Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  179

incident photon energy is transferred from the beam to energize a process in the sample, for

example, to excite an inner shell electron to a higher energy level. This is not directly useful

in determining atomic-​level structures but has been utilized in the form of resonant inelastic

soft x-​ray scattering (RIXS), which can be applied to a solution of biomolecules in the same

way as SAXS.

However, since RIXS is often associated with changes to the energy state of atomic

electrons, it is often used in biophysical investigations that involve changes to the oxidation

state of transition metal atoms in electron-​carrier enzymes, for example, those used in oxi­

dative phosphorylation and photosynthesis (see Chapter 2) but has also been applied to bio­

logical questions including solvation effects in chemoreceptors and studying the dynamics of

phospholipid bilayers.

5.3.4  X-​RAY MICROSCOPY METHODS

X-​ray microscopy methods have been developed both for transmission and scanning modes

similar to the principles of EM and optical microscopy. However, the principal challenge is

how to focus x-​rays, since no equivalent lens as such exists as for the transparent glass lenses

of optical microscopy or the electromagnetic/​electrostatic lenses of EM. The solution is to

use zone plates (Figure 5.3c), also known as Fresnel zone plates, which utilize diffraction for

focusing instead of reflection or refraction.

Zone plates are micro-​ or nanofabricated concentric ring structures known as Fresnel

zones, which alternate between being opaque and transparent. They can be used for focusing

across the electromagnetic spectrum, and in fact for any general waveform such as sounds

waves but are particularly valuable for x-​ray focusing. X-​rays hitting the zone plate will

diffract around the opaque zones. The zone spacing between the rings is configured to allow

diffracted light to constructively interfere only at a desired focus. The condition for this is

(5.12)

r

n f

n

n ⁼

−

λ

λ

2

2

4

where

rn is the radius of the switch position between the nth opaque and transparent zones

from the center of the zone plate, such that n is a positive integer

f is the effective focal length of the zone plate

Analogous to the diffraction resolution limit in optical microscopy (Chapter 4), the smallest

resolvable object feature length Δx when using a zone plate limit is given by

(5.13)

∆

∆

x

rn

= 1 22

.

Therefore, the resolution limit is really determined by the precision of the micro-​/​

nanofabrication. At the time of writing, the current reliable limit is ~12 nm.

Typical designs for a transmission x-​ray microscope (TXM) and a scanning transmission

x-​ray microscope (STXM) are shown in Figure 5.3d. “Soft” x-​rays are used typically from a

collimated synchrotron source, of wavelength ~10–​20 nm. The TXM uses two zone plates

as equivalent condenser and objective “lenses” to form a 2D image on a camera detector,

whereas the STXM typically utilizes just a single zone plate to focus the x-​ray beam onto a

sample. As a robust biophysical technique, x-​ray microscopy is still in its infancy, but it has

been tested on single-​cell samples.

An alternative to using physical focusing methods of x-​rays with zone plates is to perform

numerical focusing through similar techniques of coherent x-​ray diffraction imaging (CXDI

or CDI) and ptychography (which was discussed previously as part of optical microscopy

techniques in Chapter 4). CXDI involves a highly coherent incident beam of synchrotron x-​

rays, which scatter from the sample and generate a diffraction pattern, which is recorded by