Technology Note

2 µm

X-ray Nanotomography in the Laboratory
with ZEISS Xradia Ultra 3D X-ray Microscopes

Technology Note

X-ray Nanotomography in the Laboratory
with ZEISS Xradia Ultra 3D X-ray Microscopes
Author:ZEISS Microscopy

Date:		

May 2018

X-ray microscopy (XRM) enables non-destructive 3D investigation of a variety of samples across multiple length scales.
Nanoscale XRM with resolution down to tens of nanometers has long been developed at synchrotron radiation facilities,
driven by the development of advanced X-ray optics such as Fresnel zone plates. ZEISS Xradia Ultra is the first instrument
to bring this capability to the user’s own laboratory. In this paper, we discuss the technology behind Xradia Ultra andresulting performance, including X-ray optics, contrast modes and X-ray energy. The paper concludes with application
areas and upcoming developments.
Xradia Ultra technology
Benefits of laboratory based X-ray nanotomography:

Optical architecture
The architecture of Xradia Ultra is conceptually equivalent to an• Non-destructive 3D imaging down to 50 nm resolution

optical microscope or a transmission electron microscope (TEM).
This architecture is also called transmission X-ray microscope,• In situ and 4D imaging: Observe nanostructural

or TXM.

evolution by imaging the same specimen multiple
times under varying conditions, or over time

• A high-brightness X-ray source is focused onto the specimen
by a high-efficiency capillary condenser• A Fresnel zone plate objective forms a magnified image of the• Multiscale and correlative imaging: Bridge the gap

specimen on the X-ray camera (detector)

between micro-CT and nanometer resolution, but• An optional phase ring can be inserted into the beam path

destructive, electron microscopy techniques

to achieve Zernike phase contrast to visualize features in• Contrast for a wide range of materials, from polymers

low absorbing specimens• As the specimen is rotated, images are collected over a range

and tissue to rock, ceramics and metals

of projection angles that are then reconstructed into a 3D
tomographic dataset
On the cover: PEFC Catalyst Layer showing porosity and connected pore space.
Sample courtesy Carnegie Mellon University

X-ray
SourceCondenser
Lens

SampleObjective Lens
(Zone plate)Phase Ring

X-ray
Detector

Figure 1: Optical schematic of Xradia Ultra

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Technology Note

Capillary condensers
The purpose of the condenser lens in a microscope is to provide
even illumination of the sample across the entire field of view.
Xradia Ultra employs reflective, single bounce capillaries1 for thispurpose that image the X-ray source spot into the sample plane(see Figure 1).
Reflective capillaries have a number of advantages over Fresnel
zone plates as condenser lenses in laboratory X-ray microscopes,
namely:• Close to unity focusing efficiency• Ability to fabricate large numerical aperture (NA) condensers
to match NA of high resolution imaging zone plates

Figure 2: Capillary condenser• Ability to fabricate large diameter condensers
To prevent excessive blurring of the focal spot, which would
result in a loss of X-ray intensity within the field of view, thesurface roughness inside the capillary must be controlled tothe submicron level.
Fresnel zone platesFresnel zone plates are used as microscope objectives to provide
a magnified image of the sample on the X-ray camera. Zone
plates are circular diffraction gratings with radially decreasing
line width, acting as a focusing lens for X-rays2,3 (see Figure 3).

Figure 3: Top: Schematic of a zone plate.
Right: SEM image of a zone plate.

Some optical parameters of zone plates are listed in Appendix B.
The spatial resolution that can be achieved, determined by
the Numerical Aperture (NA) in the same way as in an optical
microscope, is about the same as the width of the finest, outerzones (ΔRn, typically a few tens of nanometers). At the sametime, the zones need to be tall (hundreds of nanometers to morethan a micron) to be efficient. This leads to a requirement forvery high aspect ratio (ratio of height to width) structures.
ZEISS XRM has developed proprietary technology to “stack”
and permanently bond zone plates with nanometer accuracy
to increase the effective zone height and therefore aspectratio4 (see Figure 4).

Figure 4: Schematic of the stacking concept,4 where two zone plates are bonded
together to increase the effective thickness of the zones. Zones need to be narrow(laterally) to achieve high spatial resolution, but thick to achieve high efficiency(which translates into imaging throughput of the X-ray microscope).

3

Technology Note

X-ray camera
The X-ray camera in Xradia Ultra is based on a scintillator
optically coupled to a CCD detector. This is the same concept
employed by the Xradia Versa family of submicron resolution
XRMs.
As is illustrated in Figure 5, X-rays are incident on a scintillator,
which converts X-rays to visible light. The visible light imageis then magnified and projected onto a CCD camera by an
Applicationimages / Grafics / etc.

optical lens assembly.

Border 0,25px 25% black
Optical performance and spatial resolution
The optical architecture described above achieves spatial
resolution below 50 nm. The spatial resolution of an imaging
system is the smallest distance two features can be separated
by to still be distinguishable from one another.5 Siemens stars,
resolution targets with radially decreasing feature size, are

X-ray
Beam

Scintillator Magnification
convert to
Opticsvisible light

CameraSensorFigure 5: X-ray camera concept

commonly used in X-ray microscopy to assess resolution(see Figure 6). Note that spatial resolution is not the sameas pixel size (or voxel size, for 3D imaging). While the voxel
size needs to be smaller than the desired spatial resolution(it is 16 nm for Xradia Ultra in High Resolution mode at
800X magnification), a small voxel size alone does nothelp distinguish features if the optical resolution of the
instrument is insufficient.5
X-ray computed tomography (CT)One of the unique properties of X-rays is their penetration
power, i.e. their ability to see through and inside opticallyopaque, thick specimens. However, a simple two-dimensional
X-ray projection image through a thick specimen with complex
internal structure is often not useful because features overlay

50 nm feature size at tip

each other. Computed tomography (CT), widely used in
the medical field, allows the reconstruction of a 3D virtual
volume from individual projections. More recently, microand nano-CT6-9 have pushed this technique to much higher
resolutions.

Figure 6: Spatial resolution of Xradia Ultra, demonstrated using a Siemens star
resolution target. The innermost features are 50 nm wide (50 nm lines, 50 nm
spaces). Image pixel size is 16 nm.

In CT, many individual projection images of the specimen are
acquired over a range of angles (viewing directions), ideallycovering 180 or 360 degrees. Industrial, micro- and nano-CT
as well as 3D X-ray microscopes typically rotate the specimen
through a stationary X-ray beam for this purpose. This is incontrast to hospital X-ray CT, where the X-ray source anddetector are rotated around a stationary patient.

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Technology Note

Figure 7: X-ray computed tomography illustrated using the example of a shale rock sample. Left: Example projection through the specimen. While some interior featuresare visible, the interior structure cannot be determined in detail from a single projection. Center: A projection series over an angular range of 180 degrees was reconstructed
into a virtual volume. The image shows an individual “slice” (virtual cross section) through the specimen. Right: Volume rendering of the reconstructed volume.

The number of projection images acquired is typically in theor elemental imaging, diffraction for crystallographic orientation,

hundreds or thousands. Computer algorithms10 are then usedor spectroscopic contrast mechanism for elemental or chemical

to reconstruct a virtual, 3-dimensional volume of the specimen.

imaging.

The most common algorithms are filtered backprojection (FBP)or Feldkamp-Davis-Krees (FDK, for cone beam CT), although

Absorption contrast

various advanced (e.g., iterative) algorithms exist and canAbsorption contrast is essentially shadow contrast, similar toyield better results under certain conditions.

standard medical X-rays. Material that absorbs strongly shows
up dark in the image, material that absorbs less shows up bright –The reconstructed volume can then be viewed “slice by slice”

like bone vs. tissue in the hospital. Absorption is typically stron-(looking at virtual cross-sections), or visualized in 3D using

ger for materials with higher density and/or atomic number.

various volume rendering methods (see Figure 7). Commonly,

The mechanism is explained in more detail in the section on

the reconstructed volume is segmented into different compo-

X-ray source energy below.

nents based on grayscale or other characteristics. Segmented
volumes can be further analyzed quantitatively in terms of

Absorption is most often used to image pore networks or otherporosity, tortuosity, particle size distribution or other properties,

voids (empty space = low/no absorption) in medium to highor be used as input for advanced modeling algorithms.

density materials, such as rock, calcified tissue, ceramics ormetals. In a multi-phase or composite material, if the compo-

The key difference between Xradia Ultra and other micro-

nents are of sufficiently different density, absorption contrast

or nano-CT instruments is the use of X-ray optics to achieve

can also be used to separate the materials (e.g. ceramic-metallic

ultrahigh resolution projections as described above.

composites, or cermets).

Absorption and phase contrast

Phase contrast

Microscopes may provide a variety of contrast mechanisms

Phase contrast11 is primarily used for imaging materials that havethat are sensitive to different properties or components of the

low absorption, or to differentiate materials of similar density.

specimen and therefore complement each other. In this section,

Phase contrast uses the optical effect of refraction rather than

we describe absorption and phase contrast, two contrast modes

absorption. It is very sensitive to the transition between different

typically used to visualize morphology of the sample and bothmaterials (edge enhancement). Note that the term “phase”

available in Xradia Ultra. Other contrast modes available in other

here refers to the phase shift of an optical wave, and not totypes of microscopes (light, electron or synchrotron based X-ray

material phases (like crystallographic phases).

microscopes) include optical or X-ray fluorescence for functional

5Technology Note

Phase contrast is essential when imaging materials of low
density or atomic number, such as polymers or soft tissue,
since absorption contrast is typically very weak. Figure 8
shows an example of a polymer membrane imaged inphase contrast.
Due to the edge enhancement properties of phase contrast,
it is also well suited to detect small features close to the resolution limit, such as fine cracks and defects, in more strongly
absorbing material. It may be used as an initial survey mode tofind small features prior to 3D imaging in absorption contrast.

5 µm

On the other hand, these same edge enhancement properties
mean that different gray scales in the image may not corresponddirectly to different materials. In such a case, phase contrast may
be more suitable to detect and visualize small features, whereas

Figure 8: Polymer fibers in a desalination membrane, imaged in phase contrast.
Such low-Z materials are essentially transparent to multi-keV X-rays and therefore
not able to be visualized in absorption contrast. Sample courtesy of Industrial
Technology Research Institute (ITRI).

absorption contrast is more suitable to quantify and segment
features based on gray scale thresholding. A comparison ofabsorption and phase contrast for a sample of shale rock isAbsorption Contrast

Phase Contrast

10 µm

10 µm

shown in Figure 9.
Multiple implementations of phase contrast imaging have beendeveloped over time for different microscope architectures.
Xradia Ultra uses the Zernike principle to achieve phase contrast(see Figure 10). This principle was invented by Frits Zernike inthe 1930s for light microscopes,12 for which he received theNobel Prize in 1953.13

Figure 9: Comparison of absorption and phase contrast for a shale rock sample.
In absorption contrast (left), the grayscales in the image directly represent different
materials or material phases in the sample, which makes it more suitable forimage segmentation. Phase contrast (right) visualizes fine cracks much more clearly.

Condenser
Aperture

Imaging
Zone Plate

Undiffracted Light

Phase Ring

Phase Ring
Image on
Detector

ObjectDiffracted Light
Hollow Cone
Illumination
Figure 10: Left: Illustration of Zernike phase contrast. The sample is illuminated by a hollow cone of X-rays. A phase ring is inserted in the back focal plane of the objective
zone plate. The “undiffracted light” (X-rays that have not interacted with the sample) passes through the phase ring and is phase shifted by a quarter wavelength.
“Diffracted light” (X-rays that have interacted with the sample and therefore have been scattered off the direct path) does not pass through the phase ring.
In the detector plane, the diffracted and undiffracted light combine (interfere), which turns phase shifts into intensity variations. Right: SEM image of a phase ring.

6

Technology Note

X-ray source energy

X-ray Absorption in Material

3D data acquisition times in a laboratory based nanoscale

1.2

XRM are on the time scale of hours. Therefore, optimizing
system. In this section, we will review how the two different
X-ray source options, 5.4 keV for Xradia 810 Ultra and 8 keV
for Xradia 800 Ultra, differ in terms of imaging properties andperformance for different materials to be imaged. To do so, we

Relative Intensity

throughput is essential to make the most productive use of the

5.4 keV
8 keV

1
0.8
1/e = 37%
0.6
0.4
0.2

will review how X-rays get absorbed in matter14 and what that0means for the resulting image contrast and feature detectability.

Propagation Distance (t)We will explain that in the context of absorption contrast,

Absorption length t0

although the concepts apply similarly to phase contrast. For
further details, see Ref. 15, which illustrates contrast, noiseand detectability in the context of medical CT.

Figure 11: Schematic illustration of X-ray absorption in matter following theLambert-Beer law. After a propagation distance t0 (which is a function of
X-ray energy), the intensity drops to 37% of its incident value.

X-ray absorption in matter

X-ray Absorption Length

Absorption of X-rays in matter follows the Lambert-Beer law:where I is the intensity after propagation distance t , I0 is theincident intensity, and t 0 is the absorption length of the material
in question at a given X-ray energy. t0 is the distance after which
the intensity falls to 1/e = 37% of the incident value. Sometimes, the absorption coefficient μ = 1/t0 is used instead.

Absorption Length (µm)

I = I0 exp(– t /t 0 )

120
100

Abs. length Al (µm)
Abs. length Fe (µm)

80
60
40
20
0
5000

6000

7000

8000

9000

Photon Energy (eV )The absorption length is a function of the material, its density
and the X-ray energy. Generally, the absorption length increases
with energy (i.e., harder X-rays are more penetrating), anddecreases with density and atomic number Z (i.e., heaver
materials are more strongly absorbing).

Figure 12: Illustration of X-ray absorption length for two example elements.
Generally, absorption length is longer for lighter elements (aluminum, Al)
compared to heavier elements (iron, Fe). Furthermore, absorption length typicallyincreases with energy, except for so-called absorption edges, which arediscontinuities in the absorption spectrum. This is illustrated for the exampleof iron, which has an absorption edge around 7.1 keV photon energy.

Looking at the two specific X-ray source energies available
for Xradia Ultra, the absorption length is generally longer at

Sample5.4 keV

8.0 keV

8 keV than at 5.4 keV. There are a few exceptions (specificallyIron*

11.7 µm

4.16 µm

vanadium, chromium, manganese, iron and cobalt), which have

Aluminum24.8 µm77.6 µm

so-called absorption edges (discontinuities in the absorption

PMMA

397 µm1337 µm

length due to the specific atomic energy levels) in between

CaCO3

16.5 µm

48.7 µm

the two energies. A few examples are listed in Table 1 below.

Silicon22.4 µm69.6 µm

To provide for sufficient penetration for imaging, the sample

Tungsten

1.14 µm

3.11 µm

thickness should be at most ~2x the absorption length.

*Note: Iron is an exception to the rule that 8 keV X-rays can penetrate further
than 5.4 keV X-rays. This is because of the iron X-ray absorption edge at
7.1 keV, above which penetration drops drastically.
Table 1: Approximate X-ray absorption length for select materials. Exact values
will depend on composition and density. Note that X-ray penetration will be larger
if material is porous.

7

Technology Note

Contrast
Contrast is the difference in light intensity that makes different

and/or throughput will be greatly improved at 5.4 keV X-ray

features in an image distinguishable from one another. To beenergy compared to 8 keV. However, for materials of higher

able to detect a feature, it must both be resolved (see Opticaldensity (such as most metals, but note the exception of iron

Performance and spatial resolution above) and have sufficiently

explained above), or thick specimens, the higher X-ray energy ofstrong contrast compared to its surroundings.

8 keV may be needed for sufficient transmission (see Figure 13).
The contrast difference is illustrated on a real world sample in

As described above, lower energy X-rays are generally absorbed

Figure 14. 5.4 keV X-rays are absorbed more strongly than 8 keV,

more strongly and therefore will provide higher contrast. Thus,

resulting in higher contrast and therefore better detectability.

as long as transmission remains sufficient, resulting image quality

X-ray Penetration: Medium Density Material

X-ray Penetration: High Density Material
1.2

1.2

Relative Intensity

0.8
0.6
0.4

5.4 keV
8 keV

0.2
0

1

Relative Intensity

Greaterintensity
drop equals
highercontrast

1

0

0.8

Transmission
insufficient
to discern
small variations

0.6
0.4

5.4 keV
8 keV

0.2

20

40

60

80

0

100

0

20

40

60

80

100

Penetration Distance (µm)

Penetration Distance (µm)

Figure 13: Illustration of 5.4 vs. 8 keV X-ray energy. Left: The greater intensity drop of 5.4 keV X-rays leads to higher contrast (and therefore higher imaging throughput).
Right: If absorption becomes too strong (dense material or sample too thick), transmission at 5.4 keV may be too low to discern small variations, in which case 8 keV is preferred.

Image Contrast
Image Intensity (a.u.)

5.4 keV
8 keV

5.4 keV

8. keVLine Profile Through Image

Figure 14: Contrast difference between 5.4 and 8 keV illustrated using virtual cross-sections of a dentin sample. The lower X-ray energy of 5.4 keV provides stronger
contrast between the bulk intertubular dentin (medium gray), peritubular dentin (light) and tubules (dark). Note that the images follow the convention of displaying
higher density materials in light colors and lower density (air) in dark. The plot on the right shows an intensity profile across the lines indicated in the images.
It is evident that the contrast (intensity difference) is stronger at 5.4 keV than at 8 keV.

8

Technology Note

Noise

Poisson Distribution for n = 50

Imaging, like any measurement process, introduces noise.

0.06

Noise is a random fluctuation of the measured value around the

0.05

expected, or “true” value. That means, even if we were to image
different pixels (or, the same pixel in multiple measurements)
would not be exactly the same.

0.04

Probability

a perfectly uniform material, the measured intensity values of

0.03—
FWHM = 2.35 √50 = 16.6

0.02
0,01

While multiple noise sources exist in an X-ray microscope, wewill concentrate here on shot noise, which is intrinsic to themeasurement of discrete particles such as X-ray photons. Shot

0
-0.01

0

20

40

50

60

80

100

Number of Photons

noise follows a Poisson distribution, which means if we expect
to measure an average number of n photons in many measurements of the same type, the distribution of actual measurements_
will have a standard deviation (noise) of √n (see Figure 15).
We can then define the Signal-to-Noise Ratio (SNR) as the

Figure 15: Illustration of Poisson distribution. Assuming we expect to measure amean of n=50 photons in many measurements of the same type, the actual number
measured in a single measurement will vary from about 30 to 70 based on the
distribution shown. It can be shown that_ the full width at half maximum (FWHM)
of this distribution is FWHM = 2.35 √n, or FWHM = 16.6 in this case.

ratio of expected number of photons and noise:__
SNR = Signal/Noise = n/√n = √n

In other words, by increasing the exposure time and therefore
counting more X-ray photons, we can decrease the noise level
relative to the measured signal. This is in analogy to photography, where in the case of low light, longer exposure times areused to decrease noise. However, the improvement follows asquare root relationship, i.e. we have to measure four times
as long to double the SNR.
This concept is illustrated again for the case of dentin in

3 hours

12 hours

Figure 16: Virtual cross section of dentin sample from a 3 hr tomogram (left)
and a 12 hour tomogram (right) at 5.4 keV X-ray energy. It is evident that thelonger exposure leads to lower noise.

Figure 16. Here, both images were acquired using 5.4 keV
X-ray source energy, meaning the contrast between the
different features is the same. However, it can be seenthat the noise is much lower for the longer exposure.
Putting it all together:
Contrast to Noise Ratio and imaging throughput
So what does all this mean for general image quality anddetectability of features in an image? Ultimately, what counts
is the Contrast-to-Noise Ratio (CNR) of the features of interest
relative to the surroundings. CNR can be increased by either
increasing contrast or decreasing noise. In other words, evenin the case of lower contrast we can detect features by
exposing longer and therefore decreasing noise.

9Technology Note

However, if we can increase contrast by using a more suitable
X-ray energy, we can achieve sufficient CNR with shorter
exposure times, which is generally preferred.

• Motion errors of the rotation stage are measured andcorrected for by a novel run-out correction system16• The precision motion control system comprises 26 axesof motion to position and align the X-ray optics, sample,

Looking back at Figure 16 again, note that contrast is the same

optical alignment microscope and other components

in both images because they were both acquired at 5.4 keV
X-ray energy. However, CNR is clearly improved with the
12 hour exposure.

Application areas
In the following, we list a number of applications where Xradia

Conclusions

Ultra and its predecessor models (Xradia nanoXCT and UltraXRM)

We have seen that for most materials, 5.4 keV X-rays arehave been used to provide 3D nanostructure data.

absorbed more strongly than 8 keV X-rays, leading to higher
contrast and therefore higher imaging throughput. In other

Materials researchwords, equivalent image quality can be achieved with shorter• Li-ion battery electrodes17-19

exposure times. If fact, it has been shown that for samples• Polymer electrolyte fuel cell (PEFC) electrodes20-22

such as rock or calcified tissue, the same contrast to noise• Solid oxide fuel cell (SOFC) electrodes23

ratio (image quality) can be achieved about 10 times faster• 3D-ordered macroporous materials for CO2 capture24

using a 5.4 keV X-ray source compared to 8 keV.

• Osmosis membranes25• Alloys26

On the other hand, for samples made of higher-Z (“heavier”)• Superconducting materials27

material, 8 keV might be needed to provide sufficient• Nanocomposites28

penetration. Ultimately, the preferred source energy varies• Cement29

by application.

• Subsurface coatings30• High voltage insulators31

Furthermore, for a given experiment, it is important to consider
what image quality is sufficient. It may be more productive toLife and environmental sciencemeasure multiple samples at lower CNR in a given time frame• Unstained tissue32

than just a single one at higher CNR, as long as the results allow• Nanoparticle uptake in protozoa or soybean roots33,34

detecting and quantifying the features of interest as required.

• Pharmaceutical particles35• Bone and dentin

Mechanical architecture
To achieve 50 nm resolution in a 3D measurement taking several

Natural resources

hours, the microscope needs to be mechanically stable over that

• Digital rock physics (DRP)36,37 or general rocktime frame. The following design features are implemented incharacterization,38,39 e.g. for carbonate rock, shale rock,

Xradia Ultra to achieve that:or tight sand

• Xradia Ultra is built on a low vibration platform to isolate
the optical system from external vibrations

Electronics• Voids and extrusions in through-silicon via (TSV)40,41• Careful thermal engineering and calibration prevents orcorrects thermal drifts on the scale of tens of nanometers
between specimen and optics

10Technology Note

Summary and outlook
Nanoscale 3D X-ray microscopy is the only technique that canIn this White Paper, we described the technology behindachieve spatial resolution down to 50 nm, non-destructively,

Xradia Ultra, the only laboratory based nanoscale X-rayon samples of tens to hundreds of microns in size. As such, it

microscope. Resolution down to 50 nm is achieved using

is particularly well suited to 4D and in situ experiments, where

X-ray focusing optics such as reflective capillary condensers

the same sample is imaged multiple times over time or underand Fresnel zone plate objective lenses. Absorption and phasevarying conditions, allowing studying microstructural evolution.

contrast modes allow imaging of a wide variety of materials.

Furthermore, nanoscale 3D XRM covers a unique length scale

Demonstrated applications cover a wide range of examples fromin a correlative suite of techniques, between micron/submicronmaterials research, life and environmental sciences, natural

XRM or micro-CT, where larger samples can be studied withresources and electronics. Emerging techniques include in situ

resolution down to one micron or slightly below, and serial

imaging, for example under mechanical load, 4D imaging, suchsectioning using electron microscopy, where smaller volumes

as monitoring corrosion, and correlative imaging across multiple

can be studied with nanometer resolution, but destructively.

length scales and using different but complementary techniques.

Appendix A: Why use X-ray optics?
The vast majority of laboratory-based X-ray microscopes and micro CT systems use the principle of cone beam projection through the sample,
followed by X-ray detection on a 2D detector. Rapid developments in the last decade have pushed the achievable spatial resolution down toabout one micron and below. Two concepts are commonly used5 (see Figure 17).
• Conventional micro CT systems typically use a small spot X-ray source and a flat panel detector
Sample with relatively large pixels (~100 µm).
Centerof Rotatation
To achieve voxel sizes below one micron, a large geometric magnification (>100x) and therefore
very small source-to-sample distance is required.

SourceThe optical magnification stage effectively provides a small• ZEISS Xradia Versa architecture uses a two-stage (geometric + optical) magnification.
Detector
pixel (down to <500 nm) detector. Voxel sizes below one micron can be achieved with low geometric magnification (<10x) andworking
distances of several centimeters.
While both of these concepts keep pushing spatial resolution further below one micron (currently ~600-700 nm), it is ultimately limited by factors
such as achievable X-ray spot size at sufficient power, X-ray detector resolution and practical limitations of acceptable exposure times to achieve

Dss nm, a projection based architecture
Dds
Geometricimpractical.
Mag
becomessufficient signal-to-noise ratio. It can be shown42 that at resolution levels below about 500
To achieve spatial resolution higher than that and into the sub-100 nm regime, a lens-based architecture using X-ray focusing optics is required.

GeometricMag

SampleCenter of Rotatation

OpticalMag

SourceDetector

Scintillator
Dss

Dds

Detector

Geometric Mag

Figure 17: (Left) Conventional micro CT architecture using a large pixel detector and high geometric magnification to achieve high resolution. This requires a small spot
X-ray source to avoid penumbral blurring, and small source to sample distance (working distance) to achieve small voxel sizes. Resolution degrades quickly as the sample
is moved away from the source. (Right) ZEISS XRM architecture using two-stage magnification. Moderate geometric magnification is followed by switchable optical
Geometric
Opticaland allows for longer working distance, which is advantageous in the case of interior tomography
magnification. This relaxes theneed for high geometric magnification
Mag
Mag(imaging a small interior subregion of a large sample at high resolution), and when using in situ sample environments.

11Technology Note

Appendix B: Fresnel zone plates
The properties of a zone plate can be specified by three parameters such as the diameter D, the outer zone width ΔRn and the wavelength λ.
Then, some other quantities of interest are the number of zones N
N = D/4ΔRnthe focal length ƒƒ = D ΔRn/λand the numerical aperture
NA = λ/2 ΔRnNote that the relationship between photon energy E and wavelength λ is given by
E = hc/λ = 1239.842 eV ⋅ nm/λ

where hc = 1239.842 eV ⋅ nm is the product of Planck’s constant h and the speed of light c.
The spatial resolution achievable by a Fresnel zone plate is determined by the outer zone width ΔRn.

Specifically, for uniform plane-wave illumination the transverse resolution δt according to the Rayleigh criterion is given by Abbe’s law:
δt = 0.61λ/NA = 1.22 ΔRn
The depth of focus, or longitudinal resolution δl, isδl = ± 2ΔRn2/λ12Technology Note

References:[1]

X Zeng, et al., “Ellipsoidal and parabolic glass capillaries as condensers for x-ray microscopes.” Appl. Opt. 47 (2008), 2376-2381.
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J Kirz, “Phase zone plates for x rays and the extreme uv.” J. Opt. Soc. Am. 64 (1974), 301-309. DOI: 10.1364/JOSA.64.000301[3]

AG Michette, Optical Systems for Soft X Rays (New York: Plenum, 1986)[4]

Y Feng, et al., “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications.” J. Vac. Sci. Technol. B 26 (2007).
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