JOURNAL OF ULTRASTRUCTURE RESEARCH
61,
124-133
(1977)
Surface Reliefs Computed from Micrographs of Heavy MetalShadowed Specimens P. R. SMITH AND J. KISTLER Department of Microbiology, Biozentrum der Universit~it Basel, Klingelbergstrasse 70, CH-4056, Basel, Switzerland Received July 6, 1977 A method has been developed which allows a topographical map of a specimen surface to be computed from a digitized micrograph of a heavy metal-shadowed specimen. Preliminary results from the application of the method to micrographs of tungsten-shadowed freeze-dried T-layers (Kistler, J., Aebi, U., and Kellenberger, E. (1977) J. Ultrastruct. Res. 59, 76) show t h a t qualitatively consistent results for the T-layer surface structure can be obtained from specimens shadowed from different directions. The method and its drawbacks are discussed with regard to the known difficulties in interpretation of the heavy metal deposit on a specimen surface.
Surface structural information about a biological object is usually obtained by the method of heavy metal shadowing of a suitably prepared specimen or replica made from it (Aberman et al., 1972). Unfortunately a micrograph of a shadowed specimen provides only indirect information about the topography of the specimen surface. In general, the microscopist infers the surface structure by analogy to a macroscopic surface obliquely illuminated with light. On observation from above, the "brightest" parts of the structure are those parts of the surface inclined nearperpendicular to the illuminating beam, those less bright areas being inclined more nearly parallel to the illumination. Parts of the structure in the shadow of elevated parts of the surface cannot be observed; however, if a shadow is cast onto a flat area, then the outline of the ridge or protuberance on the specimen which casts the shadow can often be inferred. The absolute specimen surface topography can, in principle, be obtained by applying three-dimensional reconstruction methods to projection data from tilted views of the specimen (Henderson and Unwin, 1975). The method is sophisticated, however, and demands a combination of microscopical and computational expertise not generally
available in most laboratories, even if relatively modest resolution is required. The method of metal shadowing is simple to apply and the facilities for performing it are usually available to the microscopist. Consequently it is useful to have a method which would allow information from a micrograph of a shadowed specimen to be simply converted into a topographical ~map" from which specimen surface '~elevations" could be read directly. The purpose of this paper is to propose a method for performing such surface reconstructions and to present preliminary results on its application to data obtained from freeze-dried tungsten-shadowed Tlayer cylinders (Aebi et al., 1973; Henry, 1972; Kistler et al., 1977). The following section describes a model for the accumulation of heavy metal on the specimen and shows that if this model is valid, simple image processing allows a topographical surface map of the specimen to be calculated. Successive sections present the experimental method and the results obtained in a test case. The final section discusses the results in view of the known drawbacks of the shadowing model. 1. THEORY
In order to be able to calculate the 124
Copyright © 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0022-5320
125
SPECIMEN SURFACE RELIEF
surface elevation map from an electron micrograph of a shadowed specimen, it is first necessary to have a model for the accumulation of heavy metal on the exposed specimen surface. The model we have chosen is the simplest available (Moor, 1959); that is, that heavy metal accumulates on the specimen so that the thickness of metal deposit along the line of the incident metal-ion beam is constant over the whole specimen (see Fig. 1). For the purpose of this preliminary description we will assume that the metal deposits itself uniformly onto the specimen surface without diffusing or aggregating. This model allows us to calculate the thickness of a metal deposit as seen in vertical projection. Let d be the vertical thickness of metal deposited on a horizontal fiat surface. From Fig. 1 it can be seen that the thickness of metal deposit, t, at the point denoted vectorially by r in the plane of the specimen, will be:
our model, heavy metal piles up along lines parallel to the incident metal beam (Fig. 1) over every point on the surface of the specimen. The expression given for t(r) will therefore only hold in regions where the whole surface of the specimen is accessible to the metal beam. If the object being studied is periodic and the metal deposit thickness is given by the equation above everywhere in the unit cell, then by Fourier transforming both sides of Eq. (1) we get: T(R) = ~ (R).d -
Z(R)
. (1 -
(2) exp (-2~riR.a)),
where T(R) is the Fourier transform of t(r), Z(R) is the transform ofz(r), and ~ is the Dirac delta function. Z(R) can be reconstructed from T(R) exactly, in the absence of noise, at all points R for which (1-exp(-2~iR.a)) is nonzero, by simply multiplying T(R) by the filter function F(R) = -(1 - exp(- 2~riR.a)) -1, (3)
t(r) = z(r - a) + d - z(r),
(1)
where z (r) is the height of the specimen at r and z(r - a) is the height of the specimen at the point (r - a); a is the projection of the line lying in the direction of the beam whose length is (d/tan 0), where 0 is the shadowing elevation angle. According to
::i
cidenf heovymetedbeom k~ d eQvyreefG[ deposit~
Specimln i~ FIG. i. A diagrammatic representation of the model for the deposit of heavy metal onto a specimen surface. Seen from the direction of the incident metal beam the metal appears to have the same depth over the whole specimen. Viewed in vertical projection, the metal thickness at a point is determined by the difference between the altitudes of the specimen and of the upper surface of the metal, which depends upon the amount of metal accumulated on an adjacent part of the specimen surface (see also Moor (1959), Fig. la).
called the "exact" surface reconstruction filter. The Fourier transform, T(R), should vanish along the line (R. a) = 0, since the metal shadow cannot detect ridges parallel to the incident beam direction. If the specimen has N-fold rotational symmetry with N > 2, then two estimates are always available for each Fourier coefficient, Z (R), and in this case z (r) can be reconstructed everywhere from a single micrograph. The filter function F(R) has two actions. First, it alters the phases of the Fourier coefficients, T (R), so that they once again refer to the phase origin of the surface relief; and second, the amplitudes of T(R) are changed to restore their relative magnitudes. Since the restoration of the relative positions of structural features is the most important action of the reconstruction procedure we define a phase-filter function, P(R) = F ( R ) / I F ( R ) t ,
(4)
which makes only these alterations. As
SMITH AND KISTLER
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p o i n t e d o u t b e l o w t h e c o r r e c t i o n of t h e amplitudes as well may exaggerate errors s i n c e t h e a m p l i t u d e s a p p e a r to d e p e n d m o r e c r i t i c a l l y on t h e d e t a i l s o f t h e s h a d o w i n g m o d e l . T h e r e c o n s t r u c t i o n obtained using P(R) rather than F(R) would b e e x p e c t e d to r e s e m b l e t h e s u r f a c e r e l i e f , placing structural features in their correct l o c a t i o n s b u t d i s t o r t i n g t h e i r r e l a t i v e elevations. 2. MATERIALS AND METHODS
(a) Specimen Preparation and Electron Microscopy The micrographs used in this work were drawn from the collection of micrographs of tungstenshadowed freeze-dried T-layer cylinders obtained by J. Kistler for the work described in the report of Kistler et al. (1977). The micrographs of tilted specimens were obtained using a Philips EM301 equipped with a goniometer stage capable of tilts of _+50°"
(b) Image Processing Micrographs of the T layer shadowed at elevation angles of 60° and 45° showing smooth structure and without obvious shadows were selected for processing. Their diffraction patterns were checked to ensure that the spots perpendicular to the shadowing direction either vanished or were not significantly above the noise level. Selected micrographs were enlarged onto film, densitometered, and computerfiltered as described by Aebi et al. (1973) to produce averaged unit cells of 24 × 24 sample points. The Fourier coefficients of the transform of the averaged unit cells were then multiplied by the inverse phase-filter function [Eq. (4)]. The action of this filter was to place the structural features in their correct places within the unit cell so that its symmetry center could be found. The unit-cell center was then located by searching for the point giving the best twofold least-squares residual. Reconstructions of the surface were then performed in the following two ways. (i) The phase-filtered unit cell was fourfold averaged about its twofold center. (ii) Data from the averaged unit cell was filtered using the full surface-reconstruction filter [Eq. (3), which corrects both phases and amplitudes] and then fourfold symmetrized about the previously located center. Reverse Fourier transformation applied to data processed by either of the two methods set out above should represent different approximations to the topographical map of the T-layer surface. The recon-
structions were output as projection plots making it easier to visualize the result as indicating the relative ~heights" of the specimen surface over some arbitrary zero level. Photographic output of both the averaged images of the shadowed unit cells and the surface reconstructions made from them was obtained using the method described by Aebi et al. (1976). The output device, an Optronics Photomation (P1700), was made available through the generosity of the Photography Department of the Federal Institute of Technology, Zfirich. 3. RESULTS
(a) Testing the Model for Heavy Metal Deposit T h e d e p o s i t o f h e a v y m e t a l o n t o a specim e n is a c o m p l e x p r o c e s s ( R e i m e r a n d S c h u l t e , 1966; Z i n g s h e i m , 1972), a n d t h e s i m p l e m o d e l for m e t a l d e p o s i t s e t o u t i n S e c t i o n 1 does n o t p r o v i d e a c o m p l e t e des c r i p t i o n o f it. T h e t h e o r y d o e s m a k e t w o specific p r e d i c t i o n s , h o w e v e r , a n d it is p o s s i b l e to t e s t t h e m to s e e h o w w e l l t h e s e a s p e c t s of t h e m o d e l a r e f u l f i l l e d . T h e p r e d i c t i o n s a r e a s follows: (1) A heavy metal-shadowed specimen should appear structureless when viewed in the m i c r o s c o p e so t h a t t h e e l e c t r o n b e a m is p a r a l l e l to t h e d i r e c t i o n of t h e h e a v y m e t a l - s h a d o w i n g b e a m . (2) I f t h e w h o l e specimen surface was directly accessible to t h e h e a v y m e t a l - s h a d o w i n g b e a m , t h e Fourier transform (and diffraction patt e r n ) s h o u l d s h o w a zero l i n e p e r p e n d i c u l a r to t h e s h a d o w i n g d i r e c t i o n . D u e to t h e f a c t t h a t o u r g o n i o m e t e r s t a g e for t h e m i c r o s c o p e a l l o w e d o n l y _ 5 0 ° t i l t s , w e w e r e u n a b l e to c h e c k w h e t h e r p r e d i c t i o n I w a s s a t i s f i e d for a l l s h a d o w i n g elevation angles, and consequently experi m e n t s w e r e c a r r i e d o u t b y s h a d o w i n g Tlayers at elevation angles greater than 40 °. F o r a l l t h e s p e c i m e n s i n v e s t i g a t e d , t h e u n t i l t e d o b j e c t s s h o w e d s t r o n g contrast. After a tilt in the correct direction t h e c o n t r a s t b e c a m e v e r y low a n d t h e f i n e s t r u c t u r e s e e n on t h e u n t i l t e d s p e c i m e n c o u l d no l o n g e r b e o b s e r v e d . W h a t w a s noticeable, however, was that after tilting, a low s p a t i a l f r e q u e n c y w a v e o f t h e s a m e
SPECIMEN SURFACE RELIEF
periodicity as the T-layer repeat (131 •) was still visible on the specimen, probably due to a nonlinear effect in metal deposit as discussed below. Diffraction analysis, however, indicated that it could only significantly affect the first-order spatial frequencies. The second prediction was checked by comparing diffraction patterns from areas of micrographs of specimens shadowed
127
over a range of elevation and orientation angles (see Kistler et al. (1977), Fig. 2). The general trend was quite clear. At low elevation angles (10°), shadows are clearly cast in parts of the unit cell, and the diffraction pattern shows little evidence of being damped on the line perpendicular to the shadowing direction. At a 60° elevation angle, however, Fourier coefficients on the line perpendicular to the shadowing direc-
FIG. 2. T-layer cylinders shadowed (a) at an elevation angle of 60° and an azimuth of -45 ° and (b) at an elevation angle of 45° and an azimuth of 8°. The scale bar represents 1000 A and the arrows indicate the approximate shadowing direction. The micrographs are printed so that points of high metal accumulation are bright: (a) shows lower contrast t h a n (b) due to the higher elevation angle used when shadowing this specimen; (c) and (d) are diffraction patterns recorded from square regions of (a) and (b), respectively.
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tion are strongly damped, but the strength of the damping depends on the orientation of the shadowing vector with respect to the lattice. Our conclusion is that prediction 2 is fulfilled quite well, but not necessarily for all specimen-shadowing orientations at a given elevation angle. The higher the elevation angle, the lower the image contrast and the larger the range of orientation angles for which prediction 2 seems to be satisfied. It seems desirable therefore to record many micrographs at as low an elevation angle as practicable and to select only those which appear best to satisfy proposition 2. It appears to be very difficult to decide from simple inspection of the micrograph whether shadows have been cast or not.
(b) Reconstruction of the Surface of a Shadowed T-Layer Cylinder Selected areas of two micrographs of Tlayer cylinders shadowed from elevation angles of 60° and 45° and at azimuthal orientations of -45 ° (Fig. 2a) and 8° (Fig. 2b), respectively (diffraction patterns shown in Figs. 2c and d), were digitized, and averaged unit cells (Figs. 3a and b)
were obtained from them computationally as described by Aebi et al. (1973). The vertical metal depth, d (=6 /~), lattice constant (131 A), and respective orientation angles were then substituted into Eq. (4), and phase filters were generated and then applied to the data for each of the two particles. The twofold phase centers of the phase-filtered arrays were found, and surface reliefs were then generated by fourfold averaging the phasefiltered arrays (Section 2b, method (i)). It is important to note that the fourfold averaging step is an integral part of the reconstruction procedure, which partially compensates for the failure of the phase filter to correct the amplitudes. Inspection of Eq. (2) shows that phase filtration followed by fourfold symmetrization yields amplitudes correct to within 35%. Computer tests show that such errors alter the relative elevations of structural features in an image of the T-layer but do not affect their qualitative interpretation. The results of the surface reconstruction are shown in Figs. 4a and 5a and Figs. 4b and 5b. The surface reconstructions from both particles show essentially the same features: pronounced raised regions con-
FIG. 3. (a) and (b) each show 2 × 2 computer-averagedunit cells obtained from the shadowed specimen pictured in Figs. 2a and b, respectively. The contrast is chosen so that dark parts of the image indicate absence of heavy metal deposit. The unit cells are positioned to correspondto the reconstructions shown in Fig. 4.
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129
FIG. 4. (a) and (b) each show 2 × 2 unit cells of the surface reconstructions performed using the data shown in Figs. 3a and b, respectively. Dark regions indicate high elevation. The grey-level representation has been chosen so t h a t elevations in all parts of the u n i t cell can be visualized.
a
b
FIG. 5. (a) and (b) show the projection plots of the elevation data shown in Figs. 4a and b, respectively. The vertical scale is arbitrary.
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SMITH AND KISTLER
taining a central depression Cmajor tetramer") and connected to each other with a double-arm structure with the space between the arms containing another less prominent raised region. Surface reconstructions were also performed using the "exact" reconstruction filter [Eq (3)] as described in Section 2b, method (ii). The results obtained were similar to those for the phase filter, but the double-arm structure was less well defined and the "major tetramer" was much more pronounced.
and with errors in both the heavy metal depth and the shadow orientation being made to correspond to the largest expected values in the real case. The results indicated that the reconstruction procedure was stable against broadband noise contaminating images up to a signal-to-noise (S/N) ratio of 2 in the data and against errors in shadowing azimuthal orientation up to -+5°. Errors in the shadow depth also had little effect, which was to be expected for shadow depths small in relation to the resolution distance. Surprisingly, however, the pres(c) Computational Control Experiments ence of shadows covering up to 25% of the The result of the surface reconstructions unit cell also had little effect. It seems shown above cannot be checked independ- that, as long as the shadows do not comently because the "real" surface structure pletely mask a structural feature, it will of the T-layer is not known. A number of still appear in the final reconstruction control experiments were therefore neces- although its relative elevation will be alsary to determine the sensitivity of the tered. Our conclusion from these computer reconstruction procedure to errors in the parameters it needed and the data to simulation experiments is that the surface reconstruction procedure is stable against which it was applied. Four different errors were considered; noise and errors in the parameters of the errors in the length and direction of the reconstruction filter within the range exheavy metal shadow, the presence of pected for real experiments. Furthermore "shadows" over parts of the unit cell, and the presence of areas of "shadow" in the contamination of the data with random unit cell does not lead to the generation of noise. In addition we compared the "exact" spurious structures; if features are comand the phase filters for surface recon- pletely masked by shadows, they fail to struction. Test data were computer-gener- appear in the reconstruction, but the genated from the image of a negatively eral structure of other contrasted features stained T-layer unit cell by producing a is little affected. difference picture between the image and 4. DISCUSSION itself after an appropriate translation [Eq. (1)]. Approximations to shadows cast over (a) Metal Deposit on the Specimen Surface The model we have proposed in Section the specimen were generated by "floating" this difference picture by different amounts 1 for the deposit of heavy metal onto a [essentially introducing different values specimen specifically requires that the of d in Eq. (1)] and then setting all nega- metal be deposited homogeneously withtive values to zero. Gaussian random num- out migrating, aggregating, or specifically interacting with the specimen. Recent rebers were used as representative noise. The surface reconstructions obtained us- sults (Kistler et al., 1977; Zingsheim, ing both procedures given in Section 2b 1972), however, indicate that all these were then obtained from noise-contami- processes occur to some extent in real nated data containing up to 50% of the shadowing experiments. The observed structure "in shadow" (i.e., areas which granular structure of the micrographs sugwere zeroed and contained no information) gests that, rather than having a smooth
SPECIMEN SURFACE RELIEF
131
aspect, the metal appears to be aggregated resulting in an apparent thickening or into grains on the surface of the specimen. broadening of pronounced surface fi~aEven given the formation of metal tures. All these effects would be expected to grains, the propositions made in Section 2a would be expected to be fulfilled if the work against the model presented in Secnucleation sites have a uniform random tion 1. In particular, the residual 131-Adistribution over the area of the specimen, periodicity wave which is still observed on as viewed from the direction of the inci- the tilted specimens could reasonably be dent metal-ion beam. In this case the explained by point 1 above since the :resimple model given in Section 1 would not gions of high metal accumulation seem to be expected to give a realistic view of have preferentially accumulated addimetal accumulation over areas containing tional material. In general, however, we only one or two unit cells. However, after would expect that these nonlinear effects averaging over 50 to 100 unit cells, the could be limited to some degree by minigranularity should be smoothed away and mizing the amount of metal deposited on the averaged picture should behave as we the specimen, a procedure we have folhave described. lowed in this work. The key to the interpretation of the image is therefore the random distribution (b) The T-Layer Surface Structure of grains over the projected specimen area. A comparison of Figs. 4a and 5a with 4b If decoration (Bassett, 1958)occurs, i.e., if and 5b shows them to be essentially the there are sites on the specimen which same in their gross features: in detail, preferentially nucleate the growth of however, there are small differences. metal grains, then the averaged image These are most noticeable in the structure will no longer correctly reflect the topog- of the arms which appear weaker in Fig. raphy of the specimen surface. We believe 4b than in Fig. 4a. This can be explained that although decoration is likely to occur in part from Fig. 3b where it seems that to some extent it is not a serious problem part of the arm structure is obscured ]by for this specimen surface since the images the major tetramer and therefore not conshow high contrast and no *'highly illumi- trasted by the metal. In Fig. 3a, however, nated" areas independent of shadowing the arms in both lattice directions are orientation can be seen. accessible to the metal, and consequently Besides the possibility of decoration more detailed structural information is there are other effects which would limit transmitted to the reconstruction. the application of our simple shadowing The largest metal-collecting region of model. (1) Growing grains would even- the T-layer surface is clearly the major tually be expected to begin to cast their tetramer, and this contributes strongly to own shadows restricting the deposit of the first-order spatial frequency in the metal on the specimen behind them. (2) transforms of the images in Figs. 2a and The grain size probably determines the 2b. The tilting experiments (Section 3a) resolution since large metal grains are demonstrated, however, that there is a unlikely to be able to contrast fine features nonlinear effect which overemphasizes the of the specimen surface. (3) The size of the overall contrast over the unit cell and grain could alter the apparent position of whose principal contribution is to the firstfeatures, since the center-of-mass of a order spatial frequencies. The surface regrain is unlikely to coincide with its point constructions therefore almost certainly of nucleation. Strongly "illuminated" show the central region of the unit cell to areas (large metal deposits) would be more be much higher than it should be relative affected than weakly "illuminated" ones, to the height of the double arms. This
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SMITH AND KISTLER
effect is much more pronounced in the quite obvious, it is nevertheless difficult reconstructions performed with the exact to bear in mind that the amount of metal surface reconstruction filter [Eq. (3)] deposited on a structural feature is priwhich further enhances the first-order re- marily determined by its slope with reflections. spect to the evaporation source rather than Previous work on T-layer cylinders its elevation. Surface reconstruction, howshowed that they possessed a coarse outer ever, does not eliminate the microscopist's and a relatively smooth inner surface interpretive responsibility, since decora(Kistler et al., 1977). It is therefore reason- tion and other nonlinear effects not considable to expect that the image obtained ered by our shadowing model must be from a negatively stained T-layer will allowed for. Since the deposit of metal grains on the mostly be due to the coarse outer surface. Our surface reconstruction images, when specimen surface is statistical, averaging compared to the images of averaged nega- over a sufficiently large number of identitively stained T-layer unit cells (Aebi et cally shadowed objects is vital if data suital., 1973; Kistler et al., 1977), show a able for surface reconstruction are to be strong similarity to the third-order filtra- obtained. Periodic objects are particularly tions. Since the three-dimensional nega- satisfactory specimens from this point of tive stain distribution is not known, these view since all objects (unit cells) have images unfortunately provide no more been prepared and imaged under identical than a general confirmation of the surface conditions and are regularly arranged in reconstruction result. respect to one another. The most interesting feature of the 5. CONCLUSIONS method is that it has allowed images of This article has presented a new method two specimens of the T-layer shadowed which allows a topographical map to be from different directions and providing generated from the image of a heavy inequivalent representations of similar metal-shadowed specimen and has pre- structural information to be converted, via sented preliminary results from its appli- the surface reconstruction procedure, to a cation to freeze-dried tungsten-shadowed representation where their information T-layer cylinders. The results indicate content can be directly compared. The that consistently good qualitative results shadowing model we have presented, and can be expected if the simple theoretical upon which the results are based, suffers model we have presented in Section 1 is from several inadequacies which so far used as a basis for the surface reconstruc- preclude the reconstruction method from tion of real data. providing quantitative topographical maps We believe that the method is likely to of the specimen surface. We believe that be found to be particularly valuable as an improved understanding of the process an aid in interpreting micrographs of of heavy metal shadowing will lead to a shadowed specimens, even at the qualita- better theoretical model and allow more tive level, because it removes one of the accurate maps to be obtained. Given the interpretation steps which stand between simplicity and general applicability of the microscopist and an understanding of heavy metal shadowing as a specimen the surface structure of the specimen. This preparation technique we feel that work interpretation step is not trivial since the in this direction will be particularly valualtitude of a particular part of the speci- able. men must be inferred from the way in which the whole structure has been ~'illuWe are particularly grateful to Prof. K. S. Ludwig of the Anatomy Department of the University minated." While this is in some respects
SPECIMEN SURFACE RELIEF of Basel for allowing us access to his EM301 with its goniometer stage. We would like to thank Dr. A. Engel for discussions which helped us to formulate the shadowing model and Dr. U. Aebi for his critical reading of the manuscript. The EDV-Department of F. Hoffmann-La Roche Ltd. provided our computing facilities; without their help the work could not have been completed. This work was supported in part by the Swiss National Science Foundation through Grant No. 3.433.74 to PRS. REFERENCES ABERMANN, R., SALPETER, M. M., AND BACHMANN, L. (1972) in HAYAT, M. A. (Ed.), Principles and Techniques of Electron Microscopy, Vol. 2, pp. 197-217, Van Nostrand Reinhold, New York.
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AEBI, U., SMITH,P. R., DUBOCHET, J., HENRY, C., AND KELLENBERGER, E. (1973) J. Supramol. Struct. 1, 498. AEBI, U., BIJLENGA, R. K. L., TEN HEGGELER, B., KISTLER, J., STEVEN, A., AND SMITH, P. R. (1976) J. Suprarnol. Struct. 5, 475. BASSETT, G. A. (1958)Phil. Mag. 3, 1042. HENDERSON, a., AND UNWIN, P. N. W. (1975) Nature (London) 257, 28. HENRY, C. M. (1972) DisH. Abstr. Inst. 33, 73-2878, 4409-B. KISTLER, J., AEBI, V., AND KELLENBERGER,E. (1977) J. Ultrastruct. Res. 59, 76. MooR, M. (1959)J. Ultrastruct. Res. 2, 393. REIMER, L., AND SCHULTE, Ch. (1966) Naturwissenschaflen 53, 489. ZINGSHEIM, H. P. (1972) Biochim. Biophys. Acta 265, 339.
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Surface Reliefs Computed from Micrographs of Heavy MetalShadowed Specimens P. R. SMITH AND J. KISTLER Department of Microbiology, Biozentrum der Universit~it Basel, Klingelbergstrasse 70, CH-4056, Basel, Switzerland Received July 6, 1977 A method has been developed which allows a topographical map of a specimen surface to be computed from a digitized micrograph of a heavy metal-shadowed specimen. Preliminary results from the application of the method to micrographs of tungsten-shadowed freeze-dried T-layers (Kistler, J., Aebi, U., and Kellenberger, E. (1977) J. Ultrastruct. Res. 59, 76) show t h a t qualitatively consistent results for the T-layer surface structure can be obtained from specimens shadowed from different directions. The method and its drawbacks are discussed with regard to the known difficulties in interpretation of the heavy metal deposit on a specimen surface.
Surface structural information about a biological object is usually obtained by the method of heavy metal shadowing of a suitably prepared specimen or replica made from it (Aberman et al., 1972). Unfortunately a micrograph of a shadowed specimen provides only indirect information about the topography of the specimen surface. In general, the microscopist infers the surface structure by analogy to a macroscopic surface obliquely illuminated with light. On observation from above, the "brightest" parts of the structure are those parts of the surface inclined nearperpendicular to the illuminating beam, those less bright areas being inclined more nearly parallel to the illumination. Parts of the structure in the shadow of elevated parts of the surface cannot be observed; however, if a shadow is cast onto a flat area, then the outline of the ridge or protuberance on the specimen which casts the shadow can often be inferred. The absolute specimen surface topography can, in principle, be obtained by applying three-dimensional reconstruction methods to projection data from tilted views of the specimen (Henderson and Unwin, 1975). The method is sophisticated, however, and demands a combination of microscopical and computational expertise not generally
available in most laboratories, even if relatively modest resolution is required. The method of metal shadowing is simple to apply and the facilities for performing it are usually available to the microscopist. Consequently it is useful to have a method which would allow information from a micrograph of a shadowed specimen to be simply converted into a topographical ~map" from which specimen surface '~elevations" could be read directly. The purpose of this paper is to propose a method for performing such surface reconstructions and to present preliminary results on its application to data obtained from freeze-dried tungsten-shadowed Tlayer cylinders (Aebi et al., 1973; Henry, 1972; Kistler et al., 1977). The following section describes a model for the accumulation of heavy metal on the specimen and shows that if this model is valid, simple image processing allows a topographical surface map of the specimen to be calculated. Successive sections present the experimental method and the results obtained in a test case. The final section discusses the results in view of the known drawbacks of the shadowing model. 1. THEORY
In order to be able to calculate the 124
Copyright © 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0022-5320
125
SPECIMEN SURFACE RELIEF
surface elevation map from an electron micrograph of a shadowed specimen, it is first necessary to have a model for the accumulation of heavy metal on the exposed specimen surface. The model we have chosen is the simplest available (Moor, 1959); that is, that heavy metal accumulates on the specimen so that the thickness of metal deposit along the line of the incident metal-ion beam is constant over the whole specimen (see Fig. 1). For the purpose of this preliminary description we will assume that the metal deposits itself uniformly onto the specimen surface without diffusing or aggregating. This model allows us to calculate the thickness of a metal deposit as seen in vertical projection. Let d be the vertical thickness of metal deposited on a horizontal fiat surface. From Fig. 1 it can be seen that the thickness of metal deposit, t, at the point denoted vectorially by r in the plane of the specimen, will be:
our model, heavy metal piles up along lines parallel to the incident metal beam (Fig. 1) over every point on the surface of the specimen. The expression given for t(r) will therefore only hold in regions where the whole surface of the specimen is accessible to the metal beam. If the object being studied is periodic and the metal deposit thickness is given by the equation above everywhere in the unit cell, then by Fourier transforming both sides of Eq. (1) we get: T(R) = ~ (R).d -
Z(R)
. (1 -
(2) exp (-2~riR.a)),
where T(R) is the Fourier transform of t(r), Z(R) is the transform ofz(r), and ~ is the Dirac delta function. Z(R) can be reconstructed from T(R) exactly, in the absence of noise, at all points R for which (1-exp(-2~iR.a)) is nonzero, by simply multiplying T(R) by the filter function F(R) = -(1 - exp(- 2~riR.a)) -1, (3)
t(r) = z(r - a) + d - z(r),
(1)
where z (r) is the height of the specimen at r and z(r - a) is the height of the specimen at the point (r - a); a is the projection of the line lying in the direction of the beam whose length is (d/tan 0), where 0 is the shadowing elevation angle. According to
::i
cidenf heovymetedbeom k~ d eQvyreefG[ deposit~
Specimln i~ FIG. i. A diagrammatic representation of the model for the deposit of heavy metal onto a specimen surface. Seen from the direction of the incident metal beam the metal appears to have the same depth over the whole specimen. Viewed in vertical projection, the metal thickness at a point is determined by the difference between the altitudes of the specimen and of the upper surface of the metal, which depends upon the amount of metal accumulated on an adjacent part of the specimen surface (see also Moor (1959), Fig. la).
called the "exact" surface reconstruction filter. The Fourier transform, T(R), should vanish along the line (R. a) = 0, since the metal shadow cannot detect ridges parallel to the incident beam direction. If the specimen has N-fold rotational symmetry with N > 2, then two estimates are always available for each Fourier coefficient, Z (R), and in this case z (r) can be reconstructed everywhere from a single micrograph. The filter function F(R) has two actions. First, it alters the phases of the Fourier coefficients, T (R), so that they once again refer to the phase origin of the surface relief; and second, the amplitudes of T(R) are changed to restore their relative magnitudes. Since the restoration of the relative positions of structural features is the most important action of the reconstruction procedure we define a phase-filter function, P(R) = F ( R ) / I F ( R ) t ,
(4)
which makes only these alterations. As
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p o i n t e d o u t b e l o w t h e c o r r e c t i o n of t h e amplitudes as well may exaggerate errors s i n c e t h e a m p l i t u d e s a p p e a r to d e p e n d m o r e c r i t i c a l l y on t h e d e t a i l s o f t h e s h a d o w i n g m o d e l . T h e r e c o n s t r u c t i o n obtained using P(R) rather than F(R) would b e e x p e c t e d to r e s e m b l e t h e s u r f a c e r e l i e f , placing structural features in their correct l o c a t i o n s b u t d i s t o r t i n g t h e i r r e l a t i v e elevations. 2. MATERIALS AND METHODS
(a) Specimen Preparation and Electron Microscopy The micrographs used in this work were drawn from the collection of micrographs of tungstenshadowed freeze-dried T-layer cylinders obtained by J. Kistler for the work described in the report of Kistler et al. (1977). The micrographs of tilted specimens were obtained using a Philips EM301 equipped with a goniometer stage capable of tilts of _+50°"
(b) Image Processing Micrographs of the T layer shadowed at elevation angles of 60° and 45° showing smooth structure and without obvious shadows were selected for processing. Their diffraction patterns were checked to ensure that the spots perpendicular to the shadowing direction either vanished or were not significantly above the noise level. Selected micrographs were enlarged onto film, densitometered, and computerfiltered as described by Aebi et al. (1973) to produce averaged unit cells of 24 × 24 sample points. The Fourier coefficients of the transform of the averaged unit cells were then multiplied by the inverse phase-filter function [Eq. (4)]. The action of this filter was to place the structural features in their correct places within the unit cell so that its symmetry center could be found. The unit-cell center was then located by searching for the point giving the best twofold least-squares residual. Reconstructions of the surface were then performed in the following two ways. (i) The phase-filtered unit cell was fourfold averaged about its twofold center. (ii) Data from the averaged unit cell was filtered using the full surface-reconstruction filter [Eq. (3), which corrects both phases and amplitudes] and then fourfold symmetrized about the previously located center. Reverse Fourier transformation applied to data processed by either of the two methods set out above should represent different approximations to the topographical map of the T-layer surface. The recon-
structions were output as projection plots making it easier to visualize the result as indicating the relative ~heights" of the specimen surface over some arbitrary zero level. Photographic output of both the averaged images of the shadowed unit cells and the surface reconstructions made from them was obtained using the method described by Aebi et al. (1976). The output device, an Optronics Photomation (P1700), was made available through the generosity of the Photography Department of the Federal Institute of Technology, Zfirich. 3. RESULTS
(a) Testing the Model for Heavy Metal Deposit T h e d e p o s i t o f h e a v y m e t a l o n t o a specim e n is a c o m p l e x p r o c e s s ( R e i m e r a n d S c h u l t e , 1966; Z i n g s h e i m , 1972), a n d t h e s i m p l e m o d e l for m e t a l d e p o s i t s e t o u t i n S e c t i o n 1 does n o t p r o v i d e a c o m p l e t e des c r i p t i o n o f it. T h e t h e o r y d o e s m a k e t w o specific p r e d i c t i o n s , h o w e v e r , a n d it is p o s s i b l e to t e s t t h e m to s e e h o w w e l l t h e s e a s p e c t s of t h e m o d e l a r e f u l f i l l e d . T h e p r e d i c t i o n s a r e a s follows: (1) A heavy metal-shadowed specimen should appear structureless when viewed in the m i c r o s c o p e so t h a t t h e e l e c t r o n b e a m is p a r a l l e l to t h e d i r e c t i o n of t h e h e a v y m e t a l - s h a d o w i n g b e a m . (2) I f t h e w h o l e specimen surface was directly accessible to t h e h e a v y m e t a l - s h a d o w i n g b e a m , t h e Fourier transform (and diffraction patt e r n ) s h o u l d s h o w a zero l i n e p e r p e n d i c u l a r to t h e s h a d o w i n g d i r e c t i o n . D u e to t h e f a c t t h a t o u r g o n i o m e t e r s t a g e for t h e m i c r o s c o p e a l l o w e d o n l y _ 5 0 ° t i l t s , w e w e r e u n a b l e to c h e c k w h e t h e r p r e d i c t i o n I w a s s a t i s f i e d for a l l s h a d o w i n g elevation angles, and consequently experi m e n t s w e r e c a r r i e d o u t b y s h a d o w i n g Tlayers at elevation angles greater than 40 °. F o r a l l t h e s p e c i m e n s i n v e s t i g a t e d , t h e u n t i l t e d o b j e c t s s h o w e d s t r o n g contrast. After a tilt in the correct direction t h e c o n t r a s t b e c a m e v e r y low a n d t h e f i n e s t r u c t u r e s e e n on t h e u n t i l t e d s p e c i m e n c o u l d no l o n g e r b e o b s e r v e d . W h a t w a s noticeable, however, was that after tilting, a low s p a t i a l f r e q u e n c y w a v e o f t h e s a m e
SPECIMEN SURFACE RELIEF
periodicity as the T-layer repeat (131 •) was still visible on the specimen, probably due to a nonlinear effect in metal deposit as discussed below. Diffraction analysis, however, indicated that it could only significantly affect the first-order spatial frequencies. The second prediction was checked by comparing diffraction patterns from areas of micrographs of specimens shadowed
127
over a range of elevation and orientation angles (see Kistler et al. (1977), Fig. 2). The general trend was quite clear. At low elevation angles (10°), shadows are clearly cast in parts of the unit cell, and the diffraction pattern shows little evidence of being damped on the line perpendicular to the shadowing direction. At a 60° elevation angle, however, Fourier coefficients on the line perpendicular to the shadowing direc-
FIG. 2. T-layer cylinders shadowed (a) at an elevation angle of 60° and an azimuth of -45 ° and (b) at an elevation angle of 45° and an azimuth of 8°. The scale bar represents 1000 A and the arrows indicate the approximate shadowing direction. The micrographs are printed so that points of high metal accumulation are bright: (a) shows lower contrast t h a n (b) due to the higher elevation angle used when shadowing this specimen; (c) and (d) are diffraction patterns recorded from square regions of (a) and (b), respectively.
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tion are strongly damped, but the strength of the damping depends on the orientation of the shadowing vector with respect to the lattice. Our conclusion is that prediction 2 is fulfilled quite well, but not necessarily for all specimen-shadowing orientations at a given elevation angle. The higher the elevation angle, the lower the image contrast and the larger the range of orientation angles for which prediction 2 seems to be satisfied. It seems desirable therefore to record many micrographs at as low an elevation angle as practicable and to select only those which appear best to satisfy proposition 2. It appears to be very difficult to decide from simple inspection of the micrograph whether shadows have been cast or not.
(b) Reconstruction of the Surface of a Shadowed T-Layer Cylinder Selected areas of two micrographs of Tlayer cylinders shadowed from elevation angles of 60° and 45° and at azimuthal orientations of -45 ° (Fig. 2a) and 8° (Fig. 2b), respectively (diffraction patterns shown in Figs. 2c and d), were digitized, and averaged unit cells (Figs. 3a and b)
were obtained from them computationally as described by Aebi et al. (1973). The vertical metal depth, d (=6 /~), lattice constant (131 A), and respective orientation angles were then substituted into Eq. (4), and phase filters were generated and then applied to the data for each of the two particles. The twofold phase centers of the phase-filtered arrays were found, and surface reliefs were then generated by fourfold averaging the phasefiltered arrays (Section 2b, method (i)). It is important to note that the fourfold averaging step is an integral part of the reconstruction procedure, which partially compensates for the failure of the phase filter to correct the amplitudes. Inspection of Eq. (2) shows that phase filtration followed by fourfold symmetrization yields amplitudes correct to within 35%. Computer tests show that such errors alter the relative elevations of structural features in an image of the T-layer but do not affect their qualitative interpretation. The results of the surface reconstruction are shown in Figs. 4a and 5a and Figs. 4b and 5b. The surface reconstructions from both particles show essentially the same features: pronounced raised regions con-
FIG. 3. (a) and (b) each show 2 × 2 computer-averagedunit cells obtained from the shadowed specimen pictured in Figs. 2a and b, respectively. The contrast is chosen so that dark parts of the image indicate absence of heavy metal deposit. The unit cells are positioned to correspondto the reconstructions shown in Fig. 4.
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129
FIG. 4. (a) and (b) each show 2 × 2 unit cells of the surface reconstructions performed using the data shown in Figs. 3a and b, respectively. Dark regions indicate high elevation. The grey-level representation has been chosen so t h a t elevations in all parts of the u n i t cell can be visualized.
a
b
FIG. 5. (a) and (b) show the projection plots of the elevation data shown in Figs. 4a and b, respectively. The vertical scale is arbitrary.
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SMITH AND KISTLER
taining a central depression Cmajor tetramer") and connected to each other with a double-arm structure with the space between the arms containing another less prominent raised region. Surface reconstructions were also performed using the "exact" reconstruction filter [Eq (3)] as described in Section 2b, method (ii). The results obtained were similar to those for the phase filter, but the double-arm structure was less well defined and the "major tetramer" was much more pronounced.
and with errors in both the heavy metal depth and the shadow orientation being made to correspond to the largest expected values in the real case. The results indicated that the reconstruction procedure was stable against broadband noise contaminating images up to a signal-to-noise (S/N) ratio of 2 in the data and against errors in shadowing azimuthal orientation up to -+5°. Errors in the shadow depth also had little effect, which was to be expected for shadow depths small in relation to the resolution distance. Surprisingly, however, the pres(c) Computational Control Experiments ence of shadows covering up to 25% of the The result of the surface reconstructions unit cell also had little effect. It seems shown above cannot be checked independ- that, as long as the shadows do not comently because the "real" surface structure pletely mask a structural feature, it will of the T-layer is not known. A number of still appear in the final reconstruction control experiments were therefore neces- although its relative elevation will be alsary to determine the sensitivity of the tered. Our conclusion from these computer reconstruction procedure to errors in the parameters it needed and the data to simulation experiments is that the surface reconstruction procedure is stable against which it was applied. Four different errors were considered; noise and errors in the parameters of the errors in the length and direction of the reconstruction filter within the range exheavy metal shadow, the presence of pected for real experiments. Furthermore "shadows" over parts of the unit cell, and the presence of areas of "shadow" in the contamination of the data with random unit cell does not lead to the generation of noise. In addition we compared the "exact" spurious structures; if features are comand the phase filters for surface recon- pletely masked by shadows, they fail to struction. Test data were computer-gener- appear in the reconstruction, but the genated from the image of a negatively eral structure of other contrasted features stained T-layer unit cell by producing a is little affected. difference picture between the image and 4. DISCUSSION itself after an appropriate translation [Eq. (1)]. Approximations to shadows cast over (a) Metal Deposit on the Specimen Surface The model we have proposed in Section the specimen were generated by "floating" this difference picture by different amounts 1 for the deposit of heavy metal onto a [essentially introducing different values specimen specifically requires that the of d in Eq. (1)] and then setting all nega- metal be deposited homogeneously withtive values to zero. Gaussian random num- out migrating, aggregating, or specifically interacting with the specimen. Recent rebers were used as representative noise. The surface reconstructions obtained us- sults (Kistler et al., 1977; Zingsheim, ing both procedures given in Section 2b 1972), however, indicate that all these were then obtained from noise-contami- processes occur to some extent in real nated data containing up to 50% of the shadowing experiments. The observed structure "in shadow" (i.e., areas which granular structure of the micrographs sugwere zeroed and contained no information) gests that, rather than having a smooth
SPECIMEN SURFACE RELIEF
131
aspect, the metal appears to be aggregated resulting in an apparent thickening or into grains on the surface of the specimen. broadening of pronounced surface fi~aEven given the formation of metal tures. All these effects would be expected to grains, the propositions made in Section 2a would be expected to be fulfilled if the work against the model presented in Secnucleation sites have a uniform random tion 1. In particular, the residual 131-Adistribution over the area of the specimen, periodicity wave which is still observed on as viewed from the direction of the inci- the tilted specimens could reasonably be dent metal-ion beam. In this case the explained by point 1 above since the :resimple model given in Section 1 would not gions of high metal accumulation seem to be expected to give a realistic view of have preferentially accumulated addimetal accumulation over areas containing tional material. In general, however, we only one or two unit cells. However, after would expect that these nonlinear effects averaging over 50 to 100 unit cells, the could be limited to some degree by minigranularity should be smoothed away and mizing the amount of metal deposited on the averaged picture should behave as we the specimen, a procedure we have folhave described. lowed in this work. The key to the interpretation of the image is therefore the random distribution (b) The T-Layer Surface Structure of grains over the projected specimen area. A comparison of Figs. 4a and 5a with 4b If decoration (Bassett, 1958)occurs, i.e., if and 5b shows them to be essentially the there are sites on the specimen which same in their gross features: in detail, preferentially nucleate the growth of however, there are small differences. metal grains, then the averaged image These are most noticeable in the structure will no longer correctly reflect the topog- of the arms which appear weaker in Fig. raphy of the specimen surface. We believe 4b than in Fig. 4a. This can be explained that although decoration is likely to occur in part from Fig. 3b where it seems that to some extent it is not a serious problem part of the arm structure is obscured ]by for this specimen surface since the images the major tetramer and therefore not conshow high contrast and no *'highly illumi- trasted by the metal. In Fig. 3a, however, nated" areas independent of shadowing the arms in both lattice directions are orientation can be seen. accessible to the metal, and consequently Besides the possibility of decoration more detailed structural information is there are other effects which would limit transmitted to the reconstruction. the application of our simple shadowing The largest metal-collecting region of model. (1) Growing grains would even- the T-layer surface is clearly the major tually be expected to begin to cast their tetramer, and this contributes strongly to own shadows restricting the deposit of the first-order spatial frequency in the metal on the specimen behind them. (2) transforms of the images in Figs. 2a and The grain size probably determines the 2b. The tilting experiments (Section 3a) resolution since large metal grains are demonstrated, however, that there is a unlikely to be able to contrast fine features nonlinear effect which overemphasizes the of the specimen surface. (3) The size of the overall contrast over the unit cell and grain could alter the apparent position of whose principal contribution is to the firstfeatures, since the center-of-mass of a order spatial frequencies. The surface regrain is unlikely to coincide with its point constructions therefore almost certainly of nucleation. Strongly "illuminated" show the central region of the unit cell to areas (large metal deposits) would be more be much higher than it should be relative affected than weakly "illuminated" ones, to the height of the double arms. This
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effect is much more pronounced in the quite obvious, it is nevertheless difficult reconstructions performed with the exact to bear in mind that the amount of metal surface reconstruction filter [Eq. (3)] deposited on a structural feature is priwhich further enhances the first-order re- marily determined by its slope with reflections. spect to the evaporation source rather than Previous work on T-layer cylinders its elevation. Surface reconstruction, howshowed that they possessed a coarse outer ever, does not eliminate the microscopist's and a relatively smooth inner surface interpretive responsibility, since decora(Kistler et al., 1977). It is therefore reason- tion and other nonlinear effects not considable to expect that the image obtained ered by our shadowing model must be from a negatively stained T-layer will allowed for. Since the deposit of metal grains on the mostly be due to the coarse outer surface. Our surface reconstruction images, when specimen surface is statistical, averaging compared to the images of averaged nega- over a sufficiently large number of identitively stained T-layer unit cells (Aebi et cally shadowed objects is vital if data suital., 1973; Kistler et al., 1977), show a able for surface reconstruction are to be strong similarity to the third-order filtra- obtained. Periodic objects are particularly tions. Since the three-dimensional nega- satisfactory specimens from this point of tive stain distribution is not known, these view since all objects (unit cells) have images unfortunately provide no more been prepared and imaged under identical than a general confirmation of the surface conditions and are regularly arranged in reconstruction result. respect to one another. The most interesting feature of the 5. CONCLUSIONS method is that it has allowed images of This article has presented a new method two specimens of the T-layer shadowed which allows a topographical map to be from different directions and providing generated from the image of a heavy inequivalent representations of similar metal-shadowed specimen and has pre- structural information to be converted, via sented preliminary results from its appli- the surface reconstruction procedure, to a cation to freeze-dried tungsten-shadowed representation where their information T-layer cylinders. The results indicate content can be directly compared. The that consistently good qualitative results shadowing model we have presented, and can be expected if the simple theoretical upon which the results are based, suffers model we have presented in Section 1 is from several inadequacies which so far used as a basis for the surface reconstruc- preclude the reconstruction method from tion of real data. providing quantitative topographical maps We believe that the method is likely to of the specimen surface. We believe that be found to be particularly valuable as an improved understanding of the process an aid in interpreting micrographs of of heavy metal shadowing will lead to a shadowed specimens, even at the qualita- better theoretical model and allow more tive level, because it removes one of the accurate maps to be obtained. Given the interpretation steps which stand between simplicity and general applicability of the microscopist and an understanding of heavy metal shadowing as a specimen the surface structure of the specimen. This preparation technique we feel that work interpretation step is not trivial since the in this direction will be particularly valualtitude of a particular part of the speci- able. men must be inferred from the way in which the whole structure has been ~'illuWe are particularly grateful to Prof. K. S. Ludwig of the Anatomy Department of the University minated." While this is in some respects
SPECIMEN SURFACE RELIEF of Basel for allowing us access to his EM301 with its goniometer stage. We would like to thank Dr. A. Engel for discussions which helped us to formulate the shadowing model and Dr. U. Aebi for his critical reading of the manuscript. The EDV-Department of F. Hoffmann-La Roche Ltd. provided our computing facilities; without their help the work could not have been completed. This work was supported in part by the Swiss National Science Foundation through Grant No. 3.433.74 to PRS. REFERENCES ABERMANN, R., SALPETER, M. M., AND BACHMANN, L. (1972) in HAYAT, M. A. (Ed.), Principles and Techniques of Electron Microscopy, Vol. 2, pp. 197-217, Van Nostrand Reinhold, New York.
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AEBI, U., SMITH,P. R., DUBOCHET, J., HENRY, C., AND KELLENBERGER, E. (1973) J. Supramol. Struct. 1, 498. AEBI, U., BIJLENGA, R. K. L., TEN HEGGELER, B., KISTLER, J., STEVEN, A., AND SMITH, P. R. (1976) J. Suprarnol. Struct. 5, 475. BASSETT, G. A. (1958)Phil. Mag. 3, 1042. HENDERSON, a., AND UNWIN, P. N. W. (1975) Nature (London) 257, 28. HENRY, C. M. (1972) DisH. Abstr. Inst. 33, 73-2878, 4409-B. KISTLER, J., AEBI, V., AND KELLENBERGER,E. (1977) J. Ultrastruct. Res. 59, 76. MooR, M. (1959)J. Ultrastruct. Res. 2, 393. REIMER, L., AND SCHULTE, Ch. (1966) Naturwissenschaflen 53, 489. ZINGSHEIM, H. P. (1972) Biochim. Biophys. Acta 265, 339.
