
2λ
.
(1.14)
The longitudinal coherence after a monochromator is usually determined by the rocking curve of the crystal or grating used in the monochromator, which defines λ//λ.
For a perfect crystal with insignificant mosaicity, λ is limited by the so-called Dar-