X-ray microlaminography with polycapillary opticsK. M. Dąbrowski, D. T. Dul, A. Wróbel, and P. Korecki Citation: Appl. Phys. Lett. 102, 224104 (2013); doi: 10.1063/1.4809583 View online: http://dx.doi.org/10.1063/1.4809583 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v102/i22 Published by the American Institute of Physics. Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

X-ray microlaminography with polycapillary optics

K. M. Dabrowski, D. T. Dul, A. Wr�obel, and P. Koreckia)

Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krak�ow, Poland

(Received 3 April 2013; accepted 19 May 2013; published online 4 June 2013)

We demonstrate layer-by-layer x-ray microimaging using polycapillary optics. The depth resolution

is achieved without sample or source rotation and in a way similar to classical tomography or

laminography. The method takes advantage from large angular apertures of polycapillary optics and

from their specific microstructure, which is treated as a coded aperture. The imaging geometry is

compatible with polychromatic x-ray sources and with scanning and confocal x-ray fluorescence

setups. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4809583]

Since their discovery, x-rays have been used to visualize

the internal structure of objects. The depth information is,

however, lost in a single x-ray projection. Imaging of slices

localized at particular depths is possible by means of x-ray

laminography.1 It was invented before the era of computed

tomography (CT)2 and is also referred to as classical or lin-

ear tomography.3 Nowadays laminography is mainly used in

geometries with limited angle access in medical imaging4 or

for material testing.5 More recently, laminography was

implemented for x-ray microscopy using synchrotron radia-

tion6,7 and extended to phase-contrast imaging.8,9

The original geometry of laminography is presented in

Fig. 1(a). When the x-ray source and the film are translated

synchronously in opposite directions only objects located at

the so called focal plane are imaged sharply. Projections of

objects located at different depths are blurred. Contemporary

approaches use 2D detectors and by means of digital tomo-

synthesis10 or computed laminography5 reconstruct the 3D

image of the object. X-ray laminography can be performed

using multiple sources or as demonstrated more recently,

using multi-beam sources based on carbon nanotube field-

emitters.11 The sources can be flashed either sequentially or

simultaneously. In the latter case, the projections formed by

individual beams overlap and a specific arrangement of sour-

ces12 and the so called coded aperture approach13,14 is

required for object visualization.

A unique possibility to generate multiple x-ray micro-

beams is provided by polycapillary optics.15,16 Polycapillary

elements are arrays of a large number (104 � 106) of glass

capillaries in which x-rays travel by means of total external

reflections. A special bending of capillaries allows one to

focus radiation from laboratory x-ray sources or synchrotrons

into micro-spots. Importantly, angular apertures of polycapil-

lary optics are orders of magnitude larger compared to typical

x-ray optics17 and can reach 10� � 20�. Very recently, we

demonstrated a method for x-ray imaging of objects inside

the focal spot of polycapillary optics.18 This method is based

on the coded aperture concept and resolves lateral details of

objects smaller than the focal spot dimensions.

In this letter, we demonstrate depth-resolved x-ray

microimaging with polycapillary optics based on the com-

bined ideas of laminography and coded aperture imaging.

This approach does not require sample or source rotation and

takes advantage from specific microstructure and large angu-

lar apertures of polycapillary optics.

The idea of x-ray microlaminography with polycapillary

optics is presented in Figs. 1(b) and 1(c). Radiation from an

x-ray tube is focused by polycapillary optics having focal

length f. The object is placed at z ¼ f þ Dz and the x-rays are

recorded using a 2D detector placed at z¼D. The enlarged

geometry of image formation from Fig. 1(c) can be compared

to the geometry of classical laminography. For an object

placed in the focal plane, all beams from individual capilla-

ries produce, magnified by a factor of D/f, projections of the

object which are replicated over the entire area of the detec-

tor. On the other hand, objects located below or above the

focal plane are imaged only by a limited number of beams.

Hence, for large jDzj, the x-ray image can be interpreted as a

simple projection of the object relative to the focal point.

This qualitative change in the character of the x-ray image

will provide a basis for depth-resolved x-ray imaging.

In order to realize x-ray microlaminography with polyca-

pillary optics, we used an experimental setup with a W target

x-ray tube having a 75 lm spot (Oxford Instruments, XTF

5011) operated at 1 mA and 50 keV. Polycapillary focusing

FIG. 1. Principle of x-ray microlaminography with polycapillary optics. (a)

Image formation in laminography (classical tomography). (b) Schematics of

the experimental setup for x-ray microlaminography and a microscope

image of the exit surface of the polycapillary optics. (c) Image formation for

polycapillary optics. (d) Measured x-ray intensity distribution near the focal

spot. The line plot shows a profile along the z axis.

a)Author to whom correspondence should be addressed. Electronic mail:

pawel.korecki@uj.edu.pl

0003-6951/2013/102(22)/224104/4/$30.00 VC 2013 AIP Publishing LLC102, 224104-1

APPLIED PHYSICS LETTERS 102, 224104 (2013)

optics (IfG) had an output focal length f¼ 14 mm and exit sur-

face diameter DA ¼ 2:4 mm, which corresponds to an angular

aperture a � DA=f � 9:8�. Figure 1(b) shows a microscope

image of the surface of the optics revealing a hexagonal mesh

of capillaries and a coarser mesh corresponding to bundles of

capillaries. Figure 1(d) presents the measured intensity distri-

bution in the vicinity of the focal spot. The focal spot has an

approximate Gaussian shape with FWHM of 41 lm in the lat-

eral plane and a Lorentzian shape with FWHM of 1.5 mm

along the optical axis. Note that when polycapillary optics is

used in scanning or confocal geometries, the dimensions of

the focal spot set the limit of the spatial resolution.19–21 The

flux in the beam having a mean energy of 22 keV was �108

photon/s. X-ray images were measured using a scintillator

coupled to a CMOS sensor (Rad-Icon, RadEye1) with

1024� 512 pixels spaced by 48 lm. The camera was placed

at a distance D¼ 165 mm from the exit surface of the lens.

Let us first demonstrate the transmission from projection

imaging to coded aperture imaging, which makes it possible

to achieve depth resolution. Data in Fig. 2 were obtained for

a 20 lm thick Cu finder grid. Figure 2(a) presents images of

the grid for different displacements Dz from the focal plane.

All x-ray images are shown as I=I0, where I and I0 denote

exposures with and without the object, respectively. For a

large distance Dz ¼ 15 mm, the focal spot of the optics can

be treated as a secondary source producing a magnified

point-projection of the object. As shown in the zoom, the pe-

numbra blur results in a poor resolution being of the order of

the lateral dimensions of the focal spot.

In images recorded for smaller Dz, a characteristic hex-

agonal structure of polycapillary bundles becomes very dis-

tinct (mesh of individual capillaries is not resolved due to a

limited detector resolution). This means that the object

placed near the focal plane influences all the beams emerg-

ing from the exit surface of the optics. For Dz ¼ 1 mm, a dis-

torted low-resolution projection of the object can be still

recognized in the data. However, for Dz ¼ 0, the projection

of the object disappeared and the structure of the object is

encoded in the fine structures of the visible hexagonal mesh.

Formally, for Dz ¼ 0 the intensity I(r) at the detector

can be written as a convolution:18

IðrÞ � 1

D2T

r

1�M

� �G

r

D

� �h i� S

r

M

� �; (1)

where r is the coordinate in the lateral plane, M¼ (f � D)/f,T denotes the transmission of the object, and G is a Gaussian

with FWHM of �2:35hc characterizing the angular diver-

gence of the beams from individual capillaries. hc is the criti-

cal angle for total external reflection. The function S(r)

describes the spatial distribution of the capillaries as well as

their transmission properties.28 Equation (1) suggests that a

deconvolution can be used for imaging of the object. For this

purpose, the knowledge of S(r), which plays the role of the

coded aperture is fundamental. As seen from Eq. (1), for a

point-like object, the image I(r) is up to a constant factor

equal to S(r/M). Hence, a low-pass approximation of S was

measured at the beginning of the experiment using a 5 lm

pinhole placed in the focal spot. This radius of the pinhole is

well fitted to the resolution of the system, which for a given

magnification is mainly limited by the detector resolution.

The crucial point is that the deconvolution can be limited to

a set of discrete frequencies, which correspond to the perio-

dicity of the microstructure of the optics.18 As demonstrated

in Fig. 2(a), the signal coming from objects displaced from

the focal plane is incommensurate with the periodicity of the

capillary structure and will be strongly suppressed after

deconvolution.

Images in Fig. 2(b) present slices reconstructed from

data recorded at different Dz. Actually, the field-of-view

(FOV) of a single exposure is limited to the area of the focal

spot. Therefore, in order to increase the FOV, the sample

was scanned in the lateral xy plane with steps Dx ¼ Dy¼ 10 lm, which were smaller than the lateral size of the

focal spot. The final image V was composed from 15� 15

partially overlapping images Uij decoded from single x-ray

exposures (1 s acquisition time each), accordingly to

Vðx; yÞ ¼P

i;j Uijðxþ iDx; yþ jDyÞ, where i and j enumer-

ate the scan positions. This acquisition principle was

adopted from x-ray ptychography22 and was shown to

improve the data quality.18

For Dz ¼ 0, the reconstruction procedure provided an

image of the object with a lateral resolution of dx � 8lm,

which is much better than the lateral size of the focal spot.

However, with increasing Dz, the image of the object

becomes less intense and, most importantly, blurred. This

blurring denotes that the depth resolution depends on the fre-

quency of the object in the lateral plane. In classical lami-

nography, the depth resolution resulting from blurring of the

out-of-focal plane signal can be estimated as3

dzð�Þ � 1

a�; (2)

where � denotes the frequency in the lateral plane and adescribes the range of viewing angles. Hence, for

Dz�dzð�Þ=2 all frequencies in the decoded images that are

higher than � will be strongly suppressed.

Let us use Eq. (2) for a qualitative description of our

data. In such a case, a denotes the angular aperture of the

FIG. 2. Transmission from projection to coded aperture imaging, which pro-

vides the basis for depth-resolved imaging. (a) X-ray images of the object (a

finder grid) for different Dz. The zoom in the left image shows a blurred pro-

jection of the letter “U”. For Dz ¼ 0, the projection of the object disappears

but the structure of the object is encoded in the fine structures of the hexago-

nal pattern. (b) A series of slices reconstructed from x-ray images recorded

at different Dz. For Dz < 0, a similar blurring can be observed.

224104-2 Dabrowski et al. Appl. Phys. Lett. 102, 224104 (2013)

polycapillary optics. While a is very large compared to angu-

lar apertures of other types of x-ray optics, it is relatively

small compared to angular ranges in classical laminography.

This results in a limitation of the resolution along the depth

direction. For example, for the highest resolved frequency of

�max ¼ 1=ð2dxÞ, Eq. (2) predicts a limit of the depth resolu-

tion as dzmin � 93 lm. However, for lower spatial frequen-

cies, dz is proportionally larger as visible in Fig. 2(b).

In order to directly demonstrate the depth resolution,

experiments were performed for two pairs of grids (Au, thick-

ness 20 lm) spaced with a kapton film. Grids with a 600 mesh

(pitch 42 lm, bar 5 lm) were spaced by 150 lm and grids

with a 1000 mesh (pitch 25 lm, bar 6 lm) were spaced by

100 lm. Figure 3 unambiguously demonstrates the depth reso-

lution. However, in both cases, a clear contrast between grids

was obtained for jDzj greater than the grid half spacing. This

denotes that the spacings of the grids were slightly below the

depth resolution for the fundamental frequency of the images,

related to the pitch of the grids. On the other hand, the depth

resolution for higher frequencies (e.g., related to bar widths)

makes it possible to resolve objects with spacing which is an

order of magnitude smaller than the dimension of the focal

spot along the optical axis and is rather comparable to the

dimensions of the focal spot in the lateral plane [cf. Fig. 1(d)].

The most important question is whether polycapillary

optics give the possibility to image slices in a thick, com-

pared to the depth resolution, complex object. In order to

demonstrate this, an x-ray microlaminography dataset was

acquired for a microSD card. This molded memory card has

thickness varying from 0.7 to 1.1 mm. Simultaneously, such

cards have relatively small dimensions (11 mm� 15 mm)

and the tomographic data could be measured with a high spa-

tial resolution in a full angular range. For characterization of

the object, we used a lCT scanner (SkyScan 1172) with a

80 keV source having spot size of 5 lm and a cooled CCD

detector having 4000� 2672 pixels with size of 9 lm.

Tomographic reconstruction was performed with the cone-

beam reconstruction software (NRecon, SkyScan). A frag-

ment of the 3D tomographic reconstruction with visible wire

bonds between traces and the memory die is shown in Fig.

4(a). The poor contrast between silicon and the material of

the mold makes the die invisible.

A side projection of the reconstruction shown in Fig.

4(b) makes it possible to identify two layers of traces as well

as to visualize the shape of the bonding wires. Also note the

very weak line (marked with an arrow), which corresponds

to a metallic layer on the die. Fig. 4(c) shows a fragment of a

raw x-ray projection taken with the lCT scanner for compar-

ison with x-ray laminography data. The resolution of this

projection is approx. 10 lm. The region of the projection is

marked with rectangles in Figs. 4(a) and 4(b).

Figure 4(d) presents slices of the object reconstructed

from laminographic data measured for different Dz. Each

slice was reconstructed from a set of 38� 38 x-ray images

(1 s exposure each) with the object scanned in the lateral

plane. The resolution in these slices is better than the resolu-

tion of the projection from Fig. 4(c). The most apparent ob-

servation is the very distinct smearing of either bond wires

and pads (for larger Dz) or traces (for smaller Dz). This allows

one to unambiguously identify the stacking sequence of these

components. Furthermore, in slices for Dz ¼ �600 lm and

Dz ¼ �300 lm, the vertical traces seem to be more intense

than the horizontal ones. Hence, the stacking sequence

of these layers can be identified as well—vertical traces are

located in the lowest layer. Next, in the image for

Dz ¼ 300 lm, the bond wires show intensity changes which

can be related to the presence of two groups of such wires as

shown in Fig. 4(b). Interestingly, in the slice for Dz ¼ �300

lm, one can recognize weak features (marked with arrows)

terminating at the bond pads. Most probably, they are located

in the top layer of the die and correspond to the thin line in

Fig. 4(b). In the top projection from Fig. 4(c), these features

are not resolved due to a low sensitivity of a conventional

projection compared to depth-resolved data.

FIG. 3. Depth resolution. Slices reconstructed from data recorded for differ-

ent Dz for grids with a pitch 42 lm spaced by 150 lm (a) and for grids with

a pitch 25 lm spaced by 100 lm (b). Left images show the orientation of the

grids.

FIG. 4. X-ray images of a microSD

memory card in the region of the mem-

ory die. (a) 3D tomographic reconstruc-

tion of lCT data. (b) Side projection of

the reconstruction (highly distorted as-

pect ratio). (c) Small fragment of a raw

x-ray projection taken with the lCT

scanner. (d) Slices of the object recon-

structed from x-ray microlaminography

datasets recorded for different Dz.

224104-3 Dabrowski et al. Appl. Phys. Lett. 102, 224104 (2013)

Since the lCT scanner was equipped with high-

resolution components, it is hardly possible to compare the

quality and resolution of tomographic and laminographic

data. However, already in this proof-of-principle experiment,

we showed that the limited depth-resolution is compensated

by a high sensitivity and resolution in the lateral plane, which

is a hallmark of laminography. The use of high-resolution

detectors, micro-focus sources, and short focal length optics

could provide at least one order of magnitude improvement

in both the lateral and the depth resolution. The FOV of a sin-

gle exposure is limited to the focal spot size. However, larger

areas can be examined by using ptychographic-like scan-

ning.22 Moreover, for choosing the region-of-interest, low-

resolution (limited to the size of the focal spot) projection

imaging can be used.

In summary, it was shown that polycapillary optics is ca-

pable to perform depth-resolved microimaging. Submicron

lateral resolution and depth resolution at the level of 10 lm

seems to be possible with commercially available optics. The

presented experimental geometry is, in particular, suited for

imaging of large flat samples and can be realized with labora-

tory x-ray sources or with synchrotron radiation. X-ray micro-

laminography with polycapillary optics could be applied for

nondestructive imaging of microscopic subvolumes within

large heterogonous samples, for example, in minerals,19 bio-

samples23 as well as in forensic samples24 and in paint

layers.20 It is compatible with scanning and confocal x-ray

fluorescence microscopy setups for chemical mapping, which

use two crossed polycapillary elements.25,26 Hence, lamino-

graphic data could serve as a high-resolution reference for 3D

element sensitive imaging. At synchrotrons, it could be also

combined with x-ray absorption spectroscopy.27

This work was financially supported by the Polish

National Science Center (Grant No. 2011/01/B/ST3/00506).

lCT measurements were carried out with the equipment pur-

chased thanks to the financial support of the European

Regional Development Fund in the framework of the Polish

Innovation Economy Operational Program (Contract No.

POIG.02.01.00-12-023/08).

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224104-4 Dabrowski et al. Appl. Phys. Lett. 102, 224104 (2013)