Hawkes P.W., Spence J.C.H. (Eds.) Science of Microscopy. V.1 and 2

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Chapter 7 Cryoelectron Tomography (CET) 565

The second major characteristic of a CCD camera is the sensitivity,

quantitatively expressed in the detection quantum efﬁ ciency (DQE). In

combination with the conversion efﬁ ciency (number of created pixel

electrons per primary electron) the DQE describes the inﬂ uence of

the detector noise on the SNR of a transferred image and is deﬁ ned as

the ratio of the square of the SNR at the output to the same quantity

at the input of the detection device (Herrmann and Krahl, 1982; Fan

and Ellismann, 2000). There are essentially four main sources of noise:

(1) variations in the electron conversion of electrons into photons, (2)

ﬂ uctuations in the generation of electron hole pairs on the chip, (3) dark

current noise, and (4) preampliﬁ er noise. To reduce the dark current

noise, which mainly stems from the electronics, the whole array is

cooled down to a temperature of −30°C.

Depending on the scintillator material and thickness, the primary

energy of the electrons, and the coupling of the scintillator to the

capacitors the detector will show slightly different characteristics

(Fan and Ellisman, 1996). The scintillator has the key role in the

performance of an image converter since it primarily determines sen-

sitivity, resolution, and noise contribution. Typically, single crystals

(YAG = Y

:Ce

) or polycrystalline phosphor scintillators

(e.g., P43 = Gd

S:Tb

) are used in commercially available CCDs.

Since high resolution is of major interest in materials science, CCDs

for this purpose are normally equipped with very thin scintillator

coatings to minimize the point spread function and to obtain the best

transfer, especially in the high-frequency domain. On the other hand,

the detection sensitivity and the ampliﬁ cation of the incoming signal

are of minor interest since the specimens are not subject to restricted

illumination conditions. This is in contrast to biological applications,

where low-dose exposure schemes are typically used, demanding a

very high sensitivity of the detection device and thus a somewhat

greater scintillator thickness. The optimum thickness of the scintillator

depends on the application and on the acceleration voltage used. While

the performance for CCDs in the voltage range below 200 kV is satis-

factory, it drops dramatically for intermediate or high acceleration

voltages.

However, in principle both are needed; the highest sensitivity com-

bined with the maximum transfer of low and high frequencies. But

these two requirements are in conﬂ ict with each other; the higher the

sensitivity, the thicker the scintillator layer, and the greater the pos-

sibility of electron backscattering and multiple light scattering, result-

ing in a severe damping of high-frequency information, especially at

primary energies at and above 300 keV.

Clearly, the ideal detector for cryo-ET has not yet been invented, but

there are possible ways to overcome the shortcomings of “classical”

CCDs, at least to some extent: modiﬁ ed CCDs (Fan et al., 2000), lens-

coupling (Mooney and Krivanek, 1994; Mooney, 2004) instead of ﬁ ber

coupling, “decelerators” in combination with CCDs (Downing et al.,

2000; Downing and Mooney, 2004), and active pixel detectors (APS;

Fan et al., 1998; Faruqi et al., 2003a,b; Evans et al., 2005). In lens-coupled

systems the glass ﬁ ber array, transferring the light without magniﬁ ca-

566 J.M. Plitzko and W. Baumeister

tion, has been replaced by huge optical lenses focusing the photons

arising from one electron onto the CCD chip. A free-standing scintil-

lator foil generates the light, which is then deﬂ ected by a 45° mirror

into the lens-coupling system. In this way scattering from the interface

between scintillator and glass ﬁ bers, and from within the glass ﬁ bers

is eliminated and moreover the detection of X-ray quanta is completely

bypassed, since they are not reﬂ ected in the optical mirror. The setup

provides a deﬁ nite gain in resolution, while the detection efﬁ ciency is

more or less kept constant if compared to highly sensitive ﬁ ber-coupled

CCDs (Agard; Mooney, 2004). The main technical difﬁ culty in lens

coupling is the quality and thus the performance of the optical lens

system to guarantee an undistorted transfer (mainly geometric distor-

tions) of the light onto the full array of the CCD chip. Deceleration of,

e.g., 300 keV electrons to 100 keV is technically difﬁ cult, because it is

necessary to slow down the electrons with a “countervoltage” of, e.g.,

200 kV (Downing and Mooney, 2004) before detection. This counter-

voltage is generated with an electrostatic deﬂ ector stack ﬂ oated at a

voltage comparable to the acceleration voltage of the microscope. The

CCD, the associated electronics, and the electrostatic deﬂ ector are

enclosed within an insulated high-voltage tank. However, the shield-

ing of the CCD against AC magnetic ﬁ elds and against possible dis-

charges is still a major technical difﬁ culty, which will have to be

addressed in the future.

While lens-coupled systems and decelerators have been designed

and tested for 300 kV instruments and represent bulky apparatuses,

detectors based on the active or hybrid pixel sensor designs [mainly

based on complementary metal oxide semiconductors (CMOS)] come

in sizes comparable to “classical” CCDs, with the possibility of detect-

ing the incoming electrons directly. Pixel detectors have been success-

fully used in the ﬁ eld of X-ray crystallography and condensed matter

physics and they do possess some distinct advantages; instead of indi-

rect detection of the incoming electrons, pixel detectors detect the

signal directly, the lateral resolution is dramatically increased, and

moreover dark noise (mainly from the electronic readout) is quasi-

nonexistent (Turchetta et al., 2001). The signal produced by pixel detec-

tors is intrinsically digital, thus allowing very fast readouts, but one

major handicap is their “radiation hardness”; while CCDs can continue

to be used, pixel detectors do have a somewhat limited lifetime.

However, recent developments based on the latest CMOS technology

have shown that the radiation hardness can be increased, e.g., if the

size of the CMOS capacitors is reduced (Evans et al., 2005).

All three of these different detection “philosophies” are currently

being tested in prototypes in combination especially with 300-kV

instruments to ﬁ nd an optimum recording device and a long-term

solution for digital TEM imaging.

3.4.6 Energy Filter

To image thick specimens such as vitriﬁ ed cells, the development and

the subsequent integration of energy ﬁ lters (Krivanek et al., 1991, 1995)

have been a major breakthrough for biological imaging and especially

Chapter 7 Cryoelectron Tomography (CET) 567

for ET. Electrons interacting with the sample atoms can be scattered

elastically (no loss in energy but change in direction) or inelastically

(loss of energy due to interaction with core shell electrons). The mean

free path Λ

of inelastically scattered electrons (the path length after

an inelastic scattered electron has been scattered once on average) is

about 280 nm in vitriﬁ ed ice at 300 kV at liquid nitrogen temperature

and around 210 nm at liquid helium temperature (Schweikert et al.,

a thickness in the range above 200 nm multiple scattering is inevitable

(Figure 7–14). For biological specimens and vitriﬁ ed ice, which are

almost exclusively built up of light atoms, inelastic scattering is much

stronger than elastic scattering. However, the elastically scattered elec-

trons carry the main portion of structural information of the specimen,

whereas inelastically scattered electrons form a strong inelastic back-

ground and thus contribute signiﬁ cantly to the shot noise of the image

background, obscuring ﬁ ne details. Because of the different energies

of inelastically scattered electrons, they are slightly “out of focus” and

will thus contribute to a “blurring” of the ﬁ nal image and hence they

decrease the SNR.

Energy ﬁ lters are in principle electron energy loss spectrometers with

the additional ability to image the sample at a speciﬁ c kinetic energy.

Introduced in the early 1990s (Krivanek et al., 1992; Probst et al., 1993;

Gubbens et al., 1993) they are widespread in materials science for the

inelastic

mixed

unscattered

elastic

thickness [nm]

fraction of detected electrons

2007; Plitzko et al., 2004; Wright et al., 2006). Thus for specimens with

area) scattering channels for vitreou s ice as a function of thickness for 300 kV, in nm). The dashed

Figure 7–14. Distribution of scattered electrons for vitreous ice. Distribution (without an aperture)

lines mark fractions of single (elastic or inelastic) scattering.

over the elastic (lower intermediate grey area), inelastic (upper dark grey area), and mixed (light grey

568 J.M. Plitzko and W. Baumeister

analysis of the chemical composition, either by high resolution electron

energy loss spectroscopy (EELS) or electron spectroscopic imaging

(ESI). For a complete description of energy ﬁ lters see Reimer (1995) and

for electron energy loss spectroscopy see Egerton (1996). Energy losses

can be selected that are speciﬁ c to certain elements to obtain so-called

elemental maps, visualizing the elemental distribution in one single 2D

image (Figure 7–15). However, the dose typically used for an elemental

map is in the order of 10,000 e

−

/Å

, thus orders of magnitude higher than

what would be allowed for the investigation of biological structures.

Nevertheless, instead of using the speciﬁ c energy loss of elements

(characteristic ionization edges) for “inelastic ﬁ ltering” it is always pos-

sible to operate the energy ﬁ lter for “elastic” ﬁ ltering or to use a more

common expression for “zero-loss” ﬁ ltering. The energy-selecting slit

aperture is positioned around the energy of the primary beam, selecting

only the unscattered and elastically scattered electrons for imaging. The

energy window is typically in the range of 20 eV or slightly larger, but

it has to be smaller than the smallest relevant energy loss in the sample

(in most cases the 20–25 eV single plasmon loss peak).

Basically the energy ﬁ lter is built up from one or several magnetic

prisms. If an electron travels through a homogeneous magnetic ﬁ eld it

will move in circles whose radius is proportional to the kinetic energy

of the electron, and in this way electrons of different energy are sepa-

rated. In the so-called energy-selective plane (or plane of energy dis-

persion) they are located in different positions, and produce a spectrum,

which is called the EELS. A mechanical slit aperture can be inserted

in this plane to select electrons with a speciﬁ c energy. There are basi-

cally two types of energy ﬁ lters: postcolumn energy ﬁ lters (Krivanek

et al., 1991) and in-column energy ﬁ lters (Rose and Plies, 1974; Lanio,

1986; Lanio et al., 1986). For the postcolumn ﬁ lter only one 90° magnetic

prism is utilized and placed at the lower end of an EM behind the

Figure 7–15. Electron spectroscopic imaging of microtubulis embedded in virtiﬁ ed ice. With the help

of an energy ﬁ lter one can select energy losses speciﬁ c to certain elements to obtain so-called elemental

maps. The maps shown here are created with the three-window technique. Two images have been

acquired in front of the ionization edge (pre-edge images) and one directly after it (post-edge image).

The two pre-edge images are used to calculate the background intensity, which is extrapolated and

subtracted from the post-edge image, resulting in the net-signal of the element under scrutiny. a)

Shows the elemental distribution of oxygen, b) of carbon and c) of nitrogen.

Chapter 7 Cryoelectron Tomography (CET) 569

projective lens system. In-column energy ﬁ lters, mainly omega (Ω)

ﬁ lters, are placed above the projective lens system of the microscope

within the column. In omega ﬁ lters the beam has to pass through four

magnetic prisms in a symmetric path corresponding to the greek letter

omega.

Energy ﬁ lters are additional optical elements and therefore they will

add optical distortions of different kinds (spectral aberrations both

transmissivity and nonisochromaticity as well as geometric distor-

tions; Uhlemann and Rose, 1996) to the ﬁ nal image, which have to be

compensated by adding additional multipole lenses to the system. In

the case of the postcolumn energy ﬁ lter (Gatan Imaging Filter, GIF,

Gatan, Pleasanton, CA) several quadrupoles and hexapole lenses are

placed behind the magnetic prism to correct these distortions up to a

certain degree. These lenses have to be aligned on a day-to-day basis,

to ensure the best performance of the system and, to make life easier,

the necessary alignment routines have to be computer controlled and

automated.

Because of the symmetry of the in-column omega ﬁ lter, a number of

aberrations are canceled out in this type of energy ﬁ lter, simplifying

the alignment procedure. Furthermore, the pre- and postﬁ lter electron

trajectories are parallel, which makes the in-column ﬁ lter design an

obvious choice. However, in-column ﬁ lters cannot be included in an

existing TEM column, in contrast to postcolumn energy ﬁ lters, which

lack the symmetry, but which can be attached to almost every existing

microscope column.

Moreover, with the addition of energy ﬁ lters the whole electron

optical path will be increased, thus naturally resulting in an additional

magniﬁ cation factor. In the case of the in-column ﬁ lter this magniﬁ ca-

tion factor is quite small, while for the postcolumn ﬁ lter the magniﬁ ca-

tion factor ranges between 20 and 40 depending on the acceleration

voltage used. Obviously, this postmagniﬁ cation is well suited for high-

resolution work, as typically used in materials science. However, to

apply the ﬁ lter to biological specimens, the magniﬁ cation range, in

which the objective lens is excited (to allow focus adjustments), has to

be extended to much lower magniﬁ cations. Therefore special lens

series have to be utilized, called EFTEM series, which demagnify the

image, before entering through the spectrometer entrance aperture

into the energy ﬁ lter. In this way, the magniﬁ cation factor is reduced

to a value in the range of 2–3 if compared to images observed on the

viewing screen. Recently, larger entrance apertures (5 mm in diameter)

for the energy ﬁ lter have been introduced (Brink et al., 2003) to increase

the collection angle and thus allow the magniﬁ cation factor to be

further reduced. Especially in biological applications in cryoconditions

where limitations include the dose and thus the applied magniﬁ cation,

this has proven to be beneﬁ cial because the ﬁ eld of view (FOV) can be

considerably increased.

The application of zero-loss ﬁ ltering for collecting high-resolution

structural data from ice-embedded biological macromolecules, which

are normally small in size compared to cellular structures, provides

only a minor improvement, and therefore it is rarely used (Langmore

570 J.M. Plitzko and W. Baumeister

and Smith, 1992; Schroeder et al., 1993; Frank et al., 1995; Zhu et al.,

1997; Angert et al. 2000). Typically these ice-embedded isolated parti-

cles are thinner and thus smaller than the inelastic mean free path and

therefore the inﬂ uence of inelastically scattered electrons is compara-

bly small. However, zero-loss ﬁ ltering allows the use of smaller defocus

values without impairing the accuracy of the subsequent alignment of

the particles as required for averaging (see Section 2.2). In electron

crystallography, energy ﬁ ltering has its advantages even for thin speci-

mens, as shown by Yonekura et al. (2002). Overall the effect of energy

ﬁ ltering (especially zero-loss ﬁ ltering) for thick specimens in the thick-

ness range above the mean free path (∼200 nm for 300-keV electrons) is

more obvious, because details can be observed with a higher contrast

and higher resolution than in the unﬁ ltered case (Figure 7–16). More-

over in very thick specimens, in which most of the electrons have been

inelastically scattered, it is possible to choose an energy-selective

window close to the most probable, instead of the zero-loss value

(Olins et al., 1989; Han et al., 1996; Bouwer et al., 2004). Moreover,

energy ﬁ ltering allows us to estimate or, if the mean free path is known,

to determine the absolute specimen thickness quickly and simply by

means of the so-called log-ratio technique (Malis et al., 1988; Grimm

et al., 1996b); by taking the logarithm of the ratio between an unﬁ ltered

image and a zero-loss image the relative thickness of the specimen can

be obtained in units of the inelastic mean free path. If the inelastic

mean free path is known this value can be easily converted to the

absolute thickness. This simple procedure can be additionally utilized

for the determination of the inelastic mean free path, if the thickness

of the specimen has been determined by other techniques (Grimm

et al., 1996b; Feya and Aebi, 1999). Thickness determination is advanta-

geous to ascertain suitable sample areas for follow-up in-depth struc-

tural investigation and thus represents a quality criteria, especially for

automated acquisition schemes.

Figure 7–16. Inﬂ uence of zero-loss ﬁ ltering on the investigation of ice-embedded thick specimens

(Thermoplasma acidophilum, images courtesy of C. Koﬂ er, MPI of Biochemistry, Martinsried, Germany).

Unﬁ ltered (a) and zero-loss (b) ﬁ ltered images of a Thermoplasma acidophilum cell. The specimen thic-

kness is almost 500 nm, which is greater than the mean free path of 300 kV electrons in ice at liquid

nitrogen temperature. The slit-width was 20 eV. c) shows a section through a tomographic reconstruc-

tion based on the ﬁ ltered image set.

Chapter 7 Cryoelectron Tomography (CET) 571

3.4.7 Automation

Experimentally, the acquisition of a tomogram requires recording of a

“tilt series,” which is a sequence of micrographs from different angles

containing the feature of interest. However, it took more than a decade

after the pioneering work of Hart and Hoppe to establish angular

acquisition schemes, especially under cryoconditions as a routine and

robust method in structural biology (Hart, 1968; Hoppe et al., 1968;

Figure 7–17). This is due to the fact that the specimen, or the feature of

interest, inevitably moves out of the ﬁ eld of view during physical tilting

of the specimen holder as a result of the mechanical inaccuracies of the

tilting device (see Section 3.4.3; Figure 7–18A). The adjustment of the

microscope optics, the recentering of the specimen in the electron

beam, focusing, and the ﬁ nal recording of the electron micrograph

were exclusively done by hand in the ﬁ rst experiments. However, the

additional exposure time required for these steps resulted in the over-

exposure of the specimen and thus in extensive beam damage, which

ﬁ nally culminated in the loss of the sample. Manual recording of a tilt

series is therefore inappropriate and the implementation of automated

acquisition, which includes “tracking” (recentering) of the specimen,

refocusing with a minimum additional exposure (Dierksen et al., 1992;

Figure 7–17. Experimental setup for automated tomography based on an intermediate voltage (300 kV)

instrument (1) equipped with an energy ﬁ lter (2). The CCD camera (3) makes the image formation avail-

able instantaneously and, in conjunction with a computer (4), allows measurement of deviations from a

perfectly eucentric tilt geometry. This information is then used, in a feedback loop to the microscope, to

activate auto-tuning functions that compensate for the mechanical imperfections of the system.

572 J.M. Plitzko and W. Baumeister

Koster et al., 1992; Braunfeld et al., 1994; Rath et al., 1997), and image

acquisition, was essential for the success of ET in structural biology.

Clearly, only with the introduction of computer-controlled electron

microscopes was automation within reach.

Automated tomography includes three major steps for every tilt

angle: tracking, focusing, and ﬁ nal image acquisition (Figure 7–18B).

normally carried out adjacent to the area of interest, to reduce the dose

that is delivered to the specimen area. These areas are positioned along

the tilt axis with respect to the actual acquisition area to determine the

correct shift and focus levels prior to ﬁ nal image recording. During the

tracking step a micrograph with a very low exposure time at a higher

binning mode of the CCD camera is acquired, which is correlated with

a micrograph from the previous tilt. Utilizing cross-correlation or by a

manual inspection of prominent features (e.g., gold beads), the shift

relative to the preceding micrograph can be determined. Depending

on the SNR of the image, the cross-correlation algorithm might fail and

must be supported by suitable image processing routines, e.g., band-

pass ﬁ ltering or the use of a Hanning window. This is especially the

case at higher tilt angles where the projected thickness increases. The

shifts are typically compensated by moving the beam with the image

deﬂ ection coils back to the region of interest. To obtain a higher accu-

racy (better than 1%) with autotracking the procedure can be repeated

several times. The offset in z between the object and the tilt axis z

can

be minimized by setting the eucentric height. Procedures have been

developed to adjust the sample z height automatically until minimum

image movement is detected while the goniometer is wobbling within

a speciﬁ ed angular range (“Explore3D,” automated tomography soft-

ware of FEI Company, Eindhoven, Netherlands; Schoenmakers et al.,

2005). However, due to mechanical imperfections of the goniometer, it

Figure 7–18. a) Geometric model of specimen rotation around a tilt axis. b) Automated data collection

scheme for the ‘full-tracking/ full-focusing’ case. For tracking, focusing and the ﬁ nal image acquisi-

tion the same magniﬁ cation is used and the beam is adjusted in a way that the areas where tracking,

times in combination with high binning values (4 × 8 or even 8 × 8) the exposure to the sample in

auto-tracking and auto-focusing can be minimized. (See color plate.)

change tilt angle

‚image shift‘ correction

Focus correction

image acquisition

ilt

Tracking

Focus

Exposure

focusing and exposure is done do not overlapp (blue and green circle). Using very short exposure

Under strict low-dose conditions, the tracking and focusing steps are

Chapter 7 Cryoelectron Tomography (CET) 573

is very difﬁ cult to tune z

to zero. As a result, the uncorrected residue

of z

can still be severe enough to make the object disappear from the

ﬁ eld of view at high magniﬁ cation and lead to signiﬁ cant focus changes

during the acquisition of a tilt series. Furthermore, it is observed that

this offset in z depends not only on the actual sample being used but

also varies from point to point within a sample. This can be attributed

to many factors including nonuniform thickness and ﬂ atness of the

specimen. Therefore z

has to be determined during data collection for

each selected tilt angle.

Automated focusing or autofocusing is achieved by acquiring images

with different beam tilts (Koster et al., 1992; Koster and de Ruijter, 1989;

Ziese et al., 2003) prior to the ﬁ nal exposure. It is based on the fact that

tilting the illuminating beam will result in an image displacement, if

the image is out of focus. The amount of this displacement, measured

by means of crosscorrelation, is proportional to the focus change

and can be used to readjust the objective lens current, rather than using

the z adjustment of the stage. The amount of shift and focus change

that occurs during data collection depends on the goniometer and

specimen holder. In most experiments, accumulated shifts are in

the order of 1–3 µm during the acquisition of a complete tilt series,

provided that the specimen was set as accurately as possible to the

eucentric height.

Image shifts are measured by determination of the peak position of

the cross-correlation function (XCF) of an image recorded after setting

a new tilt angle with a reference image that was recorded previously.

Since the two correlated images are acquired at different tilt angles,

they will not only be shifted relative to each other but they will also

differ to some extent as a result of their different projection angles.

Moreover, a tilted image (assuming the tilt axis is parallel to the y-axis

and in the center, of the image) will exhibit a defocus difference between

the left side of the image, the center, and the right side of the image.

Thus defocus determination by the beam-tilt method for tilted samples

is impaired by an elongation of the cross-correlation peak, which has

contributions from areas with different defocus values. Therefore, prior

to the computation of the cross-correlation function, “stretching” of the

image at a higher modulus can be applied (Guckenberger, 1982; Ziese

et al. 2003). “Stretching” is typically done perpendicular to the tilt axis

by a factor of cos(α − α

)/cos α or a similar expression depending on

the sign of the actual tilt angle α and the tilt angle increment α

(Koster

et al., 1997). Instead of stretching the image, the focus determination

can also be done in the center region of the image provided that beam

tilting is done along the tilt axis to minimize errors in the autofocus

procedure. The accuracy of the beam-tilt autofocus procedure without

stretching can be as good as ±50 nm (Dierksen et al., 1993).

Since the effective thickness of the specimen in the beam direction

varies during tilting, the portion of “absorbed” electrons will increase

with the tilt angle. There are two possible ways to account for this effect:

a tilting scheme with a ﬁ ner sampling at higher tilt angles and an

increase in exposure time for higher tilt angles to obtain a similar SNR

574 J.M. Plitzko and W. Baumeister

within the projections of a tilt series. A tilting scheme according to

Saxton has been widely adapted (“Saxton scheme”; Saxton et al., 1984).

Since this scheme was proposed for crystalline specimens a slightly

different expression is typically used in electron tomography:

n+1

= α

+ arcsin(sin α

⋅ cos α

To achieve a uniform SNR in the single projections of a tilt series

and to prevent an insufﬁ cient SNR at high tilt angles, and an unneces-

sarily high SNR at low tilts, the exposure time can be varied in differ-

ent ways. Instead of using the constant exposure scheme (t = t

) it is

possible to use an exponential scheme or a cosine scheme to allow for

the thickness increase at high tilts:

tt T=⋅

−

()

[]

exp

cosα

tt=⋅

cosα

tt=⋅

[]

exp cosα

where T is the relative specimen thickness in units of the mean free

path (Grimm et al., 1998; see Section 3.4.6). For the reconstruction, the

images have to be normalized with respect to the exposure time, so

that the incident beam dose will stay nominally constant for all tilt

angles. Since the thickness of the sample under investigation is nor-

mally not known beforehand, the cosine scheme is favored and is pri-

marily used for the acquisition of a tilt series.

To minimize the electron dose that is delivered to the specimen, the

images required for these automated procedures have to be recorded

on areas that do not coincide with the chosen area of interest. This way

almost all of the total dose (97%) can be employed for the acquisition

of the single projections and only a fraction of it (3%) is used for the

autoadjustment procedures. In less strict low-dose schemes, these nec-

essary steps can be performed directly on the region of interest, but

with different illumination and exposure settings, which will then

sum up to 10–15% of the total applied dose.

Clearly, tracking and autofocusing prior to the ﬁ nal exposure are

time consuming. However, with the improvements made in electron

optics, stage designs, and specimen cooling, even of the already com-

puter-controlled microscopes, it became feasible to use calibration and

prediction schemes to dramatically reduce the amount of time typically

used for the acquisition of a tilt series (Zheng, 2004; Ziese, 2002).

The acquisition schemes and software packages of today can be

grouped in roughly three major domains: the almost classical “full-

tracking/full-focusing,” the “precalibrated,” and the “on-the-ﬂ y or

dynamic prediction” procedure. Naturally, there are various deriva-