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

Подождите немного. Документ загружается.

828 S.W. Hell and A. Schönle

these states are longer than 10 ns such proteins may permit much larger

saturation factors than those used in STED microscopy today. The most

attractive solution, however, involves ﬂ uorescent proteins that can be

“switched on and off” at different wavelengths (Hell et al., 2003). An

example is as FP595 (Lukyanov et al., 2000), insertion of the published

data into Eq. (27) predicts saturated depletion of the ﬂ uorescence state

with intensities of less than a few W/cm

and, under favorable switch-

ing conditions, spatial resolutions of better than 10 nm.

The involved

intensities should also enable parallelization of saturation through an

array of minima or dark lines.

Initial realization of very low-intensity depletion microscopes may

be challenged by switching fatigue (Irie et al., 2002) and overlapping

action spectra (Lukyanov et al., 2000). Nevertheless, the prospect of

attaining nanoscale resolution with regular lenses and focused light is

an incentive to surmount these challenges by strategic ﬂ uorophore

modiﬁ cation (Hell et al., 2003) and this or similar types of ﬂ uorescent

proteins are a good starting point for these efforts.

5 Conclusion

The coherent use of opposing lenses enables the axial resolution of a

far-ﬁ eld microscope to be improved by a factor of 3–7. The improvement

in resolution occurs if the spherical wavefronts of illumination are coher-

ently added at the focus, or the emerging spherical wavefronts of ﬂ uo-

rescence are coherently added at the detector, because in both cases the

total aperture of the system is enlarged. The latter fact is the basic tenet

of the concept of 4Pi microscopy. The mere implementation of interfer-

ence of low aperture (or ﬂ at) wavefronts is insufﬁ cient, because the “4Pi

concept” of aperture increase is the underlying physical element of the

improvement in resolution. Consequently, the success of increasing the

axial resolution by two opposing lenses fully relies on large aperture

angles and on the degree to which the aperture angle is utilized in the

particular implementation.

Adding the spherical wavefronts both for illumination and detec-

tion, (multiphoton) 4Pi confocal microscopy of type C utilizes the

lenses’ aperture as much as possible. As a result, this imaging mode

features a contiguous and weakly modulated effective OTF that is

robust enough for live cell imaging in an aqueous environment. On the

other hand, I

M uses a mutually incoherent set of ﬂ at standing waves

with varying spatial frequency for illumination. To be viable, I

M adds

the spherical wavefronts of ﬂ uorescence emission at the detector; in

other words, it uses a 4Pi scheme for detection. The compromise in the

illumination path with regard to the “4Pi concept” bestows the OTF of

the I

M with internal regions of very weak frequency transfer. The I

is therefore more prone to artifacts and probably not reliably applicable

in live cells.

With the 4Pi idea as the key physical element in the process, it is not

surprising that both 4Pi microscopy and I

M would beneﬁ t from lenses

with higher semiaperture angles than those currently available. An

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 829

increase of the semiaperture angle even by only a few degrees would

make a large difference in I

M. This difference would be even more

decisive than in 4Pi microscopy, which already exploits the available

aperture to the highest possible degree.

Although 4Pi microscopy has demonstrated a 3D resolution in the

100 n m range following deconvolution, the method is still limited by

diffraction. The latter is no lo nge r t he ca s e w it h the emerging approaches

exploiting a reversible saturable transition between two states of a

marker, which we termed RESOLFT. In a microscope using the

RESOLFT principle, the resolution is no longer limited by diffraction

but by the attainable level of saturation of a (linear) optical transition

in the marker molecule. Therefore the “hard” theoretical resolution

barrier is replaced by a “soft” barrier determined solely by practical

conditions such as available laser power, cross sections, and the stabil-

ity of the dye and the sample. The enhanced resolution has already been

demonstrated (Hänninen, 2002) in a number of imaging experiments.

It is important to realize that while an effectively nonlinear interac-

tion between light and dye is the basis for this resolution increase, these

methods do not require transitions involving more than one photon at

a time, such as m-photon excitation, mth harmonics generation, or coher-

ent anti-Stokes–Raman scattering (Sheppard and Kompfner, 1978; Shen,

1984). This means that the required intensities are not determined by

the very small cross sections of these processes and the requirement for

ultrahigh (peak) intensities. By contrast, the saturation of a linear optical

transition depends on the basic kinetics of the population of the involved

states. Consequently, pulse-length requirements are less strict and, most

importantly, the required intensities can be signiﬁ cantly reduced by

choosing appropriate spectroscopic systems.

To date STED microscopy is the most advanced implementation of

the RESOLFT principle. It has been well characterized by its applica-

tion to single ﬂ uorescent molecules and has been applied to imaging

ﬁ xed and live, albeit simple biological specimens. Improvements in

resolution by a factor of up to eight have already been demonstrated

and the resulting ﬂ uorescent volumes are the smallest that have ever

been created with focused light. The results hitherto obtained with

STED must not be considered as a new limit but as proof of the viability

of the concept of RESOLFT and STED microscopy in particular. Because

this method is very young, future research on spectroscopy conditions

and on practical aspects (Stephens and Allen, 2003) should lead to

further improvements.

Nevertheless, due to the rather fast relaxation of the excited state

STED requires intensities of the order of at least several tens of MW/

. Hence, there will be a practical limit to the applicable intensity and

to the saturation level attainable under practical conditions. Intrigu-

ingly, the intensities required for obtaining a high saturation level can

be fundamentally lowered in other implementations of the RESOLFT

concept. This is particularly true when utilizing optically bistable

markers, such as photoswitchable dyes and photochromic ﬂ uorescent

proteins. Both are very promising candidates for providing high levels

of saturation at ultralow intensities of light (Hell et al., 2003). In fact, we

830 S.W. Hell and A. Schönle

expect them to play an important role in translating nanoscale resolu-

tion into the noninvasive, all-optical imaging of live cells. Dedicated

synthesis or protein engineering might eventually uncover a whole new

range of suitable markers.

Light microcopy is still commonly portrayed as fundamentally reso-

lution limited. However, about a decade ago, concepts emerged that

broke the diffraction barrier postulated by Abbe in 1873. These devel-

opments are poised to radically extend the ﬁ eld of application for far-

ﬁ eld light microscopy and eventually lead to far-ﬁ eld “nanoscopes”

operating with regular lenses and visible light.

Acknowledgments. The authors thank all mem bers of the Department

of NanoBiophotonics for contributions to this work and valuable dis-

cussions. Much of the results described in this chapter have been

adopted from original work with signiﬁ cant contributions by A. Egner,

M. Nagorni (4Pi), M. Dyba, V. Westphal, B. Harke, and J. Keller (STED).

We thank J. Jethwa, J. Bewersdorf, and G. Donnert for valuable discus-

sions and critical reading of the manuscript.

References

Abbe, E. (1873). Beiträge zur Theorie des Mikroskops und der mikroskopischen

Wahrnehmung. Arch. Mikr. Anat. 9, 413–420.

Albrecht, B., Failla, A.V., Schweizer, A. and Cremer, C. (2002). Spatially modu-

lated illumination microscopy allows axial distance resolution in the nano-

meter range. Appl. Opt. 41(1), 80–87.

Bahlmann, K. and Hell, S.W. (2000). Polarization effects in 4Pi confocal micros-

Bahlmann, K., Jakobs, S. and Hell, S.W. (2001). 4Pi-confocal microscopy of liver

366, 44–48.

ﬂ uorescence confocal microscopy. J. Microsc. 157, 3–20.

Bloembergen, N. (1965). Nonlinear Optics. (Benjamin, New York).

Born, M. and Wolf, E. (1993). Principles of Optics, 6th ed. (Pergamon Press,

Oxford).

Carrington, W.A., Lynch, R.M., Moore, E.D.W., Isenberg, G., Fogarty, K.E. and

Fay, F.S. (1995). Superresolution in three-dimensional images of ﬂ uores-

cence in cells with minimal light exposure. Science 268, 1483–1487.

Denk, W., Strickler, J.H. and Webb, W.W. (1990). Two-photon laser scanning

ﬂ uorescence microscopy. Science 248, 73–76.

Bonifacino, J.S., Davidson, M.W., Lippincott-Schwartz, J. and Hess, H.F.

(2006). Imaging intracellular fluorescent proteins at nanometre resolution.

copy studied with water-immersion lenses. Appl. Opt. 39(10), 1653–1658.

Science 313, 1642–1645.

unknown phase difference in 4Pi-confocal microscopy through the image

218103.

intensity. Opt. Commun. 206, 281–285.

Bertero, M., Boccacci, P., Brakenhoff, G.J., Malfanti, F. and Van der Voort, H.

barrier in fluorescence microscopy by optical shelving. Phys. Rev. Lett. 98,

T.M. (1990). Three-dimensional image restoration and super-resolution in

cells. Ultramicroscopy 87, 155–164.

resolution in ﬂ uorescence microscopy by standing-wave excitation. Nature

*Betzig, E., Patterson, G.H., Sougrat, R., Lindwasser, O.W., Olenych, S.,

Bailey, B., Farkas, D.L., Taylor, D.L. and Lanni, F. (1993). Enhancement of axial

*Bretschneider, S., Eggeling, C. and Hell, S.W. (2007). Breaking the diffraction

Blanca, C.M., Bewersdorf, J. and Hell, S.W. (2002). Determination of the

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 831

microscope reveals structural plasticity of mitochondria in live yeast. Proc.

Natl. Acad. Sci. USA 99, 3370–3375.

Eigen, M. and Rigler, R. (1994). Sorting single molecules: Applications to diag-

nostics and evolutionary biotechnology. Proc. Natl. Acad. Sci. USA 91,

5740–5747.

Elson, E.L. and Rigler, R. Eds. (2001). Fluorescence Correlation Spectroscopy.

Theory and Applications. (Springer, Berlin).

Failla, A.V., Spoeri, U., Albrecht, B., Kroll, A. and Cremer, C. (2002). Nanosiz-

ing of ﬂ uorescent objects by spatially modulated illumination microscopy.

Appl. Opt. 41(34), 7275–7283.

Freimann, R., Pentz, S. and Hörler, H. (1997). Development of a standing-wave

ﬂ uorescence microscope with high nodal plane ﬂ atness. J. Microsc. 187(3),

193–200.

Göpper-Mayer, M. (1931). Über Elementarakte mit zwei Quantensprüngen.

Ann. Phys. (Leipzig) 9, 273–295.

Goodman, J.W. (1968). Introduction to Fourier Optics. (McGraw-Hill, New

York).

Gugel, H., Bewersdorf, J., Jakobs, S., Engelhardt, J., Storz, R. and Hell, S.W.

(2004). Cooperative 4Pi excitation and detection yields 7-fold sharper optical

sections in live cell microscopy. Biophys. J. 87, 4146–4152.

Gustafsson, M.G., Agard, D.A. and Sedat, J.W. (1996). 3D wideﬁ eld microscopy

with two objective lenses: Experimental veriﬁ cation of improved axial reso-

lution. In: Three-Dimensional Microscopy: Image Acquisition and Processing III.

Proc. SPIE.

Gustafsson, M.G.L. (1999). Extended resolution ﬂ uorescence microscopy. Curr.

Opin. Struct. Biol. 9, 627–634.

Gustafsson, M.G.L. (2000). Surpassing the lateral resolution limit by a factor of

two using structured illumination microscopy. J. Microsc. 198(2), 82–87.

Gustafsson, M.G.L., Agard, D.A. and Sedat, J.W. (1995). Sevenfold improve-

ment of axial resolution in 3D wideﬁ eld microscopy using two objective

lenses. Proc. SPIE 2412, 147–156.

Gustafsson, M.G.L., Agard, D.A. and Sedat, J.W. (1999). I5M: 3 wideﬁ eld light

microscopy with better than 100 nm axial resolution. J. Microsc. 195, 10–16.

S.W. (2007). Fluorescence nanoscopy in whole cells by asynchronous

163901.

Dyba, M. and Hell, S.W. (2003). Photostability of a ﬂ uorescent marker under

42(25), 5123–5129.

Hänninen, P. (2002). Beyond the diffraction limit. Nature 419, 802.

Andresen, M., Stiel, A.C., Jakobs, S., Eggeling, C., Schönle, A. and Hell,

11445.

emission depletion microscopy. Nature Biotechno. 21(11), 1303–1304.

Dyba, M., Jakobs, S. and Hell, S.W. (2003). Immunoﬂ uorescence stimulated

fluorescence nanoscopy. Biophys. J. 92, L67–L69.

pulsed excited-state depletion through stimulated emission. Appl. Opt.

localization of photoswitching emitters. Biophys. J. 93, 3285–3290.

Jahn, R., Eggeling, C. and Hell, S.W. (2006). Macromolecular-scale resolution

Egner, A., Jakobs, S. and Hell, S.W. (2002). Fast 100-nm resolution 3D-

Jahn, R., Jakobs, S., Eggeling, C. and Hell, S.W. (2007). Two-colour far-field

Dyba, M. and Hell, S.W. (2002). Focal spots of size 1/23 open up far-ﬁ eld

*Donnert, G., Keller, J., Medda, R., Andrei, M.A., Rizzoli, S.O., Luhrmann, R.,

ﬂ uorescence microscopy at 33 nm axial resolution. Phys. Rev. Lett. 88,

*Donnert, G., Keller, J., Wurm, C.A., Rizzoli, S.O., Westphal, V., Schönle, A.,

in biological fluorescence microscopy. Proc. Natl. Acad. Sci. USA 103, 11440–

*Egner, A., Geisler, C., von Middendorff, C., Bock, H., Wenzel, D., Medda, R.,

832 S.W. Hell and A. Schönle

Hell, S.W. (2003). Toward ﬂ uorescence nanoscopy. Nature Biotechnol. 21(11),

1347–1355.

Hell, S.W. (2004). Strategy for far-ﬁ eld optical imaging and writing without

diffraction limit. Phys. Lett. A 326(1–2), 140–145.

Hell, S.W. and Kroug, M. (1995). Ground-state depletion ﬂ uorescence micros-

copy, a concept for breaking the diffraction resolution limit. Appl. Phys. B

60, 495–497.

Hell, S.W. and Nagorni, M. (1998). 4Pi-confocal microscopy with alternate

interference. Opt. Lett. 23(20), 1567–1569.

Hell, S.W. and Stelzer, E.H.K. (1992b). Fundamental improvement of resolution

with a 4Pi-confocal ﬂ uorescence microscope using two-photon excitation.

Opt. Commun. 93, 277–282.

Hell, S.W. and Wichmann, J. (1994). Breaking the diffraction resolution limit

by stimulated emission: Stimulated emission depletion microscopy. Opt.

Lett. 19(11), 780–782.

Appl. Phys. A 77, 859–860.

Microsc. 185(1), 1–5.

Holmes, T.J. (1988). Maximum-likelihood image restoration adapted for non-

coherent optical imaging. JOSA A 5(5), 666–673.

Holmes, T.J., Bhattacharyya, S., Cooper, J.A., Hanzel, D., Krishnamurthi, V.,

Lin, W., Roysam, B., Szarowski, D.H. and Turner, J.N. (1995). Light micro-

scopic images reconstruction by maximum likelihood deconvolution. In

Handbook of Biological Confocal Microscopy (J. Pawley, Ed.) 389–400 (Plenum

Press, New York).

diffraction barrier at low light intensities by using reversibly photoswitchable

Hänninen, P.E., Lehtelä, L. and Hell, S.W. (1996). Two- and multiphoton excita-

tion of conjugate dyes with continuous wave lasers. Opt. Commun. 130,

29–33.

Hecht, B., Bieleﬂ edt, H., Inouyne, Y., Pohl, D.W. and Novotny, L. (1997).

Facts and artifacts in near-ﬁ eld optical microscopy. J. Appl. Phys. 81,

1492–2498.

Heintzmann, R. and Cremer, C. (1998). Laterally modulated excitation micros-

copy: Improvement of resolution by using a diffraction grating. SPIE Proc.

3568, 185–195.

Heintzmann, R., Jovin, T.M. and Cremer, C. (2002). Saturated patterned excita-

tion microscopy—a concept for optical resolution improvement. J. Opt. Soc.

Am. A: Opt. Image Sci. Vision 19(8), 1599–1609.

Hell, S. and Stelzer, E.H.K. (1992a). Properties of a 4Pi-confocal ﬂ uorescence

Hell, S.W. (1990). Double-scanning confocal microscope. European Patent.

Hell, S.W. (1997). Increasing the resolution of far-ﬁ eld ﬂ uorescence light micros-

copy by point-spread-function engineering. In Topics in Fluorescence Spec-

rescence beads at 100–200 distance with a two-photon 4Pi-microscope

imaging by fluorescence photoactivation localization microscopy. Biophys. J.

Hell, S.W., Jakobs, S. and Kastrup, L. (2003). Imaging and writing at the

troscopy (J.R. Lakowicz, Ed.), 361–422 (Plenum Press, New York).

microscope. J. Opt. Soc. Am. A 9, 2159–2166.

Hell, S.W., Schrader, M., Hänninen, P.E. and Soini, E. (1995). Resolving ﬂ uo-

91, 4258–4272.

working in the near infrared. Opt. Commun. 117, 20–24.

proteins. Proc. Natl. Acad. Sci. USA 102, 17565–17569.

cence microscopy with three-dimensional resolution in the 100 nm range. J.

*Hell, S.W. (2007). Far-field optical nanoscopy. Science 316, 1153–1158.

*Hess, S.T., Girirajan, T.P.K. and Mason, M.D. (2006). Ultra-high resolution

Hell, S.W., Schrader, M. and van der Voort, H.T.M. (1997). Far-ﬁ eld ﬂ uores-

*Hofmann, M., Eggeling, C., Jacobs, S. and Hell, S.W. (2005). Breaking the

nanoscale with focused visible light through saturable optical transitions.

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 833

Levene, M.J., Korlach, J., Turner, S.W., Foquet, M., Craighead, H.G. and Webb,

W.W. (2003). Zero-mode waveguides for single-molecule analysis at high

concentrations. Science 299, 682–686.

Lukosz, W. (1966). Optical systems with resolving powers exceeding the clas-

sical limit. J. Opt. Soc. Am. 56, 1463–1472.

Lukyanov, K.A., Fradkov, A.F., Gurskaya, N.G., Matz, M.V., Labas, Y.A., Sav-

itsky, A.P., Markelov, M.L., Zaraisky, A.G., Zhao, X., Fang, Y., Tan, W. and

Lukyanov, S.A. (2000). Natural animal coloration can be determined by a

nonﬂ uorescent green ﬂ uorescent protein homolog. J. Biol. Chem. 275(34),

25879–25882.

Magde, D., Elson, E.L. and Webb, W.W. (1972). Thermodynamic ﬂ uctuations

in a reacting system—measurement by ﬂ uorescence correlation spectros-

copy. Phys. Rev. Lett. 29(11), 705–708.

Nagorni, M. and Hell, S.W. (1998). 4Pi-confocal microscopy provides three-

dimensional images of the microtubule network with 100- to 150-nm resolu-

tion. J. Struct. Biol. 123, 236–247.

Nagorni, M. and Hell, S.W. (2001a). Coherent use of opposing lenses for axial

resolution increase in ﬂ uorescence microscopy. I. Comparative study of

concepts. J. Opt. Soc. Am. A 18(1), 36–48.

Nagorni, M. and Hell, S.W. (2001a). Coherent use of opposing lenses for axial

resolution increase in ﬂ uorescence microscopy. II. Power and limitation of

nonlinear image restoration. J. Opt. Soc. Am. A 18(1), 48–54.

Pawley, J., Ed. (1995). Handbook of Biological Confocal Microscopy. (Plenum Press,

New York).

Pohl, D.W. and Courjon, D. (1993). Near Field Optics. (Kluwer, Dordrecht).

Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1993).

Numerical Recipes in C, 2nd ed. (Cambridge University Press,

Cambridge).

Irie, M., Fukaminato, T., Sasaki, T., Tamai, N. and Kawai, T. (2002). A digital

ﬂ uorescent molecular photoswitch. Nature 420(6917), 759–760.

Kastrup, L. and Hell, S.W. (2004). Absolute optical cross section of individual

ﬂ uorescent molecules. Angew. Chem. Int. Ed. 43, 6646–6649.

Kastrup, L., Blom, H., Eggeling, C. and Hell, S.W. (2005). Fluorescence ﬂ uctua-

tion spectroscopy in subdiffraction focal volumes. Phys. Rev. Lett. 94(17),

178104.

Klar, T.A., Engel, E. and Hell, S.W. (2001). Breaking Abbe’s diffraction resolu-

beams of various shapes. Phys. Rev. E 64, 1–9.

Klar, T.A., Jakobs, S., Dyba, M., Egner, A. and Hell, S.W. (2000). Fluorescence

microscopy with diffraction resolution limit broken by stimulated emission.

Proc. Natl. Acad. Sci. USA 97, 8206–8210.

Krishnamurthi, V., Bailey, B. and Lanni, F. (1996). Image processing in 3-D

standing wave ﬂ uorescence microscopy. Proc. SPIE 2655, 18–25.

New York).

two-photon excitation of ﬂ uorescence. Photochem. Photobiol. 64, 632–635.

Lanni, F. (1986). Applications of Fluorescence in the Biomedical Sciences, 1st ed.,

D.L. Taylor, Ed. 520–521. (Liss, New York).

Laurence, T.A. and Weiss, S. (2003). How to detect weak pairs. Science 299(5607),

667–668.

type A with 1-photon excitation in biological fluorescence imaging. Opt.

Lakowicz, J.R. (1983). Principles of Fluorescence Spectroscopy. (Plenum Press,

Express 15, 2459–2467.

tion limit in ﬂ uorescence microscopy with stimulated emission depletion

*Lang, M., Müller, T., Engelhardt, J. and Hell, S.W. (2007). 4Pi microscopy of

Lakowicz, J.R., Gryczynski, I., Malak, H. and Gryczynski, Z. (1996). Two-color

834 S.W. Hell and A. Schönle

Sheppard, C.J.R., Gu, M., Kawata, Y. and Kawata, S. (1993). Three-dimensional

transfer functions for high-aperture systems. J. Opt. Soc. Am. A 11(2),

593–596.

Stephens, D.J. and Allen, V.J. (2003). Light microscopy techniques for live cell

Nuovo Cimento Suppl. 9, 426–435.

Weiss, S. (2000). Shattering the diffraction limit of light: A revolution in ﬂ uo-

Westphal, V., Blanca, C.M., Dyba, M., Kastrup, L. and Hell, S.W. (2003). Laser-

diode-stimulated emission depletion microscopy. Appl. Phys. Lett. 82(18),

3125–3127.

Westphal, V., Kastrup, L. and Hell, S.W. (2003). Lateral resolution of 28 nm

(λ/25) in far-ﬁ eld ﬂ uorescence microscopy. Appl. Phys. B 77(4), 377–380.

Westphal, V.H. and Hell, S.W. (2005). Nanoscale resolution in the focal plane

of an optical microscope. Phys. Rev. Lett. 94(14), 143903.

Wilson, T. and Sheppard, C.J.R. (1984). Theory and Practice of Scanning Optical

Microscopy. (Academic Press, New York).

Xu, C., Zipfel, W., Shear, J.B., Williams, R.M. and Webb, W.W. (1996). Multi-

photon ﬂ uorescence excitation: New spectral windows for biological non-

linear microscopy. Proc. Natl. Acad. Sci. USA 93, 10763–10768.

microscopy reveals that synaptotagmin remains clustered after synaptic

Schmidt, M., Nagorni, M. and Hell, S.W. (2000). Subresolution axial distance

measurements in far-ﬁ eld ﬂ uorescence microscopy with precision of 1 nano-

Schneider, B., Albrecht, B., Jaeckle, P., Neofotistos, D., Söding, S., Jäger, T. and

Cremer, C. (2000). Nanolocalization measurements in spatially modulated

illumination microscopy using two coherent illumination beams. Proc. SPIE

3921, 321–330.

Schönle, A. and Hell, S.W. (1999). Far-ﬁ eld ﬂ uorescence microscopy with

repetetive excitation. Eur. Phys. J. D 6, 283–290.

Schönle, A. and Hell, S.W. (2002). Calculation of vectorial three-dimensional

transfer functions in large-angle focusing systems. J. Opt. Soc. Am. A 19(10),

2121–2126.

Schönle, A., Hänninen, P.E. and Hell, S.W. (1999). Nonlinear ﬂ uorescence

through intermolecular energy transfer and resolution increase in ﬂ uores-

cence microscopy. Ann. Phys. (Leipzig) 8(2), 115–133.

Schrader, M. and Hell, S.W. (1996). 4Pi-confocal images with axial superresolu-

tion. J. Microsc. 183, 189–193.

Schrader, M., Bahlmann, K., Giese, G. and Hell, S.W. (1998). 4Pi-confocal

imaging in ﬁ xed biological specimens. Biophys. J. 75, 1659–1668.

Shen, Y.R. (1984). The Principles of Nonlinear Optics, 1st ed. (John Wiley, New

York).

Sheppard, C.J.R. and Kompfner, R. (1978). Resonant scanning optical micro-

scope. Appl. Optics 17, 2879–2882.

253, 358–379.

II. Structure of the image ﬁ eld in an aplanatic system. Proc. R. Soc. Lond. A

by stochastic optical reconstruction microscopy (STORM). Nature Methods

Richards, B. and Wolf, E. (1959). Electromagnetic diffraction in optical systems

rescence microscopy? Proc. Natl. Acad. Sci. USA 97(16), 8747–8749.

imaging. Science 300, 82–91.

3, 793–796.

Toraldo di Francia, G. (1952). Supergain antennas and optical resolving power.

vesicle exocytosis. Nature 440, 953–959.

*Rust, M.J., Bates, M. and Zhuang, X.-w. (2006). Sub-diffraction-limit imaging

meter. Rev. Sci. Instrum. 71, 2742–2745.

*Willig, K.I., Rizzoli, S.O., Westphal, V., Jahn, R. and Hell, S.W. (2006). STED

*References added since the first printing.

835

Principles and Applications of Zone

Plate X-Ray Microscopes

Malcolm Howells, Chris Jacobsen, and Tony Warwick

1 Introduction

1.1 Background

In the 1949 issue of Scientiﬁ c American, an article by Stanford physicist

Paul Kirkpatrick on “The X-ray Microscope” (Kirkpatrick, 1949) was

described by the editors as follows:

“It would be a big improvement on microscopes using light or electrons, for

X-rays combine short wavelengths, giving ﬁ ne resolution, and penetration. The

main problems standing in the way have now been solved.”

With the perspective of a half century, we might change “improvement

on” to “complement to” and say that further problems were solved after

1949, but here in essence is the character of X-ray microscopes.

In this chapter, we outline some of the properties of X-ray microscope

systems in operation today, and highlight some of their present applica-

tions. We will not discuss the history of X-ray microscopes prior to

about 1975 but instead refer the reader to a series of conference proceed-

ings known as “X-ray Optics and X-ray Microanalysis,” which began in

1956. Originally these had valuable material on X-ray microscopy but

this diminished after about 1970. The ﬁ rst ﬁ ve were at Cambridge (1956)

(Cosslett et al., 1957), Stockholm (1959) (Engström et al., 1960), Stanford

(1962) (Pattee et al., 1963), Orsay (1965) (Castaing et al., 1966) and Tub-

ingen (1968) (Molenstedt et al., 1969). We also recommend the historical

perspectives by A. Baez (Baez, 1989, 1997) and the book by Cosslet and

Nixon (1960). There is a recognisable thread of continuity between

today’s status of the ﬁ eld and efforts that began slowly around 1975

(Niemann et al., 1976; Parsons, 1978; Kirz and Sayre, 1980c; Parsons,

1980) and blossomed with the availability of synchrotron light sources

and nanofabrication technologies; this thread can be traced in part via

the proceedings of another conference series that began in 1984

(Schmahl and Rudolph, 1984a) and has continued until today (Sayre et

al., 1988; Michette et al., 1992; Aristov and Erko, 1994; Thieme et al.,

1998b; Meyer-Ilse et al., 2000b; Susini et al., 2003). Zone-plate X-ray

836 M. Howells et al.

microscopes now exist at roughly two dozen international synchrotron

radiation research centers (see Table 13–3), and commercial lab-based

instruments are also available. Three types are in especially wide-

spread use. Transmission X-ray microscopes (TXMs) specialize in the

rapid acquisition of 2D images using high ﬂ ux sources, and in the col-

lection of tilt sequences of projection images for 3D imaging by tomog-

raphy. Scanning transmission X-ray microscopes (STXMs) specialize in

the acquisition of reduced dose images and point spectra with high

energy resolution for elemental and chemical state mapping, and

require high source brightness. Scanning ﬂ uorescence X-ray micro-

probes (SFXMs) are similar to STXMs except that ﬂ uorescence X-rays

are collected by energy-resolving detectors for trace element mapping.

All three approaches are now working below 100 nm resolution, to the

point of reaching 15 nm resolution in some demonstrations (Chao et al.,

2005). While many of the new technical developments continue to be

pursued by specialists in X-ray optics and microscopy, much of present-

day activity comes from scientists in other ﬁ elds of research who are

using X-ray microscopes to address their particular questions. This

chapter is mainly aimed at scientists from the latter group as well as

those from the other communities represented in the content of this

series of books.

1.2 X-Ray Interactions

A microscope requires illumination, magniﬁ cation, and contrast. The

characteristics of X-ray interactions with matter affect all three. In

Figure 13–1, we show the cross-section (Hubbell et al., 1980) for photo-

electric absorption, coherent (elastic or Thomson) scattering, and inco-

100

Cross section (barns=10

-24

)

10 1 0.1 0.01

λ (nm)

Energy (eV)

(absorption)

coh

(coherent)

incoh

(incoherent)

-1

-2

Carbon

Figure 13–1. X-ray interaction cross sections in carbon. At energies below

about 10 keV, absorption dominates so that images are free from the complica-

tions of multiple scattering. [Data from Henke et al. (1993) and the NIST XCOM

database (Saloman and Hubbell, 1987).]

Chapter 13 Principles and Applications of Zone Plate X-Ray Microscopes 837

herent (inelastic or Compton) scattering for carbon. Below 10 keV,

absorption dominates, so multiple X-ray scattering is usually not of

concern (an X-ray is much more likely to be absorbed following any

scattering event than scattered again) nor is inelastic scattering.

However, what is not evident in Figure 13–1 is the fact that the propa-

gation of X-rays in materials can also include refractive effects, and in

fact it was Einstein (1918) who ﬁ rst pointed out that the refractive index

is slightly less than unity. The X-ray refractive index for a wave forward

propagated as exp[−i(kñx − ωτ)] is often written as ñ = 1 − δ − iβ where

δ represents the phase-shifting part of the refractive index and β rep-

resents absorption according to a linear coefﬁ cient µ = 4πβ/λ in the

Lambert-Beer law I = I

exp[−µt]. In an anomalous dispersion model,

the refractive index terms can furthermore be written as (δ + iβ) = αλ

( f

+ if

) with α = n

/2π, where n

= ρN

/A gives the number density of

atoms, r

= 2.82 × 10

−15

m is the classical radius of the electron, and ( f

+ if

) represents the frequency-dependent oscillator strength of an

atom. This oscillator strength ( f

+ if

) has been tabulated with very

good absolute accuracy for all elements by Henke, Gullikson et al.

(Henke, 1993) over the energy range 10–30,000 eV (see Figure 13–2). In

examining Figure 13–2, two features immediately jump out: f

is some-

what constant except near absorption edges, so the thickness t

= λ/2δ

= 1/(2αλf

) needed to provide a phase advance exp[ikδt

] equal to π

increases as λ

−1

, while, because f

scales as E

−2

or λ

, the thickness 1/µ

= 1/(4παλf

) that produces an attenuation of 1/e increases as E

or λ

−3

As a result, phase contrast becomes the dominant contrast mechanism

as one goes to shorter wavelengths (Schmahl and Rudolph, 1987).

1000 100 10 1

λ (Å)

0.01

0.10

1.00

10.00

100.00

10 100 1000 10000

Energy (eV)

Gold

Carbon

1 and

Figure 13–2. The frequency-dependent oscillator strength (f

+ if

) for carbon

and gold. At X-ray absorption edges (such as 290 eV for carbon), f

has step

increments, while f

undergoes anomalous dispersion resonances. (Reprinted