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Introduction

"To see a World in a Grain of Sand" (William Blake) [1] - "not only one world and not only in a grain of sand," a researcher working in the field of super-resolution microscopy might comment. Advanced far-field light-optical methods have become an indispensable tool in the analysis of nanostructures with applications both in the field of material sciences and in the life sciences. Tremendous progress has been made in recent years in the development and application of novel super-resolution fluorescence microscopy (SRM) techniques. As a joint effort by researchers in multiple disciplines, including chemistry, computer sciences, engineering, and optics, the development of SRM has its own place in the long history of light-optical microscopy, culminating in the 2014 Nobel Prize in Chemistry being awarded to Eric Betzig, Stefan Hell, and William E. Moerner for their achievements in the advancement of single-molecule detection and super-resolution imaging [2]. More precisely, these researchers succeeded in developing revolutionary new microscopy techniques that can be used, for example, in the investigation of fluorescent cell samples down to the level of individual molecules, that is, they cleared the way for new approaches that have proven invaluable for a wide range of applications in biomedical research. This is due to the fact that after specific labeling of a target structure with fluorescent markers, a fluorescence readout can be analyzed with respect to its spatial and temporal distribution, and thus it provides great detail about the underlying structure [3]. As the background in fluorescence imaging is typically close to zero, the resulting contrast allowed even the detection of single molecules [4]. Despite these developments, none of the novel SRM techniques has so far invalidated Abbe's (1873) or Rayleigh's (1896) limits for the resolution of light-optical microscopy; methods of circumventing these limitations have been discovered. By implementing these methods it became possible for the first time to, for example, directly observe the molecular machinery of life by far-field light microscopy.

This introduction presents the basic physical concepts behind the limits in optical resolution and offers an up-to-date diachronic overview of some important landmarks in the development of SRM methods. The next two chapters focus on the physicochemical background (Chapter 2) and required hardware and software (Chapter 3). The next four topic-specific chapters are dedicated to a description and evaluation of structured illumination microscopy (SIM) (Chapter 4), localization microscopy, and in particular single-molecule localization microscopy (SMLM) (Chapter 5), stimulated emission depletion (STED) microscopy (Chapter 6), and multi-scale imaging with a focus on light-sheet fluorescence microscopy (LSFM) and optical projection tomography (OPT), as well as on sample preparation techniques such as clearing and expansion microscopy (ExM) (Chapter 7). These application-oriented chapters are not restricted to a mere description of the respective techniques but offer a thorough discussion and evaluation of the specific potentials and problems of the various methods. Each of these advanced light-optical microscopy techniques responds in its own specific way to the research question and challenges at hand, and each of them comes with its own set of benefits and disadvantages. The discussion (Chapter 8) finally tries to push the limits by shedding light on potentially promising progressive approaches and future challenges in this ever-growing and extremely fast developing field. A particular focus in all of the discussions will be on the application of advanced light-optical microscopy in studies of biological cell samples.

In the visible range of the electromagnetic spectrum, cells can be considered thick, transparent objects that can be analyzed in three dimensions by means of far-field light microscopy either after fixation in a preserved state or possibly as live samples. However, the images produced by this analysis method lack structural information owing to the limited resolution of light microscopy. In recent years, a number of methods of fluorescence microscopy have been developed to narrow down the spread of the blur in microscopic images or to facilitate the separate detection (localization) of individual fluorescent molecules within samples and, thus, to prevent the "Abbe limit of microscopic resolution" from being applicable to the final microscopic image, resulting in the transition from microscopy to nanoscopy. The realization of focused nanoscopy-based STED and localization microscopy-based photoactivated localization microscopy (PALM) techniques represents culminating points of a long history of attempts to overcome the so-called Abbe limit: In 1873, Ernst Abbe, the colleague of Carl Zeiss, in his pioneering developments of advanced microscopy, stated that "[...] the limit of discrimination will never pass significantly beyond half the wavelength of blue light [...]," which corresponds to approximately 200 nm. A similar limit for the possibility to distinguish two "point-like" luminous objects was given by Lord Rayleigh in 1896. Point-like means that the dimensions are much smaller than the wavelength used for imaging. From this time on, for about a century, the 200 nm value of the Abbe limit has generally been regarded as the absolute limit for obtaining structural information by far-field light microscopy. However, already in his famous contribution (1873) on the fundamental limits of optical resolution achievable in (far-field) light microscopy, Abbe stated that the resolution limit of about half the wavelength used for imaging is valid only "[...] so lange nicht Momente geltend gemacht werden, die ganz außerhalb der Tragweite der aufgestellten Theorie liegen [...]."1) As seemingly foreseen by Abbe, only by deviating from the experimental conditions stated in his original work could super-resolution by STED and PALM be achieved.

1.1 Classical Resolution Limit

In 1873, Ernst Abbe derived from theoretical considerations a criterion for the resolution limit of a light microscope. The considerations that led to its formulation are as brilliant as they are simple: He understood that an object consisting of small structural features gives rise to diffraction, which is known to be stronger for smaller structures. The plethora of structural features present in a real object might be approximated locally by a superposition of stripes of different orientations, stripe widths, and strengths. This will help us in what follows to understand the concepts behind the image blur. Let us consider a fine grating structure with lattice constant d (spacing between two stripes), embedded in a medium with refractive index n, which is illuminated centrally with light of wavelength ?/n (? being the vacuum wavelength). This will result in constructive interference of order m observed under an angle a if the following condition is fulfilled:

When imaged by a lens, such an interference pattern will only be transmitted under the condition that, in addition to the central non-diffracted beam, at least the m = ±1 orders are collected by the lens, i.e., two fine object features have a minimum distance dcentr.illum. = ?/(n sin(a)). If oblique illumination is used, the minimum distance d for which diffraction arising from the structure is collected by the lens is half the value of dcentr.illum.. From this Abbe derived his famous formula for the resolution limit in optical microscopy [5]:

which describes the minimum distance d of two structural features to be resolved by the microscope, where n sin (a) is the numerical aperture of the detection objective lens, n is the refractive index of the sample, and a is half of the opening angle defined by the rays of light that are detected by the objective lens (acceptance cone); a is the so-called half-aperture angle of the objective lens.

In general terms, Abbe stated a formula for the smallest distance d that two point-like object details can have so that they can still be discriminated (resolved) by microscopy. According to his formula (1.2), the smallest distance d is determined by the vacuum wavelength ? of the light used for imaging and the numerical aperture n sin(a). For a perfect lens with no spherical aberration, the intensity of the 2D diffraction pattern of such a single "point source" in the (perfect) focal plane is shown in Figure 1.1a. This diffraction pattern is described [6] by the formula

Figure 1.1 Microscopic image of a "point source" (a) or two "point sources" in close proximity (b). Scale bar equals full width at half-maximum (FWHM) of the diffraction pattern of a single "point source." See text for numeric values.

where J1 is the first-order Bessel function of the first kind, and v is the (generalized) lateral optical coordinate, related to the image coordinate by

Knowing the lateral magnification of the microscope system, the image coordinate r can easily be transferred to the object...