CHEMPHYSCHEM REVIEWS DOI: 10.1002/cphc.201301086

Structured Illumination Microscopy for Superresolution John R. Allen,[a] Stephen T. Ross,[b] and Michael W. Davidson*[a]

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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CHEMPHYSCHEM REVIEWS The ability to image beyond the diffraction limit is the central tenet of the burgeoning field of superresolution fluorescence microscopy, also referred to as optical nanoscopy. The advent of superresolution has revolutionized biological fluorescence microscopy and the field at large. However, much of that excitement has been tempered by prohibitive imaging requirements. Achieving superresolution entails certain sacrifices, namely imaging speed, choice of fluorophore, ease of multicolor and three-dimensional imaging, and generally more complex instrumentation as compared to standard widefield imag-

1. Introduction Structured illumination microscopy (SIM) is a family of several conceptually similar microscopy techniques exploiting the use of patterned illumination. The term SIM thus encompasses several structured illumination-based techniques with differing imaging requirements and capabilities. Before discussing the resolution capabilities of SIM, it is important to more carefully define the terms “superresolution” and “nanoscopy”. For the purposes of this review, these terms will refer to any method providing an increase in resolution surpassing the diffraction limit, but not necessarily diffraction-unlimited. Also, these terms do not refer in any way to the optical sectioning capabilities of a technique. While some SIM methods do not provide resolution gains surpassing those of traditional widefield or confocal microscopy, others are capable of beating the diffraction limit or are even diffraction-unlimited. Available SIM instruments are capable of doubling conventional diffraction-limited resolution from approximately 200 nanometers (nm) laterally and 700 nm axially resolution to about 100 nm and 300 nm, respectively. Other superresolution methods offer even greater gains in resolution; single-molecule localization microscopy (SMLM)[1–3] is capable of approximately 10–30 nm lateral resolution on most systems. Others, including STED[4] and similar RESOLFT-based methods,[5, 6] are capable of matching that level. It should be noted that SMLM and STED are diffraction-unlimited, whereas existing commercial SIM instruments are not. However SMLM and STED suffer from different sets of limitations that, depending on the experimental requirements, can make SIM an attractive option. The performance of SIM in comparison to SMLM and STED will be more thoroughly explored, but the theoretical basis and instrumentation of the most popular varieties, as well as recent developments in the field, will first be reviewed. [a] J. R. Allen, Dr. M. W. Davidson National High Magnetic Field Laboratory and Department of Biological Science The Florida State University 1800 East Paul Dirac Drive Tallahassee, FL 32304 (USA) E-mail: [email protected] [b] Dr. S. T. Ross Nikon Instruments, Incorporated 1300 Walt Whitman Road Melville, NY 11747 (USA)

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www.chemphyschem.org ing techniques. Several techniques utilizing structured illumination occupy an intriguing middle ground between the ease of use associated with traditional fluorescence microscopies and the unprecedented resolving power of modern superresolution methods, resulting in undeniably robust imaging techniques. Presented here is a review of the conceptual basis of structured illumination and its implementation, including its performance in comparison to other nanoscopies and the most recent developments in the field.

SIM comes in several varieties. Earlier methods use structured illumination to create thin optical sections with a capacity similar to confocal microscopy.[7–9] The most popular iterations employ a single spatial frequency grid projected onto the specimen, illumination appearing as a line-pattern of sinusoidally alternating intensity maxima and minima. Contrast of the projected pattern is only maintained in the focal plane, resulting in effectively uniform illumination of features removed from the focal plane. Out-of-focus fluorescence can be computationally discriminated and removed from the final image. This approach will be referred to as optical sectioning SIM (OSSIM). It should be noted that OS-SIM as defined herein does not include superresolution approaches and will only be discussed in brief. Superresolution SIM (SR-SIM)[10–12] methods use the projection of a high-frequency pattern within the excitation light, the most popular of which use the same line-type pattern as OSSIM. Illumination with structured illumination results in modulation of the spatial frequencies of sample details, making normally unobservable frequencies accessible by down-modulation into conventionally observable space. Displaced information can be computationally identified and restored to its proper place in the image space. A more advanced iteration of this approach, termed non-linear SIM (NL-SIM),[13, 14] is capable of even greater resolution gains by incorporating non-linear effects into the illumination pattern.

2. Optical Sectioning SIM The potential of structured illumination was first theorized in 1963,[15] but not realized until 1993[16] with the introduction of standing-wave fluorescence microscopy (SWFM). This technique uses interference of a pair of slightly offset counterpropagating coherent lasers to create a pattern of alternating nodes and anti-nodes along the optical axis. Features located within the bright anti-node fields are selectively excited. Adjusting the angle of incidence between the two beams shifts the phase of the nodes, making it possible to scan the sample. This technique was demonstrated imaging 50 nm thick optical sections, effectively opening the door for structured illumination in microscopy. Techniques in the OS-SIM category are limited to those that provide optical sectioning ability but without achieving superresolution. OS-SIM as developed by Wilson and colleagues[7] will be primarily discussed. ChemPhysChem 2014, 15, 566 – 576

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CHEMPHYSCHEM REVIEWS John Allen received his B.S. in Biological Science from Florida State University in 2010. Since that time he has been working as a microscopist in the laboratory of Dr. Michael Davidson, using light microscopy to help characterize novel fluorescent protein fusion chimeras and address other biologically relevant questions. His microscopy experience includes work with widefield, confocal, TIRF, as well as superresolution techniques, including singlemolecule localization and structured illumination. Stephen Ross, Ph.D. is General Manager of the Product and Marketing Division at Nikon Instruments Inc., responsible for North and South America. Ross earned his Ph.D. in Neuroscience at the University of California, Irvine, working in the area of neuroplasticity. During his graduate research, Steve worked in the laboratory of Ivan Soltesz at the University of California, Irvine–College of Medicine on synaptic plasticity related to head trauma, learning, and memory using a combination of optical imaging and electrophysiology. Additionally, Ross worked in the laboratory of Joseph Fetcho, Ph.D. (Cornell University) where the pioneering work on the zebra fish as a model system for imaging physiology was done. Ross has been with Nikon for more than twelve years since beginning his career as an Applications Scientist, and has played a major role in the company’s product development roadmap. Steve has a passion for microscopy education, and has taught microscopy “bootcamp” at the MBL Physiology course for 10 years, in addition to being featured in multiple didactic lectures recorded for the iBiology initiative (http://www.ibiology.org/). Michael W. Davidson is a research faculty member affiliated with the Department of Biological Science and the National High Magnetic Field Laboratory at the Florida State University. Davidson’s laboratory is involved in development of educational websites that address all phases of optical microscopy, including brightfield, phase contrast, DIC, fluorescence, confocal, TIRF, and multiphoton. In addition to his interest in educational activities, Davidson is also involved in research involving the performance of traditional fluorescent proteins and optical highlighters in fusions for targeting and dynamics studies in live cells. Davidson’s digital images and photomicrographs have graced the covers of over 2000 publications in the past two decades and he has licensed images to numerous commercial partners. The proceeds of these licensing fees support Davidson’s research.

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www.chemphyschem.org 2.1. OS-SIM Theory Requiring few changes to a standard widefield upright or inverted microscope, OS-SIM can be used to create optical sections with a thickness comparable to that possible using laserscanning confocal microscopy (LSCM). Using an incoherent source of illumination, the pattern is projected in the focal plane and three images are acquired, each at a different phase of the grid pattern (0, 2 p/3, 4 p/3). Fluorescence is modulated in the direction of the pattern, reproducing the projected variations in intensity. However, with increasing defocus the pattern contrast is compromised, resulting in axially displaced features being effectively Kohler illuminated and weaker than those in the focal plane. Consequently, out-of-focus fluorophores do not exhibit modulated fluorescence when comparing the three raw images. The grid pattern mask can be removed on a pixel-by-pixel basis using Equation (1): IOS ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ðI1  I2 Þ2 þðI1  I3 Þ2 þðI2  I3 Þ2 

ð1Þ

The axial full width at half max (FWHM) of the grid pattern can be estimated using Equation (2): FWHMz ¼ 

ð3:83=16 pÞ  ðl  103 Þ   h  sin2 ða=2Þ  vg  1  vg =2

ð2Þ

where l is the excitation wavelength given in nm, h is the refractive index of the sample medium, a is the objective aperture angle, and vg is the effective grid frequency in the focal plane [Eq. (3)]: vg ¼

Mlv b  NA

ð3Þ

where M is the nominal objective magnification, v is the actual grid frequency, b is the instrument-dependent magnification factor for the reflected light beam path, and NA is the numerical aperture. It should be noted that this is not a linear operation and caution should be exercised when treating such data quantitatively. This is especially true when imaging under low signal-to-noise conditions where the effects of non-linearities may become more exaggerated. Popular commercial implementations include the Zeiss ApoTome and ApoTome.2. Illumination can also be generated by interference of two or more lasers[9] or using spatial light modulators (SLMs),[17, 18] as discussed later.

3. Superresolution SIM As previously stated, SR-SIM is capable of doubling resolution in both the lateral and axial directions.[19] However, though SRSIM instrumentation is relatively straightforward, the required computational approaches are much more complex. Thus, before discussing instrumentation and the latest developments in the field, the theoretical basis of the technique will be explored. First image formation and resolution in optical microChemPhysChem 2014, 15, 566 – 576

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scopes will be briefly reviewed, then the use of structured illumination for superresolution evaluated.

3.1. Resolution in an Optical Microscope Traditionally resolution in optical systems has been limited to approximately 200 nm in the lateral Figure 1. The diffraction limit in real and Fourier space. The graph on the left displays the intensity fluctuations of directions and 700 nm in the a pair of idealized sinusoidally-variant spatial frequencies in real space, one coarse (red) and the other fine (green). On the right the locations of these frequencies in Fourier space are illustrated. The transfer function speciaxial due to the diffraction of fies the fidelity with which contrast is maintained, and approaches a zero-value cut-off point corresponding to the light occurring between the Abb diffraction limit at 1/d, where d is the period of the high-frequency pattern. sample and the detector. Though a single point emitter may have sub-nanometer di3.2. Structured Illumination and Image Formation mensions, due to diffraction it appears as a much larger blurred three-dimensional area known as the point-spread function Applying a Fourier transform to the microscope PSF yields the (PSF). One can think of the PSF as a property of the microoptical transfer function (OTF) of the system. The OTF has two scope, an inherent blurring function that is applied to each components: the phase transfer function (PTF) and the modupoint emitter resulting in the observed pattern of fluorescence. lation transfer function (MTF). The latter is the amplitude comMost measures of resolution are fundamentally the same, with ponent of the OTF, and thus serves as the measure of how only subtle differences in defining the degree to which PSFs well contrast is conserved. With increasingly fine frequencies from pairs of point emitters can overlap and still be defined as the amplitude of the OTF (contrast) approaches zero, resulting optically resolved from one another. One commonly employed in a certain cut-off frequency past which finer frequencies are metric is the Abbe diffraction limit, which is given by rendered unobservable, as illustrated by Figure 1. This is analoEquations (4) and (5): gous to a pair of PSFs arising from separate point emitters Resolutionx,y ¼ l=2½h sinðaÞ

ð4Þ

Resolutionz ¼ 2 l=½h sinðaÞ2

ð5Þ

where l is the wavelength of the excitation illumination, h is the refractive index of the imaging medium, and the term h sin(a)the objective numerical aperture. The Abbe equations also have frequency space analogs, specifying maximum observable spatial frequencies and given by Equation (6): k0 ¼ 2 NA=lem

ð6Þ

where k0 is the magnitude of the maximum observable spatial frequency, NA is the numerical aperture, and lem is the emission wavelength. A Fourier transform can be applied to a function in order to switch it between the spatial and frequency domains. Thus while Equations (4) and (5) specify minimum resolvable distances between emitters, Equation (6) specifies a minimum resolvable spatial frequency. Spatial frequencies can be difficult to visualize, coarse frequencies correspond to structures that change gradually over several pixels while finer frequencies are attributed to much sharper, sudden changes in emitter density (Figure 1). There are certain advantages to working in the frequency, or Fourier, domain that are pivotal to the success of SIM.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

overlapping to the point where they cannot be distinguished as originating from separate entities. Spatial frequencies below the cut-off point are said to fall within the OTF support, and thus within the microscope passband. The OTF support can be visualized (in the lateral dimensions) as a circle where low-frequency information is closer to the origin and higher-frequency information towards the periphery, as illustrated by Figure 2 b. When an image is formed, the real-space position (r) of the object D(r) is multiplied by the illumination pattern I(r),

Figure 2. Illustration of OTF support expansion in the lateral dimensions kx,y. a) Moir fringes are created when two fine patterns are superimposed, representing modulated spatial frequencies that have been brought into observable region of frequency space, also known as the OTF support, and illustrated by (b). Note that the magnitude of the finest observable frequency k0 is along the edge of the support and equal to 2 NA/l. Structured illumination of frequency k0 results in the creation of harmonics centered at  k0 as shown by the points in (c). Extended OTF support regions are created centered at these points (d). Acquiring images at different orientations of the grid pattern allows one to circumscribe an expanded OTF support with approximately twice the diameter of the original. Reprinted with permission from ref. [10].

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which is then convolved with the microscope PSF, denoted by PSF(r), to yield the observed image E(r) [Eq. (7)]: EðrÞ ¼ ½DðrÞ IðrÞ  PSFðrÞ

ð10Þ

ð7Þ

The convolution function, denoted by , is an operation on a pair of functions that yields a function for finding the area overlap as one is translated with respect to the other. According to convolution theorem, the Fourier transform of a convolution operation is equivalent to the point-wise product of the respective Fourier transforms of each expression. Thus applying the Fourier transform to Equation (7) yields Equation (8): ~ ~ EðkÞ ¼ ½DðkÞ  ~IðkÞ OTFðkÞ

~i ðkÞ ¼ 0:5½DðkÞ ~ ~ þ k 0 Þ þ 0:5eifi Dðkk ~ þ 0:5eifi Dðk E 0 ÞOTFðkÞ

ð8Þ

The observed frequency information now has three harmonics: ˜ (k)), another one at the origin of the original OTF support (D ˜ ˜ centered at k0 (D(k+k0)), and the last at -k0 (D(k-k0)). Now the challenge is separating the signals produced by each harmonic so that spatial details can be correctly reassigned to their true place in frequency space. To do this requires images at several different phases of the illumination pattern. If the image contains m harmonics, then m different phases of the pattern should be imaged, resulting in equal numbers of linear combinations of the Fourier components, as there are unknown information components. These terms can be combined in a single m  m square matrix of the form (for three harmonics), given by Equation (11):

where tildes (~) specify the Fourier transform, k is spatial frequency, and OTF(k) is the Fourier transform of PSF(r). Applying 2 3 2 32 3 the Fourier transform allows one to switch between working in D0 1 1 1 E1 the spatial and frequency domains. The Fourier transform of 6 7 1 6 i1 7 i2 i3 76 D ð11Þ e e 5 4 E2 5 4 k0 5 ¼ 4 e a uniform, trivial illumination pattern such as I(r) = 1 results in 3 i1 i2 i3 D e e e E the Dirac delta function d(k) which, as the identity for convoluk0 3 tion, leaves any function with which it is convolved unchanged. Thus when a sample is Kçhler-illuminated, whether Next the inverse of this matrix is found and applied pixel-wise or not a spatial frequency is observable is dependent only to each phase-shifted image. The result can also be realized upon the condition that OTF(k) > 0 for a frequency k. However using Equation (12): if non-trivial structured illumination is utilized, the   result is the creation of several harmonics in the OTFðkÞD0 ðk ÞOTFðk þ k0 ÞDk0 ðk þ k0 Þ þ OTFðk  k0 ÞDk0 ðk  k0 Þ ð k Þ ¼ E SR Fourier transform of the illumination pattern, each ½jOTFðkÞj2 þjOTFðk þ k0 Þj2 þjOTFðk  k0 j2 þw 2  convolved with the spatial frequency information ð12Þ ˜ (k) and visually apparent in the form of given by D Moir fringes (Figure 2 a). where ESR(k) is the superresolved set of spatial frequencies, and w is the Wiener parameter. It can be used to modify the OTF Moir fringes are generated by frequency mixing whenever support range to help eliminate artifacts. Performing the intwo signals are multiplied. Thus if the structured illumination verse Fourier transform on ESR(k) will yield the real-space superpattern has a frequency given by k1, then mixing with each resolution image. One must still perform this process with sevsample frequency k results in the creation of Moir fringes at eral orientations of the grid pattern in order to circumscribe each difference and sum frequency k  k1. Normally inaccessithe full extended OTF support, as illustrated by Figure 2. ble spatial frequencies are thus observable if they are modulated into the OTF support, specifically if j k  k1 j < k0. In order to One of the shortcomings of two-dimensional SIM is that maximize sensitivity, the grid pattern frequency given by k1 axial resolution is left unaffected. In three dimensions the OTF should be made close to k0, resulting in a maximum observasupport has a torus-like shape, featuring a missing cone of inble frequency of up to 2 k0. The result is a virtual doubling of formation along the kz axis (Figure 3). An objective only illumithe OTF support in the  k1 directions. Sinusoidally structured nates and collects light from a limited range of angles [a; a] illumination as previously described is most popular [Eq. (9)]: determined by the numerical aperture of the objective. This determines the coherent transfer function (CTF) of the objec1 ð9Þ It ðr Þ ¼ ½1 þ sinð2 pkr þ t Þ tive. It should be noted that high-NA objectives can collect 2 a broader range of angles. In three-dimensional frequency space the CTF appears as a wedge-shaped cap of a sphere. where It(r) is the local illumination intensity, f is the phase of The PSF of an imaging system is the square of the modulus of the illumination pattern, and k is the frequency of the pattern. the amplitude point spread function (APSF), thus the OTF is The frequency of the pattern is made as close to the theoretiequal to the convolution of the Fourier-transformed amplitude cal value of k0 as possible, equal to 2 NA/l from Equation (6). A(x) with its own complex conjugate, represented by A*(x). Finer frequencies do not fall within the OTF support, and thus In Fourier space this equates to a convolution of the two will not be transmitted through the microscope; conversely terms [Eq. (13)]: coarse patterns as used for OS-SIM do not appreciably extend the support region. Taking the Fourier transform of It(r) and ˜ (k) from equation (8) yields Equation (10): convolving it with D  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

~Ik ¼ A ~k  A ~* k

ð13Þ

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www.chemphyschem.org NA/l. The result is greater overlap of OTF support regions, filling in the missing cone and allowing for optical sectioning with modest gains in lateral resolution.[20] These techniques allow for the acquisition of superresolution z-series. 3.3. SR-SIM Instrumentation

When designing a SIM imaging system one of the foremost requirements is the creation of a structured illumination pattern and the ability to modulate it. The simplest SR-SIM design uses the interference of two laser beams to create the pattern of sinusoidally varying illumination intensity.[10] This pattern is created by using a phase grating to diffract a collimated and linearly polarized laser beam into several orders. Only the  1 diffraction orders are allowed to pass, all others being stopped by a beam block, and form the pattern of illumination. The frequency of the pattern can be maximized by ensuring that both beams just enter the periphery of the objective back aperture. The optical train of a typical SIM setup is Figure 3. Optical transfer function support region in two and three dimensions with both conventional and structured illumination techniques. a) Conventional OTF support with trivial illumination patterns, note the missing presented in Figure 4. In order cone of information located along the kz axis. b) OTF from (a) represented in three dimensions, appearing as to give the pattern three-dimena toroid shape. c) Extended OTF support region realized using two-dimensional SR-SIM with three harmonics with sional structure, as needed to 3 different phases at a single orientation of the pattern. d) Extended OTF support of three-dimensional SR-SIM sharpen axial resolution, the 0th with seven harmonics, note that this new pattern fills in the missing cones of the components created using three harmonics alone. e) Three rotations of the pattern from (d) are used to extend the OTF in all directions. order is unblocked and allowed f) Wave vectors representing the three illumination beam directions for 3D SR-SIM. g) The three harmonics created to interfere. The result is that the by a two-beam illumination pattern and h) the seven harmonics by three-beam illumination. i) Lateral view of the pattern will vary sinusoidally OTF from (e) and a bird’s-eye view in (j). Reprinted with permission from ref. [19]. along the optical axis as well. In order to modulate the pattern phase and orientation, the graIn practice convolution of these two terms results in a three-diting is mounted on a rotatable closed loop translation device. mensional OTF with the described missing cone of information Images are generally acquired using three or five rotations of along the kz axis (Figure 3 a). Extending the axial OTF support the pattern in order to maximize imaging speed or sensitivity, entails adding axial structure to the illumination pattern. respectively. By adding sinusoidally varying axial structure, several addition More recently alternative pattern projection systems have harmonics offset not only along the lateral axes kx,y, but the become popular. LED arrays,[21] liquid-crystal spatial light modaxial kz are created. Four of the new components are displaced ulators (SLMs),[17, 18, 22] and digital mirror devices (DMDs)[23, 24] along the kz axis and act to fill in the missing cones, as shown have been demonstrated as powerful methods for creating by Figure 3, thus extending the axial extent of the OTF supstructured illumination. These devices provide great flexibility port. In practice an approximately two-fold increase in axial in terms of pattern generation, as they can be used either as resolution is realized. A second solution involves a modification a patterned mask for OS-SIM-type applications or as a grating to two-dimensional SR-SIM, instead of maximizing the frequento generate interference illumination patterns, and they allow cy of the pattern to equal 2 NA/l, it is instead made close to the user to optimize the frequency of the pattern without  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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www.chemphyschem.org was used to capture superresolution optical sections from a specimen 30 mm thick. Perhaps most exciting is the combination of light-sheet microscopy and SIM. One approach uses coarse structured illumination of standard light sheets to increase optical sectioning capability.[29] The other uses much finer light sheets generated using self-reconstructing Bessel beams to achieve SR-SIM, with fast 300 nm isotropic resolution having been demonstrated.[30, 31] Recently several novel applications of SR-SIM have been explored. An interesting recent application of SIM has been towards DIC imaging,[32] yielding a two-fold increase in lateral resolution over that conventionally possible with the described setup. SIM has also been employed to increase the resolution of flow cytometers.[33] Also recently, correlative SR-SIM and SMLM has been demonstrated;[34] the techniques being used to interchangeably identify and correct for imaging artifacts.

4. Non-Linear SIM Figure 4. Diagram of a two-beam interference SR-SIM setup. A laser beam is delivered to the microscope via an optical fiber and subsequently collimated and linearly polarized. The beam is diffracted into several orders and either the first orders left unblocked (2D SR-SIM) or both the zero and first orders (3D SR-SIM), resulting in the depicted illumination pattern. The proper orders are allowed to just enter the objective back aperture, projecting the pattern on the sample and recording fluorescence on a CCD. Reprinted with permission from ref. [19].

having to mechanically switch between different gratings. The primary benefit of using such technologies is increased speed in comparison to using a motorized grating; this is especially important for live-cell and multi-color imaging. 3.4. SIM Variations and Developments Axial resolution with SR-SIM can be extended even further by using a two-objective approach. The technique, termed I5S[25] to denote the combination of I5M[26] with SIM, is capable of 100 nm isotropic resolution. Plasmonic SIM (P-SIM)[27] is capable of even greater lateral resolution gains than conventional SRSIM. P-SIM uses a pattern generated by the interference of surface plasmons. The transmittance of surface plasmon spatial frequencies is not limited by the NA of the system and can thus be used to generate a pattern with a frequency greater than that possible using light. Using this approach a three-fold increase in lateral resolution over that possible with widefield microscopy has been demonstrated, however the technique is difficult to implement.[27] Greater axial resolution remains elusive, however many new optical sectioning SR-SIM approaches have been proposed. SR-SIM can be combined with TIRF microscopy,[17] combining the lateral resolution gains of the former with the ability to selectively excite molecules located within about 200 nm of the coverglass–medium interface of the latter. Another approach combines the resolution enhancement of SIM with the quick optical sectioning ability of line-scanning microscopy,[28] and  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Utilization of non-linear effects to sharpen the resolution in an SR-SIM system was theorized in 2002 with the concept of saturated pattern excitation microscopy (SPEM).[13] The first practical implementation came in 2005 with the introduction of non-linear SIM (NL-SIM),[14] specifically saturated SIM (SSIM), attaining 50 nm lateral resolution using fluorescent beads. One of the major hurdles associated with the SSIM approach is how to introduce and utilize a non-linear fluorophore response. 4.1. NL-SIM Theory With SSIM non-linearities are introduced by saturating fluorescent emission such that fluorophores exhibit a non-linear response to increasing excitation intensities. If the excited (S1) state is saturated, the sample will exhibit a non-linear fluorescence response to increasing excitation intensities. This effectively encodes higher-order harmonics into the illumination pattern that are multiples of k, where k is the frequency of the illumination pattern. 50 nm resolution was achieved using four total harmonic orders.[14] It should be noted that a non-linearity that can be described by a polynomial of order s results in the creation of s1 new harmonics. However, those that are nonpolynomial, as created by saturated excitation, result in a theoretically infinite number of harmonics. Ultimately the number of accessible harmonics m is limited by more practical considerations, such as photobleaching and signal-to-noise ratio. The contribution of each harmonic is determined in the same manner as for SR-SIM, requiring one to image m different phases of the pattern at each orientation in order to fill out the matrix in Equation (11). 4.1.1. Difficulties Using Fluorescence Saturation One of the fundamental difficulties with SSIM is the required illumination intensities for saturating fluorophores in the excited state. Such high intensities result in photobleaching and can be phototoxic. This is mitigated to a degree by using pulsed illumination, with pulse lengths on the order of about half ChemPhysChem 2014, 15, 566 – 576

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CHEMPHYSCHEM REVIEWS a nanosecond. SSIM also requires a much larger set of raw widefield images to create a reconstruction. Using nine total harmonics (three additional orders created by non-linearities) to extend resolution requires one to image nine different phases of the pattern. Additionally, the increased area of the desired OTF support requires several more orientations of the pattern in order to simulate circumscription of the entire extended support region. Originally twelve pattern orientations were employed. The result is that a single SSIM reconstruction requires 108 raw widefield images. In addition to photobleaching, sample drift can be become problematic due to the extended imaging time and sensitivity of the technique. 4.1.2. NL-SIM using Photoswitchable Fluorescent Proteins In order to mitigate the effects of photobleaching, alternative mechanisms for introducing non-linearities have been explored. A promising recent approach makes use of the photoswitchable fluorescent protein Dronpa to decouple the linear relationship between excitation and emission intensity.[35] This method has been demonstrated using approximately 6-fold lower excitation intensities than required for saturation as described above. Dronpa is reversibly switchable between two states: a fluorescent state excitable by blue light and a nonfluorescent that absorbs UV/Violet light. When activated the non-fluorescent state is switched back to the fluorescent and excitation of the fluorescent results in decay back to the nonfluorescent. Technically the saturation of either state can be used to introduce non-linearities, but saturation of the non-fluorescent was found to yield higher signal-to-noise, allowing for better identification of higher order harmonics.

5. Comparison with Other Superresolution Microscopies 5.1. Single-Molecule Localization Microscopy SMLMs, including STORM,[1] dSTORM,[36] PALM,[2] FPALM,[3] GSDIM,[37] and related methods, are premised upon the ability to temporally isolate and then localize individual fluorescent emitters to a super-resolved area. Photochemical properties of fluorescent molecules are exploited to exercise temporal control over the proportion of the ensemble allowed to fluoresce, allowing one to image emission from small non-overlapping subsets of fluorophores. Most often a Gaussian fit is applied to the emission profile and the centroid position identified with accuracy proportional to the number of emitted photons. With enough data, typically hundreds to thousands of frames, a superresolution composite reconstruction image can be created. Though 20 nm lateral and 70 nm axial resolution is typical,[38] advanced iterations of these techniques can go even further. Reductive fluorophore caging has been shown to increase photon output,[39] allowing for near-single nm resolution. Twoobjective approaches using an I5M type of approach make 10 nm isotropic resolution possible.[40, 41] SR-SIM resolution is several-fold worse than achieved in a typical SMLM experiment. However NL-SIM can be used with  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org FPs to afford a lateral resolution of 40 nm, close to that of typical PALM experiments. With SMLM the full resolution potential is not always realized, especially in more demanding experiments. One reason is that the sampling density is too low and thus does not satisfy the Nyquist frequency criterion[42] for the resolution at which individual emitters can be localized. This is especially common in live-cell experiments because a limited sampling time per reconstruction is required to prevent motion artifacts.[43] Only a limited of fluorophores have been found suitable for SMLM, and among them photon count, as well as other key properties, can vary widely.[44] The best synthetic dyes are capable of emitting approximately 6000 photons per burst, compared to a value approximately 1–2 orders of magnitude smaller for fluorescent proteins.[1, 44] There are several difficulties associated with SMLM that can detract from the utility of the technique. The necessity of acquiring so many frames of data makes SMLM decidedly slow, reducing its capacity for live-cell imaging. Live-cell imaging with FPs typically requires on the order of 30 s to acquire a usable reconstruction,[43] but as low as 1 s with 30–60 nm resolution using select organelle-specific synthetic dyes.[45] This is compared with reported 90 ms frame rates with 100 nm resolution for several hundred time points with TIRF-SIM.[17] In general SR-SIM is decidedly faster than SMLM, and without the same degree of resolution compromise under the more demanding imaging conditions presented by live-cell imaging. Though it is important to note that even under such strict conditions, SMLM is still fundamentally capable of greater resolution gains that SR-SIM. Additionally, extended SMLM sampling durations creates a requirement for a drift-correction step, usually executed either by tracking fiducial markers or employing a model-based algorithm. This is especially necessary given the sensitivity of SMLM methods. SMLM multi-color imaging must either be executed sequentially with spectrally distinct fluorophores,[36] extending imaging time and introducing possible chromatic aberration, or simultaneously with spectrally similar[46] or identical fluorophores.[1] The latter type of approach relies upon different ratiometric techniques for assigning fluorescence to the correct channel, and thus suffers from considerable amounts of crosstalk. Though 2–3-channel imaging is typical, six-color imaging has been realized.[47] Four-color imaging is typical for SR-SIM and can be performed on commercially available systems. An example 4-color SR-SIM image is given by Figure 5. A major advantage of SR-SIM is the lack of cross-talk between imaging channels, assuming the use of spectrally distinct probes and proper filter sets. Sample preparation for SMLM is generally more difficult in part because of the small pool of effective fluorophores. Additionally, many dyes for SMLM require different complex imaging formulations, making it difficult to identify formulations that work well for each and every probe in the sample. OS-SIM and SR-SIM can be used with almost any standard fluorophore, best performance being based on conventional criteria such as brightness, photostability, and so forth. However NL-SIM is currently limited to a small number of very specific reversibly photoswitchable probes and has only been demsonstrated with a single probe and imaging channel.[35] ChemPhysChem 2014, 15, 566 – 576

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Figure 5. Four-channel SR-SIM and corresponding widefield image of various cytoskeletal and nuclear components in a fixed mink uterus endometrium epithelial cell, GMMe line (ATCC CRL-2674). DAPI is pseudo-colored blue, Lamin B1 is labeled with ATTO647N and colored cyan, Vimentin is labeled with Alexa Fluor 488 and colored green, and F-Actin is labeled with a Phalloidin—Alexa Fluor 568 conjugate colored red. a) Whole-cell widefield image where (b) is a zoomed-in area marked by the boxed ROI in (a). c) SR-SIM image corresponding to the widefield image in (a). d) Zoomed-in SR-SIM image corresponding to the widefield image in (b). Imaging was performed on a Zeiss Elyra PS.1 system.

SMLM is also often used in conjunction with TIRF microscopy. This allows the creation of very thin optical sections of objects near the coverglass-medium interface. TIRF has also been used in conjunction with SWFM.[48] Three-dimensional SMLM imaging is generally performed with a depth of focus of less than 1 micrometer and almost exclusively in thin samples,[38] though some more advanced techniques overcome this by employing either a biplane imaging scheme[49] or a two objective approach.[40, 41] Three-dimensional SR-SIM can be used to acquire optical sections and z-series more quickly than most SMLM methods, but at decreased resolution. Optical sectioning of thick specimens is especially difficult with SMLM, but has been demonstrated to a limited degree using approaches such as two-photon activation.[50] The thickest specimen imaged that we are aware of is still only 200 micrometers thick,[51] additionally only a small set of optical sections were imaged, not a full-resolution z-series. 5.2. STED Microscopy STED microscopy is the most popular iteration of several similar techniques utilizing the concept of reversibly saturable optical fluorescence transitions (RESOLFT).[52] STED specifically  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org relies upon the phenomenon of stimulated emission to decrease the volume of the excitation PSF to a sub-diffractionlimited level.[4] Stimulated emission is a process whereby an excited-state electron can be returned to the ground state without fluorescent emission by interaction with a photon of a certain frequency, causing emission of a photon of the same energy as the incident photon and traveling in the same phase and direction. In practice stimulated emission is achieved using a very high-powered depletion laser (also known as a STED beam) whose spectrum is usually within the emission bandwidth of the probe. A helical phase ramp is used to introduce a zero-intensity node in the depletion laser center of focus. In two dimensions the PSF of the laser appears as hollow ring, and in three as a donut-shaped toroid. A typical Gaussian-distributed excitation laser can be centered through the depletion laser PSF, exciting structures located only within the zeronode. Processes other than stimulated emission can be employed using this approach, including saturation of the metastable triplet state for GSD[5] and the use of photoswitchable probes for the technique termed “RESOLFT”.[6, 52–55] The greater the depletion laser intensity, the smaller the area of the zero node where fluorescence can occur, resulting in an effective superresolution excitation PSF (PSFex). Often this translates into depletion laser powers several hundreds of times higher than the saturation intensity of the sample, but whose effects are mitigated in part by using pulsed lasers. The reduced PSFex is raster-scanned through the sample similar to LSCM. 30–80 nm lateral resolution is typical with commercially available systems, a decreased range in comparison to that typical of SMLM (10–30 nm) but similar to that realized using NL-SIM. 100 nm axial resolution is possible with STED using specialized depletion schemes.[56] This is worse than comparable SMLMs but 3-fold better than three-dimensional SR-SIM. However, some approaches are capable of down to about 30 nm isotropic resolution,[57] including iso-STED,[58] a two-objective scheme combining STED and 4Pi microscopy. This approaches the resolution gains of similar SMLM methods, and is an order of magnitude greater than that afforded by 3D SRSIM. Like SMLM, STED has been demonstrated using twophoton excitation.[59] However 3D SR-SIM is still superior in terms of collecting data from a large number of optical sections, as performed when acquiring a z-series. Photobleaching due to high depletion laser intensities affects structures outside of the focal plane as well, complicating the collection of serial optical sections. One consequence of the reduced size of the PSFex is the need to increase the sampling rate. For example, a 60 nm wide PSFex would need to be scanned approximately every 30 nm in order to satisfy the Nyquist criterion. Having to use a 30 nm pixel size significantly decreases the speed of the technique in comparison to LSCM, especially over larger areas. Combined with high intensities, photobleaching can be problematic. Approximately 40 different probes[60] have demonstrated compatibility with STED, a relatively small pool similar in size to that of SMLM. One approach uses the imaging of nitrogen vacancy centers in diamond to achieve 6 nm lateral resolution.[61] Though NL-SIM also is limited to a small number of potential fluorophores, OSChemPhysChem 2014, 15, 566 – 576

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CHEMPHYSCHEM REVIEWS SIM and SR-SIM are compatible with virtually any standard fluorophore making sample preparation less restrictive. Multicolor STED is usually implemented using a combination of four beams,[62] with a set of excitation and depletion lasers corresponding to each fluorophore. STED is currently capable of up to three-color imaging,[63] similar to the range typical of SMLM. SR-SIM is commonly used to image up to four channels, without additional specialized detection schemes. However one of the greatest challenges associated with STED is the acquisition of video-rate live-cell data. The fastest biologically-relevant implementation we are aware of was demonstrated with 28 frames per second at 62 nm resolution,[64] but only with a 2.5 mm  1.8 mm field of view. Recently the use of RESOLFT techniques utilizing reversibly photoswitchable fluorophores has proven promising for overcoming several of the limitations imposed by STED microscopy. RESOLFT allows for the use of illumination intensities approximately five orders of magnitude lower than required for STED or SSIM.[6, 54, 55] The imaging process can be parallelized in a manner similar to NL-SIM, featuring an array of zero nodes and allowing the user to significantly expedite the imaging process. One recent implementation was demonstrated with imaging times as low as 1–4 s for a 120  100 mm field.[54] Such a RESOLFT approach has an advantage over NL-SIM-type RESOLFT in that they use isotropic zero nodes and do not require mathematical post-processing of the data to reconstruct an image.

6. Summary and Outlook SIM is a versatile family of techniques able to satisfy a variety of demanding experimental requirements. OS-SIM provides a great alternative to confocal microscopy, providing fast three-dimensional multi-color optical sectioning capabilities. Linear SR-SIM approaches provide superresolution details quickly, and generally without change to standard sample preparation methods. NL-SIM closes the resolution gap between SIM and other superresolution techniques by a significant margin. As part of the veritable renaissance of superresolution imaging, these techniques continue to prove their merit. Given the wealth of new SIM methods that have been developed, there is little reason to believe that important factors such as speed and resolution will not continue to improve on pace with other superresolution methods such as SMLM and STED. Commercial SR-SIM systems are available from several major microscope companies, including Nikon, Zeiss, and Leica. Combined with an overall user friendliness, the future of SIM as a high-impact superresolution technique appears bright.

Acknowledgements The authors declare a conflict of interest: S.T.R. is employed by Nikon Instruments, Inc., which manufactures an SR-SIM microscope.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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Received: November 19, 2013 Revised: December 23, 2013 Published online on February 4, 2014

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