Laboratory Soft X-Ray Cryo Microscopy:Source, System and Bio Applications

Doctoral Thesis No. 21, 2017KTH Royal Institute of Technology

Engineering SciencesDepartment of Applied PhysicsSE - 100 44 Stockholm, Sweden

EMELIE FOGELQVIST

There once was a woman in science Who met in the lab such defiance She struggled for years Through sweat, toil and tears Until the lab showed her compliance.

In loving memory of a wonderful, kind and strong grandmother.

Giv psaltare och lyra, då mödan görs oss lång. Betag oss ej den dyra, den ljuva lust till sång. Låt klinga våra dagar som vind i gröna hagar, som hav i böljegång. - E. A. Karlfeldt

Soft x-ray microscopes routinely perform high-resolution 3D imaging of biological cells in their near-native environment with short exposure times at synchrotron radiation facilities. Some laboratory-sized microscopes are aiming to make this imaging technique more accessible to a wider scientific community. However, these systems have been hampered by source instabilities hindering routine imaging of biological samples with short exposure times. This Thesis presents work performed on the Stockholm laboratory x-ray microscope. A novel heat control system has been implemented, improving the stability of the laser-produced plasma source. In combination with recent upgrades to the imaging system and an improved cryofixation method, the microscope now has the capability to routinely produce images with 10-second exposure time of cryofixed biological samples. This has allowed for tomographic imaging of cell autophagy and cell-cell interactions. Furthermore, a numerical 3D image formation model is presented as well as a novel reconstruction approach dealing with the limited depth of focus in x-ray microscopes.

Röntgenmikroskop vid synkrotronljuskällor producerar rutinmässigt högupplösta 3D-rekonstruktioner av celler under närmast naturliga förhållanden med korta exponeringstider. Ett flertal kompakta röntgenmikroskop har utvecklats och strävar efter att göra denna avbildningsteknik mer tillgänglig för en bredare forskarkrets. Hitintills har dock instabila röntgenkällor förhindrat rutinmässig avbildning av biologiska prover med korta exponeringar. Denna avhandling presenterar arbete utfört på det kompakta röntgenmikroskopet i Stockholm. Ett nytt värmeregleringssystem har implementerats, vilket förbättrar stabiliteten hos laserplasmakällan. I kombination med nya uppgraderingar av mikroskopets design och ett förbättrat protokoll för kryopreparation, kan nu röntgenmikroskopet rutinmässigt producera bilder av kryofixerade prover med 10 sekunders exponeringstid. Detta har resulterat i tomografisk avbildning av autofagi i celler, samt interaktion mellan celler. Slutligen presenterar denna avhandling en numerisk avbildningsmodell i 3D, samt föreslår en ny rekonstruktionsalgoritm som tar hänsyn till det begränsade fokusdjupet i röntgenmikroskop.

D. H. Martz, M. Selin, O. von Hofsten, E. Fogelqvist, A. Holmberg, U. Vogt, H. Legall, G. Blobel, C. Seim, H. Stiel, and H. M. Hertz, High average brightness water window source for short-exposure cryomicroscopy, Opt. Lett. 37, 4425-4427 (2012).

E. Fogelqvist, M. Selin, D.H. Martz, A. E. Christakou, and H. M. Hertz, The Stockholm laboratory cryo x-ray microscope: towards cell-cell interaction studies, Proc. 11:th Int. Conf. X-ray Microscopy, 463-466 (2013)

E. Fogelqvist, M. Kördel, M. Selin, and H. M. Hertz, Stability of liquid-nitrogen-jet laser-plasma targets, J. Appl. Phys. 118, 174902 (2015)

E. Fogelqvist, M. Kördel, V. Carannante, B. Önfelt, and H. M. Hertz, Laboratory x-ray microscopy for 3D cell imaging, manuscript.

M. Selin, E. Fogelqvist, A. Holmberg, P. Guttmann, U. Vogt, and H. M. Hertz, 3D simulation of the image formation in soft x-ray microscopes, Opt. Express 22, 30756-30768 (2014).

M. Selin, E. Fogelqvist, S. Werner, and H. M. Hertz, Tomographic reconstruction in soft x-ray microscopy using focus-stack back-projection, Opt. Lett. 40, 2201-2204 (2015).

Meaning AFM Atomic force microscopy ART Algebraic image reconstruction technique DGCBP Defocus-gradient corrected back-projection FBP Filtered back-projection FDM Finite differential method FSBP Focus-stack back-projection LAC Linear attenuation coefficient LPP Laser-produced plasma MLM Multilayer mirror MTOC Microtubule-organizing center NA Numerical aperture NK Natural killer PALM Photoactivated localization microscopy PSF Point spread function SIRT Simultaneous image reconstruction technique STORM Stochastic optical reconstruction microscopy TEM Transmission electron microscopy TXM Full-field transmission x-ray microscopy WD Working distance ZP Zone plate

Abstract ...................................................................................................... iv Sammanfattning .......................................................................................... v List of papers .............................................................................................. vi List of abbreviations .................................................................................. vii 1 Introduction .......................................................................................... 1

A brief history of biological imaging ............................................. 1 The resolution limit ...................................................................... 2 Imaging beyond the diffraction limit of visible light ................... 4 This Thesis .................................................................................... 8

2 Soft x-ray microscopy: the instrument ............................................... 11 Introduction ................................................................................ 11 Soft x-ray sources ........................................................................ 12 X-ray source brightness .............................................................. 17 Condenser optics ........................................................................ 18 Samples for x-ray microscopy ..................................................... 21 Zone plate objectives .................................................................. 22 Detector ...................................................................................... 26

3 Soft x-ray microscopy: imaging and applications ............................. 27 Introduction ............................................................................... 27 X-ray interactions with matter ................................................... 27 Imaging with x-ray microscopes ................................................ 28 3D reconstruction methods ........................................................ 30 Biological applications ............................................................... 33

4 The Stockholm x-ray microscope ...................................................... 37 Introduction ............................................................................... 37 The microscope arrangement .................................................... 37 Improvements to the Stockholm x-ray microscope ................... 38 3D image formation model ........................................................ 43 3D reconstruction and the depth-of-focus challenge ................ 44

Overall performance of the Stockholm x-ray microscope ......... 46 Biological examples .................................................................... 47

5 Conclusions ......................................................................................... 51 Summary ..................................................................................... 51 Outlook ........................................................................................ 51

Summary of papers ................................................................................... 53 Acknowledgements ................................................................................... 55 Bibliography .............................................................................................. 57

Using lenses to obtain a magnified image of an object has been in practice since the late 16th century when spectacle-makers were experimenting with lenses in a tube. Exactly who invented the microscope is debated, but the Dutch spectacle-maker Zacharias Janssen is often accredited for the invention. Ever since Antonie van Leeuwenhoek constructed a single-lens microscope and turned it towards the human body [1], microscopy has been one of the integral tools for biological sciences. Using this new imaging technique, Leeuwenhoek was the first to document observations of, e.g., bacteria and muscle fibers. Another early discovery with this ground-breaking new imaging technique was done by Robert Hooke and documented in his famous volume Micrographia in [2]. He observed and sketched the microscopic structure of cork and coined the term cell (from latin cellula) after the plant-cells’ resemblance to the small living chambers of monks. The imaging technique was further developed by Carl Zeiss and Ernst Abbe [3] who introduced diffraction-limited compound microscopes similar to those we have today, based on an illumination system designed by August Köhler [4].

Figure 1.1: First image of plant cells in cork [2].

The microscope, however, did not allow biologists to look deep into tissue, due to absorption of the visible light. This limitation was overcome in 1895 when Wilhelm Conrad Röntgen, while doing research on cathode rays, discovered new type of radiation which he called x-rays [5]. This type of radiation could penetrate deeper into tissue and non-invasively image the interior of the human body. This was a major step towards modern health-care both when it comes to diagnostics and treatment of disease. Both visible light and x-rays can be described as waves and belong to different regions of the electromagnetic spectrum, cf. Fig. 1.2. The x-ray region extends over hard x-rays with wavelength shorter than around

nm, through soft x-rays around nm to extreme ultraviolet radiation around nm [6]. The regions have no sharp boundaries and the name for a region may differ between scientific diciplines.

When using electromagnetic radiation for far-field imaging there is an inherent limit to what can be resolved, cf. Fig. 1.3. According to Lord Rayleigh [7], the minimal distance x between two separable point sources is given by the expression

, (1.1)

Figure 1.2: The electromagnetic spectrum reaching from infrared to hard x-rays.

1 μm 100 nm 10 nm 1 nm 1 Å

IRIR VISVISUV

EUV

Soft x-raysSoft x-rays

Hard x-raysHard x-rays

where is the wavelength of the light and NA is the numerical aperture of the objective given by , where is the half-angle of the collected light cone and is the refractive index of the immersion medium.

A comprehensive explanation to why NA determines the resolution is found by considering Fourier optics. Any object can be described by a composition of spatial frequencies diffracting the incoming radiation, where the high frequency features give larger diffraction angles, cf. Fig. 1.4.

Figure 1.4: Basic concept of Fourier optics.

Lens ImageObject

Figure 1.3: (a) The Airy diffraction patterns from two point sources, separated by the minimum resolvable distance, i.e., the distance from the Airy disk maximum to its first zero. (b) Images of two Airy diffraction patterns moving towards each other until the individual points are no longer resolvable.

Distance [a.u.]-10 -5 0 5 10

Inte

nsity

[a.u

.]

0

0.2

0.4

0.6

0.8

1Intensity drop = 25.6 %

This results in the light diffracted by the higher frequency features not being collected by the lens, which thereby acts as a low-pass filter on the incoming radiation. If the lens is in the far-field of the diffracting structures, the Fraunhofer diffraction pattern describes the field at the lens and it is simply the Fourier transform of the object. The far-field region is where the antenna designer’s formula is fulfilled, where z is the object distance, D is the size of the diffracting aperture and is the wavelength of the light [8]. In this case, the imaging can simply be described as the object diffracting light, creating a Fourier transformed image of the sample in the lens plane, which is low-pass filtered by the lens and inverse transformed onto the image plane. This is the reason why a larger NA results in a better representation of high spatial frequencies in the image. The highest NA is in theory obtained when . A typical immersion oil with would give and for specialized immersion oils it could be even higher. However, since the objective needs to be infinitely wide and infinitely close to the specimen for a half-angle of

, this theoretical limit is never reached. In practice, a more realistic number for NA is . This together with the shortest wavelength in the visible spectrum, nm, yields a maximum resolution of nm full-period in conventional far-field visible microscopy.

Over the last century, several imaging techniques have been developed that overcome this resolution limit of visible light. One workaround is simply to use radiation with a shorter wavelength, since the resolution is directly proportional to the wavelength of the light. X-ray microscopy and electron microscopy are examples of such high-resolution imaging techniques. Other techniques to circumvent the Rayleigh limit are super-resolution visible light microscopy techniques utilizing fluorescence such as, e.g., stimulated emission depletion (STED) and stochastic optical reconstruction microscopy (STORM). Atomic force microscopy (AFM) is another high-resolution technique, where the surface of a sample is mapped by physically probing it by a sharp tip.

Just like photons exhibit both wave and particle behavior, a particle can be described as a wave with a certain wavelength. The wavelength of the particle is given by its de Broglie wavelength , where h is the Planck constant and p is the momentum of the particle. The de Broglie wavelength of an electron is only a few pm for a typical electron-microscope acceleration voltage [9]. Since the Rayleigh criterion (Eq. 1.1) states that a shorter wavelength yields higher resolution, the electron microscope should in theory be able to resolve features separated by a few pm. However, there are other limitations such as thermal magnetic field noise limiting the resolution of aberration-corrected microscopes to pm [10]. The downside of using electrons instead of photons to increase the resolution, is that the penetration depth of electrons into the sample is very shallow. A typical biological sample such as a human cell needs to be sectioned into ultrathin slices ( nm) that can be imaged individually. For example, if one wants to image a whole primary NK cell ( μm diameter) one would need to image around individual sections.

In atomic force microscopy (AFM), instead of imaging the sample by illuminating it with light or electrons, the surface of the sample is scanned by a sharp tip at the end of a cantilever. The height of a structure is measured by a laser beam that is reflected off the bent cantilever onto a quad photodiode. Bending of the cantilever is detected as a vertical shift of the laser beam, whereas lateral forces cause a torque in the cantilever, resulting in a horizontal offset. In this way, the topography of the sample can be mapped with both vertical and lateral resolution down to ~ nm. The AFM is only able to touch the sample at the surface, but it can provide mechanical information of the sample, such as its rigidity, surface friction and weak dipole forces [11].

Over the last decades, methods have been developed that can generate visible light microscopy images with higher resolution than the Rayleigh

resolution limit. Stimulated emission depletion (STED) [12-14] is one example of such a technique, where a sample is stained with a fluorescent dye. The fluorophores in the sample are then excited by focusing laser light onto it. In this excitation step, the minimum size of the focus spot is still set by the classical Rayleigh diffraction limit. The next step is to deplete the fluorophores in the outer region of the focus spot using a very intense donut-shaped laser beam, which only allows fluorophores in an area smaller than the focus spot to remain excited and fluoresce. This technique can reach resolutions of few nanometers and there is a trade-off between the resolution and scan speed. Another super-resolution microscopy technique is stochastic optical reconstruction microscopy (STORM) [15], also known by the name photoactivated localization microscopy (PALM) [16]. This method relies on the stochastic switching of fluorescent molecules. Illuminating the sample using a low intensity activation beam results in that only a few of the fluorophores are in the fluorescent state at every instance, making them individually detectable. When acquiring several snap-shots over time showing a random subset of the molecules, the center-position of each fluorescent molecule in the sample can be calculated. Conventional STED and STORM/PALM are suitable for thin samples, but for 3D samples the signals from different planes may overlap. This can be circumvented by more sophisticated illumination schemes [17].

Another technique that overcomes the resolution limit for conventional visible light microscopy is x-ray microscopy. Since the resolution is directly proportional to the wavelength (see Eq. 1.1), simply decreasing the wavelength results in higher maximal resolution. In the case of soft x-rays, the maximal resolution is a few nanometers.

Biological imaging in the water window For imaging small biological samples such as, e.g., single cells, the soft x-ray region between the carbon and oxygen K-absorption edges is especially beneficial. This region ( ), also known as the water window,

provides a natural contrast between the highly absorbing carbon rich structures, e.g., protein and fatty acids, and the surrounding cytosol which mainly consists of the more transparent water, cf. Fig. 1.5.

Figure 1.5: The water window, illustrating the large difference in x-ray attenuation length between water and protein. The protein formula used is Mulder’s protein formula [18]. The x-ray attenuation data was obtained from Ref. [19].

One of the main advantages of x-ray microscopy is the possibility to image wet samples such as biological cells in suspension and in vitro-like conditions. No staining or sectioning is required and an entire cell or a group of cells can be imaged in a fraction of a second at modern x-ray light sources such as synchrotron radiation facilities. A full tomographic dataset can be obtained within an hour [20]. The total exposure time is min depending on the thickness of the specimen, so the temporal bottle neck is not the image acquisition time, but the rotation and realignment of the sample [20].

Table 1.1. shows a short summary of the strengths and weaknesses of the different high-resolution microscopy techniques discussed earlier in this section.

Wavelength [nm]1 2 3 4 5 6

Att

enua

tion

leng

th [μ

m]

1

10

λ = 2.478 nm

ProteinW

ater

O edge

C edge

In this thesis, technical improvements are presented that have been implemented in the Stockholm laboratory x-ray microscope. These improvements to the microscope have resulted in stable operation with short exposure times which allows for routine cryogenic biological imaging in 2D and 3D. The key technology development is a long-term stable laser-produced plasma source in combination with a high-reflectivity condenser mirror. This allows for tomographic imaging with s projections with total exposure time around minutes. The system performance is demonstrated by tomographic imaging of cryofixed biological samples with 10 s exposure times. Primary NK cells interacting with HEK293T target cells have been tomographically imaged and the 3D sample morphology was reconstructed. 2D and 3D imaging of autophagic organelles in starving HEK293T cells have also been demonstrated. Chapter 2 discusses the general arrangement of soft x-ray microscopes including soft x-ray sources and optics. In Chapter 3, 2D and 3D imaging and reconstruction algorithms are discussed. Previous work on x-ray microscopy with biological samples is presented as well as the samples in

Technique Strength Weakness

Electron microscopy + Availability

+ Stability

+ <1 Å resolution

+ Short exposure times

- Low transmission

- Sectioning required

- Radiation damage - Fixation required for sectioning

AFM + Mechanical information

+ 1 nm resolution

+ No radiation damage

- No internal information

- Long scan times

STED/STORM + In vivo imaging

+ Few nanometer resolution

- Staining required

- Long scan times for 3D samples

X-ray microscopy + Thick objects

+ No staining

+ No sectioning

+ Short exposure times

- Availability

- Radiation damage

- Cryofixation required

Table 1.1: Comparison of four high-resolution microcopy techniques.

this Thesis. Recent improvements to the Stockholm laboratory x-ray microscope arrangement are presented in Chapter 4 as well as examples of short-exposure time images obtained with the microscope. Chapter 4 also briefly discusses a new image formation model and novel 3D reconstruction algorithm.

As mentioned in Chapter 1, soft x-ray microscopy enables imaging with higher resolution than conventional visible light microscopes in thick objects. The technique allows for 3D imaging of cryofixed biological samples without staining or sectioning using the inherent contrast between water and carbon rich structures in the water window. To make tomography a feasible imaging method for x-ray microscopy, a bright x-ray source is needed in combination with efficient x-ray focusing optics to obtain a high x-ray flux through the sample and onto the detector. Figure 2.1 shows the standard arrangement of a full-field transmission x-ray microscope. The main components are the x-ray source, condenser optics, sample, imaging optics and a detector. The arrangement is quite similar to that of a conventional visible light microscope. However, the x-ray optics rely on diffraction or reflection instead of refraction.

Sample Detector

Condenser optics Focusing optics

Source

Figure 2.1: The principal arrangement of a full field x-ray microscope.

If the image of the source in the sample plane is sufficiently large to illuminate the entire sample simultaneously, or if a small focus spot is rotated to illuminate the entire field of view during a single exposure, the method is called full-field transmission x-ray microscopy (TXM). Lens-less soft x-ray microscopy techniques such as scanning transmission x-ray microscopy and ptychography also exist, but this Thesis will focus on full-field microscopes. In this chapter, we will discuss synchrotron and compact sources for soft x-rays as well as different condenser and focusing optics.

Today, most x-ray microscopy research is performed at electron storage rings called synchrotrons. When the negatively charged electrons are bent in a circular path by a bending magnet (BM), this corresponds to an acceleration of the particles towards the circle center. When a relativistic charged particle is accelerated, it emits bremsstrahlung in a broad range of energies with emission cone angle , where is the Lorentz factor of relativistic length contraction given by the electron speed

and the speed of light [6]. These bending magnets are basic components in all synchrotron facilities. Over the years, more advanced insertion devices with alternating magnetic field have been developed, cf. Fig. 2.2.

Wigglers (W) increase the brightness of the emitted broadband radiation by bending the electrons several times using an array of strong bending magnets. The emission cone angle for a wiggler is given by , where is the number of magnet periods. Wigglers can be thought of as an array of bending magnets with brighter emission and smaller radiation cones. Undulators (U) both increase the brightness of the emitted radiation and manipulates the emitted spectrum. This is done by alternating magnetic segments so tightly packed that an electron’s angular deviation from its original trajectory is smaller than the width of the radiation cone. Such small angular deviations are termed undulations, hence the name of the insertion device. The radiation cones from an undulator are very narrow, since is large and . Due to interference between the overlapping radiation cones, certain wavelengths are enhanced and others are suppressed, resulting in narrow radiation peaks. The peak wavelengths can be tuned by changing the undulator gap which in turn changes the strength of the magnetic field and the electron undulations [21].

Figure 2.2: (a) Principal model of a modern 3rd generation synchrotron with straight sections containing insertion devices. (b) Simplified sketch of bending magnet, wiggler and undulator.

Hard x-rays

Soft x-raysUV

e-

Undulator

Wiggler

Bending magnet

e-

e-

The properties of the radiation emitted by the insertion devices, such as wavelength, coherence and spectral resolution are further controlled by subsequent optics in the optics hutch and experimental hutch at each beamline. Various imaging techniques can be performed at a single synchrotron, spanning from soft x-ray microscopy to crystallography. These large research facilities have contributed largely to the field of x-ray microscopy and are highly attractive to researchers all over the world.

As a complement to synchrotrons, compact soft x-ray sources have emerged over the past decades. These compact sources are based on pinch plasmas [22], laser-produced plasmas (LPPs) with gas puff targets [23], solid targets [24-26] and liquid jet targets [27-30], cf. Fig. 2.3. The common goal of all these compact sources is to extend the availability for imaging techniques such as x-ray microscopy to a larger community of researchers. They could also facilitate preparatory studies for beamtime experiments resulting in more efficient data acquisition at the synchrotron.

Figure 2.3: Compact x-ray sources operating in the water window.

Pinch plasma

Gas puff LPP

Solid tape LPP

Liquid jet LPP

Other emerging table top sources are high-harmonic generation (HHG) sources, producing EUV and soft x-rays by frequency conversion of infrared laser pulses [31]. These sources will not be described further in this Thesis.

Pinch plasma sources A plasma can be created by an electric discharge in a surrounding gas [32, 33]. One method to achieve a pinch plasma is to drive a high-current pulse through a conductor inducing a discharge plasma in the gas. The current creates a strong magnetic field in the center of the source, further compressing or “pinching” the plasma until it reaches a temperature high enough for soft x-ray emission. This method of creating a pinch plasma using induction can operate without having a gradually degrading electrode in the plasma [22]. Pinch plasma sources in the soft x-ray region are commercially available and have been implemented in soft x-ray microscopes with a flux of through the sample [34].

Laser-produced plasma sources Another way to produce x-rays is to focus a high power pulsed laser onto a target material, heating it up and creating a thermal plasma with each pulse. It is important to have a regenerative target since the plasma destroys the target material. One way to create a regenerative target material is to use a moving solid target. The moving target can be for example tantalum (Ta) mounted on a translation stage [24] or an unfolding mylar tape [25] that continuously present a new area for the laser to focus on. These laser-produced plasma sources give several emission lines or broadband radiation. The bulk or tape target sources are typically hampered by debris that can damage or coat sensitive optics close to the x-ray source [35]. Other examples of regenerative targets are gas-puffs or liquid jets. The target material can vary between, e.g., argon ( nm), xenon (

nm), methanol ( nm) and nitrogen ( nm) [36]. For x-ray microscopy in the water window, nitrogen is a popular choice, since it gives high transmission and does not create carbon debris like methanol.

The gas puff target is delivered by a double nozzle where the shape of the working gas (nitrogen/argon) is controlled by a surrounding flow of low Z-number gas, e.g., helium [23, 37]. The liquid nitrogen target is delivered to the vacuum chamber in the form of a jet with diameter μm and typical speed m/s [38, 39]. Liquid jet targets have higher density and smaller source size and thereby higher brightness than gas puff targets. When a nitrogen plasma is formed from a gas puff or liquid jet, the nitrogen atoms are highly ionized. A broadband bremsstrahlung spectrum is emitted from free electrons interacting and recombining with the nitrogen ions. However, x-ray microscopy requires monochromatic radiation and therefore the characteristic line emissions from bound electron transitions are more interesting. In the water-window, the hydrogen-like NVII (

nm) and helium-like NVI ( nm) emission lines from highly ionized nitrogen are suitable for x-ray microscopy. A laser plasma has an electron density gradient that increases towards the plasma center. The laser beam can penetrate the plasma until the electrons in the plasma have a density larger than the critical density given by [6, 40]

, (2.1)

above which the laser light with wavelength will be reflected instead of transmitted. As the laser beam propagates into the plasma, its energy is absorbed through the process of inverse bremsstrahlung, where an incoming photon raises the kinetic energy of a free electron as it collides with a nucleus [41-43]. The plasma emission lines are broadened by Doppler-shift due to the velocity of the emitting ions in the plasma, Stark broadening due to electric fields and broadening due to electron-ion collisions. Also, broadening is caused by the opacity of the plasma, since it suppresses the line emission peak [40, 44].

Laser-produced plasmas typically have high electron densities and temperatures around K [40]. The broadband bremsstrahlung emission from such hot, dense plasmas can be described by black-body radiation [40]. Ideally, the peak of the blackbody emission should coincide with the peak of the emission line. Using the Wien displacement law for black-body radiation,

peak , (2.2)

we see that for the NVII emission line, the optimal nitrogen plasma temperature is K, corresponding to an electron energy of

eV.

A figure of merit commonly used to compare different x-ray sources is their spectral brightness (B) defined as

(2.3)

which takes into account the source size, emission angle and limits the relative spectral bandwidth of the radiation to . In general, the spectral brightness is a suitable measure of a source’s usefulness for imaging. However, for full-field x-ray microscopy, the spectral brightness is perhaps not the most relevant figure of merit for a source. For example, a small x-ray source such as an undulator will have a higher brightness than a larger source but as long as the image of the source falls inside the desired field of view, the larger source size is not a drawback. Furthermore, the very narrow emission cones from undulators favor them in terms of brightness, but as long as the source emission angle matches the NA of the objective a larger solid angle works just as well. A more relevant benchmark for full-field microscopes is the x-ray flux through the sample and this measure gives a fairer comparison between compact sources and synchrotrons.

The brightness of liquid nitrogen jet LPP sources is around orders of magnitude lower than that of current bending magnets, cf. Fig. 2.4. Nevertheless, the source has now reached the brightness of early bending magnets used at 1st generation synchrotrons.

Figure 2.4: A comparison of spectral brightness from different x-ray sources operating in the water window. Data obtained from [23, 39, 45, 46].

Condenser optics, or collectors, are used to focus x-rays onto the sample plane. A number of different x-ray focusing techniques have been developed and the most frequently used x-ray collector optics will be described below.

A Fresnel zone plate (ZP) is a circular diffraction grating which can be used in x-ray microscopes to image the source onto the sample plane, cf. Sect. 2.6 [29, 47]. When using a ZP as condenser, an order sorting aperture is commonly used to remove background from other diffraction orders [48].

Photon energy [eV]100 101 102 103 104 105

Avg

. spe

ctra

l brig

htne

ss [p

h/(s

mra

d2

mm

2 0

.1%

BW

)]

108

1010

1012

1014

1016

1018

1020

ALS (W)

ALS (BM)

BESSY II (BM)

ALBA (BM)

BESSY II (U)

Liquid jet target LPP

Gas puff target LPP

At normal incidence angles the reflectivity from the interface between two materials ( , ) is given by the simplified Fresnel equation [49],

. (2.4)

It is clear that in the soft x-ray region where the refractive index is very close to unity ( ), cf. Sect. 3.2, the reflectivity is very low. However, for sufficiently small grazing angles, total external reflection can be obtained. This happens when the grazing angle is smaller than the critical angle given by , where is the real part of the complex refractive index of the reflecting surface, cf. Sect. 3.2 [6]. Total external reflection is utilized in polycapillary condensers [50], where the x-rays are bent in several reflections with grazing incidence angles inside hollow capillaries, arranged in an elliptically curved trajectory. Another method to focus x-rays using grazing incidence is to use Kirkpatrick-Baez mirrors [51]. The focusing system consists of two slightly curved mirrors that focus the x-rays in the vertical and horizontal direction respectively. The mirrors must be carefully aligned for their foci to coincide in the sample plane. Wolter mirrors [52] have various paraboloid shapes and focus the x-rays by grazing incidence reflections.

Even though the soft x-ray reflectivity from single interfaces is very low at near-normal incidence angles, the reflectance can be enhanced by using reflection from several interfaces that interfere constructively. This principle is used in multilayer mirrors (MLMs), consisting of multiple bilayers with alternating high and low refractive indices, cf. Fig. 2.5. The reflections interfere constructively according to Bragg’s law,

, (2.5)

where d is the bilayer thickness and is the grazing angle for the incoming radiation.

One may assume that the refraction is small, since the refractive indices are close to unity in for both the multilayer materials. For normal incidence mirrors ( ) the Bragg condition for constructive interference boils down to the condition .

Since the layer thickness is optimized to create constructive interference for a specific wavelength, the multilayer condenser also works as a monochromator by suppressing wavelengths that do not interfere constructively. Thus, the MLM acts as a bandpass filter on the incoming radiation, with spectral resolution ( ) proportional to the number of layer pairs [6]. For water-window applications, the multilayer material combinations Cr/Sc ( [53]), Cr/Ti ( [54]) and Cr/V ( [55]) are common. To avoid intermixing of the layers at the boundaries, thin diffusion barrier layers (C or B4C) are frequently used [56].

In x-ray microscopy it is important to understand the influence of partial coherence in the image formation process. This has been investigated in Paper F and it was found that partial coherence can improve the quality of the reconstructed image, compared to incoherent image reconstruction. One commonly used metric for the coherence degree is the ratio of the numerical apertures of the illumination optics and the ZP objective [57].

nlowd nhigh

Figure 2.5: Reflections from different planes in the multilayer mirror, interfering constructively.

The coherence parameter is given by the ratio of the numerical apertures of the condenser and objective, . When , the imaging is fully coherent and when it is completely incoherent. However, already at the imaging can be regarded as incoherent and the effects of partial coherence are more pronounced when [58]. By varying the shape of the illumination cone by, e.g., blocking parts of the condenser optics, one can vary the coherence degree. This could be useful for low-contrast samples, since partial coherence has the potential to enhance features with low contrast and thereby make them distinguishable.

When imaging a sample with high resolution it is important that the sample morphology does not change due to radiation damage. When done correctly, cryogenic fixation does not alter the cell morphology and protects the sample from radiation damage, cf. Sect. 2.5.3. When performing cryofixation the goal is to achieve highly amorphous ice since larger ice crystals would distort the sample structure. It is also important to keep the sample very stable during one exposure to avoid motion blur. For dry samples it may be enough to mount the samples firmly on a sample holder, whereas wet samples need to be fixed in ice in order to not move around in the liquid during the exposure. Cryofixed samples must be kept at a controlled temperature to avoid thermal drift in the sample.

One way to freeze the sample is to plunge it into liquid ethane cooled down to its freezing point ( K) by surrounding liquid nitrogen. To achieve amorphous ice with ice crystals no larger than nm, the freezing process must be very rapid and the cooling rate must supersede K/s [59]. Liquid ethane has proven to be a more efficient cooling medium than liquid nitrogen, since the latter tend to induce bubble formation on the sample, insulating it and impeding heat transfer. For samples larger than a few μm, such as biological cells with typical diameters in the range μm,

obtaining amorphous ice is not feasible through the entire sample without using a cryoprotectant [60]. One may therefore assume that the ice is at least partially crystalline for larger samples.

The high-pressure freezing technique was developed to prevent ice-crystal formation when cryofixing thicker samples without using cryoprotectants. This method allows for samples of thickness up to μm. The sample is subjected to a pressure of bar for a few milliseconds before it is rapidly cooled by immersion in liquid nitrogen [61]. Ideally, the sample shows no morphological changes due to the sudden increase in pressure.

The ice layer does not only fix the cell in space, it also makes the cell more resistant to large radiation doses. Radiation damage is caused by three mechanisms. Primary radiation damage is caused directly by breaking chemical bonds by the absorption of the ionizing radiation. The ionizing radiation also creates free radicals (•OH, •H) through radiolysis of water, which cause secondary radiation damage as they migrate and create a cascade of chemical reactions in the sample. Tertiary damage is when hydrogen gas is produced in the sample, causing large morphological distortions [62]. The secondary damage can be reduced by cooling the sample, which results in slower diffusion of free radicals [63]. A hydrated cell that is not cryofixed can withstand a dose of Gy but if it is encapsulated in amorphous ice it can tolerate doses up to Gy without undergoing visible morphological changes [64].

A zone plate is a circular grating which focuses x-rays by diffraction and constructive interference. The simplest ZP consists of interchanging opaque and transparent radially symmetric zones with gradually decreasing zone width towards the periphery. The pattern is designed so that the difference in optical path from the focal point to two neighboring transparent zones is one wavelength. By this design, the light emerging from all transparent zones will be in phase at the focal point and there they will interfere constructively, whereas the light that would interfere

destructively is blocked by the opaque zones. A method to improve ZP efficiency is to replace the opaque zones (typically gold) by semi-transparent phase shifting zones (typically nickel) and thereby reduce the loss due to x-ray absorption by the opaque zones [65]. For x-ray microscopy imaging the focus of the 1st diffraction order is most commonly used. At this point, the path difference between light emerging from neighboring transparent zones is one wavelength. However, the criterion for constructive interference is met by several other focal points, e.g., all points where the path difference between neighboring transparent zones is an odd integer number of wavelengths. These foci are referred to as the focus of the 3rd, 5th, …, mth order and are found at a distance ,

, …, from the ZP objective, cf. Fig. 2.6.

In a ZP design where the area of all zones are equal, the even orders will cancel out, but for zone plates with fabrication flaws, even order foci may exist [6]. The focal length for a ZP is given by

, (2.6)

where D is the ZP diameter, is the outermost zone width, m is the diffraction order used for imaging and is the wavelength of the x-rays. Fresnel zone plates are commonly used as objectives in x-ray microscopes

DrN

l

F1F3F5

Figure 2.6: A Fresnel zone plate with the foci from the 1st, 3rd and 5th diffraction order.

and their resolution is determined by the outermost zone width and the diffraction order used for imaging: . For a ZP with opaque zones, of the radiation incident on the ZP is absorbed, but for phase-shifting zone plates the absorption is smaller. Half of the transmitted radiation ends up in the 0th diffraction order, goes to the negative diffraction orders, goes to the 1st positive diffraction order and only is distributed on the higher positive diffraction orders [6, 66]. Thus, imaging at higher diffraction orders is a trade-off between resolution and x-ray intensity. High-resolution imaging at higher diffraction orders has been done at synchrotrons where nm half-pitch structures were clearly resolved [67].

In a perfect imaging system with a perfectly monochromatic x-ray source, the resolution is diffraction limited and only depends on the outermost zone width. However, in real soft x-ray microscopes other factors such as aberrations can come into play. For example, the ZP could be astigmatic due to elliptical zones or a tilted alignment. Also, no perfectly monochromatic x-ray sources exist so there is always some spread in wavelength, which results in different foci for different wavelengths. This means that the different wavelengths from the source will image the object onto different planes, which will be defocused with respect to the detector plane and hence contribute to a blurred image. A rule of thumb is to tolerate chromatic aberrations as long as the focal planes of the different wavelengths fall within the depth of focus (DOF) of the ZP [6]. The DOF of a ZP is determined by the displacement from the focal plane over which the on-axis intensity decreases by no more than

:

. (2.7)

The rule of thumb demands that the number of zones ( ) in the ZP should be smaller than the spectral resolution of the x-rays,

. (2.8)

Bear in mind that the tolerated chromatic aberrations are relative to the focal spot size. A ZP with a typical diameter ( μm) with a small outermost zone width ( nm) requires a highly monochromatic source

if the system is not to be limited by chromatic aberrations, whereas a broader outermost zone width ( nm) allows for a less monochromatic source . Thus, the rule of thumb states for what number of zones one can expect near-diffraction-limited performance, but contains no information about the absolute size of the chromatic blur. In summary, two important factors that determine the resolving power of a laboratory x-ray microscope are the resolving power of the focusing system and the bandwidth of the radiation. However, if vibrations or thermal drift are present in the sample plane, the imaging will instead be limited by motion blur. It is therefore very important to damp any vibrations and control the temperature when imaging cryofixed samples.

For tomography it is important that the sample can be rotated without hitting the mechanical structure on which the ZP is mounted. For this reason, the ZP should ideally be placed far away from the sample, i.e., have a sufficiently long working distance (WD). The WD for a ZP is determined by the equation

. (2.9)

The equation tells us that either increasing the ZP diameter or outermost zone width will result in a longer working distance. However, a larger results in lower resolution for an aberration-free system, as well as a decrease in NA, since the working distance increases while the diameter is unchanged. On the other hand, increasing the diameter of the ZP will not affect the NA, but it may enhance aberrations, which in turn can cause the resolution to be aberration limited instead of diffraction limited.

To adequately describe an image with features of periodic frequency , the frequency of pixels describing the features must be at least twice that frequency ( ). This is known as the Nyquist sampling theorem. If this condition is not fulfilled, the features will not be represented accurately in the image and aliasing may occur, cf. Fig. 2.7.

In x-ray microscopes, the magnification can be adjusted until a sufficient number of pixels are describing the features of interest for a certain experiment.

Figure 2.7: Siemens star illustrating aliasing when imaged with too few pixels.

As stated in the introduction x-ray microscopy allows for high-resolution tomographic imaging of thick biological samples in their near-native state. Here we review the imaging process and discuss the biological samples imaged in this Thesis.

In the x-ray regime, all materials have a refractive index smaller than , with some exceptions close to resonance frequencies. The complex refractive index is given by [6, 66, 68]

, (3.1)

where is the dispersive part, describing the phase-shift of the incident wave field as it passes through the material and describes the absorption. The transmitted light intensity as a function of traversed material thickness is given by the equation

, (3.2)

where is the incident light intensity, is wavelength and is the traversed thickness. The linear attenuation coefficient (LAC) is given by

and is typically used to describe the x-ray absorption by a certain chemical compound. In the water window at eV, carbon has

and water has [19]. The big difference in LAC

provides an excellent contrast mechanism when imaging water-carbon objects such as biological samples. The sub-unity real part of the refractive index indicates that x-rays can be focused with concave lenses. However, is typically very small ( ) in the soft x-ray regime, which means that the dispersive real part of the refractive index is very close to unity and therefore x-rays are very weakly refracted. For soft x-rays, where stacking of concave lenses is not an option due to absorption, soft x-ray lenses need to focus the light through either diffraction or reflection.

In absorption contrast imaging, a 3D object is projected onto a 2D detector, cf. Fig. 3.1.

The absorption by each feature in the sample depends on the LAC of that specific material. Therefore, the transmission through the sample is given by the Beer-Lambert law:

, (3.3)

Figure 3.1: Two projections ( ) through a 3D sample.

P1

P2

where is the linear attenuation coefficient and and are the boundary planes for the sample. However, in x-ray microscopy the projections are not collimated rays, but there is a limited depth of focus. Methods on how to correct for the limited DOF in 3D reconstructions are discussed in Sect. 4.5.

When performing tomographic imaging with full-field x-ray microscopes, several things need to be considered, such as the tilt range of the sample and the number of projections needed to obtain the desired resolution. The range of useful projection angles may be limited by a number of different things. The height of the sample holder in combination with the working distance of the ZP objective decides if and when the rotating sample holder will collide with the ZP. The tilt range can also be limited by shadowing by the bars of a TEM grid or the window frame of a silicon nitride window. Another limiting factor can be the thicker ice layer of a tilted sample, where the x-ray attenuation may lead to a low signal-to-noise ratio. The missing wedge is normally quite large for cryofixed samples, where is a typical tilt range. Reconstructions from tomographic data with a large missing wedge can be improved somewhat by using an iterative reconstruction technique. To obtain a certain resolution throughout the sample volume, the angular increments must be considered. The number of projections needed to reconstruct an object with diameter with a full-period resolution throughout the sample volume is given by the Crowther criterion [69]:

. (3.4)

When imaging a spherical object with μm diameter over a full tilt of , a full-period resolution of nm in the reconstructed volume can be achieved with equally spaced projections. This corresponds to an increment angle of . However, the DOF for soft x-ray microscopes is typically smaller than the object, which means that even with sufficient sampling, the entire sample volume is not imaged sharply.

There are several reconstruction algorithms that can be used to obtain the 3D volume from a dataset of tomographic projections. The most basic algorithm is filtered back-projection (FBP) [70], where each image intensity is back-projected through the volume and summed in each voxel. Before back-projecting the images they are processed by a ramp filter in the frequency domain to enhance edges and avoid blurring in the reconstructed image. Why this frequency filtering is needed is explained in Sect. 3.4.1. Other, more sophisticated, iterative techniques such as the algebraic reconstruction technique (ART) [71] and simultaneous iterative reconstruction technique (SIRT) [72] usually give better reconstructions with less streak artifacts in the final reconstructed volume compared to FBP. Iterative reconstruction algorithms work by solving a system of linear equations and correcting for errors in the reconstructed volume. The corrections are done by calculating projections from the volume and comparing them to the actual projections. Many variations of ART and SIRT exist and a hybrid of the two techniques is the simultaneous algebraic reconstruction technique (SART) [73]. However, in this section will only focus on the direct reconstruction algorithm FBP.

When performing tomography, the sample morphology is often not known a priori. When projecting a 2D slice of an unknown object onto a detector, the 1D detector function is obtained for this projected slice. The Fourier transform (FT) of the 1D detector function for a projection at an angle corresponds to sampling a straight line at angle through the 2D Fourier transform of the 2D object itself, cf. Fig 3.2. This is known as the Fourier slice theorem [70]. The 2D Fourier transform of the 2D object can be obtained by making more 1D projections and adding them together in Fourier space.

However, when doing this it is clear that the lower spatial frequencies are over-represented in the frequency space compared to the higher frequencies where the lines are sparser. This means that low spatial frequency objects will be heavily over-represented, which leads to a blurring of high frequency components such as sharp edges. The same reasoning applies to imaging of 3D objects, by simply adding together several 2D slices in the 3D Fourier domain.

To avoid blurring of edges by low-frequency features in the object, the 2D projections need to be ramp filtered in the Fourier domain before they are back-projected over the sample volume. A simplified 1D sketch of the filtering is shown in Fig. 3.3.

Figure 3.2: Illustration of the Fourier slice theorem.

FT

df(x)

2D object

FT

Projection

Fourier slices for all angles

n

Df(n)

1D detector function

x

n

f

f

n

The ramp filter enhances high frequency noise, which can be removed by applying an additional low-pass filter. After filtering, the 2D projections are back-projected over a 3D volume, smearing the intensities from each pixel in the 2D image onto all voxels along their back-projected path, cf. Fig. 3.4.

Figure 3.4: Illustration of back-projection of projection data.

Figure 3.3: An illustration of ramp filtering in the Fourier domain.

FT

1D detector function

x

df(x)

IFT

Ramp filter

x

Filtered 1D detector functiond’f(x)

Df(n)

D’f(n)

Filter

n

n

n

In the past decade, a wide range of biological samples have been imaged using x-ray microscopes. Soft x-ray microscopy beamlines at modern synchrotron radiation facilities routinely produce tomograms of hydrated, cryofixed biological samples. An early work in x-ray cryotomography was done at the XM-1 beamline at the Advanced Light Source where 3D imaging of eukaryotic schizosaccharomyces pombe cells was presented [74]. The HZB-TXM at BESSY II has produced several biologically relevant cryotomograms and 3D reconstructions. Mouse adenocarcinoma cells ( μm thick) have been tomographically imaged over with s exposure time per projection angle. In the 3D reconstruction intracellular components such as mitochondria, lysosomes, endoplasmic reticulum, vesicles, plasma membrane, nucleoli and nuclear envelope, pores and channels were clearly visible [75]. In another study, starved and cryofixed HEK293 cells containing autophagosomes were imaged and reconstructed with a tilt range [76]. 3D imaging of the internal structure of vaccinia virus ( nm thick) and vaccinia virus infected PtK2 cells were also obtained at the HZB-TXM beamline with tilt range [77, 78]. As for laboratory microscopes, the Stockholm compact x-ray microscope has also produced several biological studies in the past. One study showed stereo images of spironucleus salmonicida parasites and 3D reconstructions of yeast cells (diameter μm) with second exposure time covering [79]. A tomogram of a necrotic HEK293T cell has been obtained with minute exposure time per projection covering [80]. Colloidal samples have been imaged in wet and dry conditions, illustrating the importance of imaging a sample in its natural state [81].

To demonstrate the applicability of the Stockholm x-ray microscope, biological tomographic imaging has been performed on human embryonic kidney cells (HEK293T) in different stages of starvation. Cell-cell

interactions between primary NK cells and HEK293T cells have also been tomographically imaged.

Autophagy in mammalian cells After a few hours of nutrient deficiency, the cell starts a process termed autophagy in which it collects, degrades, and recycles intracellular components. The process of autophagy starts with a double-membrane structure called the isolation membrane or phagophore forming in the cytoplasm. The membrane expands and closes itself, engulfing cytoplasm and organelles in the process. These spherical double-membrane organelles are called autophagosomes with sizes ranging from μm in mammalian cells [82]. The autophagosomes gather in the perinuclear region where they merge with lysosomes creating autolysosomes. Only the outer membrane fuse with the lysosome membrane, while the inner membrane and its contents are degraded by lysosomal hydrolases and recycled [83, 84]. As the starvation increases the cells may undergo autosis, a non-apoptotic cell death induced by autophagy [85].

The immune synapse As part of the innate immune system, natural killer (NK) cells interrogate cells they encounter by forming the so called immune synapse. If the target cell is foreign to the body, e.g., presents antigen or lacks self-markers, the NK cell is activated and initiates targeted cell killing. The microtubule-organization center (MTOC) in the NK cell migrates towards the synapse, transporting lytic granules containing cytotoxic mediators such as granzymes, granulysin and perforin. The killing is done by secretion of the contents of the lytic granules into the synaptic cleft where the perforin creates a hole in the target cell membrane through which the other cytotoxic components enter and trigger apoptosis [86]. This target-specific delivery of cytotoxic mediators is termed directed secretion and allows the NK cell to kill a target cell while leaving surrounding cells unharmed.

NK cells have a range of inhibitory receptors, e.g., killer immunoglobulin like receptors (KIRs). These inhibitory receptors bind to target cell ligands displaying the major histocompatibility complex molecule-I (MHC class I) which is a self-indicator, cf. Fig. 3.5. If the target cell has a downregulated expression of the self-indicator molecule MHC class I, the NK cell will kill the target cell.

Figure 3.5: Model of the immune synapse between an NK cell and target cell.

Lytic granules

Ligands and receptors

NK cellTarget cell

Nucleus

MTOC

Nucleus

This section will describe the present Stockholm x-ray microscope arrangement and recent upgrades. The goal of this Thesis has been to achieve long-term stable operation of the compact x-ray microscope with the capability to routinely perform tomographic imaging of biological samples. Improvements to the x-ray source stability and upgrades in the imaging system are described in this chapter along with examples of biological applications. This chapter will also discuss recent improvements to our image formation model and a comparison between different 3D reconstruction techniques.

Figure 4.1 shows the principal arrangement of the compact x-ray microscope. A pulsed W Nd:YAG laser with kHz repetition rate is focused onto a jet of liquid nitrogen, creating a thermal plasma. This plasma emits soft x-rays in all directions. The x-rays are collected by a curved MLM and focused onto the sample plane. The sample is then imaged by a ZP onto the CCD, using the 1st diffraction order. The direct x-rays and laser light are blocked using a central stop and an aluminum filter, respectively.

To make routine tomography of cryofixed biological samples possible, several upgrades have been implemented in the microscope arrangement. The stability of the laser-produced plasma source has been improved by implementing a heating element around the nozzle orifice. The x-ray flux through the sample has increased thanks to the source stability in combination with a condenser mirror with higher reflectivity. A novel protocol for cryofixation has improved the quality and reproducibility of biological samples. New zone plates with large diameters and long working distance have been fabricated for the tomographic imaging experiments.

The Stockholm x-ray microscope is based on a liquid-jet laser-produced plasma source. The liquid nitrogen jet needs to be spatially stable in order for the focused laser pulses to efficiently hit it and create a plasma. However, when the liquid nitrogen is ejected into vacuum, the jet cools down rapidly due to evaporation. This phenomenon was investigated theoretically in Paper C using a model for evaporative cooling described in Refs. [87, 88]. The rapid temperature drop typically causes freezing in the jet or at the nozzle orifice. Frozen nitrogen at the nozzle orifice may induce

Figure 4.1: The Stockholm x-ray microscope arrangement.

Pulsed laser Liquid jet (LN2)

Sample

Detector

CS ZP

Aperture

Al filter

MLM

Heat coil

a larger initial disturbance that can cause spray, violent breakup in the semi-frozen nitrogen or completely clog the nozzle orifice, cf. Fig 4.2.

Jet imaging arrangement In order to monitor the jet during operation of the x-ray microscope, a flash-imaging system has been implemented in the microscope. The arrangement is shown in Fig. 4.3. A frequency-doubled Nd:YAG laser with 4 ns pulses is used to illuminate a fluorophore inside the vacuum chamber. The fluorophore emits short pulses of red-shifted light that back-illuminates the nozzle and nitrogen jet. A camera exposure is triggered at each laser pulse ( Hz) with ms exposure time in order to capture a single plasma event ( kHz) per image. A nm rejection filter is placed in front of the camera to avoid saturation of the camera by laser speckles in the images.

Fluorophore

Camera

532 nm rejection filter

Liquid nitrogen jet

Laser Lens

Figure 4.3: Flash-imaging arrangement.

Figure 4.2: Violent and unpredictable breakup due to freezing.

Jet stabilization To stabilize the jet we manufactured a radiative heating system that could be controlled from outside the microscope, cf. Fig. 4.4. A resistive Ni/Cr wire was coiled tightly in two loops around the nozzle orifice. The heating applied to the nozzle tip could be carefully controlled by regulating the current that was driven through the wire. Further details are found in Paper C. When designing this system one had to take into account that too tightly bent loops would result in stress in the wire, causing it to break when heated. However, if the coil was too loose one would need to drive more current through the wire since the heating power to the nozzle decreases like . This would result in gradual deformation and subsequent breaking of the wire.

The implementation of the heating wire resulted in a spatially and temporally stable jet allowing for plasma operation far from the nozzle. The heat wire has been especially useful in the jet startup procedure, where there is a high risk of nitrogen ice clogging the nozzle orifice. Once produced, the plasma itself would act as a heat source and the current through the wire could be slightly down-regulated. When operating the plasma at different distances from the nozzle tip, the heat current needs to be adjusted accordingly.

Figure 4.4: Resistive wire coiled tightly around the nozzle orifice.

A new MLM has greatly improved the reflectivity from previously to [55], increasing the x-ray flux through the sample by a factor eight.

The new Cr/V MLM has multilayer pairs and a reflectivity of more than over the entire reflective area, cf. Fig. 4.5. Thin diffusion barrier layers

prevent mixing of the materials at the interfaces. The new mirror efficiently acts as a monochromator with a spectral bandpass of . The donut shape of the reflectivity makes the mirror optimal for a microscope operating with a central stop and .

Hydrated biological samples are typically prepared on Au TEM grids with a thin carbon film. Adherent cells are cultivated on the grids, whereas non-adherent samples are pipetted onto the grid. When cryofixing samples for soft x-ray microscopy it is crucial to obtain a very thin ice layer. Therefore, controlling the process of blotting the sample to remove excess liquid before plunging it into liquid ethane is crucial for a successful cryofixation. If the ice layer is too thick, ice crystals will alter the sample morphology and the x-ray transmission will be low. On the other hand, the sample must

Figure 4.5: Reflectivity measurement at 1.5° angle of incidence. The condenser mirror has over 4% reflectivity over the entire area and an average reflectivity of 4.58% in the donut shaped area used for imaging.

not be allowed to dry out completely since dry and wet samples may look quite different. To optimize the plunge-freezing procedure and make it more reproducible, an imaging arrangement with side illumination has been implemented. With this setup the liquid layer thickness is monitored and recorded during the blotting procedure. The grid is typically plunged when the liquid surface on the gold wells start appearing concave. This indicates that the ice layer is thinner than μm. The sample preparation is described further in Paper D. Due to the short working distance of many zone plates it is important to consider the risk of hitting the ZP substrate when tilting the sample holder. A new cryo-sample holder with an indentation to achieve high tilt range for standardized mm TEM grids has been implemented in the microscope.

Currently two sets of nickel zone plates are in use at the Stockholm x-ray microscope. One set consists of large diameter zone plates ( μm) with nickel thickness nm. The zone widths are , yielding a focal length of , which is also the working distance of the ZP. The long working distance zone plates are ideal for tomographic imaging, where a large tilt range is required. The maximal resolution for these zone plates is full-period. The number of zones are , which means that chromatic aberrations are likely to influence the resolution with our source ( ) [89]. The other set consists of zone plates with smaller diameters ( ) with outermost zone width and thickness. These allow for high-resolution imaging ( full-period) with less chromatic aberrations. The working distance is mm, which makes these zone plates suitable for single projection or stereo imaging.

The image of the sample is detected by a pixel uncoated back-illuminated CCD ( ) with μm pixel separation and quantum efficiency at eV. The light collecting area is mm, which for a magnification of × corresponds to μm in the sample plane. The μm pixel separation corresponds to nm in the sample

plane, which fulfills the Nyquist sampling criterion ( ) for features separated by more than nm. This is sufficient for a nm ZP where the diffraction limited resolution is nm full-period. In order not to be pixel-limited, the optimal resolution of the ZP in use should always be taken into account when selecting magnification for a specific imaging project. In the current microscope arrangement, the maximum distance between ZP objective and detector is around m and therefore the largest possible magnification is given by where is the focal length of the ZP in millimeters.

In order to predict the outcome of imaging a sample with certain illumination properties such as partial coherence and limited DOF, it is beneficial to have an accurate model of the image formation. Previously, models have been developed that can handle one-dimensional objects [64], flat 2D and thick 2D objects [90, 91], weakly scattering 3D objects [92] and thick 3D objects with incoherent illumination [93]. In Paper E, we present a novel 3D image formation model that allows for varying degrees of coherence. It starts with the assumption that every point on the condenser mirror can be treated as a secondary point source [57]. The coherent field from each individual secondary point source is propagated through the sample and imaged by the objective onto the

Figure 4.6: The electric field from simulated point sources at the condenser is propagated through the sample and imaged by the zone plate onto the detector.

Sample DetectorZPMLM

k

BA Dz

yz

x

detector plane. Subsequently the contributions from all point sources are summed in the detector plane, cf. Fig. 4.6. For simplicity, the slowly varying electric field envelope, a.k.a. amplitude modulation function, is separated from the quickly oscillating component in the calculations of how the electric field propagates through the sample. As the electric field envelope traverses the sample, the wave-propagation model utilizes the finite differential method (FDM). In each step the evolution of the field is calculated using the 4th order Runge-Kutta (RK4) method to solve the parabolic wave equation. Transparent boundary conditions are used in the sample, i.e. energy can flow out but is not reflected. As the electric field from a point source exits the sample, it is imaged by the ZP through filtering by the aperture function of the ZP and scaling by the magnification. The intensity contributions from all individual point sources are summed incoherently at the detector plane, and the resulting image is obtained on the detector. The performance of this 3D wave propagation-based image formation simulation method has been compared with previous methods through simulation and experiment. The experimental data was obtained at the TXM-U41 beamline at BESSY II in Berlin. A freshwater diatom frustule was imaged with μm focus steps and the experimental images of a single areola were compared with the simulation of a model diatom.

The FBP reconstruction algorithm assumes projection data where all features in the sample volume are simultaneously sharp. However, this is not the case in x-ray microscopy where the depth of focus is typically around μm. This means that some features in the sample volume are out of focus in each image and that they contribute to an erroneous reconstruction when using the conventional algorithms. Therefore, other reconstruction methods for imaging systems with limited DOF have been developed.

Two examples of such reconstruction algorithms are defocus-gradient corrected back-projection (DGCBP) [94, 95] and the novel algorithm focus-stack back-projection (FSBP) which is presented for the first time in Paper F. In the paper, these two reconstruction methods have been compared to the classical FBP. The three algorithms were compared by reconstructing a 3D volume from the projections of a simulated 3D object. Additionally, FSBP was compared to FBP by tomographic reconstruction of a real 3D sample, a diatom frustule, imaged at the TXM-U41 beamline at BESSY II in Berlin. Both the reconstruction of the simulated tomographic dataset and the experimentally obtained dataset showed that FSBP generated the best reconstruction. DGCBP is a back-projection method in which the images are deconvolved with a defocus-dependent point spread function (PSF) before they are ramp filtered and back-projected. The FSBP reconstruction algorithm requires a focus stack for each rotation angle. Each image is filtered and back-projected individually as in FBP, but under the influence of a window function that ensures that each image contributes only to the region of the reconstruction volume where it is in focus. The window functions should be chosen so that the total voxel weight is unity. In Paper F, triangular window functions were used, cf. Fig. 4.7.

In conclusion, Paper F shows that taking focus stacks at each projection angle and using the FSBP algorithm has the potential to improve 3D reconstructions with x-ray microscopes. This would yield a more accurate reconstruction of large 3D samples when working with a limited DOF.

The improved stability of the LPP source allows for reliable imaging on a daily basis. The microscope runs stably for several hours, allowing for tomographic imaging of cryofixed samples with seconds exposure time. When operating the source with W laser power, the flux onto the detector is around photons/(second×pixel) in the current setup optimized for tomography. In this setup the magnification is ×, giving a pixel size corresponding to nm in the sample plane and a μm field of view. A tomographic dataset can now be obtained with a total exposure time of minutes and the bottleneck is currently the rotation and alignment of the sample.

Weight1

0F1 F2 F3

F1 F2 F3

Figure 4.7: Illustration of three focus planes which are weighted in the reconstruction with respect to their focus region.

The primary goal of this Thesis has been to make the compact x-ray microscope stable enough to make biological studies in 3D with short exposure times. 2D and 3D imaging of autophagy in HEK293T cells and cell-cell interactions between primary NK cells and HEK293T cells have been demonstrated in Paper D. Other images from this study are presented below. Figure 4.8 shows -second exposures of starving HEK293T cells. The size and number of autophagic organelles (dark dots) increase as the autophagy progresses. A stereo image (for cross-eyed viewing) of a starved HEK293T cell is shown in Fig. 4.9 at tilt angles and at . In some starved HEK293T cells the nucleus becomes more visible.

Figure 4.8: 10-second exposures of starving HEK293T cells.

Figure 4.9: Stereo image of a starved HEK293T cell with 10 s exposure time per image.

Figure 4.10 shows -second exposures of HEK293T cells in different stages of starvation. The cells on the left hand side do not show any visible signs of starvation. In the healthy state the cells are stretched out and adhered to the carbon film of the TEM grid. The starved cells on the right appear more round and show several autophagic organelles (a) and visible nuclei with their nucleoli (n). Similar images can be found in Paper D, where a comparative study has been performed using confocal laser scanning microscopy. Paper D also shows a 3D reconstruction of a starved HEK293T cell.

Figure 4.10: 30-second exposures of healthy HEK cells (left) and increasingly starved HEK cells (right).

Figure 4.11 shows -second exposures of primary NK cells and HEK293T cells that are interacting. The target cells were starved so that the autophagic organelles could be used as fiducial markers in the 3D reconstruction in Paper D. More -second exposures and comparisons with confocal laser scanning microscopy are found in Paper D as well as a 3D reconstruction of interacting cells.

To summarize, these images show whole, unstained cells in their near-native state, demonstrating the strength of x-ray microscopy in the water window. Protruding actin filaments and intracellular structures are clearly distinguished thanks to the natural contrast between water and carbon-dense structures. With reliable source operation and short exposure times, the Stockholm x-ray microscope could become an attractive instrument for external users.

Figure 4.11: 10-second exposures of cell-cell interactions between primary NK cells and HEK cells.

In this Thesis we have demonstrated upgrades to the Stockholm x-ray microscope arrangement allowing stable, reliable, high-resolution operation, resulting in successful 3D tomographic imaging of biological samples. The stability of the liquid nitrogen jet has been improved by a heating device, which allows routine operation of the microscope on a daily basis. The stable high-brightness laser-plasma source in combination with a high-reflectivity multilayer condenser allows for -second exposure time imaging of whole, unstained cells. This has enabled us to perform tomographic imaging of autophagy in HEK293T cells and cell-cell interactions with a total exposure time of minutes and render 3D reconstructed volumes. In addition, a novel image formation model for thick samples has allowed us to investigate the influence of coherence on image contrast. Compared to previous image formation models, this model better describes the image formation of thick samples of arbitrary geometry, which is highly relevant for, e.g., biological samples. Furthermore, a new reconstruction technique based on focus-stack back-projection is addressing the DOF-problem for thick samples in x-ray microscopy.

In the future, more work on simulating the influence of coherence on imaging will be performed using the novel image formation model. This

allows for optimization of the illumination geometry for each sample, e.g., for contrast enhancement in low-contrast samples. To facilitate the microscope operation in the future, automation of the tomographic imaging procedure could be implemented. The tilting, re-focusing and correction for sample runoff could be implemented in the control software for the microscope stages and image acquisition. In future tomographic imaging, the focus stack procedure could also be automated, rendering a focus stack at each projection angle. This would make DOF-corrected 3D-reconstructions using the focus-stack back-projection feasible.

This Thesis is based on the six papers listed below. The author had the main responsibility for paper B-D, for which she designed the experimental setups, planned and performed experiments, analyzed data and wrote the manuscripts. In paper A, the author contributed by developing a reliable cryofixation procedure and took part in both planning and performing the experiments. In papers E and F, the author contributed with proposing suitable samples, sample preparation in dry condition, participated in both the planning stage and execution of the experiments and contributed actively in discussions.

Paper A reports on an upgrade to a kHz slab laser system, creating a brighter liquid nitrogen jet laser plasma source with capability to obtain images of cryofixed B-cells with s exposure time, albeit somewhat noisy. The spectrum and size of the plasma source were measured and presented in the paper along with a brightness calculation.

Paper B describes the first steps towards imaging cell-cell interactions between NK cells and HEK293T cells. Images of possible interactions were obtained with long exposure times, due to x-ray source instabilities.

Paper C reports on improved temporal and spatial stability of the liquid nitrogen jet by applying radiative heating to the nozzle tip. The paper contains comparative measurements of source stability with and without heating, calculations of evaporative cooling and a demonstration of long-term source stability.

Paper D exploits the improved stability of the x-ray microscope to produce several -second exposures of cryofixed HEK293T cells in different stages of autophagy as well as cell-cell interactions between primary NK cells and HEK293T cells. 3D reconstructions of a starved HEK293T cell as well as cell-cell interactions were presented. The tomographic reconstructions were made from tomographic datasets obtained with seconds per projection. Each tomogram was obtained with a total exposure time of minutes.

Paper E presents an improved 3D wave-propagation and image-formation model applicable to samples with thickness larger than the depth of field. The model is compared by simulation and experiment to existing models such as projection-based models that do not consider a limited DOF and PSF-enhanced projection models.

Paper F presents the novel tomographic reconstruction technique focus-stack back-projection (FSBP). The paper compares three different tomographic reconstruction techniques by simulation and experiment for varying degrees of coherence. Focus-stack back-projection is proposed as a suitable reconstruction technique for x-ray microscopy where the limited depth of field is taken into account as it provides superior results compared to the other techniques.

This work would not have been possible without my excellent supervisors Hans Hertz and Ulrich Vogt, thank you for sharing your ideas and many years of experimental experience. Many thanks to my closest colleagues Mikael Kördel and Mårten Selin, for sharing memories of breakthroughs, milestones and despair during many, many hours in the laboratory. It has been a pleasure working with you, discussing with you and getting to know you on a personal level. I look forward to seeing you again in our future professions and at barbecues. To our past team members, Anders Holmberg and Jussi Rahomäki, thank you for sharing your knowledge in the nanolab and for providing excellent zone plates for the x-ray microscope. And to our newest team members, Jonas Sellberg and Thomas Frisk, thank you for good discussions about biology, be it cells or giant amoeba viruses. You have both been excellent sounding boards and with you on the team, I feel that the project is left in safe hands. Thank you Kjell Carlsson for encouraging me to do my master thesis at BioX and for always being very helpful and supportive. Big thanks to my office-mate Jakob Larsson for being a good friend, sports organizer and office gardener. Thank you for the floorball events and for keeping the office palm-tree alive and well. and to my dear friends and travel companions Athanasia Christakou and Tunhe Zhou, I hope that our paths meet again somewhere (yes, I would like to visit you in Oxford and Paris). And to all colleagues at BioX, you have made my doctoral studies very memorable. I have learned so much from all the fun discussions over lunch and coffee. A big thanks to Stockholms Akademiska Damkör and all my dear friends outside the office, you mean a lot to me.

To my inspiring teachers in early years, Jennifer Baker, Ulla Pilhoffer and Anders Palm, thank you for showing me the beauty of math and natural sciences. Thank you Erik Borgström for being my scientific inspiration and role model throughout my ten years of studies at KTH. You showed me that pursuing a PhD was possible. To my dear mentor, Eva Sjöwall, thank you for your moral support and inspiration. Thank you Evelina Vågesjö and Mattias Heldesjö for support, toast mastering, taking me cross-country skiing while I was writing my thesis and for always putting a wide smile on my face. Joakim Kohls, thank you for always showing interest in my research and for musical vacations for the mind. Finally, I want to thank my family. I will always be grateful for all the years I got with my wonderful grandmother Daga Hansson. Thank you for encouraging my interest in stereo images and 3D puzzles. You taught me to master the art of crosswords and you made the best pancakes. I will always carry with me your wit, wisdom, kindness and patience. To my grandfather Curt Hansson, thank you for teaching me endurance in tennis matches with countless tiebreaks and waiting in silence for the bass to bite when fishing all night long. This has prepared me for the lab work. I want to thank my dear father Tommy Hansson for encouraging my dreams, boosting my self-confidence and for gathering our family around well-cooked dinners. Thank you dear mother, Agneta Hansson for unconditional love, warm hugs and therapeutic walks. And last but not least, a big thanks to my sister Helena Hansson for being an inspiration in life, sharing your wisdom and helping me keep track of what really matters. I love you all very much. This thesis could not have been written without your support.

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