Contrast Formation in Electron Microscopy of Biological Material

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS.VOL. 63

Contrast Formation in Electron Microscopy of Biological Material E. CARLEMALM Department of Microbiology Biozentrum, Uniuersity of Basel Basel, Switzerland

C. COLLIEX Laboratoire de Physique des Solides UniuersitP de Paris-Sud Orsay, France

E. KELLENBERGER Department of Microbiology Biozentrum, University of Basel Basel, Switzerland

I. Introduction. . . . .

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11. T h e o r y . , . . . . . . . . . . . , . . . . . . . . . . . . . . . , , . . . . . . . . . . A. Basic Equations for the Single-Scattering Approximation . . . . . . . . . . . .

111. IV.

V.

VI.

B. Multiple Scattering . . . . , . . . . . . . , , , . . . . . . , . . . , . . . . . . C. Contrast Formation. . . . , . . . . . . . . . . . . . . . . , . . . . . . . . . . D. Treatment of Superpositions: The Dilution Theorem . . . . . . . . . . . . . . Scattering Cross Sections and Constants , . . , , . . . . . . , . . . . . . . . . . A. Atomic Scattering Cross Sections , . , , , . . . . . . . . , . . . . . . . . . . B. Cross Sections for Composite Matter , . . . . . . . . . . , . . . . . . . . . . Contrast with Unstained Sections of Aldehyde-Fixed Biological Material . . . . . A. Calculated Values of Scattering Constants for Different Materials . . . . . . . B. Thickness Dependence of Scattering . . , , . . . . . . . . , . . . , . . . . . . C. Influences of Thickness, Density, and Scattering on BF and D F Contrasts. . . D. Influence of Thin-Section Relief Compared for the Two Imaging Modes . . . E. How to Calculate Contrast of Real Biological Structures . , . . . . . . . . . . Experimental Confirmations , . . . . . . , . . . . . . . . . . . . . . . . . . . . . A. Definition of Test Object . , . . . . . . . . , , , . . . . . . . . . . . . . . . . B. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. R e s u l t s . . . . , , . . . . , , . . . . . . , . . . . . . . . . . . , . . , . . . . . D. Positive Stain in Thin Sections . . . , . . . . , , . . . . . . . . . . . . . . . . Discussion of the Consequences for the Interpretation of Micrographs . . . . . . A. Introduction: Different Densities. ,

270 276 276 27 8 28 1 284 286 286 29 1 294 294 295 298 302 306 309 309 310 311 316 319 319

269 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-014663-0

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B. Characteristics of the Specimen That Produce Contrast . . . . . . . . . . . . C. Contrast in Conventional Imaging . . . . . . . . . . . . . . . . . . . . . . . . D. Contrast in Ratio Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Discussion of Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Beam-Induced Destruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Plastic Deformations in Thin Sections . . . . . . . . . . . . . . . . . . . . . . C. Limitations due to Positive Stain Overcome by the Possibility of Observing Unstained Sections . . . . . . . . . . . . . . . . . . . . . . . . . D. Limitations due to Negative Stain and Potential of Observing Frozen-Hydrated Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Limitations due to Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

321 322 326 321 321 328 329 330 330 33 I 332

I. INTRODUCTION

Besides fulfilling the requirements of geometric optics, any imaging is possible only when some properties of the specimen can become reflected as intensity differences which eventually are visible to the eye. Vision and classical light microscopy are based on light absorption. In the thickness range which allows sharp imaging, electrons are not absorbed but only scattered. Among the basic treatises on electron microscopy (Zworykin et al., 1945; von Ardenne, 1940;von Borries, 1949a,b)the last author emphasized contrast tormation with biological specimens; he, and later Hall (1953)derived the basic equations expressing the relation between specimen properties and the resulting contrast. Assuming that contrast is mainly due to the elimination of electrons scattered into wide angles, these authors postulated that contrast in conventional bright-field imaging is essentially dependent on the mass density p and the thickness x of the specimen. As we will see in this chapter, this is true when only the unscattered electrons are considered or, approximatively, when multiple scattering is neglected. A critical mass thickness ( p x ) , can become defined at which, on average, each electron is scattered once. This value is indeed about 90-100 nm g/ml and is nearly independent of the matter considered. However, already at that time the big problem was the question of the density of a specimen which has sufferedextensive damage from the beam. For the contemporaries of these pioneers, it was rather obvious to take dry distillation as a model for such processes; the remains would essentially be a carbon skeleton comparable to charcoal. The thickness would have been preserved and thus only a reduced density has to be considered. It was common practice to assume that this “biological carbon” would have a reduced density of about 1 g/ml.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

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As we will discuss in this review, the role of hydrogen in determining the scattering properties of organic matter has now become central. Indeed, among the atoms involved in biological matter, hydrogen presents peculiar scattering properties. Studies of beam-induced destruction also tend to show that hydrogen does not leave the matter preferentially (Dubochet, 1975); oxygen seems to depart most easily (Egerton, 1980). The ways in which contrast has been dealt with in regard to instrumentation are highly tortuous. In the first European instruments with electromagnetic lenses (Siemens and Philips) the objective aperture had to ensure usage of only the central part of the lens and thus to eliminate the extremely high spherical aberration inherent in electron optics. It was also believed that contrast was produced by this central objective aperture by adequately eliminating scattered electrons. These microscopes had a tendency to expose the specimen to much higher doses than needed for imaging. Electrostatic lenses have the particular feature that it is not possible to accommodate an aperture in a central position. Despite this and by using a sufficiently narrow illuminating beam, it was possible with electrostatic lenses to produce about the same contrast as with an electromagnetic lens with central aperture. This fact might have had its influence in the following further developments. Hillier, one of the constructors of the Canadian electron microscope (Burton, Hillier, Prebus, et al.)and later director of the development of the RCA electron microscope, was working with biological specimens and therefore rethought contrast formation (Hillier, 1949; Hillier and Ramberg, 1949). He introduced an adequately narrow illuminating beam and showed that the electromagnetic lens without aperture is also able to achieve a usable contrast. Later he introduced the contrast aperture, which-in the objective lens-is positioned in the plane of the image of the condensor aperture (approximately in the back focal plane). At this place, a maximum of scattered electrons can become eliminated. This position is now currently favored. Experimenting with long- and normalfocal-length lenses and small contrast apertures, workers found limitations mainly on the practical side: apertures below some 15pm are difficult to make round, and in particular are extremely sensitive to contamination-induced irregularly and thus to astigmatism. The possibility of compensating contamination-caused astigmatism by a stigmator is extremely limited; contamination layers do not produce a stable electrostatic field, but rather oscillating ones. In addition, the Abbe theory of imaging shows that the contrast aperture in the back focal plane-the Fourier plane-determines resolution by cutting off high spatial frequencies. The compromise with theory is fortunately beyond practical limitations. The above-mentioned findings led at that time to a certain consensus as to how the electron microscope should be conceived for biologists, particularly cytologists: a relatively long focal length (6-9 mm) and a 20-30-pm

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contrast aperture; illumination with rad. With such microscopes, the stain produced by OsO, fixation provided sufficient contrast for observing thin sections. At that time it was already well known that the spherical aberration decreases with shorter focal lengths of the lens. Designers of electron microscopes thus put a great deal of effort into constructing such “highpower” lenses. With the practical limitations in producing contrast apertures, it is obvious that the instrumental ability to produce contrast decreased again. This relative lack of contrast was compensated by more intensive heavy-metal staining and by using still narrower illuminating beams. Two side effects promoted the consensus for using this new type (narrow beam, short focal length) of microscopes in biology: (i) The micrographs showed very fine interference noise which was believed to represent real images of the fine “atomic” structure of matter; this interference noise allowed also the definition of a new type of resolution test on carbon films, which demonstrated instrumental resolving powers in the range of few angstroms. (ii) Still unexplained, the unequal thicknesses within one thin section no longer led to “cloudiness”; the yield of nice micrographs of thin sections became markedly increased. Narrow-beam, high-coherence imaging was adopted by cytologists for these reasons. Through the laser, high-coherence optics was simultaneously developed very far. It had the advantage over incoherent optics of allowing for much further-going calculations. No wonder that this imaging mode in electron microscopy became calculated and investigated very thoroughly (Lenz, 1954;Thon, 1966;Hanszen and Trepte, 1971; Misell, 1975; Burge, 1973). Since interference involves phase differences, it was reasonable to call this imaging mode “phase contrast.” Unfortunately, this was misleading to the biologist, because there is-besides phase differences-no common basis with what is called phase contrast in optical microscopy. Although Zernike (1935) developed theoretically the principle by using the coherent case, the practically usable phase-contrast light microscope requires a maximally incoherent illumination (according to Kohler), in order to give sensefull images (Kellenberger et al., 1985). The theoretical basis of electron microscopic phase contrast showed, however, through the contrast transfer functions, that contrast is produced for specimen details above the interference noise, details which could become related to real structural features (Ericson and Klug, 1971). This was and is still used as a basis for image processing, where statistical noise from all sources. including interference noise, can be eliminated by averaging over repeated structures.

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It is obvious that phase contrast occurs as a result of interference between electrons of equal velocity; i.e., phase contrast must be the result of interference between unscattered and elastically scattered electrons. Highresolution specimens should be thin; in such a case, the number of elastically scattered electrons used in imaging is very small when compared to the unscattered ones. This was obvious to many and stimulated some to undertake thorough investigations of dark-field imaging (Ottensmeyer, 1969, Dubochet et al., 1971; reviewed by Dubochet, 1973); when unscattered and most inelastically scattered electrons are eliminated imaging depends essentially on the elastically scattered electrons. This should produce a theoretically simpler situation that is more accessible to experimental tests. Dark-field imaging turned out to be rewarding with such small biological molecules as small polypeptides (Ottensmeyer et al., 1975)and DNA (reviewed in Brack, 1981),but very disappointing with larger structures and thin sections (Weibull, 1974; Sjostrand et al., 1978; Jones and Leonard, 1978). One major limitation is due to the recording mode of conventional transmission microscopes: indeed, a dose is needed in dark field which is 30-80 times that for bright-field imaging. This leads obviously to beam-induced specimen destruction (Thach and Thach, 1971; Dubochet, 1975; Isaacson, 1977; Egerton, 1980a, 1982a).With the STEM, this problem can be overcome. Still, with thicker specimens, and particularly with unstained thin sections (below 50 nm), satisfactory sharpness could not become routinely achieved, as was possible with bright field CTEM on stained material. Most specialists explained this failure by multiple scattering. In the present chapter we will review our findings (Carlemalm and Kellenberger, 1982) which show that the surface relief plays an equally determinant role in this lack of sharpness with completely unstained specimens. In 1970 Crewe and Wall introduced scanning transmission electron microscopy (STEM). One of the several potential advantages of this imaging mode resides in the possibility of collecting separately electrons scattered in different ways. The collected signals can then be processed individually or interactively to modulate the image intensities. For very thick specimens with a high proportion of multiple scatter Crewe and Groves (1974) and Groves (1975) had compared the respective advantages of CTEM and STEM. Many of their considerations are taken up in the present chapter, which concern current biological specimens prepared so as to be optimal for retrieving relevant structural information. Their thickness is such that multiple scatter is not predominant. For the other extreme, the imaging of atoms, Crewe had proposed to use the ratio of elastically over inelastically scattered electrons. The contrast is then mainly a function of the atomic number 2 (Crewe et al.,

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1975). We had introduced this mode of imaging for the observation of biological material, particularly of sections (Carlemalm and Kellenberger, 1982) and have shown that by use of this imaging mode the influence of the surface relief can apparently become reduced very substantially. By ratio contrast it was thus possible to obtain a higher resolution of completely unstained specimens than with the dark-field mode. Ratio contrast on unstained normal biological specimens was rightly criticized (Egerton, 1982b; Ottensmeyer and Arsenault, 1983) because, when first presented (Carlemalm and Kellenberger, 1982), multiple scattering was not considered. Real specimens that are usefull in biology, even the most perfect ones of 10-50 nm thickness, show some multiple scattering. This multiple scattering is relevant whenever we consider either conventional imaging and phase contrast or ratio contrast. For a given specimen thickness the influence obviously becomes stronger with denser matter. The influence of multiple scatter is thus much more considerable with positively or negatively stained material-as is needed in phase-contrast bright-field imaging-than with unstained samples which are viewed with ratio contrast. Ratio or 2 contrast was also not acceptable to those believing that organic materials cannot show sufficient differences in their atomic composition to produce contrast. These questions will be discussed in the present chapter by comparing the influences of varying composition of matter on contrast formation in conventional and ratio-contrast imaging. To do this on real specimens, we had to progress by successive approximations; we thus obtain qualitative answers: First, we will use throughout only the particle aspect of the electrons. We felt that it is today possible to describe biological matter in regard to its electron scattering abilities fairly simply, while its description by charges and potentials is likely to be not only overcomplicated but also feasible with approximations only, which would lead to much less precision than the Heisenberg uncertainty involved in the particle approach. Second, we restricted contrast evaluations in relation to matter in considering elastically and inelastically scattered electrons only. For conventional contrast formation the elastically scattered electrons are essential either directly in the dark-field mode or indirectly in producing phase contrast in narrow-beam, high-coherence imaging. For ratio contrast both types of scattered electrons are involved. Third, after reviewing multiple scatter in Section KB, we neglect it in the following sections related to practical examples. Let us repeat once more that we are fully aware that treatment of contrast by the particle interaction only, as we do here, is an approximation. It is a relatively perfect one for ratio-contrast and dark-field, but much less so for conventional bright-field imaging. In our opinion, however, this most spread type of imaging is also the least understood despite all the calculations

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available. Some of us firmly believe that the assumptions to be made for such calculations are much too approximate to be applicable to real biological specimens. While we believe that most conventional electron microscopy specimens behave as near ideal scatterers, the theoreticians have to assume ideal phase scatterers, the theoreticians have to assume ideal phase objects to be able to use wave theory. Only very recently, a real phase phenomenon was observed in a new type of embedding of membranes where lipid seems t 9 be preserved. By defocusing, contrast reversal was easily produced (Westphal et al., 1984). Frozen-hydrated particle suspensions (Adrian et al., 1984) also showed contrast in conventional bright field, which suggest them to be phase objects: puzzling unpublished observations (in collaboration with J. Dubochet, EMBL, Heidelberg) suggest a lack of contrast correlation with the compactness- i.e., concentration-of proteins. We owe the reader also some explanation as to how we “quantify” contrast. We start from a physiological definition of contrast: two areas of gray can be distinguished as different when the two grays, measured as optical densities (negative logarithm of transparency or of reflectance), differ by at least a minimal, threshold value. The physiologically defined law of WeberFechner states that for a wide range of intensities this threshold is a constant. In the case of photographic electron recording, it is known (Valentine, 1966) that the optical density obtained on the negative is proportional to the electron dose received. We have also investigated the situation in STEM and found that here too the optical density on the photograph of the screen is strictly proportional to the voltage of the arriving signal S. In these cases, it is obvious that to the threshold of optical density AG,, corresponds a AZth of the electron dose. Therefore we base our contrast considerations on AZ (AS). (The signal S is derived as linear combinations of scattered and/or unscattered electron.) In the literature this definition is not frequently used; very often authors use A l l 1 instead, in an incorrect analogy with photographic recording of light. In another paper we shall discuss these problems in more detail, in comparing, e.g., direct recording of electrons with the recording by intermediate light produced by a fiber plate and outside photograph. We are obviously aware that the above-mentioned way of considering contrast is applicable and relevant for the visual detection of structural details of micrographs which are large relative to the noise. For small details and obviously for the detection of atoms, the signal-to-noise ratio is more important than the contrast as defined above. In a forthcoming paper we will show examples with real, very small biological structures where it is obvious that the contrast is by far the predominant criterion for judging detectability.

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11. THEORY A . Basic Equations for the Single-Scattering Approximation

The probability of scattering for an incident electron by an atom is governed by a cross section a which is defined as dl

=

-1oNdx

(1)

where N is the number of atoms per unit volume, d x is the length of the electron path, and I is the number of incident electrons. One generally considers elastic scattering (with its ae,cross section) for electrons scattered at large angles without energy loss, and inelastic scattering (with its din cross section) for electrons which have suffered measurable energy loss. The total scattering cross section is then 0

+ ai,

= (T,I

In Section I11 we shall discuss how these cross sections can be calculated from Z , the atomic number. The number N of atoms in compact matter is described by the experimentally determinable mass density p, from which we obtain N = (L/A)P

with L being Avogadro's number 6.023 x loz3and A the atomic weight. The basic equation (1) then becomes with I = I ( x )

d l = -1apdx

(1')

For a convenient separation of variables, one introduces the K factors defined as

As we will see later (Fig. 5 and Table 11), K is to a first approximation a universal constant independent of the matter considered, except for hydrogen and helium. The Kel and Kin,however, depend on Z and A as shown also in Fig. 5. The basic differential equation for unscattered electrons then becomes dl dl = -IKpdx, -= d l n l = - K p d x ( 1'7 I which, integrated, is I,,

= loexp( - k p x )

Iun

= 10 ~ X PPX/PX~I

C

(3) (3')

CONTRAST FORMATION IN ELECTRON MICROSCOPY

277

Despite its simplicity, this equation deserves some discussion.’ The unscattered electrons will reach the value of e - ’ = 0.37 when (px), = 1/K; px was called the “mass thickness” by the pioneers of electron microscopy, and is nothing else than the mass per unit surface; (px),, the critical mass thickness, when expressed in nanometers (for x) and grams per milliliter for p , is 100 2 10 for all relevant substances. The fact of the symmetry of p and x is of extreme interest for rapid calculations of contrast for we can use it answer the question as to how much p must vary to provide the same effect as a variation of the thickness x or the reverse. Or one can ask how much heavy-metal stain must be added to any embedded substance to double the contrast, e.g., in a thin section. Let us take up this last example: A compact protein with p = 1.3 in a resin of p = 1.2 is sectioned to 50 mm. We obtain a px of 65 for the protein and of 60 for the resin, i.e., a A(px) = 5. How much must the density of the protein be changed by a heavy-metal stain to reach A ( p x ) = lo? When the volume change is neglected the density of the stained protein must be 1.4. Next question: How large a thickness variation of the resin would also produce a A( px) = 5? Answer: 4 nm! From these simple considerations it becomes obvious how useful this symmetry of p and x in this formula and the constancy of (px), are. We will see later, in Section IV, that most of the calculations presented there can be very well approximated by the above considerations. The authors of today’s literature often introduce the “mean free path A,” which is the average distance x, = A traveled by a beam electron between two consecutive interactions. From the above, A = l/Kp, which says essentially that the mean free path is inversely proportional to the density p . It seems obvious to us, from what we said above, that A does not help us in any qualitative considerations while (px), does. As long as the number of scattered electrons remains small in comparison to the number of unscattered electrons, Eq. (1’) can also be integrated to provide the thickness behavior of both elastic and inelastic electrons: dl,, = I,, K e l p dx,

dIi,

= I,,Ki,p

dx

replacing I,, by Eq. (3) and integrating, we get IeI(x)

= (KeI/K)IoC’ - exp(-Kpx)l

Iin(x) = (Kin/K)IOCl - exp(-Kpx)I We check that Z,,(x)

’

+ lel(x)+ Zi,(x) = I,.

(4) (5)

The formal analogy of the law of Eq. (3’) with that of Lambert-Beer applicable, e.g., in the case of the absorption of light in solutions might be noted here: I / I , = exp-licx, with c the concentration of a solution and x the thickness of the cell. This becomes -In l / l , = od = kcx (see also Section A).

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E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

Forming the ratio of elastic and inelastic intensities, one shows that

(6) r = 1 e J l i n = KeI/Kin = b e l / b i n from which formula both p and x have disappeared. The result now depends only on the cross sections, which in turn depend on 2;this is nothing else than Crewe's 2 contrast (Crewe et al., 1975). It is therefore only dependent on the elementary composition of the specimen. B. Multiple Scattering

The simplified description presented above is only valid as long as the number of scattered electrons is small compared to that of the unscattered ones. With increasing thicknesses, more numerous multiple scatterings occur and one has to use statistical methods to describe more satisfactorily the interaction of the incident electrons with the specimen. Every biologist with a modern education knows the Poisson distribution and uses it in many of his problems such as virus infection, one- and multiplehit phenomena (as, for example, first-order kinetics in chemistry and inactivation in radiobiology). The interaction of electrons with matter also obeys the Poisson distribution (von Borries, 1949a; Lamvik and Langmore, 1977). The probability P(n) for n rare events to occur on one individual target is

P(n) = (m"/n!)exp( - m)

(7)

with m the average number of events per target in a population. Within the specimen we associate a cylinder of cross section n (be,,bin)and height x with each electron. Scatter of the electron will occur once or more, according to the number of atoms (represented by one point) contained in this cylinder. When using the definition of cross sections, one finds that m = 0 L/A px

= Kpx

(7') As discussed in the preceding section, we obtain the critical mass thickness (px), = 1/K for the case m = 1. As we see in Table 11, this critical mass thickness is, within k lo%, a matter-independent constant and therefore of large practical value for qualitative estimations. This definition will be used throughout in preference to A = 1 /K p . Purely formally, m can be expressed by x/A, which is mathematically elegant, but practically of little use. Since we know ( p x ) , to be about 100, when p is expressed in grams per milliliter and x in nanometers, we thus can immediately estimate m for any practically used specimens as m = p x / ( p x ) , = A p x . Knowing m, we can read in Table I the distribution of single- and multiple-scattering events. For sections with little or no stain and 100 kV, the distribution lies between 0.2

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279

and 0.4. For rn = 0.4, only 20% are multiple among the scattered electrons. For negative stain layers around structures of some 20 nm we reach values of m = 1. Multiple scatter affects here already 40% of the scattered electrons. Considering scattering per se, with a given rn value, one easily calculates the proportion of unscattered electrons: P(0) = exp( -rn)

that is, Iun/lo= exp( - Kpx) as above; the proportion of single-scattering events: P( 1) = rn exp( - m) that is ll/Io = Kpx exp( - Kpx); the proportion of scattering events, including single and multiple events.

f

i=l

I,,,,,- 1 - exp(-Kpx)

P(i) = 1 - ~ ( 0=) 1 - exp(-rn),

10

and the proportion of multiple events is similarly a2

1 P(i) = I

i=2

-

P(O)- ~ ( 1 = ) I -(I

+ rn)exp(-rn)

-

which can be developed, when rn remains small, into pmUl, rn2 - + ( I - m)m2 (8) It increases approximately with the square of rn. Some typical values are tabulated in Table I. To apply Poisson statistics, the assumption of a straight electron path, and thus also of a straight associated vertical cylinder is needed and entirely correct for single-scattering events. This is only approximately true for multiple scattering: for a single-scattering event we know that the large majority of scattered electrons are still within a scattering angle below TABLE 1 PROPORTIONS OF UNSCATTERED, SINGLY, DOUBLY, AND MULTIPLY SCATTERED ELECTRONS CALCULATED WITH THE POISSON DISTRIBUTION m 0.1

P(0) P(1) P(2) P(>2)

0.905 0.0904 0.0045 0.0001

0.2

0.4

1

0.82

0.67 0.26 0.05 0.02

0.37 0.37 0.18 0.08

0.16

0.016 0.004

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E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

10- rad. Treating double-scattering events with Poisson statistics is thus still a very good approximation, leading only to very small errors. For practical purposes we rarely deal with specimen thicknesses allowing for substantial numbers of more than two consecutive scattering events. At least this is so as long as we use no, or only restricted, amounts of heavy metals, i.e., when the density p is within the range 0.9-1.3, as we have to consider for unstained biological material embedded in resins with and without heavy metal. We can then also apply the Poisson distribution to calculate the relative proportions of I,,, Zin, and Iel. For a single-scattering event we obtain P( 1) = rn exp( - rn) = p x ( K i ,

+ Kel)exp( - K p x )

(9)

with Pi,( 1) = Iin/Io= pxKi, exp( - K p x )

and

(9’) peI(1) = IeI/Io = pxKelexP(-Kpx)

For a double-scattering event we have to introduce the binomial distribution and we obtain the following relative proportions:

+

P(2) = i ( p ~ ) ~ ( K : 2KelKi, ~

+ K?,)exp(-Kpx)

(10)

from this we deduce for the proportion of double elastic scatter for the elastic-inelastic scattered proportion Pel/in(2)= I e l / i n / l o

= (pxI2Ke1Kinexp( -

KP~)

(1 1b)

and for the double inelastic scatter (1 1 4 Pinjin(2) = Iin/in/lo = i(px)’K?n exp(-Kpx) For the remaining multiple-scatter events above 2, binomial distributions with n are obtained in analogy, but, as observed above will, become increasingly approximate:

with i from 0 to n. From Eqs. (7) and (9) we might calculate the proportion of electrons which have suffered at least one elastic scatter: 1 - P(0) -

m

C Pi,(i) i= 1

CONTRAST FORMATION IN ELECTRON MICROSCOPY

28 1

Useful approximations to these formulas were given for the first time by Crewe and Groves (1974). Similar ones have been used by several other authors (Egerton, 1982a; Colliex and Mory, 1984). When the angular distribution of the scattered electrons has also to be taken into account, only approximations can be made. Elastic electrons are distributed into rather wide angles, a few rad, while the inelastic ones remain mainly within a few rad. This is actually an important factor when one wants to develop calculations for quantitative agreement. With experimental conditions one has then to consider the given angular acceptance of the detectors. Moreover, multiplescattering events may redistribute the scattered electrons between the categories defined above; for example, double elastic scattering can advance an electron in the forward direction, so that it can no longer be distinguished from the unscattered beam, or on the contrary, the two angles can add up so that it is scattered outside the maximum acceptance angle of the detector. The real situation is much more satisfactorily described by using the Monte Carlo approach. Each type of scattering event is characterized by a set of parameters (energy loss, angular deviation, length between successive interactions) and one simulates many possible trajectories for an incident electron arriving on the specimen by random access to these parameters. The transmitted electrons are then classified according to the angular acceptance and energy window of the used detectors (Jouffrey, 1983; Reichelt and Engel, 1984) for application to typical organic materials, as illustrated in Fig. 1. C. Contrast Formation

In any imaging disposition of electron microscopy, contrast is achieved by eliminating or selecting part of the transmitted beam. With the conventional EM column (CTEM), scattering contrast has long been distinguished from phase contrast. In the first case, one deals with intensities within well-defined solid angles (bright field, tilted dark field), while in the second mode, one uses interference effects between the unscattered and the elastically scattered wave, with high-coherence illumination. This latter contrast seems to govern highresolution studies; it is particularly important for periodic structures and outof-focus conditions. This will not be considered in this chapter. On the other hand, recent developments with STEMS offer new possibilities for using scattering contrast. These are mainly due to the flexible possibilities for efficient angular and energy selection on the transmitted beam: annular dark-field detectors (ADF) can collect all electrons scattered at large angle; magnetic spectrometers can discriminate any energy loss electrons and, as a special case, can separate all inelastic electrons from those with no energy loss.

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E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

FIG. 1. Representation of the calculated angular and energy distribution after passing through a 50-nm-thick protein layer. (Courtesy of Dr. R. Reichelt.)

Figure 2 shows some typical angular configurations for the most largely used imaging modes in CTEM and STEM. The signals in CTEM can be described by using a single-scattering approximation as sCTEM = I un + alin + ble, BF (12) SICTEM DF

=

+ b’lel

(12‘) where a, b, a’ and b’ must be calculated from the geometry of the incident and collected beams. In CTEM modes, it is only possible to discriminate electrons allin

283

CONTRAST FORMATION IN ELECTRON MICROSCOPY Inelastic

i\

and bright fielddetector

Spectrometer Briaht-field ~

lens

~

~

r

'

C

c

operture

l

o

r

k detector - f i e

l

d

Specimen

(a1

(b)

FIG.2. Image formation in (a) bri&--t-fieldCTEM with parallel illumination and (b) STE 1 using annular dark-field detector and EEL spectrometer. In the CTEM all electrons deflected at angles larger than 0, are removed by the objective aperture and cause scattering contrast. In STEM the dark-field signal is formed by the electrons scattered to a larger angle than 0, and recorded on the dark-field detector; electrons scattered to an angle smaller than 0, are recorded by the spectrometer.

of different energies by a rather complicated column modification [introduction of a prism-mirror configuration (Castaing and Henry, 1962; Ottensmeyer and Andrew, 1980; Henkelman and Ottensmeyer, 1974),or of its completely equivalent magnetic filter]. The important signals in STEM are

When the system has been designed so that the spectrometer acceptance angle is equal to the minimum acceptance angle of the annular dark-field detector, c=l-c'

each of the collection factors a, b, c, d is smaller than one and depends mainly on the optical geometry of the microscope and slightly on the elementary composition of the matter considered. The angular distribution of scattered electrons varies with the atomic composition of the matter. Elastically scattered electrons have usually a much broader distribution than the inelastic ones. Eusemann et al. (1982) have introduced instead the notion of effective cross section. In our nomenclature oeff= ba in the above example and accordingly

284

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

in the other cases described below. We have modified the formulas of Eusemann et al. accordingly, so as to get a mathematical expression for these collection factors; they can easily be calculated from the known geometry of the microscope (see Section 111,A). In dark-field CTEM (beam tilt), a’ and b’ represent a rather complicated geometry (Langmore et al., 1973) and it will not be dealt with here. For hollowcone dark field in CTEM and for dark field in STEM, the factors are easily described by the geometric parameters of the dark-field detector. For STEM Z contrast, we form the ratio between the signals obtained from the dark-field detector and the spectrometer

By ideal collection, this ratio would be equal to r = ge,/oin.In reality the angular dark-field detector collects less than 100% of the elastically scattered electrons and in addition some inelastically scattered electrons, as shown by Eqs. (1 3) and (1 4). We define r’ = (c

+ dr)/c’

(15)

This constant is, however, of very little practical importance, since it does not help very much for the cases considered here (Table 111). The signal S is easily modified electronically by the gain and by subtracting a constant value. Such electronic manipulations may change the contrast but obviously not increase the information contained in the signal. When considering the effect of multiple scattering (as described by either the Poisson or the Monte Carlo method), one has to point out that there is no possibility to discriminate in energy those electrons collected by the annular dark-field detector. Consequently, IADF= I , ,

+ lin/el

as defined by Eqs. (9) and (1 1). D. Treatment of Superpositions: The Dilution Theorem

In practice, it rarely occurs that different substances of a specimen are nicely arranged side by side. Embedded biological structures will be surrounded by embedding material above and below and on the sides. In thin sections of such embedded material, many biological structures might span the slice from surface to surface, but many others will be partly or wholly included in the slice. The matter-specific constants p, K , and Ke, are thus discontinuous along x.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

1

285

1

FIG. 3. Schematic drawing illustrating the “dilution theorem” described in the text on Section I,D. Arrows indicate path of one electron with its associated cylinder.

Locally, around a “point” of the specimen, the matter has to be considered in a strict treatment as being layered. This situation is mathematically easy to deal with in the case of the unscattered electrons I , , [3], but it becomes very complicated for I , , and Ii, [4] and [S]; in these formulas we already made the simplification of only considering single-scattering events. For thin specimens we can easily evaluate this distribution of discontinuities or layered specimens. In Fig. 3 we see part of a specimen composed of one matter (crosses) with a layer of a second matter (circles). The associated cylinders of the crosses and circles is given. The numbers of crosses and circles contained in the corresponding associated cylinders determines the frequencies when entered in the Poisson distribution. It seems obvious to us that another distribution of the circles, as indicated in Fig. 3 by the cylinder to the right, will not affect the frequencies. In a first approximation, valid for thin specimens, the distribution of matter along the depth x of the section is thus irrelevant. This distribution only becomes relevant when multiple scatter has to be considered. In theory, any discontinuous distribution of matter along x would be reflected in different characteristics of the image according to the two possible orientations of the specimen during observation. This was indeed a point of contention in the early days of electron microscopy and comes up again as a question in every practical electron microscopy course. With a strong influence of multiple scatter, the resulting image should be strongly and significantly different according to whether the supporting film or the structure per se were turned toward the lens. Such a difference should be particularly strong, e g , with shadowed or negatively stained specimens on thick organic supporting films. No significant, striking difference was ever found and/or published. Based on the theoretical considerations above, the consensus nevertheless recommends orienting the side with the specimen toward the lens.

286

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

We therefore think that neglecting multiple scatter in treating the examples in Section IV,E and Fig. 13, is a fully justified approximation which allows for correct qualitative assessments.

111. SCATTERING CROSSSECTIONS AND CONSTANTS A. Atomic Scattering Cross Sections

The scattering power of an isolated atom on an incident high-energy electron is defined by its scattering cross section, which represents its effective target area. It can only be deduced from complex calculations involving refined potential descriptions of the Coulombic field of the nucleus and its orbital electrons. Results are presented either in terms of differential cross sections for scattering within a given solid angle or of total cross sections which measure the probability of elastic or inelastic events as introduced in the theory above. Another way of adapting these calculations for practical use is to weight the total values with an efficiency factor which depends essentially on the experimental conditions. 1. Elastic Cross Sections There are several theoretical studies available in the literature (Burge and Smith, 1962; Crewe et al., 1975; Euseman et al., 1982; Schafer et al., 1971), and the problem is to decide which one is the most suitable for practical applications. In the case of elastic cross sections, there is not too much difference between the published results when one is not interested in accurate values for forward scattering at very small angles. In the following we give the resulting cross sections r~ and scattering constants K in function of the atomic number 2, as obtained (i) by the coarse approximation of Crewe et al. (1975) and (ii) by the equations used by Eusemann et al. (1982). For the approximation according to Crewe et al. (1975) we used

From Eusemann et al. (1982), we have kept the following equations in which the angular parameters are taken into account. For CTEM, bright-field

CONTRAST FORMATION IN ELECTRON MICROSCOPY

287

configuration:

where f (0) is the forward scattering amplitude and 8, is the characteristic scattering angle, estimated from the tables of Schafer et al. (1971). In the simple screened Coulombic potential, 8, can be estimated analytically as

8, = 1/2na where a = a(Z) = 0.885802-'/3 is the screening radius for atomic number Z. Similarly for STEM, with the annular dark-field configuration:

Oo is in CTEM the limiting angle of the objective aperture; in STEM it represents the angle of the illumination cone. 2. Inelastic Cross Sections Though most of the energy transfer between the incident electron and the specimen takes place with the peripheral atomic electrons which are not well described in any of the single models, it is useful to consider first an atomic description, the validity of which will be discussed later on. We have therefore tried to estimate, similarly to the elastic case, some values for total inelastic cross sections by summing over all possible excitations. From Wall et a/.(1974) we can calculate a general 2 dependence following cln= (1.5 x 1 0 ~ 4 / ~ 2 ) 2 ' ~ 2 1 n ( 2 / 8 , )

(20)

In this formula, a characteristic inelastic angle gE= =/2E,, fi = V / c , 2E0 = p2 (V, + mc2),with relativistic correction and the average energy loss AE is supposed to be equal to 62. This assumption is valid for l o w 4 materials, such as most organic substances as checked by Isaacson (1977), but cannot be extended simply to high-Z atoms. The angular efficiency for inelastic scattering has been evaluated from the formulas of Eusemann et al. (1982). They are CTEM:

TABLE I1 RELEVANT CONSTANTS FOR CONTRAST FORMATION I N STEM AND CTEM AT 100 KV Average atomic Hydrogen Carbon Nitrogen Oxygen Phosphorus Carbohydrate Protein Lipid (lecithin) Nucleic acid” HM20 K4M Epon Ice Sn-methacrylate resin 0s-fixed proteinb Potassium phosphotungstate a

P

1 6 7 8 15 4.14 3.83 3.21 5.26 3.34 3.57 4.01 3.33

1 12.01 14.01 16.0 30.97 7.72 7.10 5.75 10.24 6.12 6.53 7.52 6.01

3.78 4.5 1 22.86

-

oe,

10-19

x

10-19

K,, x lo4

K ; . x 104

K x 104

(px): = 1 x

K

10.8

1.4 1.3 1 1.6 1.09 1.23 1.24 0.92

0.35 7.89 8.43 8.95 33.10 4.56 4.29 3.60 6.65 3.70 3.91 4.65 3.22

6.10 10.55 11.40 12.16 13.31 8.82 8.57 7.98 9.57 8.16 8.34 8.74 8.12

2.12 3.96 3.62 3.37 6.44 3.55 3.64 3.76 3.91 3.64 3.61 3.73 3.23

36.41 5.29 4.90 4.58 2.58 6.88 7.27 8.36 5.63 8.04 7.69 7.00 8.15

38.59 9.25 8752 7.94 9.02 10.43 10.91 12.12 9.54 11.69 11.30 10.73 11.38

9.6 9.2 8.3 10.5 8.6 8.8 9.3 8.8

7.27 8.80

1.24 1.63

5.92 6.46

8.02 8.64

4.95 4.42

6.70 5.91

11.64 10.34

8.6 9.7

53.47

5.1‘

60.9 1

12.87

6.86

1.45

8.32

12.0

2 -

Density value represents Na salt.

’0s-fixed protein containing 20% (w/w)0 s . Data from Brown et al. (1977).

( p x ) , is the mass per surface area that statistically leads to one scattering event per incident electron.

-

CONTRAST FORMATION IN ELECTRON MICROSCOPY

289

STEM:

The angular parameters involved, GE, e,, and O,, have already been defined; Izc is the Compton wavelength (2.4263 x m) and q is a fitting constant which has been found to be q E 1.09. For comparison with the efficiency factors introduced above [Eqs. (12)-(14)], for CTEM:

for STEM:

The results of these calculations are shown both on Fig. 4, and in Tables I1 and 111, which concern, respectively, total cross sections and geometrydependent factors (a, b, c‘, d ) in the case of single scattering. We also considered the scattering constants K :

These constants have also been plotted in Fig. 5, which shows that K is approximately constant, except for hydrogen and helium. On the contrary, the ratio r = K,,/Ki, displayed in Fig. 6 varies substantially. Of the two, the more

N

E

u

m

10 20

30 40 50 60 70 80 90

20 30 10 50 60 70

10

Atomic number

80 90

Atomic number

FIG. 4. Elastic scattering cross sections ueIand inelastic scattering cross sections u," in function of Z for 100 kV calculated according to (a) Langmore et al. (1973) and (b) Eusemann et a!. (1982). TABLE 111 GEOMETRICAL PARAMETERS DETERMINING ELECTRON COLLECTION AND RATIOCONTRAST

STEM^

CTEM"

Ratio

Substance

a

b

C

C(

d

r

r'

r/r'

Hydrogen Carbon Nitrogen Oxygen Phosphorus Carbohydrate Protein Lipid (lecithin) Nucleic acid HM20 K4M Epon Ice Sn-methacrylate resin 0s-fixed protein Potassium phosphotungstate

0.887 0.835 0.805 0.780 0.790 0.835 0.843 0.854 0.824 0.850 0.846 0.844 0.834

0.170 0.162 0.123 0.099 0.168 0.133 0.143 0.153 0.141 0.148 0.143 0.151 0.104

0.065 0.095 0.110 0.123 0.122 0.095 0.090 0.085 0.100 0.087 0.089 0.090 0.094

0.934 0.905 0.890 0.877 0.878 0.905 0.910 0.915 0.900 0.913 0.911 0.910 0.906

0.409 0.433 0.483 0.526 0.486 0.476 0.460 0.450 0.480 0.453 0.460 0.450 0.519

0.058 0.748 0.739 0.736 2.565 0.517 0.500 0.449 0.699 0.453 0.470 0.532 0.397

0.025 0.463 0.401 0.442 1.418 0.376 0.353 0.314 0.484 0.319 0.334 0.361 0.331

2.32 1.62 1.35 1.67 1.81 1.38 1.42 1.43 1.44 1.42 1.40 1.47 1.20

0.849 0.838

0.149 0.134

0.087 0.093

0.913 0.907

0.518 0.521

0.739 0.747

0.514 0.531

1.44 1.41

0.720

0.129

0.150

0.850

0.624

4.733

3.474

1.36

~~

~

CTEM, 0, = 7.5 mrad. STEM, 0, = 28 mrad. ' r = uel/uin. r' ,= ,S,/,,S, with the signals collected on the annular dark-field detectors and the LEL in the spectrometer.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

0

,

,

,

,

20

10

,

,

30

I

I

LO

,

I

I

I

.

60

50

.

I

.

.

29 1

.

70

80

90 Z

70

80

9OZ

Atomic number

RAREEARTH ELEMENTS

I

11

11110 20 H CNO P S

30

40

50

60

Atomic number

FIG.5. Scattering constants at 100 kV plotted as a function of Z. Filled columns represent the K,, and open the Kinparts of the total K. The data in (a) are calculated according to Langmore et al. (1973) and in (b) according to Eusemann et al. (1982).

sophisticated calculations using Hartree-Fock models clearly reveals the periodicity of electron shells with increasing 2. B. Cross Sections for Composite Matter

The different organic matters that we consider are composed essentially of H, C, N, and 0 with additional P i n nucleic acids. Other components like S are

present only in small amounts. In some cases, we will consider the influence of

292

E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

30 25 .c _

b

\

a,

20 15

b

10

5 0

10

20

30 40 50 60 70 80 90 Atomic number

FIG.6. 2-dependent signal r

=

uc,/uinin function of the atomic number.

heavy metals, like 0 s and Sn, respectively, introduced during specimen preparation either as a fixative-stain or covalently bound in an embedding resin, respectively. We will also take into account the possible staining brought about by charge-neutralizing ions, stemming from the buffer used. A general assumption is to calculate average cross sections by summing over the cross sections of all atoms present in a molecule and dividing by the total number of atoms. This procedure implies that the scattering properties of single atoms are the same as those of atoms bound to others. In the case of elastic scattering, most of the cross section is due to interaction with the Coulombic field due to the charge of nuclei; the influence of the neighboring atoms is to modify the distribution of the outer electrons, so that the potential at long distance is slightly modified. Consequences can be found for smallangle scattering but they do not involve noticeable changes concerning the large-angle elastic scattering considered here. For inelastic scattering, the situation is rather different because most of the relevant cross section is due to these outer orbitals. A typical energy loss spectrum of organic matter (Fig. 7) exhibits the following major features: a narrow and intense zero-loss peak, a major inelastic contribution in the low-energy-loss (LEL) range, that is, between 10 and 40 eV, consisting in a large and smooth maximum which does not contain

CONTRAST FORMATION IN ELECTRON MICROSCOPY

293

any atom-related feature, and, at higher energy losses (above 50eV), a continuously decreasing tail on which are superposed a succession of characteristic small edges due to atomic core electrons. One notices that at least 30% of the inelastic intensity is contained within this low-energy-loss peak; the general shape of which remains very similar in all organic substances. Consequently, the recording of an “inelastic” image consists in collecting at the exit of the spectrometer LE1 electrons contained within an energy window from typically 10 to 50 eV. For contrast quantitation, the relevant inelastic cross sections can be calculated in two ways. The first method is to average atomic inelastic cross sections in a new way as for the elastic term. The second approach consists in evaluating the total intensity in a real EEL spectrum with a Lorentzian-type fit (Wall et al., 1974). If one compares the two calculations for a typical adenine specimen, the results fit within 10%(Colliex et al., 1984).When one is interested in organic and biological substances in the absence of heavier elements, the atomic calculation constitutes a satisfactory source of inelastic scattering cross sections.

150 v)

c

0

-aaJJ V

100

U

E aJ

0 0

50

100

150

ENERGY LOSS (eV 1 FIG.7. Average EEL spectra of HM20 showing the low energy-loss (LEL)electrons used in ratio contrast; 80 keV. (Courtesy of Dr. R. Reichelt.)

294

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

Iv.

CONTRAST WITH UNSTAINED SECTIONS OF

BIOLOGICAL MATERIAL

ALDEHYDE-FIXED

A. Calculated Values of Scattering Constants for Diflerent Materials

As did von Borries (1949a) and Hall (1953) in the pioneering days of electron microscopy, we chose as variables in our theoretical equations the thickness x, the mass density p, and introduced the scattering constants K = KeI+ Kin: The latter are obtained from the matter-specific average scattering cross sections (T = oel+ oinby multiplication by L / A (2). This (a)

10-

G

-baJ

1

b

08 -

Sn-Cesin

06-

‘PO/

-

oc!d40r

-

bon

ig,!

04 02-

Nuclelc

pro Carbohydrate HM?y K ~ M 0 ICe /A0 // I

1

1

1

.

I

-

FIG.8. Z-dependent signal r = uc,/uinas (a) a function of the average Z and (b) of the hydrogen content of organic matter. On the right scale in (b) we indicate the elastic and inelastic scattering cross sections u,, and uin.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

295

choice revealed itself judicious because then the signal Iei/Ii,,is reduced to the For conventional imaging the signal depends on px very simple form oel/oin. as a product that a commutative on both p and x with equal influence, but also on the scattering constants Kel, K i n ,and K . In the next section we will explore the degree to which these scattering constants are involved in contrast formation. Tables I1 and 111 present the calculated values of these matter-specific constants for substances involved in biological electron microscopy. From these data and using the simple equations in Section 111 it should be easy to calculate any signal for any other substance not listed in Tables I1 and 111. For the range of biological materials, the ratio r = oel/oin can be presented either as a function of an average 2 (Fig. 8a), or, more conveniently, as a function of decreasing hydrogen content (Fig. 8b). Only those matters which contain P or Sn (or any “abnormal” atoms other than N, C, 0),are not on the curve, but more or less far above it. As we will show further below, this fact illustrates the extremely high sensitivity of Z contrast to 2, which is much stronger than in conventional imaging contrast. This has important practical consequences, in that small amounts of metals incorporated into organometallic resins or into ice produce with Z-imaging manifold the contrast that is obtained with conventional imaging (Carlemalm et al., 1982b). It implies also that specific labeling with heavy metals requires very much smaller probes or tags when imaging with 2 contrast than with the conventional modes. For the same reason, a general heavy-metal stain or shadowing-if still requiredcan be used in very much smaller amounts than usual. B. Thickness Dependence of Scattering

By using a Poisson distribution for the description of multiple scattering (Section II,B), we have introduced the critical mass thickness (px), = 1/K as the one at which, on average, one scattering event occurs per incident electron. In this case, 37% of the electrons are still passing unscattered, 37% are single scattered, and the remaining 26% are multiply scattered. Some typical values of ( p x ) , are listed in Table 11. Its variance for all matters considered is 12%,but with extremes of 8.3 and 12.0, indicating that for more precise calculations, we have also to take into account the variations, rather small, of K besides the more important ones in p, x , and Kel. In Fig. 9a we have plotted the curves of I,,,, Zel, and Ii, in function of x and calculated from single scattering. In this case, Iel/Iin= oel/oin= const. Only very thin specimens of about p x = 10 nm g/ml can be approximated correctly by these equations. Specimens of such thicknesses are seldom available or can be made only at the cost of preparation-method-induced deformations. Thin

296

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

I I10

10

I

I (a)

08

08

06

06

01

04

L

- Inelastic 02 Elastic - scattered

-

0

0

50

100

150

02

0

0

nrn

I

50

100

150

nrn

I10

08

06

tc

04

04

t

02

0

0

50 nm

100

0

50

100

nm

FIG.9. Plots of calculated signals in function of thickness x. (a) Scattered electrons calculated with the statistical method (Section 11,B). HM20, 100 kV, 28 mrad. (b) Calculated signals, taking 0, into account. HM20,lOO kV, 28 mrad. Note that the curve for the A D F signal is almost straight when compared with the curve for elastically scattered electrons in (a); this is due to electrons multiply scattered to a larger angle than 0, and thus falling onto the A D F detector. (c) The thickness dependence of the A D F signal is much larger than that of the ratio signal at the same contrast. The curve 2.3 x A D F signal is the ADF signal recalculated to the same contrast as the ratio signal at x = 50 nm. HM20-protein, 100 kV, 28 mrad (protein, ------, HM20, -). (d) The signals calculated with the Monte Carlo method for a different 0,. Protein, 100 kV 13 mrad. (Courtesy of Dr. R. Reichelt.)

CONTRAST FORMATION IN ELECTRON MICROSCOPY

297

sections, for example, have two surfaces which are heavily distorted by plastic deformation to a depth reaching easily 5 nm on each side (Section IV,D). A good compromise is reached with sections of 30-50 nm. This is still about half to two-thirds of (px),, when considering unstained material. In Fig. 9b we have plotted corresponding curves obtained with Eqs. (8)-(1 l), by which up to six multiple scattering events have been included. We have assumed that all scattered electrons with at least one elastic scatter will fall on the annular darkfield (ADF) detector. The remaining unscattered and inelastic scattered electrons will be collected in the central aperture; they are dispersed by the spectrometer and the LEL electrons detected. The ratio S A D F / S L E L between the two signals is measured and provides the ratio contrast. In Fig. 9c we have plotted the curves calculated for both the embedding resin HM20 and for an average protein. When comparing 9b with 9c, we first find that the ADF signal increases nearly linearly with the specimen thickness, far further than the I,, alone. This is due to multiple scatter which removes some of the electrons from the central, near-axial part and shifts them to larger angles. In consequence, the proportion of collected LEL electrons decreases. The ratio S,D,/SL,L increases with x , with an x-dependent contrast comparable to that of the ADF signal alone. This confirms the authors who calculated this dependence on x (e.g., Egerton, 1982a). Why then d o we maintain the claim that the ratio contrast is relief independent as is observed experimentally? This is easily understandable when comparing the contrast between sections of a protein and of resin HM20 of an equal thickness of 50 nm. In dark field, we obtain a contrast ASD of about 0.02. The same contrast is obtained by a thickness variation of Ax = 9 nm of HM20. For the ratio contrast, however, we obtain ASR = 0.055, which is 3.3 times the contrast obtained in dark field. We can electronically amplify the dark-field signal (“more gain”) by 3.3, so as to obtain ASD = ASR= 0.055. The same contrast is achieved by a variation of AX, = 9 nm of the resin. In order to obtain the same with ratio contrast A x R = 27 nm! This simply means that, e.g., knife marks, strongly visible in the dark-field mode, will disappear in the ratio contrast. This is demonstrated in Fig. 10, where we show an image with knife marks, one half recorded with ratio contrast the other half with dark field. In conclusion, we can say that the relative, matter-specific contribution to contrast is very much larger with ratio contrast than with dark field; in just the reverse manner, the influence of thickness variations is very much higher with dark field than with ratio contrast. The practical consequence of this situation is that the influence of relief is negligible with ratio contrast applied to unstained material. It is obvious, but worth mentioning, that with the heavy stain used in current routine methods, the influence of relief becomes negligible in any case. The limitations due to stain will be discussed later (Section VI1,C).

298

E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

The above calculations are based on somewhat arbitrary decisions about the distribution of scattered electrons on the two detectors. This can be done very much precisely by applying Monte Carlo procedures (Reichelt and Engel, 1984).These authors have done this for our Vacuum Generators HB-5 STEM and our homemade spectrometer. The ratio-contrast results obtained with different matters are given in Fig. 9d. There we see again that the contrast AS, is nearly independent of x and therefore also approximately the same as the 2 contrast at x = 0. From the above it becomes quite clear that contrast calculations based on the formulas of single scatter, i.e., formulas strictly valid only for very thin specimens, give throughout some overestimates. This estimated error in calculated contrast is, however, barely larger than some lo%, and thus certainly within other errors due to other approximations in the basic assumptions of the theories. In what follows, we therefore use again the singlescatter approximations. C. lnjluences of Thickness, Density, and Scattering on BF and DF Contrasts

In conventional bright field, most inelastic electrons are collected in the recorded image and only contribute to a general background. The contrast is then essentially produced by partly eliminating the elastically scattered electrons, while in conventional dark-field imaging we use practically only the elastically scattered electrons. In one way or the other, the I , , are thus responsible for contrast. From Eq. (4) we see that their amount depends on p, x, K,,, and K . As we see from Table I1 for organic materials, neither K , , nor K is constant when we consider hydrogen in the calculations. Biological material is variably rich in hydrogen. Hydrogen is no more sensitive to beam-induced loss than is phosphorus (Thach and Thach, 1971), and phosphorus behaves comparably to carbon (Dubochet, 1975). Most sensitive among the atoms involved is oxygen (Egerton, 1980), obviously depending on its bonding. A preferential, beam-induced loss of oxygen would therefore increase the relative amount of hydrogen. It is thus reasonable to calculate contrast for biological materials without yet considering beam-induced modification. Beam damage would indeed tend to improve contrast. These simplifying assumptions are in good agreement with the experimental results reported in Section V. In order to appreciate the influences of the four variables ( p , x, KelrK ) on contrast in conventional imaging, we differentiate the expression (4) for I,, and obtain the sum of the partial differentials for each of the four variables. To

CONTRAST FORMATION IN ELECTRON MICROSCOPY

299

obtain simpler expressions we divide the resulting Ielby run[Eq. (33)]:

Ale, lun

- Ke,pAx

1 + Ke,xAp + -[exp(Kpx) K

Ke, + 7[1 K

- exp(K px)

-

l]AKel

+ K px]AK

Keeping all A’s of the variables at 0, except one, we can calculate units for each of the four variables which produce the same contrast. For these equioalent contrast units (ecu’s) we obtain

0.012 Ke1P

u, = -,

up=-

0.0 12 Kelx ’

0.012K - exp(K p x ) - 1’ -

uKeI

UK

=

0.012K KeIC1 - e x ~ ( K PX)

+ K PXI

Equation (25) can now be written by means of these equivalent contrast units as ux

up

(25’)

uK,~

In this equation, the differences of the four variables are expressed as multiples of the ecu’s. If this difference is now exactly one unit, then the resultingcontrast is 0.012. In Table IV we give for different biological substances and embedding media the equivalent contrast units, as calculated with formulas (26) and using TABLE IV EQUIVALENT CONTRAST UNITSFOR Ax, A p , A K , , , AND A K

Substance

u x (nm)

Ice HM20 K4M Epon Sn-methacr ylate Carbohydrate Lipid Nucleic acid Protein 0s-fixed protein

4.0 3.0 2.7 2.6 2.0 2.4 3.2 1.9 2.5 1.7

up

(g/ml)

0.093 0.082 0.083 0.080 0.061 0.085 0.080 0.077 0.082 0.068

UK.1

UK

0.26 x 0.21 0.18 0.18 x 0.18 0.16 x 0.23

10-3

0.14

10-3

10-3 10-3 10-3 10-3

10-3

10-3

0.17 10-3 0.13 x 1 0 - 3

-4.70 x I O - ~ -2.90 x 10-3 -2.26 x 10-3 -2.17 x 10-3 -1.6 x 10-3 -1.76 x 10-3 -3.37 x 10-3 -1.21 x 10-3 -2.00 x 10-3 -1.01 x

300

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

the data computed in the previous tables and figures of this paper. These units also depend on the thickness, and in the table we have provided ecu’s for 40 nm. We see for example that u, for HM20 is 3 nm, a thickness difference which-under favorable circumstances in dark-field observation-we estimate to lead to a just visible contrast. All other ecu’s tabulated lead to exactly the same contrast. For practical biological work, x = 40 nm is a good average. As we will see, this value seems to be optimal for thin sections. Even if beam damage would result in a complete carbonization, we should not be induced to compare such 40-nm organic slices with 40-nm-thick carbon. During carbonization of most organic material, the dimensions are approximately kept and the resulting carbon is porous. Such porous carbon has been called “biological carbon” (von Borries, 1949a) and has been considered to have a density of less than 1 g/ml (charcoal!). In some few cases, the organic material might melt during carbonization. Then the density might be higher, but the thickness is reduced accordingly. From Table IV we can already learn several interesting facts: it shows, e.g., that the u, is the highest for ice, followed by lipid and HM20. This signifies that these substances are not very efficient when transforming thickness variations into contrast. More informative, however, is Table V, which expresses contrast between embedded biological substances and embedding material in ecu’s, taken from Table IV. To do this, we had to make approximations: First, we kept x constant throughout as 40 nm. Second, the calculated differences p, K , , ,and K had to be expressed in em’s in order to be useful for interpretations. Neither the ecu of the embedding medium nor that of the embedded substances is completely correct for this purpose, but they are the only available ones. We therefore simply tabulated both, giving some sort of lower and higher estimate of the resulting contrast. In regard to contrast, it becomes obvious from Table V that ice is throughout the best embedding medium for unstained biological substances. It is interesting that lipids would lead to negative contrast with all organic embedding media (HM20, K4M, Epon). This fact is relevant obviously only in those cases in which lipids are not extracted. Extraction always occurs (Weibull et al., 1983) except at temperatures below -60°C (Weibull et al., 1984). Epon is particularly unsuitable for the observation of unstained proteins. In very general terms, it is obvious from Table V that p does not have a very much greater influence than K , , . Nor is there any correlation at all between the two differences. When considering conventional imaging of unstained material, it is therefore an extremely crude approximation when speaking of essentially px-dependent contrast formation.

RELATIVE CONTRAST BETWEEN

TABLE V BIOLOGICAL SUBSTANCES AND EMBEDDING MEDIA IN CONVENTIONAL IMAGING

Carbohydrate eCU

from h

Ice

AP K

1

AK

2.0

8.6

ecu from

ecu from

b

a

5.7 2.0 5.9 13.6

0.9 2.0 -0.2 2.7

~

~~

AP

HM20

-0.4

AP

Total

2.0 -0.3 0.4 2.1

AP AKel AK Total

2.0 - 1.0 0.1 1.1

AP

2.6 -7.8 0.8 -4.4

~~

K4M

AKel

AK ~~

Epon

3.8

AKel AK Total

~~

Sn-

AKel

methacrylate

AK

~~

Total

0.4 3.4

Nucleic acid

ecu from a

5.2 1.2

Total

Lipid

3.6 -0.6 0.7 __ 3.1

~

- 1.1

1.9 - 1.1 0.2 1.o

~

3.1 - 1.1

0.5 -0.1 __ -0.7

-2.8 0.8 - 0.4 - 2.4

- 2.9

2.0

0.5 2.1

-0.2 ~

0.6 - 0.2 __ -0.7

- 0.4 ~

1.o 2.3

~

~

- 3.0 0.2 -0.6 - 3.4

~

ecu from

ecu from

ecu from

ecu from

ecu from

a

h

a

h

a

1.4 2.6 0.4 10.4

9.0 4.9 1.4 14.3

4.1 1.6 0.1 5.8

4.6 2.9 0.2 7.7

7.6 7.7 0.3 __ 15.6

2.6

6.6 3.7 0.5 10.8

6.3 1.3 0.7 8.3

~

~

6.7 2.0 1.7 10.4

- 2.5

7.1

4.9 2.2 1.4 8.5

- 3.0

4.6 1.1 0.6 6.3

4.8 1.4 0.9 __ 6.1

0.8

-0.5 ~

~

0.1 - 0.4 - 3.3

~

~

1.9

- 4.0

- 3.0

6.1

4.8

- 8.8

- 6.6

- 5.2

- 5.7

- 7.4

0.7

~

~

- 6.2

-0.3 10.9

~

-0.1 8.3

~

0s-fixed protein

ecu from b

4.6 1.7

0.9

~

Protein

1.3 1.7

~

~

~

0.1 0.2 0.2 1.1

0.8 -0.5 -0.1 __ 0.2

~

0.4 3.0

~

7.9 6.0 1.3 15.2

1.1

5.9 6.2 1.o __ 13.1

0.7 -0.5 -0.1 0.1

4.9 3.8 0.2 __ 8.9

5.7 5.3 0.4 11.4

0.2

~

~

4.8 4.5 0.4 9.7

~

0.5

~

0.7

6.4

- 7.1

- 3.0

0.4

~

- 5.8

~

0.7 0.2

1.o

~

- 0.9

0.0

- 7.3

1.7

~

2.6 0.0 0.3 2.9

~

11.3 15.3 1.3 21.9

~

- 6.6

0.8 4.2

~

~

5.7 -4.1 1.3 2.9

302

E. CARLEMALM, C. COLLIEX, AND. E. KELLENBERGER

We conclude by saying that the contrast of embedded biological material in conventional imaging is not sufficiently described by considering only the density p. For material not containing heavy atoms, the scattering constants have particularly important influence. They reflect here the hydrogen content of the material. For heavy-atom-containing material, either obtained by 0 s fixation or represented by an Sn-containing embedding resin, both p’ and K,, gain additional influence.

D. Injluence of Thin-Section Relief Compared for the Two S T E M Imaging Modes In a first paper (Carlemalm and Kellenberger, 1982),we proposed that the unsharp imaging of unstained thin sections (40 nm) by dark-field imaging is not due to optical causes and multiple scattering, but rather to a consequence of the surface relief on both faces of the slice. Due to plastic deformations associated with the tearing forces of the cleavage process of ultramicrotomy, this relief obviously would not faithfully represent the biological structures. Since in ratio-contrast imaging the influence of Ax vanishes and with that most of the influence of such relief, this would explain why unstained sections lead to very well-defined micrographs (Fig. 10) in the meantime, Williger, from our laboratory, has investigated these reliefs by careful fine grain shadowing (Fig. 11). They estimated the thickness variations to be between 3 and 5 nm. We evaluated the influence of such relief on contrast in STEM ADF imaging by assuming an embedded compact protein in a section of constant thickness. We calculated its contrast with the surrounding embedding material by using formulas (4), (13), and the data of Tables I1 and 111. We then reduced the thickness of the protein by a Ax which was calculated so as to reduce the contrast by exactly the same amount as that provided between protein and embedding material in a section without thickness variation. When the thickness of the embedded protein, but not of the embedding, is reduced by the calculated matching thickness difference, then the contrast between protein and surroundings disappears. If this difference is comparable in magnitude to that of the relief, then our hypothesis is verified: the influence of a relief of 3-5 nm provides contrast differences similar to the density differences of the embedded material. In Table VI we give several numerical examples. From the examples above we have learnt that the relief of sections of unstained embedded biological material has an influence on contrast which is comparable to that due to specific differences of the matter, as reflected in p, K , and K e , .When we consider also the quality of this relief, as shown in Fig. 15,

CONTRAST FORMATION I N ELECTRON MICROSCOPY

303

FIG.10. (a) Ratio-contrast and (b) ADF image of a section from rat duodenum, with knife marks showing up as strong diagonal lines in the A D F image but very much suppressed in the ratio-contrast image. (a) and (b) do not represent two independent micrographs; they were obtained as a single photographic record from one complete scan during which the imaging mode was switched. This is demonstrated also by the very weak continuations of the knife marks from the right into the left part of the micrograph. Note also the white “halos” or “shadows” associated with nearly all structures of the right part and their absence-except one-in (a). This is due to thickness variations as discussed in Sections 1V.D and V,C.

the unsharp imaging is understandable as a consequence of the surface deformations. As theory predicts and experiments have shown (Carlemalm and Kellenberger, 1982), imaging by ratio contrast reduces the influence of the distorted surface reliefs when compared to dark-field imaging. To further explore this situation we calculated the resulting contrastexpressed by AS-for a protein of 5-nm dimension positioned differently in respect to the surface of a 40-nm-thick section. In this case we calculated the contrast for both modes of imaging (ADF and ratio) and for different embedding media. From Fig. 12 we learn immediately that the position of the protein has virtually no effect in ratio contrast. Letting half of the protein protrude from the surface leads with ADF imaging to doubling and in some cases even to a more than tenfold increase of contrast. Increasing protrusion

304

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

FIG. 11. Section of HMZO-embedded phage T4 adsorbed onto E . coli envelopes and shadowed with tungsten-tantalum alloy, revealing the relief of one of the two surfaces.

of the protein out of a tin resin or Epon even produces a contrast reversal when conventionally imaged, but a nearly unaltered contrast when using ratio-contrast imaging. From these calculations it becomes obvious that for unstained structures in the range of 5-10 nm, dark-field imaging of thin sections cannot be expected to provide meaningful results, because the contrast differences between the same structures inside of a section and those partly protruding are so strong that interpretation becomes most difficult. Either a very strong staining of the structure or ratio contrast leads to interpretable results, in which the distorted surface reliefs are not predominant in contrast formation. It should be noted here that already a relief of 1-2.5 nm is sufficient to create this queer contrast situation. From the examples in Fig. 12 we learn also that the tin-containing embedding resin is perfect for ratio contrast, but not usable in conventional

TABLE VI

INFLUENCE

OF A p AND Ax ON CONTRAST'

.I

........ .. .. .. .. .. .. ...;.....;.....;. . : . : . ..~............

/

Ax

COMPACT'PROTEINS

Density Section thickness (nm)

Protein Unstained

40

1.3

40 100

0s-stained

1.63

1.3

Thickness variation leading to the same contrast A.x (nm)

Resin p

Ap

HM20 1.09 Epon 1.24 K4M 1.23

0.21 0.06 0.07

7.06 (6.4) 0.38 (1.8) 2.94 (2.1)

Ice

0.92

0.38

15.73 (1 1.6)

Epon 1.24

0.39

15.70 (9.6)

Ice

0.38

29.2

0.92

Range of predominance of relief (5 nm) Border range

Range of predominance of structures inside of the section

a A cylinder formed of compact protein is resin embedded and sectioned, such that it spans the section; the thickness variation Ax of the protein is calculated, leading to the same contrast as does the density difference Ap between protein and resin; the values in parentheses are calculated with a constant K (K = 10.65 x

306

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

Protruding raction

0.25

0.5

AS

AS

0 AS

Embedded

AOF

ratio

AOF

ratio

ADF

ratio

x10-2

x10-2

x10-*

x10-2

x10-2

x10-2

Ice

-0.15

-0.25

-0.25

-0.24

-0.35

-0.24

HM20

-0.094

-0.38

-0.18

-0.37

-0.26

-0.36

K4M

-0.029

-0.21

-0.12

-0.20

-0.20

-0.20

Epon

-0.017

0.12

-0.11

0.12

-0.20

0.12

0.23

2.21

0.11

2.14

0

2.08

-0.34

-1.85

-0.43

-1.79

-0.

-1.14

in

~~

Sn-methacrylate

0 s - f i xed

protein i n Epon

FIG.12. Contrast AS of a large (5-nm) embedded protein (slippled square)in relation to the fraction of the protein that protrudes out of a 40-nm-rhick section. Negative values mean that the embedded material is bright against a dark background. The values are calculated for an annular dark-field collection angle of 28 m a d to m and 100 k V .

imaging because of the contrast reversal that occurs as soon as the structures protrude from it. This is confirmed experimentally. E . How to Calculate Contrast of Real Biological Structures

In order to simplify argumentation, we have considered until now only extended compact proteins. This is a putative entity which never exists in this simple form as a biological structure. It is well known, however, that protein molecules are generally rather compact in that they contain in the interior of

CONTRAST FORMATION I N ELECTRON MICROSCOPY

307

their domains no, or at best only very few water molecules. Bound water is in the form of a thin “hydration shell” of two to three layers on the outside of hydrophilic areas of proteins. Larger biological structures are composed of many protein molecules or subunits acting as building blocks. Therefore, water-filled spaces necessarily exist between subunits in such “supramolecular protein structures.” The water will eventually be replaced by resin, negative stain, or transformed into ice. Because of the superposition in depth, the “effective”concentration of such protein assemblies is therefore easily reduced by some 20-300/,. The same is true for polysaccharides, which form gels containing frequently more than 80% water, and for any form of DNA and chromatin. As long as the effective resolution has not reached that of individual molecules, reduced concentrations have to be used for contrast calculations. Pro rata of the initial water “content” a resulting density has to be calculated as a mixture of biological substance and embedding material. All biological structures, except lipids and proteins within lipid layers, are therefore not compact entities but rather “spongy” structures which contain water in the form of cell sap. When dried (in vacuum!) most of this water will disappear and the structure will collapse (Kistler and Kellenberger, 1977; Kellenberger and Kistler, 1979).This collapse is best avoided by keeping the structures embedded either in ice or in a resin. Biological structures, when observed in the electron microscope, have therefore to be considered as mixtures of biological material (protein, nucleic acids, and polysaccharides) with variable amounts of embedding medium. In an artifact-free preparation, the amount of the latter-measured as volume-should correspond exactly to the native water content. In Section II,D we demonstrated the “dilution theorem,” which is valid for thin specimens (up to 50 nm): After passage of the electron through a cylinder of the specimen, the frequency distribution of electrons into the three classes I,,, I,,, and I,, is not dependent on the in-depth distribution of the constituent material of this cylinder. If we assume protein and resin, it does not matter if this protein is equally distributed within the resin or localized in a compact form somewhere in the cylinder. We have illustrated such situations in Fig. 13. In Fig. 13a we show a compact substance spanning the whole thickness of a slice of resin HM20. Except for lipids and lipids with proteins, such compact substances are not encountered in nature. In Fig. 13b we show schematically two biological structures: the one composed of globular subunits (bl), the other represented by a coil of a fibrous type (b2). Both are supposed to have contained 50% of water when native. These structures exemplify in b l a protein structure, such as a virus capsid, composed of protein subunits, and in b2 a nucleic acid filament packed into a chromosome or virus. In order to treat these two cases numerically, we make use of the dilution theorem: either we distribute the biological matter of Fig. 13b equally over the

308

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

whole depth of the specimen c, or we “compact” each and separate them, as shown in Fig. 13d. When the biological structures in b had initially 50% (v/v) of water, then the compacted structures are half of their native extent. That is, the 10-nm structure is now reduced to 5 nm, and the relative volumes of resin and biological matter are now 35 : 5. This ratio allows us to calculate the average values of the corresponding matter-specific constants p, K , , , K i n ,and K of the mixture by using the data of Tables I1 and 111. This is exemplified in Fig. 13 for protein, DNA, and carbohydrate by calculating the conventional dark field and 2 contrast, expressed as a signal difference with the surrounding embedding medium (Lowicryl HM20). When considering biological matter as compact-as is unfortunately frequently done-we see in column a that compact DNA would produce in dark field about 2.5 times the contrast of compact protein. However, as soon as we consider a biologically realistic situation, as in b, the difference between DNA and protein becomes much smaller. A water content of some 75% (w/w) is found in the case of one of the most compact forms of DNA known, namely that found in the head of a bacteriophage (Earnshaw et al., 1978). For the values in Fig. 13 we note that the contrasts obtained for “real” samples by annular dark-field imaging and in the ratio-contrast mode differ by only a factor of 3. This is exactly the factor found when we studied in Fig. 9c the contrast obtained between protein and resin HM20 in the two imaging modes, but when using multiple scatter. There we also explained that by

Ratio Protein(p = 1 3 )

ONA ( p = l 61) Carbohydrote ( p =1 44)

AS

ADF

- 0 033

-00073

- 0 16

- 0 019

-0057

- 0 013

AS

Ratio - 0 0038 -0 O N -0 0062

AOF

- 0 00091 -00036 - 0 0016

FIG. 13. Examples of contrast calculations for various “real” structures, embedded in HM20. (a) Compact matter spanning the section. (b) Schematic representation of “porous” or “spongy” structures consisting of matter and resin in the ratio 1 : I ; b l represents globular and b2 fibrous matter. (c) How the matter of the structures in (b)can be regarded as diluted into resin and spanning the entire section; for details see Section II,D of the test. (d) How the matter of cases (b) is compacted and as such allows more easily for calculations.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

309

electronic amplification (“gain”), the dark-field contrast can be increased. But we should remember here that then the variations in thickness Ax also lead to enhanced contrast and thus become visible, while this is not the case in ratio contrast. Practically, the difference between the two modes of imaging lies mainly in the quality and sharpness of the images, and not so much in the contrast.

V. EXPERIMENTAL CONFIRMATIONS A . Dejinition of Test Object

With the following we will demonstrate the consistency between theory and experiment. To do this in a reasonable manner, we have selected a biological system which is biochemically and biophysically well defined such that the structures visible on micrographs can be evaluated in respect to their scientific meaningfulness. Bacteriophage T4 is one of the most thoroughly and extensively investigated viruses. Its protein composition is known and carefully related to the physical parameters of its structure (Eiserling, 1979). The agreement between structures viewed in electron microscopy by negative stain (Kellenberger et al., 1965), thin sections (Wunderli et al., 1977), and freeze fracturing (Branton and Klug, 1975) is good. The envelope of the host of this bacteriophage, E . coli, is also well investigated. There is no doubt about the existence of a biochemically defined outer membrane (Steven et al., 1977); a periplasmic space separates this outer membrane from the inner one, the plasma membrane. Only the structure of the periplasmic space and of the peptidoglycan located between inner and outer membrane are not yet completely agreed on. New electron microscopy procedures have probably settled these unanswered questions as we discuss elsewhere (Hobot et al., 1984). Fortunately, they are not relevant to the arguments which we present below. When a phage infects a bacterium, an inner tail tube is “drilled” through part of the envelope, probably up to the plasma membrane, but not piercing it (Furukawa et al., 1979; Labedan and Goldberg, 1979). The “drilling” is associated with a contraction of the tail sheath. This mechanism has been studied in detail (reviewed in Caspar, 1980, and Eiserling, 1979). In the micrographs presented in the following, we show phages, of which most have adsorbed on “empty” bacterial envelopes and which-in consequence-have a contracted tail sheath. Some of these phages have partly or fully ejected their DNA. Triggering of the DNA release from the head

3 10

E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

1 15 8

(a)

(b)

FIG. 14. Schematic drawing of the structures that embedded and sectioned give the images in Figs. 11 and 16-19. (a) A T4 phage. (b) A T4 phage after absorption onto an E . coli cell envelope; the tail sheath is now contracted and the tail core (a tube!) has penetrated the outer layers down to the cytoplasmic membrane. (c) The E . coli envelope with the outer membrane, the periplasmic gel, and the inner or cytoplasmic membrane. The inner part of the periplasmic gel is lost upon separation of the two membranes.

indeed requires contact of the tip of the tail tube with the plasma membrane (Furukawa et al., 1979). During preparation of empty cell envelopes, most of the plasma membrane becomes detached from the outer membrane and the peptidoglycan. This procedure is used in biochemistry to separate the envelopes into two fractions which in their composition are distinct. The known structural features of this phage-envelope system are summarized in Fig. 14.

B. Materials and Methods Bacteriophages T4 were produced by infection of E . coli B. The phages were purified on a sucrose gradient which was later removed by dialyses against Sorensen phosphate buffer pH 7.0. Envelopes from E . coli B were prepared by shaking bacteria, harvested in exponential phase, with ballotini beads in a Mickle apparatus. The envelopes were washed twice by centrifugation. This material was kindly provided by Dr. Jan Hobot and Cornelia Kellenberger of our laboratory. Bacteriophages were adsorbed onto the envelopes, fixed with 2% glutaraldehyde, and centrifuged to a loose pellet in a table-top centrifugation.

CONTRAST FORMATION IN ELECTRON MICROSCOPY

31 1

This pellet was serially dehydrated in ethanol at progressively lower temperatures,-embedded in Lowicryl HM20 or a tin-containing resin (Carlemalm et ul., 1982b),and sectioned with a LKB microtome. Shadowed sections were obtained by electron gun evaporation of a tantalum-tungsten source at an angle of 14" (Villiger et ul., 1984). Micrographs were recorded with a Philips EM 301 with a 30-pm objective aperture (corresponding to a half angle of about 7.5 mrad) and a Vacuum Generators HB 501 STEM (situated in the Laboratoire de Physique des Solides, Orsay, France) equipped with a Gatan EEL spectrometer. The spectrometer slit is set to collect electrons with energy losses of 5-60 eV; the collector aperture is the inner hole of the annular dark-field detector and corresponds to about 25 mrad. The outer angle of detection for ADF is about 200 mrad. For a full description of the STEM configuration used see Colliex and Mory (1 984). C. Results

From our theoretical and numerical considerations we are led to postulate for conventional imaging a strong influence of the surface relief of both faces of a thin slice, an influence that vanishes when using ratio contrast. To demonstrate this influence experimentally, we will first consider micrographs of sections obtained from embeddings in a tin-containing resin. Variations of thickness of the embedding medium will be more strongly manifest than those obtained with other embedding media, as we will see afterward. In Fig. 15 we show the putative profile of a slice of the sort that leads to the micrographs of Figs. 16 and 17. Figure 16 presents the same specimen region

E

..:.

. . ..

FIG.IS. A drawing of a cross view of a thin section as it has to be imagined to explain our experimental data. The letters point out features seen in Figs. 1 1 and 16.

312

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

FIG.16. STEM images of sectioned T4 phages adsorbed on E . coli envelopes embedded in an organometallic methacrylate resin. (a) Dark-field image formed by mainly elastically scattered electrons. (b) Image formed by inelastically scattered electrons. (c) Z-contrast image formed by the ratio of elastically over inelastically scattered electrons. (d) As in (c), but with photographically reversed contrast. Surface artifacts produced during sectioning are well emphasized due to the scattering properties of the Sn resin, which enhances the effect of the relief. Note that these effects are eliminated in (c).The letters mark features which are discussed in the text.

imaged in STEM as dark field with elastic (16a) and inelastic (16b) electrons. In Fig. 16c the ratio-contrast image is given. In regions marked (E) the outer membrane is seen in a vertical superposition. In Fig. 16c it has the expected dimension of 10-11 nm. The same dimension is also obtained on stained sections (Fig. 17). In P1 we see (partially) empty phages with contracted tail sheaths and some undefined material that remains inside the head. In Fig. 16a

CONTRAST FORMATION IN ELECTRON MICROSCOPY

313

FIG. 17. CTEM bright-field image of the same specimen as in Fig. 16, but embedded in Lowicryl HM20 and stained with uranyl acetate and lead citrate.

these phages, marked P2 and P3, clearly show something which could be the head membrane or head shell made of protein. The unwarned observer could believe that this represents new information. This is unfortunately not the case. The proteinous head shell is only about 4.5nm thick, as can be recalculated from the known protein content. This value is an upper estimate, because the shell is obviously a porous assembly of subunits, as explained in Section IV,E. The “porosity” and “unevenness” can, however, only be estimated by considering the size of substances which can or cannot penetrate through the shell (Leibo et al., 1979) and from shadowed micrographs of shells (Scraba et al., 1973; Branton and Klug, 1975; Kistler et al., 1978). Even if this is done very optimistically, we cannot even reach half of the values measured in Fig. 16a and 16b, while these dimensions are of the correct order of magnitude in 16c. The thickness in 16c corresponds to that of stained shells in Fig. 17 and other published micrograph (Wunderli el a!., 1977; Carrascosa and Kellenberger, 1978). The phage tails in P2 of Fig. 16 show again in 16a a black core, surrounded by a white cylinder, while it is only a black cylinder of 17 nm diameter in Fig. 16c. From chemistry and information processing of negatively stained

314

E. CARLEMALM, C. COLLIEX, A N D E. KELLENBERGER

tails, a diameter of 18 nm is determined (Amos and Klug, 1975; Smith et al., 1976). Again, the “beautiful” image in Fig. 16a is a misleading artifact, explainable by the relief, while that of 16c is in perfect agreement with the known features. The normal and flipped-out baseplate of the phages [schematically drawn in Fig. 14, according to Kellenberger et al. (1965);reviewed in Eiserling (1979)l are clearly visible in Fig. 16c, particles P1, P2, and Bp, but not in 16a or 16b. Still considering known structures, we have the somewhat puzzling situation that full and empty phage heads can be distinguished in both Figs. 16a and and 16b, but not in 16c. This can be explained by the fact that the ratio contrast of the phage-head DNA happens to be matched by that of the tin resin. Empty heads are obviously filled with resin, with the exclusion of remaining internal proteins. In order to make a distinction, the tin content of the resin has to be chosen differently. Some other features of biologically undefined structures are also of interest. The particles designated A and P2 (Fig. 16) have an associated dark region, always in the same direction, like a shadow. This is easily explained by a sectioning artifact reflecting in a thinner region of the resin behind the particle in respect to the direction of sectioning (Fig. 15). The regions G and G2 in Fig. 16 can, in our opinion, be interpreted much more readily in 16c than in 16a and 16b. We think that the filaments visible in region G2 of 16c are likely to be bundles of DNA. To finish the discussion of Fig. 16, we should mention that the tin resin used for these micrographs is still beam sensitive. Larger magnifications reveal a granularity above noise which precludes higher resolutions, as would be needed for resolving the tail fibers of phage T4. A new tin-containing resin is under construction and has already demonstrated the absence of beam-induced granularity. Results with biological material will be reported later. In Fig. 18 we show a section of the same biological material as in Figs. 16 and 17, but this time embedded in Lowicryl HM20, which is particularly rich in hydrogen. Figures 18a and 18b are the elastic dark-field and Z-contrast pictures, respectively. It is interesting that these two micrographs were taken on an area which was accidentally contaminated at low magnification by working with too few lines per frame. This contamination is obvious as a line pattern in 18a, but not in 18b. This contamination layer had a variable thickness which reflects in the elastic dark-field image, but not in ratio contrast. As a whole, 18b is better defined than 18a. It confirms our arguments made above (Fig. 10) and in previous papers. Finally, in Fig. 19, we present the same material embedded in Epon and observed in the ratio-contrast mode. We immediately note that the phages are now only represented by their DNA content; the proteins no longer have

CONTRAST FORMATION IN ELECTRON MICROSCOPY

315

FIG.18. STEM images of an unstained section from the same specimen as in Fig. 17:(a) an ADF image with contamination and etching marks which in the ratio-contrast image (b) are hardly visible due to the ability of ratio contrast to suppress differences of mass thickness.

sufficient contrast to be visible. As we discussed in Section IV,A, this is not unpredictable: indeed, Epon, as an epoxy resin, has a hydrogen content which is comparable to that of proteins and substantially higher than that of HM20. This fact has also been used in Fig. 10. By these observations we eliminate the possibility that contrast of the biological material might have been due only to adsorbed metal ions.

316

E. CARLEMALM, C. COLLIEX, AND E. KELLENBERGER

FIG. 19. STEM ratio-contrast image of Epon-embedded T4 phages illustrating the influence of the elementary composition on the contrast. The DNA inside the phage head is the only visible structure. For composition and scattering properties see Fig. 8 and Tables I1 and Ill.

The advantage of ratio contrast over staining will obviously become really apparent only at higher magnifications and with adequate specimens such as, e.g., the septate junctions (Garavito et al., 1982). D. Positive Stain in 7hin Sections

As we have learned, the contrast in conventional modes of imaging of slices of embedded biological material depends on the differences of the mass densities p and of the average scattering cross sections, expressed by K , , of the two components (the biological matter and the embedding medium). In conventional bright-field imaging, the contrast of unstained resin-embedded

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material is so low that one cannot work with such a material. It happens that fixation with OsO, was found very early to be preferable to all the other fixatives already known from light microscopy. It was understood by most that 0 s must also become deposited into or onto the fixed material (Bahr, 1955) and thus increase both density p and K e , . As discussed in the Introduction, at some period in the history of electron microscopy, the 0 s deposited through fixation with OsO, was sufficient for producing adequate micrographs. In our laboratory we titrated the resulting 0 s deposit by neutron activation (Carlemalm et al., 1985) and found for 0 s some 10 f 2% (w/w). By uranyl acetate treatment in aqueous solution about an equal amount is added to it. These measurements were done on a defined protein structure, the capsid of bacteriophage T4, and on whole bacteria. To find out to what extent this added amount of 0 s is reflected in increased contrast, we embedded 0s-fixed bacteria simultaneously with glutaraldehydefixed ones. The result is shown in Fig. 20a. At first sight it is astonishing how little contrast is gained by this 10% addition of heavy metal. As mentioned in the Introduction, it became customary to stain the sections with uranyl acetate and lead citrate. In Fig. 20b we show the result of a section stained with uranyl acetate and lead. Now the micrographs look acceptable. Interestingly enough, we are no longer able to distinguish by contrast whether the bacteria were fixed with OsO, or with glutaraldehyde. The small contrast increase due to the 10% 0 s deposit is therefore very much smaller than the added stain on the sections. From these observations we estimate that section staining leads to deposits which are 4-10 times those of the initial amounts; in other words, to the biological material an about equal amount of heavy metal is added. With such large amounts of heavy metal, the question arises about the location of the deposits in relation to the macromolecule. This problem can now be studied by comparing stained, conventionally observed material with unstained material observed in the ratio mode. With septate junctions it was found that hydrophobic parts of proteins are not stained by uranyl acetate (Garavito et al., 1982), but it was not yet possible to decide where the stain was in respect to the hydrophilic part of the molecule (Fig. 21). Further work on different structures is needed. Studies of only 0s-fixed, but not poststained material should not only be made in dark field (Ottensmeyer and Pear, 1975), but now also in ratio contrast (Ottensmeyer and Arsenault, 1983).It is most likely that new information will be gained. Indeed, from the values in Tables I1 and I11 we can see that the relative influences of thickness variations, i.e., of the surface reliefs, are already so strongly reduced with 20% stained material that they are negligible.

FIG. 20. CTEM bright-field images of glutaraldehyde and Os0,-fixed E . coli cells embedded together in Epon. Image (a) is recorded from a section which has not been poststained, (b) is a recording from a section that had been poststained with uranyl acetate and lead citrate. Note the minute contrast difference between the cells in (a). Despite the fact that the cell marked “0s” contains about 10% (w/w) osmium, almost all the contrast in (b) is due to the poststaining. Note that the bacteria marked Glu in (a) when observed in the ratio mode would look similar to that marked “0s” in (b)!

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FIG.21. Septate junctions of the testis of Drosophila melanogaster. The left micrograph is glutaraldehyde-fixed, fully unstained material embedded in Lowicryl HM20 and imaged by Zcontrast in STEM. The right micrograph is from sections of the same block, but now poststained with uranyl acetate and observed in CTEM. Note that the hydrophobic parts of the junction are here unstained, and that it is difficult to decide between positive or negative staining.

VI. DISCUSSION OF THE CONSEQUENCES FOR THE INTERPRETATION OF MICROGRAPHS A . Introduction: Diferent Densities

The final goal for studying different modes of producing contrast is to find out which type of contrast formation provides the most biologically useful information about the object. In conventional electron microscopy, a first obstacle, however, takes precedence over the above-mentioned goal: the differences of constitution between different unstained biological materials are so small that it is difficult to achieve any contrast! The development of electron microscopy has only followed the line of increasing resolution, completely forgetting that the limitation with biological material per se is not resolution,

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but contrast. The biologists have compromised with the physicists by introducing continuously more and stronger heavy-metal staining. But now they have become aware that the relation of heavy stain to the stained object is again a new, nearly unknown limitation. New specimen preparation methods are being devised and new imaging modes proposed that should overcome also these limitations; we shall discuss these now. One of the most noble purposes of microscopy is to provide an image. On micrographs morphological patterns are discovered which frequently indicate new biological structures. By biochemical and biophysical procedures they can then be isolated, but only if the morphological definition of the structure is kept as a continuous guide. This all sounds trivial and is illustrated by the history of mitochondria, chloroplasts, microsomes, ribosomes, viruses, various vesicles, and so on. But the limitations of electron microscopy become obvious when considering smaller objects. We cannot discuss these here and refer the reader to a review (Kellenberger and Chiu, 1982). The correct interpretation of finer details becomes crucial in any further interaction between microscopy and biochemistry toward elucidating structures below the 10-nm range. For physiological reasons, an image is composed of gray tones (or colors) associated with a morphological pattern. Gray tones, or grays as we will call them for short, are physiological impressions or sensations. It was found more than a century ago that a linear progression of grays is seen when the (reflected or transmitted) intensity of light is progressing exponentially (or “geometrically”). This law of Weber-Fechner is valid only in a limited range, but seems to hold for nearly all our sensory systems. The Weber-Fechner law simply states that the physiological sensation is proportional to the logarithm of the physical intensities. This physiological law is frequently confused by physicists with the Beer-Lambert law (see footnote to p. 277) of the decrease of intensity in absorbing matter and which shows that the optical density, defined as the negative logarithm of the transmitted intensity, decreases linearly with the thickness. According to this law, a linearly increasing thickness of an absorbing matter produces a linear progression of optical densities and therefore a linearly increasing series of grays. For our eye “twice as thick is twice as gray.” But also “twice concentrated-in a solution-twice as gray or twice as colored.” It is obvious that electron microscopists would like to correlate the gray of a micrograph with specific properties of the specimen. Here is where unpleasant confusions start! These began by calling dark parts of a micrograph electron dense, instead of electron opaque, meaning “highly electron scattering.” It was clear that confusion had to arise with data obtained by x-ray diffraction where the density of electrons, the real electron density, is directly determinant. As we will see below, the mass density p is important in

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determining the grays in micrographs and for electron diffraction. No wonder then that the measured optical densities of micrographs are transformed nearly automatically into mass densities when producing 3D reconstructions. Experts in thin sectioning realized frequently that the gray (wrongly named electron density) obtained on sections of cells is in the first approximation a reflection of concentration of matter in the initial aqueous cytosol, and in the second, a consequence of stain and specific chemical composition. A “dense,” in the sense of concentrated, cytoplasm is darker on the micrograph than a more diluted “less dense” part of it elsewhere in the cell! Water is the main component of living matter, and 80% of it is the average for a cell! We have introduced the dilution theorem (Section II,D) in the hope that it will help to dissipate some of these confusions, and thus to stop their inhibitory consequences for the progress of science. B. Characteristics of the Specimen That Produce Contrast

Knowing on each area of a specimen the number of each sort of atom and their scattering cross sections (elastic, inelastic, and total) would suffice to describe the proportions of different species of transmitted electrons. The number of atoms has, however, to be determined from the mass density p and the thickness x . It is interesting to note that atoms do not have an exactly determined volume and the density of protein, e.g., cannot yet simply be calculated as a consequence of the relative amounts of constituent C , N, 0, and H. Apparently, packing is variably compact or, in other words, the spacefilling volume of the different atoms depends on their surroundings. Unfortunately, determining experimentally the density p is not very simple, because most biological macromolecules have a hydration shell, of which the “organized” water behaves differently than the surrounding water. In vacuum, or after substitution by organic liquids, hydration shells are supposed to be totally or at least mostly removed. But in reality, very little is still known about these shells; neutron diffraction and also observation of still-frozen specimens in the electron microscope after transformation of water into vitreous ice have been recently introduced as experimental methods for studying these problems. Thickness x and density p substitute for the number of atoms when we know also the atomic weights. The latter, together with the atom-specific cross sections, are combined in the matter-specific scattering constants K , , + Kin = K . As the strict theory (Section 11) shows, the unscattered electrons decrease as P(0) = exp( - K p x ) . The calculations show in addition that the K’s for stained and unstained biological matter are nearly constant, with deviations of only + l o % .

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The inelastically and elastically, singly and multiply scattered electrons are represented by more complex functions represented by the type 1 exp( - Kpx), multiplied by either K,, or Kin, and combinations thereof. This type of equation is mathematically unwieldy; in general, by serial developments, they are simplified into linear functions with corrections for nonlinearity. The collected electrons, or those remaining after removal of a certain class and which are used for imaging, are given by rather long formulas. In STEM, the electrons collected on the annular dark-field detector happen to have a largely extended linear range, because of multiple scatter, which moves scattered electrons from the LEL detector to the annular dark-field detector. By electronic manipulations it is easy to transform a 1 - exp function back into a simple exponential by subtracting it from a constant. The essential determinants for scattered electrons are thus p and x and the relative amounts of KeIand Kin(Kin= K - K J . In conventional imaging p and x are contributing most to contrast, while in the ratio contrast this is K,,/Kin (Sections II,C and IV,C). The contrast-forming weight of matterspecific properties (Keland Kin)to that of thickness is more than three times higher in ratio contrast than in dark field. A thickness (or density) variation has to be more than three times as high in ratio contrast to produce the same contrast as in the dark-field mode (Section IV,B).

C. Contrast in Conventional Imaging

In a forthcoming paper we will detail the precise reasons why in STEM and CTEM AG is proportional to AS, which, we recall is AS z A(px)exp(- K p x ) . This means that the contrast decreases with increasing mass thickness px. This can be verified by comparing a small particle, as, e.g., a virus, positioned on something with variable thickness as, e.g., a holey film. The signal S can be transformed into light of intensity L, with L 2: S , by a fluorescent screen. The emitted light can then be transmitted to the photographic film by a fiber plate (Guetter and Menzel, 1978). The photographic response to light has historically been developed so as to achieve an extended range of linearity with G = 1nL. With so-called outside photography, as it is performed in the Zeiss EM 109, we obtain therefore AG 5 A(px). This is also experimentally verified and reported in the above-mentioned paper, These differences of response are practically relevant only for specimens with very high contrast differences. Most specimens, however, have typically a very small range. In such cases, the micrographs obtained under these two conditions have no visibly different characteristics. Over small

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ranges, part of an exponential curve can always be approximated by a straight line. In a first approximation, contrast is due either to density differences, to thickness differences, or to both: A ( p x ) = AX) when p is constant or x ( A p ) in a specimen of constant thickness but variable substance. Constant thickness is given by embedded material, if the two surfaces are perfectly flat. Ideally, this should be the case with thin sections. As we have summarized here (Section IV,D) and shown in detail elsewhere, this is not really so, and the surface reliefs (fracture surfaces) on both sides have amplitudes of the order of 3-5 nm. The density range of unstained biological matter goes only from 0.9 to 1.4. With OsO, fixation and uranyl acetate post fixation, about 20% w/w of heavy metal is deposited, which leads to densities of proteins in the range 1.5-1.7. This is not yet sufficient for conventional microscopy (Section V,D). With additional section staining, very high densities are reached which now are sufficient for eliminating most contrast problems in bright-field imaging. Obviously, we then observe the heavy-metal deposits only and not the biological material itself, which singularly narrows the possibilities for obtaining high-resolution information. Sections of unstained biological material are of extremely low contrast; only with some particularly compact structures, like bacteria, can an image exceptionally be made in the CTEM, bright-field mode (see Fig. '20a). In the dark-field mode, more contrast is achieved; even unstained material is easily observable (Weibull, 1974; Sjostrand et al., 1978; Jones and Leonard, 1978). The results were, however, disappointing in their lack of definition; we have shown here (Section IV,D) and elsewhere that the surface relief is mostly responsible: thickness differences have a much stronger influence than the density differences between unstained biological material and resin. Rapidly frozen thin films of aqueous particle suspensions without supporting film (Lepault et a/., 1983b) should lead to flat surfaces, provided the particles are smaller than the film thickness and that sublimation during or before observation is completely avoided. High-coherence, narrow-beam imaging of viruses prepared in this manner has given astonishing results (Adrian et al., 1984). Although the contrast per se is low, the background inteference noise is so small that a photographic contrast amplification is easily possible (from discussions with J. Dubochet, EMBL, Heidelberg). This could possibly be due to vitreous ice being really a phase object, in contrast to carbon films, which are likely to be excellent scatterers. A thorough theoretical consideration of these new experimental facts by physicists is needed and of the highest interest.

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With cryosections observed in the frozen-hydrated state, the problems are similar, but much more pronounced than with resin sections: (i) the surfaces of cryosections are what we are used to observing in replicas from cryofracturing, and (ii)it is still difficult to obtain sections thinner than some 100 nm. Nevertheless, biologically interesting results have been achieved with conventional bright-field imaging (Dubochet et al., 1983). With ratio contrast-in opposition to conventional imaging-the influences of thickness variations due to surface reliefs are very much decreased and the contribution of matter-specific contrast is increased. As we will discuss in the next section, ratio contrast is thus particularly indicated for observing thin sections of unstained material. The procedure of negative staining, despite its manual simplicity leads in some cases to very intricate situations which are frequently barely interpretable; we should not forget that negative stains and sustains are aqueous solutions of a few percent of matter which during dry-down lose their water completely and thus become rearranged continuously under the influence of surface tensions (including wettability) and viscosity. One should simultaneously keep in mind that the surface tension deforms either the particle (Kellenberger and Kistler, 1979) or the supporting film by wrapping it around part of the particle (Kellenberger et al., 1982; Fig. 22). In most cases, both will occur to degrees which depend on the relative deformabilities and elasticities of specimen and film. Every microscopist dreams of negatively stained specimens which end up as an embedding in heavy-metal salt and limited by two flat surfaces! This event might occur exceptionally with two-dimensional biological crystals with relatively smooth surfaces, like the purple membrane (Unwin and Henderson, 1975) but certainly do not do so as a rule. This is thecase, however, with frozen-hydrated films of particle suspensions. One should also not forget to mention that the technique using selfsupporting frozen-hydrated suspensions of particles is also applicable without difficulty when using heavy-salt solutions as the suspension medium. Negative contrast should become achievable with some 3-4 atom percents of heavy metals but only when using ratio contrast. In the case of nonflat surfaces of negatively stained preparations and 3D reconstructions by tilt, one assumes the Beer-Lambert law to be applicable and thus also the validity of our dilution theorem (Section 11,D).In this case, curves of equal optical density are interpretable as curves of equal mass density but only when both the particle and the distribution of negative stain around it are outlined individually. Any 3D reconstruction should provide the entire profile, comprising particle, negative stain, and supporting film, comparable to the schemes of Fig. 23.

FIG. 22. CTEM image of shadowed particles and schematic drawing illustrating the wrapping phenomena of a thin carbon support film. (a) 126-nm polystyrene spheres adsorbed on both sides of a thin carbon film (about 6 nm thick). The particles on one side are negatively stained with uranyl acetate (particle t o the left). The particle to the right is unstained and the specimen is shadowed on this unstained side. Note that both particles throw a shodow. (b) Same as (a) but shadowed on both sides. (c) Virus particle (TYMV) prepared as (b).

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FIG.23. Scheme showing the expected stain distributions for extreme cases of (a) rigid and (b) deformable specimens; for (c) single-support films and (d) the sandwich technique.

D. Contrast in Ratio Imaging As we have seen in the theoretical discussion (Section II), Reichelt and Engel (1984) have shown that the signal of ratio contrast leads to response curves in function of x, which are parallel for different materials (Fig. 9d). The difference AS between the curves of two biological matters stays more or less constant and nearly equal to the ratio cel/cin. AS leads in our STEM to a contrast AG 2: AS (C being measured as optical density in micrographs obtained on photographic emulsions). As we have explained by the dilution theorem, this contrast reflects the concentration of the biological material in the resin (or ice), as long as the biological macromolecules are not individually resolved. Ratio contrast therefore should allow direct determination of concentrations, provided the general category of the involved biological matter is known (nucleic acids, proteins, polysaccharides, lipids). These concentrations are meaningful only when the region to be investigated spans integrally through the slice or layer. Such concentration determinations are expected to be very useful biologically and particularly easily made with thin sections. If the structure does not span the slice or layer, the embedding above and below the structure “dilutes” the signal, as does the embedding material mixed directly with the macromolecules. The main advantage of ratio imaging is, however, a consequence of the fact that the influence of A(px) is very much reduced when compared to darkfield imaging: the surface relief resulting from the fracture involved in the

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cleavage process of cutting is practically eliminated, as are also the knife marks. The other advantages are given by the much higher influence of heavy metals: 25% of Sn integrated into an organic resin provides too much “negative” contrast in the ratio mode, but nearly none with conventional bright-field imaging (Carlemalm et al., 1982b). We might extrapolate this knowledge to the so-called negative stain, or what was frequently called a sustain. We understand that negative stain not only acts to provide contrast, but apparently sustains the structure and thus preserves it from surface-tension-induced collapses. Pure sucrose and glucose were used for that purpose (Unwin and Henderson, 1974). To provide contrast, some heavy atoms were frequently mixed into such sustains with little success. This we understand now, and have learned in addition that small amounts of heavy metals lead to very strong ratio contrast. This was verified in our laboratory by the work of M. Wurtz and M. Hanner on “sustained” bacteriophages which gave nearly no contrast in conventional bright field, but a very strong one with ratio contrast. At the same time, the preservation of the head and its dimensions were exceptionally good because of the sustain. The extreme contrast of heavy metals in ratio contrast is also the cause of the fact that cytochemically specific heavy-metal tags used on unstained sections lead to a much stronger signal with ratio contrast. The consequence of this is that smaller tags should give usable signal-to-noise ratios with ratiocontrast imaging. It should be emphasized here that the results of ratio-contrast imaging might depend on the collection angles associated with the geometries of the objective lens and the annular detector used. Much more work is needed to definitively optimize this problem.

VII. DISCUSSION OF LIMITATIONS A more detailed discussion of limitations in the electron microscopy of biological material is provided by Kellenberger and Chiu (1982); thus we will summarize here only the most important of them. A . Beam-Induced Destruction

Ultimately all electron microScopy of biological material will be limited by the extent of beam-induced destruction, although numerous other limitations are still predominant and, potentially, seem to be avoidable. We will

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nevertheless start to discuss beam-induced distortions because we have only mentioned (Section IV,C) but not yet emphasized this old, but again fashionable, phenomenon. Beam-induced distortions have been observed by one of us (E.C.) on HM20 embedded, unstained gap junctions and other fine structures, when observed with ratio contrast under low-dose conditions. The doses were about the same as those used in minimal beam conditions of conventional bright field. It will now be very important to compare scanning with conventional imaging and to keep the specimen at different temperatures. It is presently possible to observe, at 93 K, with cryostages and conventional lenses in STEM and CTEM and with cryolenses (Dietrich et al., 1977)-kept at some 1020 K-already in CTEM and soon also in a cryo-STEM (built by A. Jones and collaborators at EMBL, Heidelberg). From these studies we should obtain more information on the influence of the dose rate (or intensity) of the beam. Presently, with CTEM, all measurable effects are only dose dependent. The range of intensity variations in CTEM is, however, too small to permit definitive analysis. On frozen-hydrated material observed in CTEM, the “bubbling” effect (Chang et al., 1983) occurs suddenly when certain critical doses are reached. What will this effect become in STEM? First observations at 93 K showed that the effect is at least strongly modified. Only further work will elucidate if the effect disappears or is replaced by “microbubbling.” Nothing definitive is known about the cryoprotection factor at 10-20 K, which was claimed originally to be around 30 (Knapek and Dubochet, 1980). With better experimental systems, this factor was very much reduced (Lepault et al., 1983a),but there are still claims of substantial improvement (Chiu and Jeng, 1982)..Itis obvious that these studies have to be continued with various, adequate specimens. It is possible to construct resins that are more beam resistant, e.g., by using cyclic components as has been done with the new Sn-containing resins (J. D. Acetarin and E. Carlemalm, unpublished). This is, however, only possible with a compromise: this resin-before curing-is viscous, and cannot be used in low-temperature procedures (Carlemalm et al., 1982a). B. Plastic Deformations in 7hin Sections

The process of microtome cutting of material embedded in ice or resins is in reality a cleavage. Cleavage happens when the tensile force attains a critical value at which rupture occurs. This value is strongly matter dependent and occurs after a phase of so-called plastic flow, which, after release of tension, is not, or only partly, reversible and thus leads to a permanent deformation. The

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extent of the phase of plastic flow is extremely matter dependent. Glass, probably also vitreous ice, is-at the speeds of cutting actually used-nearly now in the plastic range. In general, anything which is called brittle has these characteristics. Very little is known as yet about embedded biological material, except that the “complementary” cleavage surfaces do in fact not complement their reliefs (Williams and Kallman, 1955) because of the different plastic flow of embedded biological matter and embedding. The cohesion between these two is also likely to play an important role and would explain why epoxy embeddings show less relief than others. Indeed, epoxys like Araldite are reputed to be among the best “glues” or cements. This would also explain why Epon embeddings have to be etched to reacting well with antibodies, while crosslinked methacrylate embeddings (Lowicryl K4M) do so immediately without any prior treatment. It is obvious that the above-described plastic flows and ensuing deformations are likely to produce some “cracks” within and between embedded matter and resin, cracks which would help to produce massive uptake of heavy-metal stain. Although very little experimental work has been published on these problems (possibly because the referees do not like to face an unpleasant reality?) we have to be aware that deformations will always be present in slices produced by current microtomy techniques. The depth of the perturbed layer might decrease by an optimization of techniques. Since ratio contrast images not only the surfaces but also the inside, an improved information is expected, as shown already on septate junctions (Garavito et al., 1982). With vitreous ice as embedding material, phase contrast might be sufficient to produce contrast with thick sections. In this case, the interior would also be predominant in forming image contrast. But, again, experimental studies (not to speak of theories) are only at their very beginning.

C. Limitations due to Positive Stain Overcome by the Possibility of Observing Unstained Sections We have already mentioned several times that nearly equal amounts of heavy metal are needed to visualize, e.g., a protein in conventionally observed sections (Fig. 20). It is clear that we know nothing about the location of heavy metal relative, e.g., to protein, particularly if we remember what we said in Section VI1,B. It is obvious to us and some others that it is high time to observe also unstained material, so as to start understanding something about these relative locations. Since ratio contrast allows the study of unstained material, this limitation is removed, but might be replaced by those described in Sections VII,A and VI1,B.

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D. Limitations due to Negative Stain and Potential of Observing Frozen-Hydrated Material We have discussed negative stain in Sections VI,C, in Section VI,D emphasized the difficulties of interpretation encountered, and have discussed their elimination by the possibilities offered by the new prospects offered the observation of frozen-hydrated thin layers of suspensions (Lepault et al., 1983b).More experimental work has to be done with different imaging modes and temperatures of observation. It seems clear to us that this technique will revolutionize electron microscopy of small, biochemically isolated structures because here the situation is simple enough to be both understandable and interpretable. By comparison with thin sections and extrapolation of the knowledge related to them, we might also learn to understand and improve over the present sectioning artifacts, so as to provide better sectioning techniques. We have to be aware that microtomy, together with cryofracturing, are the only techniques available to study fine structures in their natural context inside of the cells. No other biophysical technique is as yet available for such direct in situ studies.

E . Limitations due to Noise In order to reduce beam damage one reduces the dose as far as possible in compromising with quantum noise. The latter is enhanced with decreasing dose. It might eventually reach a level at which direct imaging is no longer possible; redundant objects might be subjected to information processing and thus the noise reduced in proportion with the number of images of the many identical objects used. In ratio contrast we have white (statistical) quantum noise in both the elastic and the inelastic signal when we work with minimal doses. The quotient of two white noises becomes a new noise of a special type, following an F distribution (Guenther, 1964). This noise is not as pleasant as white noise, because it is a skewed distribution, which could be bothersome in cytochemical labels with heavy metals (Section V1,D). These ratio-contrast noises have to be further explored, experimentally and theoretically. The problem has been overshadowed by the observation that the STEM in Orsay, Paris had a much less noisy inelastic signal than the elastic one, compared to the STEM in Basel. The cases for this are presently being explored. We tend to believe that the main reason for the differences

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should be sought in the different geometries of the detectors and the ensuing differences in collection angles, as well as the lower beam currents used in Basel.

VIII. CONCLUDING REMARKS The imaging of single atoms has been the dream of physicists occupied theoretically or with the design of electron microscopes during the last two decades. Some efforts have also been made toward a better physical understanding of the microscopy of very thick specimens. Since the times of such pioneers of biophysical electron microscopy a B. von Borries, C. Hall, and J. Hillier, the “normal” biological specimen, on the preparation of which the electron microscopist spends all his imagination and skill, has almost never been treated by the physicists. This is very understandable, because no precise theory can be formulated, and physics can become involved only in an oldfashioned qualitative manner! We have attempted this venture at understanding and describing in physical terms what hundreds or thousands of scientists do everyday when they try to interpret electron micrographs. With conventional imaging we included also the ratio-contrast techniques, which together with the recently developed cryotechniques, open new avenues to biological electron microscopy. The possibility of extending our visual knowledge of the microworld from the usual 10 or so to some 2-5 nm no longer seems to us to be a mere dream. And this, not only with regularly arrayed two-dimensional crystals, where 1-2-nm imaging is currently achieved, but also with the direct imaging of structures in situ in the cell. This is a level where electron microscopy has a monopoly. Only thin sections and cryofractures are able to provide direct information. These are very important for rounding up all the indirect evidence gathered from genetics and biochemistry.

ACKNOWLEDGMENTS We gratefully acknowledge the very competent assistance of Werner Villiger in various instances and of Renate Gyalog in thin sectioning. We also gratefully acknowledge the many and rewarding discussions with Professor T. Tschudi and Professor H. Rose (Darmstadt), Dr. J. Dubochet (EMBL Heidelberg), and Dr. Rudolf Reichelt in our laboratory. We are most indebted to Dr. R. Reichelt, Robert Wyss, and Dr. Andreas Engel for designing and constructing a spectrometer for the STEM in Basel and for EMBL, Heidelberg, so that work could also continue in these two places. We also greatly appreciate the opportunity to share the results obtained in our laboratory by Dr. R. Reichelt and Dr. A. Engel with the Monte Carlo method prior to publication. We are grateful to Elvira Amstutz and Marianne Schafer for their patient and efficient

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typewriting, to Dr. Michel Wurtz for his help with the graphic art, and to Margrit Steiner for excellent darkroom work. The Basel group is supported by Grant No. 3.069.81 from the Swiss National Science Foundation, and the Orsay group by a grant from CNRS (US120041).

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