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790

Nanoscale Resolution in Far-Field

Fluorescence Microscopy

Stefan W. Hell and Andreas Schönle

1 Introduction

The discovery of the diffraction barrier in 1873 by Ernst Abbe (1873) has

shown that, relying on propagating light waves and regular lenses, the

traditional light microscope cannot resolve spatial structures that are

smaller than about half the wavelength of the focused light. This physi-

cal insight has been accepted as an unalterable limitation of focusing

light microscopy and has consequently triggered the invention of non-

optical imaging techniques, such as electron and scanning probe

microscopy. In spite of the tremendous improvement in resolution

brought about by these methods, light microscopy has maintained its

importance in many ﬁ elds of science. The reasons are mainly a number

of exclusive advantages, the most prominent of which is the ability to

noninvasively image (living) specimens. Light microscopy also entails

the possibility of using ﬂ uorescence as a highly speciﬁ c signature of the

specimen features of interest. Fluorescence is particularly attractive

when provided by endogenous ﬂ uorescence markers, i.e., proteins in

physiologically intact cells. Mapped with a confocal or multiphoton

excitation microscope (Sheppard and Kompfner, 1978; Wilson and

Sheppard, 1984; Denk et al., 1990), ﬂ uorescence emission readily yields

protein three-dimensional (3D) distributions, or that of other ﬂ uores-

cently labeled molecules from the strongly convoluted inside of biologi-

cal specimens.

Abandoning the concept of focusing light altogether, near-ﬁ eld

optical microscopy is the earliest practically relevant attempt to over-

come the diffraction barrier with visible light (Pohl and Courjon, 1993).

To this end, scanning near-ﬁ eld optical microscopes employ ultrasharp

tips or tiny apertures to conﬁ ne the interaction of the light ﬁ eld with

the object to subdiffraction dimensions. However, applying this tech-

nique to soft biological matter has not been very successful to date and

it has to be applied carefully to avoid imaging artifacts (Hecht et al.,

1997). In any case, a near-ﬁ eld optical microscope is conﬁ ned to imag-

ing surfaces, again underscoring the importance of improving the

resolution in an optical microscope that still preserves focusing. For

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 791

convenience we refer to the traditional light microscope as a “far-ﬁ eld”

instrument.

This formidable problem has been approached by many scientists

(Toraldo di Francia, 1952; Lukosz, 1966), but only in recent years have

methods been characterized (Hell and Kroug, 1995; Hell, 1997, 2003)

that effectively broke Abbe’s diffraction barrier, implying the potential

to attain molecular resolution with regular lenses and visible light

(Hell et al., 2003; Hell, 2003; Westphal and Hell, 2005).

2 The Resolution Limit

The limited resolution of a focusing light microscope is readily

described by the form and extent of the effective focal spot, commonly

referred to as the (effective) point spread function (PSF). The PSF is the

image that an inﬁ nitely small object would create. For an incoherent

imaging mode such as ﬂ uorescence, the image is therefore given by the

convolution of the object with the PSF:

I = h ⊗ G (1)

Here I, h, and G denote the image, the PSF, and the object, respectively,

with the object consisting of, e.g., a distribution of ﬂ uorophores in

space. The convolution actually means that the object is “smeared out”

by the focal spot. While a careful analysis of the imaging properties

requires a detailed analysis of the PSF, for PSFs with a single peak,

assessing the full width half maximum (FWHM) usually gives a good

estimate of the microscope’s resolution. If identical molecules are

within the FWHM distance, the molecules cannot be separated in the

image. Therefore, it becomes evident that improving the resolution is

largely equivalent to narrowing the PSF of the microscope.

In a conventional ﬂ uorescence microscope, the FWHM of the PSF

is about λ/(2n sin α) = λ/(2 NA), with λ denoting the wavelength, n

the refractive index, α the semiaperture angle, and NA the numerical

aperture of the lens. Without changes to the principal method, the

spot size can only be decreased by using shorter wavelengths

or larger aperture angles (Abbe, 1873; Born and Wolf, 1993). However,

the lens half-aperture is technically limited to ∼70° and the wave-

length λ cannot be reduced below 350 nm because shorter wavelengths

are not compatible with live cell imaging. In the best case, established

far-ﬁ eld microscopes resolve 180 nm in the focal plane (x,y) and merely

500–800 nm along the optic axis (z) (See Figure 2–1a) (Pawley, 1995).

All attempts to improve the resolution by a mere improvement of the

optical components remain limited by diffraction. This is arguably

better understood in the frequency domain. Here, the resolving power

is described by the optical transfer function (OTF) giving the strength

with which these spatial frequencies are transferred from the object

to the image. The OTF is readily computed as the Fourier transform

of the PSF (Wilson and Sheppard, 1984; Goodman, 1968). Due to the

convolution theorem, Eq. (1) becomes

= h

= oG

(2)

792 S.W. Hell and A. Schönle

where the hat signiﬁ es a 3D Fourier transform and o is the OTF. Due

to the multiplication on the right hand side it is evident that even under

optimal imaging conditions, object frequencies are lost where the OTF

is zero. This loss is physically irrecoverable. Hence, the ultimate resolu-

tion limit is given by the highest frequency where the OTF is nonzero,

i.e., the extent of the support of the OTF.

The highest spatial frequency produced by a (quasi)monochromatic

wave passing through the setup is k = 2πn/λ. For focused light, the

Fourier transform of its electric ﬁ eld, C(k), is therefore given by a

spherical cap with radius k, as seen in Figure 12–2. The excitation prob-

ability is well approximated by the absolute square of the electric ﬁ eld,

corresponding to an autocorrelation in frequency space. This signiﬁ es

that frequencies of up to 2k are contained in the excitation OTF.

However, resolving optics can be employed both in the illumination

and the detection path. This introduces a spatially varying detection

probability for the emitted ﬂ uorescence. Since the phase of the illumi-

nating light is lost during excitation, ﬂ uorescence is emitted incoher-

ently. Therefore the effective PSF is given by the multiplication of the

excitation PSF with its normalized detection counterpart, i.e., the

detection PSF (Wilson and Sheppard, 1984), which is equivalent to a

Figure 12–1. (a) The wavefront

created by a single lens is a

spherical cap. For the highest

available semiaperture angle

(∼70°), diffraction theory dic-

tates an elongated spot along

the optic axis (z) that is approxi-

mately three times longer than

it is wide (xy). The elongation

can also be explained by the fact

that the wavefront is only a cap

rather than a sphere, bringing

about an asymmetry of the

focusing process. (b) Coherent

addition of two spherical wave-

fronts created by opposing

lenses completes a major part of

the missing wavefront toward a

more spherical one, which is the

tenet of the “4Pi concept.” (c)

The central focal spot, i.e., the

main diffraction maximum,

becomes more spherical as a

result. However, because the

wavefront is not approaching a

sphere side-maxima appear

along the optic axis.

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 793

convolution in frequency space. Thus the achievable cutoff is at 2k

det

where k

and k

det

are the frequencies corresponding to the excita-

tion and detection wavelengths in the medium, respectively.

These considerations are illustrated in Figure 12–2. As an example,

if ﬂ uorescence is excited at 488 nm and detected at around 530 nm,

the cutoff is given by (2n/488 nm + 2n/530 nm)

−1

≅ 127 nm/n,

E-Field

Exct. & Det. Effective

det

confocal

'ideal'

4Pi type C

Figure 12–2. OTF supports in frequency space. (a) For a single lens, the Fourier

transform of the electric ﬁ eld, C(k), is a spherical cap with a cutoff angle deter-

mined by the aperture angle of the objective lens, which has been technically

limited to <70°. Excitation and detection (intensity) PSFs depend on the abso-

lute square of the electric ﬁ eld; hence, the respective OTFs are given by the

autocorrelation of the cap. Finally, in a confocal ﬂ uorescence microscope, the

effective PSF is given by the product of the excitation and detection (intensity)

PSF. Its OTF is therefore the convolution of the corresponding excitation and

detection OTF, resulting in a squeezed OTF along the z direction accounting

for the degraded axial resolution. (b) With a scalar ﬁ eld a truly spherical

wavefront could ideally be generated. The autocorrelation of such a complete

spherical shell is nonzero within a sphere of radius 2k. Convolution of the

excitation and detection OTFs again results in a spherical OTF support of

radius 2k

+ 2k

det

, which is tantamount to isotropic resolution. This radius

deﬁ nes the theoretical resolution limit of all microscopes in which the resolu-

tion is solely created by the optical arrangement and in which the phase of

light is lost at the sample, as in the excitation–emission process. (c) The 4Pi

microscope of type C with coherent excitation and detection through both

lenses with large aperture angles generates the largest wavefront currently

achievable in practice. For the highest available cutoff angles of approximately

70° this results in an almost spherical effective OTF. The resulting resolution

is very close to the possible limit. While a semiaperture angle somewhat

greater than 70° would still give a better coverage, the study also shows that

the true solid angle of 4π is actually not required to gain the desired improve-

ment in axial resolution. The putative use of aperture angles approaching 80°

and higher is also complicated by the transverse nature of electromagnetic

waves.

794 S.W. Hell and A. Schönle

corresponding to approximately 83 nm for oil and 96 nm for water

immersion. Therefore, all far-ﬁ eld light microscopes relying solely on

improvements of the instrument have an ultimate resolution limit of

frequencies are transmitted and restored in the image. This theoretical

benchmark is indeed almost achieved by the 4Pi microscope described

in more detail later (Egner et al., 2002; Hell et al., 1997).

To overcome this fundamental limit, higher frequencies need to be

ties in the interaction of the excitation light with a dye: For example,

when using multiphoton (m-photon) excitation, the probability of pro-

ducing a ﬂ uorescence photon depends on the mth order of the illumina-

tion intensity (Sheppard and Kampfner, 1978; Göpper-Mayer, 1931;

Bloembergen, 1965). The original excitation OTF will be convolved m

times with itself, thus extending the support region to m times higher

frequencies. Therefore, it has sometimes been argued that superresolu-

tion can be attained by multiphoton excitation. It is, however readily

understood why the resolution limit cannot really be pushed (Denk

et al., 1990). While it is true that the excitation volume is narrower than

the focal spot, which is due to the nonlinear dependence, using m-

photon excitation to excite the same dye also means that the excitation

energy has to be split between the photons (Denk et al., 1990). Conse-

quently the photons have an m times lower amount of energy, thus an

m times longer wavelength mλ

, which results in m times larger focal

spots to begin with. Consequently, the theoretical cutoff remains equal

at 2m(k

/m) + 2k

det

= 2k

+ 2k

det

. The multiplication by m stems from

the m correlations or convolutions in frequency space and the division

from the longer excitation wavelength. Obviously, this equally holds for

excitation with several photons of different energies such as two-color

two-photon excitation (Lakowicz et al., 1996). However, in the case of

multiphoton excitation, higher frequencies within the support are

usually damped, making the resolution poorer as compared to the 1-

photon case. Multiphoton excitation is therefore not a viable option for

signiﬁ cantly increasing the resolution. In addition, multi photon excita-

tion, especially for m > 3, requires very high intensities (Xu et al., 1996)

leading to damage to the sample. Bleaching is largely restricted to the

focal plane, but there it can be much stronger than for one-photon exci-

tation. For some dyes, however, the excitation wavelength can be chosen

to be shorter than mλ

and when imaging deep into scattering samples

such as brain slices, multiphoton imaging can feature a superior signal-

to-noise ratio (SNR). In these cases, multiphoton excitation is a valuable

method for reasons unrelated to the classical resolution issue.

Recognizing that the energy subdivision prevents any resolution

increase, “multiphoton” concepts have been proposed, where the detec-

tion of a photon occurs only after the consecutive absorption of multiple

excitation photons. Since the photons induce a linear optical transition

in the dye, high intensities are not required and photon-energy subdivi-

sion does not occur (Hänninen et al., 1996; Schönle et al., 1999; Schönle

and Hell, 1999). However, these concepts require speciﬁ c conditions or

complicated dye systems, also complicating their practical realization.

just below 100 nm in all directions, even when all conceivable spatial

generated. Obviously this can be achieved by introducing nonlineari-

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 795

A radically different concept for improving the far-ﬁ eld ﬂ uorescence

microscopy resolution appeared in the mid-1990s in the form of stimu-

lated emission depletion (STED) and ground state depletion (GSD)

microscopy (Hell and Wichmann, 1994; Hell and Kroug, 1995). Both

concepts were based on one common principle: The required nonlin-

earities in the relationship between the irradiating light and the signal

detected from the dye are provided by a spatially modulated reversible

saturable optically linear (fluorescence) transition between two molec-

ular states (RESOLFT). Since there is no physical limit to the degree of

saturation, there is no longer a theoretical limit to the resolution. The

limit is largely the size of the marker molecule itself. Therefore, con-

cepts based on the RESOLFT principle, such as STED or GSD micros-

operation they can achieve nanoscale resolution in all directions (Hell,

1997; Hell et al., 2003; Heintzmann et al., 2002).

increase, an introduction to the general idea will follow in the second

part of this chapter, and we shall outline different possibilities for real-

izing the RESOLFT concept. We will see that initial applications of

RESOLFT-based superresolution microscopy have recently yielded

encouraging results, such as the ﬁ rst demonstration of a spatial resolu-

tion of λ/25 with focused light using regular lenses (Westphal et al.,

2003). A potential road map toward imaging with nanometer resolu-

tion in live cells will be discussed, opening the prospect of bridging

the gap between electron and current light micro scopy, and providing

a “nanoscope” working with focused light.

3 Axial Resolution Improvement by Aperture

Enlargement: 4Pi Microscopy and Related Approaches

Figure 12–2 illustrates that the suboptimal axial resolution of a far-ﬁ eld

light microscope can readily be motivated by the fact that the focusing

angle of the objective lens is far from covering a full solid angle of 4π.

The axially elongated PSF evidently also implies an axially compressed

OTF. If the focused wavefronts were almost spherical, so would the

focal spot, as well as the OTF of the system. In this case, the resolution

would be largely isotropic. Therefore, an obvious way to achieve

optimal optical resolution is to synthesize a focusing angle that comes

closer to the solid angle of 4π. Since the focusing angle of a lens is

limited by technical constraints, a larger wavefront can be obtained

only by pasting together two or more wavefronts. A wavefront synthe-

sis sharpening the focus along the optic axis is attained by employing

two opposing lenses (Figure 12–1) that either coherently illuminate the

sample from both sides or that detect the light through both lenses in

a coherent manner (Hell, 1990; Hell and Stelzer, 1992a; Gustafsson

et al., 1995). The resultant support of the OTF is displayed in Figure

12–2c. In the spatial domain the effect can be pictured as two counter-

propagating focused beams interfering either at the focal spot or at a

common point at the detector, for the illumination and the detection,

Fundamentally departing from earlier approaches to resolution

copy, truly break the diffraction barrier. Due to their principles of

796 S.W. Hell and A. Schönle

respectively. For the common high-angle lenses with a semiaperture

64° < α < 72°, constructive interference produces a maximum with an

approximately three to four times narrower axial FWHM. The basic

idea of the 4Pi microscope is to produce and take advantage of this

axially narrowed PSF. Due to the fact that the semiaperture angle α is

considerably smaller than 90°, the main maximum is also accompanied

by one or two axial satellite lobes originating from the “missing lateral

part” of a potentially full solid angle (Figure 12–1c).

Importantly, the narrowed main focal maximum is not λ/(4n), as

would be anticipated for a ﬂ at standing wave, but somewhat larger. By

the same token, the side maxima are not located at mλ/(2n), (m = 0, 1,

2, 3 . . .), but slightly farther away from the focal point, constantly

decreasing in height with increasing order. As we shall see later, this

difference is essential to the axial resolution improvement brought

about by the coherent use of two opposing lenses and the actual reason

why it is not possible to improve the axial resolution just by the inter-

ference of counterpropagating plane waves (Lanni, 1986; Bavley et al.,

1993). The latter is the tenet of the standing wave microscope (SWM),

which utilizes a ﬂ at standing wave of laser light and thus a set of exci-

tation nodal planes in the sample along the optic axis. The SWM uses

wide-ﬁ eld detection on a camera, like any conventional ﬂ uorescence

microscope; the ﬂ at standing wave of excitation light is produced either

with a mirror beneath the sample or by adding counterpropagating

waves from two lenses. A substantial increase in axial resolution has

initially been claimed by SWM. However, the resulting multiple thin

interference layers in a sample (Lanni, 1986) do not unambiguously

resolve features extending over a minimal axial range that is larger

than half the wavelength (0.2–0.4 µm) (Krishnamurthi et al., 1996;

Freimann et al., 1997). While SWM might prove useful for specialized

applications, it fails in delivering axial images of arbitrary objects

(Nagorni and Hell, 2001a, 2001b). An explanation for this is that the

interference excitation maxima have almost equal intensity, leading to

strongly blurred “ghost images.” The deeper-rooted physical reason is

that SWM does not increase the aperture of the system. This can be

readily observed when analyzing the SWM in the frequency space

(Figure 12–3). The excitation OTF has only three delta peaks located at

−k, 0, and k on the inverse optical axis. When convolved with the detec-

tion OTF, large gaps remain in the support of the effective OTF repre-

senting potential object frequencies that are not transferred from the

object to the image.

It is a major physical insight (into the problem of axial resolution

improvement with coherently used opposing lenses) that these gaps

can be closed only when the light is focused, that is with spherical wave-

fronts. Focusing to the same point requires the accurate alignment of

the two lenses, but the real physical challenge is to identify feasible

the side-maxima still present when focusing at 64° < α < 72°. Reduction

of the contribution from the side-maxima is equivalent to completing

the support of the OTF and eventually to avoiding imaging artifacts.

When spot-scanning confocal and nonconfocal 4Pi microscopy (Hell, 1990;

mechanisms helping to further reduce the ﬂ uorescence contributed by

Chapter 12 Nanoscale Resolution in Far-Field Fluorescence Microscopy 797

Hell and Stelzer, 1992b) (Figure 12–3) and wide-ﬁ eld I

M micro scopy

(Gustafsson et al., 1995) ﬁ nally demonstrated the improvement of axial

resolution (Hell et al., 1997; Schrader and Hell, 1996; Gustafsson, 1999;

Gustafsson et al., 1999), each method used lenses with high numerical

aperture and relied at least on one of the following three lobe-reducing

mechanisms: (1) Using both focused excitation and confocal detection

(Hell, 1990; Hell and Stelzer, 1992a) suppresses ﬂ uorescence from

higher order side lobes of the excitation PSF; (2) two-photon excitation

(TPE) (Hell and Stelzer, 1992b) emphasizes differences in the intensities

of the main and the side-maxima due to its quadratic dependence on

the excitation intensity; and (3) ﬁ nally, spatial disparities between the

maxima of excitation and ﬂ uorescence wavelengths can be used (Hell

4Pi C

4Pi TPE type A

4Pi TPE type C

SWM

det

Figure 12–3. Comparison of the supports of excitation (left column), detection

(middle column), and effective OTFs for techniques using two opposing lenses

coherently. The effective OTF is the convolution of the excitation and detection

OTFs. For two-photon excitation in the 4Pi mode, the Fourier transform of the

excitation intensity is given by the excitation OTF of the 4Pi type C microscope

but scaled by 488 nm/800 nm = 0.61. The excitation OTF is therefore very

similar to the effective OTF of 4Pi type C. Note the gaps in the support of the

SWM microscope’s effective OTF.