Low-dose three-dimensional x-ray imaging of bacterial cells ...10.1186/2192...ux of 2:4 1011 counts per second at 70 mA ring current, as measured by a pixel detector (Pilatus, Dectris)

Low-dose three-dimensional x-ray imaging of bacterial cells:supporting information

Matthias Bartels∗1, Marius Priebe1, Robin N. Wilke1, Sven P. Kruger1, Klaus Giewekemeyer1,Sebastian Kalbfleisch1, Christian Olendrowitz1, Michael Sprung2 and Tim Salditt∗1

1 Institut fur Rontgenphysik, Georg-August-Universitat Gottingen, Friedrich-Hund37073 Gottingen, Germany2 HASYLAB at DESY, Notkestr. 85, 22607 Hamburg, Germany

Email: Matthias Bartels∗- [email protected]; Tim Salditt - [email protected];

∗Corresponding author

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Experimental setup and optics

The experiment was carried out at the holographic imaging end-station of the coherence beamline P10 of

PETRA III. The source in low β configuration consists of a 5 m long undulator with a period of 29 mm,

with a source size of 36µm× 6µm (1σ, horz.× vert.). The undulator beam was monochomatized by a

Si(111) double crystal to 13.8 keV and then focused by two Kirkpatrick-Baez (KB) mirrors polished to

fixed elliptical shape positioned at a distance of 87.7 m behind the source, as described in Kalbfleisch et

al. (2011); Salditt et al. (2011). The mirror alignment and beam profile in the focal plane was controlled

by scanning horizontally and vertically aligned planar x-ray waveguides through the beam, yielding typical

focus sizes of Dhorz = 370 nm and Dvert = 200 nm (best value: Dvert = 120 nm) full width at half maximum

(FWHM), respectively, and a total flux of 2.4× 1011 counts per second at 70 mA ring current, as measured

by a pixel detector (Pilatus, Dectris) positioned at 5.29 m in the widened far-field of the KB beam. The

waveguide (WG) system was positioned in the focal plane of the KB mirror, using a miniaturized fully

motorized goniometer with optical encoders (Attocube), three translations in xyz, and two rotations along

two directions orthogonal to the optical axis. Alignment of the waveguide as well as the sample was facilitated

by use of two on-axis optical microscopes, one directed downstream and one upstream with the beam. The

focal planes of both microscopes coincide with the KB focal plane in their respective reference positions,

and allow accurate determination of the (defocus) distance z1 between waveguide exit and sample plane

(Kalbfleisch et al. 2011; Salditt et al. 2011). The sample stage is equipped with an air-bearing rotation

(Micos) for ultra-high precision turns suitable for nano-tomography. On top of the rotation, a group of

xyz piezos (Physik Instrumente) is used for aligning the sample in the axis of rotation. Additional xyz

stages (Micos) below the rotation are used for aligning the rotation axis in the x-ray beam and for distance

variation between the waveguide and the sample. The detectors were placed at a distance of z1 +z2 = 5.29 m

behind the sample, see Fig. 1 of main manuscript. To record the empty beam far-field distribution needed to

reconstruct the near-field intensity distribution of the waveguide system, a single photon counting detector

with a rather large pixel size of 172 µm (Pilatus, Dectris), and correspondingly large angular range was

used. This detector also provides a particularly large dynamic range for waveguide alignment and KB flux

calibration. The projected holograms of the biological cells needed finer sampling, and were recorded with

a single photon counting detector of 55 µm pixel size (Maxipix) (Ponchut et al. 2007) without readout noise

or dark current. This single photon characteristic is essential for phase reconstruction algorithms taking into

account the noise distribution.

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Specimen preparation

Cells of the Deinococcus radiodurans wild-type strain were cultivated from freeze-dried cultures (DSM

No. 20539 by the German Collection of Microorganisms and Cell Cultures) for one day at 37◦ C on petri

dishes covered with nutrient medium (corynebacterium agar: 10 g/l casein peptone, 5 g/L yeast extract,

5 g/l glucose, 5 g/l NaCl, 15 g/l agar). Prior to preparation the actively growing cells were washed off

the culturing medium with ca. 1.5 ml buffer solution (2 g/l KH2PO4, 0.36 g/L Na2HPO4·2H2O, pH 7.2).

After placing a droplet of cell suspension onto the substrate, a Si3N4-foil (Silson) of 1 µm thickness and

5 × 5 mm2 lateral dimensions, the cells were allowed to adhere for 60 seconds. The remaining buffer was

blotted, the frame cryoplunged into liquid ethane to prevent crystallization (Dubochet et al. 1988) and

afterwards lyophilized in a home-built freeze-drier.

Raw data processing

For all projections N = 15 intensity distributions I(n)φ were collected with 40 second dwell time for each

measurement. To correct for lateral drift the N intensity distributions I(n)φ were aligned with respect to each

other by cross-correlation methods with sub-pixel accuracy (Guizar-Sicairos et al. 2008) (upsampling factor

100). The aligned intensity distributions I(n)φ,cc where then summed up yielding Iφ =

∑n I

(n)φ,cc. Fig. 1 shows

the improvement in data quality achieved by this method. The aligned data shows more fringes in comparison

to the sum of the non-aligned intensity distributions. To correct for unhomogenous illumination the intensity

distribution I0(x, y) of the empty beam was recorded during an exposure time of 40 minutes. The normalized

intensity distribution was then calculated as Iφ(x, y) = Iφ/I0 · 40 min/10 min. Residual low frequency-

variations were removed effectively by applying a Gaussian highpass filter and a subsequent correction

through division by the mean intensity fluctuations in the regions outside the cellular area independently

for the vertical and horizontal direction (Giewekemeyer et al. 2011). We find that applying a median filter

using a 3-by-3 neighborhood prior to phase reconstruction yields superior results.

Automated generation of the support area

For tomographic datasets it is crucial to determine the support area S ⊂ R2 for all projections automatically

and accurately. As a first step the same rectangular support is chosen for all projections as an initial

guess, as shown in Fig. 2 (a) for the projection corresponding to θ = 0◦. Using 150 iterations of the phase

reconstruction algorithm an approximate reconstruction of the sample is obtained (see Fig. 2 (b)). By

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application of a threshold (−0.08 rad) to the reconstructed phase a binary image is generated. Application

of subsequent morphological operations (erosion and dilation) yield a suitable support area (see Fig. 2(c)).

Using this support area one obtains a phase reconstruction (see Fig. 2(d)) which can be used to refine the

support area by repeating the steps described above, similar to the Shrink-Wrap algorithm suitable for CDI

experiments (Marchesini et al. 2003).

Treatment of noise in iterative reconstruction

Experimental noise in the diffraction data can significantly disturb the results of iterative reconstruction

schemes (Williams et al. 2007) which are based on the implicit assumption that the measured intensity is

a noise-free representation of the diffracted intensity. To prevent possible overfitting of the noise in the

normalized intensity distribution a modified projector applied to the image intensity is used as described in

(Giewekemeyer et al. 2011). The detection plane intensity of the updated χ′n at position (x, y) then reads

|χ′n(x, y))|2 :=

(1− D

d

)I(x, y) +

D

d|χn(x, y)|2 (1)

if d > D, where d is defined by the the misfit

d2(|χn|2) := 1/N∑(x,y)

(|χn(x, y)|2 − I(x, y)

)2(2)

between the reconstructed and measured holographic intensity distribution. Here χ(x, y) = Dzeff [χ(x, y)]

denotes the near-field propagated object wave and N denotes the number of points (x, y), or pixels, at which

I was measured. The algorithm stops as soon as d ≤ D. An optimum value for the parameter D depends on

the noise statistics of the the experimental data. For the present analyis a median filter was applied prior

to phase reconstruction. A natural choice for the threshold parameter D is the standard deviation σ of the

normalized intensity distribution outside the cellular area (Giewekemeyer et al. 2011). The smallest D, for

which convergence in the sense defined above could be achieved within a reasonable amount of time (about

2000 iterations on average), was found to be in the interval of D = [0.9, 1.1]σ for all projections.

Extraction of mass density maps

As described earlier (Giewekemeyer et al. 2010) the reconstructed phase distribution ϕ(x, y) can be rescaled

into a projected electron density map σe(x, y) using the relation σe(x, y) = −ϕ/(λr0), where λ is the

wavelength of the incident radiation and r0 the classical electron radius. σe is further related to the mass

density σm as σm = A/Z · u · σe with the atomic mass unit u and A, Z denoting the atomic number and the

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mass number of the imaged material, averaged over one resolution volume. Thus one can relate the phase of

the object transmission function at point r in the object plane uniquely with an effective area mass density

σm := 2u · σe via

σm(r) = −(

2u

λr0

)· ϕ(r). (3)

The absolute area mass density is then given as σm = A/(2Z) · σm. For most biological material the factor

A/(2Z) deviates from 1 by less than 10%.

Dose

The dose quantification in this experiment relies on the single photon counting capability of the pixel de-

tectors. Summing up the photons traversing the sample and registered on the detector is easily possible,

since the support of the sample can be directly inferred from the holographic image. Taking the quantum

efficiency of the detector (Maxipix with 500 µm Si (Ponchut et al. 2007)) at 13.8 keV photon energy, ab-

sorption in window materials, and residual air-scattering into account, the dose taken up by the sample is

actually higher by 40%. However, for for the relationship between imaging resolution and dose, this dose

as measured by the detector is the relevant quantity, so that we stick to this quantity. The total (detector)

dose applied during the tomographic scan was about 1.6 · 105 Gy, based on calculations presented in Howells

et al. (2009), corresponding to a dose applied to the sample of 2.2 · 105 Gy.

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Ponchut C, Clement J, Rigal J M (2007) Photon-counting X-ray imaging at kilohertz frame rates. Nucl Instrum MethA 576:109

Giewekemeyer K, Thibault P, Kalbfleisch S et al (2010) Quantitative biological imaging by ptychographic x-raydiffraction microscopy. PNAS 107:529

Giewekemeyer K, Kruger S P, Kalbfleisch S et al (2011) X-ray propagation microscopy of biological cells usingwaveguides as a quasipoint source. Phys Rev A 83:023804

Guizar-Sicairos M, Thurman S T, Fienup J R (2008) Efficient subpixel image registration algorithms. Opt Lett 33:156

Howells M R, Beetz T, Chapman H N et al (2009) An assessment of the resolution limitation due to radiation-damagein X-ray diffraction microscopy. J El Spec Rel Phen 170:4

Kalbfleisch S, Neubauer H, Kruger S P et al (2011) The Gottingen Holography Endstation of Beamline P10 atPETRA III/DESY. AIP Conf Proc 1365:96

Marchesini S, He H, Chapman H N et al (2003) X-ray image reconstruction from a diffraction pattern alone. PhysRev B 68:140101

Salditt T, Kalbfleisch S, Osterhoff M et al (2011) Partially coherent nano-focused x-ray radiation characterized byTalbot interferometry. Opt Express 19:9656

Williams G, Pfeifer M, Vartanyants I et al (2007) Effectiveness of iterative algorithms in recovering phase in thepresence of noise. Acta Cryst A 63:36

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FiguresFigure 1

(a) Sum of the non-aligned intensity distributions, normalized by the empty beam. (b) Normalized intensity

distribution obtained by aliging N = 15 intensity distributions with respect to each other with sub-pixel

accuracy before summation.

0.9

1

1.1

0.9

1

1.1

(a) (b)

Figure 2

(a) Holographic intensity corresponding to θ = 0◦. The rectangular support (dashed rectangle) is used as

an initial guess for all projections. (b) Approximate reconstruction of the sample after 150 iterations of the

phase reconstruction algorithm. (c) Support area generated by application of a threshold and subsequent

morphological operations. (d) Phase reconstruction obtained by using the support area shown in (c).

0.92

1

1.08

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

-0.08

-0.06

-0.04

-0.02

0

1

0

(a) (b)

(c) (d)

[rad]

[ra

d]

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