Fast TIRF-SIM imaging of dynamic, low-fluorescent biological samples.

Fluorescence microscopy is the standard imaging technique to investigate the structures and dynamics of living cells. However, increasing the spatial resolution comes at the cost of temporal resolution and vice versa. In addition, the number of images that can be taken in sufficiently high quality is limited by fluorescence bleaching. Hence, super-resolved imaging at several Hertz of low fluorescent biological samples is still a big challenge and, especially in structured illumination microscopy (SIM), is often visible as imaging artifacts. In this paper, we present a TIRF-SIM system based on scan-mirrors and a Michelson interferometer, which generates images at 110 nm spatial resolution and up to 8 Hz temporal resolution. High resolution becomes possible by optimizing the illumination interference contrast, even for low fluorescent, moving samples. We provide a framework and guidelines on how the modulation contrast, which depends on laser coherence, polarization, beam displacement or sample movements, can be mapped over the entire field of view. In addition, we characterize the influence of the signal-to-noise ratio and the Wiener filtering on the quality of reconstructed SIM images, both in real and frequency space. Our results are supported by theoretical descriptions containing the parameters leading to image artifacts. This study aims to help microscopists to better understand and adjust optical parameters for structured illumination, thereby leading to more trustworthy measurements and analyses of biological dynamics.


Introduction
Proteins are molecules formed by a genetic construction plan and which are expressed in many different shapes, serving specific functions. To understand the distribution, the dynamics, the interplay and the functionality of proteins and associated molecules, the best possible visualization is essential. Both, highest spatial and temporal resolution is critical to retrieve information from image sequences of living cells to understand dynamic processes on short temporal and small spatial scales. Super-resolution techniques based on fluorophore localization have the inherent drawback of often-unacceptably long acquisition times and high bleaching rates relative to conventional fluorescence techniques. Imaging of small and highly dynamic structures like fluorescent proteins inside living cells renders the use of slow super-resolution techniques ineffective and prone to erroneous observations. Structured illumination microscopy (SIM) has proven to be an excellent compromise, between a reasonable increase in spatial resolution and a tolerable loss in temporal resolution [1][2][3] relative to conventional microscopy. A particularly successful variant is total internal reflection fluorescent structured illumination microscopy (TIRF-SIM) [4][5][6][7]. It yields higher spatial resolution than standard 2D-SIM and it needs shorter acquisition times than 3D-SIM due to its limitation to two dimensions. For linear TIRF-SIM only nine raw images have to be acquired to obtain a super-resolved image with about twice the resolution of the standard TIRF image. our experimental TIRF-SIM system used to achieve maximum image quality for dynamic, low fluorescent samples. We demonstrate and assess the system's capabilities and limits for standard fluorescent samples such as beads. Finally, we illustrate the feasibility of TIRF-SIM imaging of dynamic, low fluorescent probes such as cytoskeletal filaments inside bacteria and inside eukaryotes.

Local modulation contrast in TIRF-SIM
High modulation contrast of the illumination grating is critical for structured illumination imaging. In TIRF-SIM, usually three pairs of counter-propagating evanescent waves with k-vectors subsequently generate two-dimensional interference gratings, where the tangential component k t,ev = k 0 · n i · sin(θ i ) depends on the wave number k 0 , the refractive index of the incident material n i and the angle of the incident beam θ i . For dielectric media, the field component perpendicular to the interface (axial z-direction) decays exponentially in the optically thinner medium. The intensity I ev (x, y, z) of the interference grating is characterized by the beam intensities at the interface I 1 and I 2 , by the wave vector-difference k ev − (−k ev ) = 2k ev and the modulation contrast C mod (r ⊥ ), which depends on the lateral position r ⊥ at z=0. The wave vector k ev represents three different azimuthal illumination directions α = 1,2,3. At the position z above the interface at z=0, the fluorescence excitation intensity reads I ev,α (r ⊥ , z, φ 0 ) = (I 1 (r ⊥ ) + I 2 (r ⊥ )) · (1 + C mod (r ⊥ ) · cos(2 k ev,α · r ⊥ + φ 0 ) · exp(−z/d(θ i )) (1) with grating phase φ 0 and penetration depth d(θ i ) = λ 0 / 4π n 2 i sin 2 θ − n 2 t . C mod (r ⊥ ) depends on the local intensities I 1 and I 2 , and the local degree of spatial coherence γ s (r ⊥ ) C mod (r ⊥ ) = 2 I 1 (r ⊥ )I 2 (r ⊥ ) I 0 (r ⊥ ) · γ s (r ⊥ ), where I 0 (r ⊥ ) = I 1 (r ⊥ ) + I 2 (r ⊥ ) is defined by the magnitude square of the beams' electric fields I 1/2 (r ⊥ ) = |E 1/2 (r ⊥ )| 2 . For the beam intensities I 1/2 , the vector characteristics of the E-fields needs to be taken into account. According to Axelrod [23], the three-dimensional intensity distribution of the evanescent field depends on the incident angle θ i , the polarization angle Ψ 1/2 , the electric field amplitudes E 0 and the ratio of the refractive indices of the incident and transmitting medium n ti = n t /n i . The intensity for both I 1 (r ⊥ , z) and I 2 (r ⊥ , z) reads Where E 0P and E 0S are the electric field amplitudes for p-and s-polarization, respectively. The functions f 1 , f 2 and f 3 are described by Axelrod [23] and all the variables introduced above are prone to perturbations in the optical beam path resulting in changes in the modulation contrast. Consequently, the modulation contrast is often locally compromised and needs to be optimized locally to obtain high-resolution images over the entire field of view.

Quantitative assessment of local interference contrast via standard deviation
The (coherent or fluorescence) image p(x,y) is obtained by convolution of a signal L(r)·s(r) (emitted field or intensity) with the 3D detection PSF(r), where L(r) = L 0 (x, y) · e −z/d is the illumination function, L 0 is the interference grating and s(r) is the object (sample) distribution. Usually, convolving the signal with a 2D PSF(x,y) is sufficient, since no adjacent objects can be separated in axial direction within the penetration depth d of the evanescent wave. At PSF position z 0 = d/2, we approximate for the camera image p(x, y, z) Within the extent of the PSF, the object information is averaged (integrated). Since the penetration depth d is shorter than the axial extent ∆z of the PSF det , i.e. d < ∆z = 2λ / (n-ncosα), the approximation in the 2nd line of Eq. (5) is justified.
For the coherent case, used in Fig. 1, we measure the interference of electric fields L 0 (r) = E 1 (r) + E 2 (r), i.e. |p(x, y)| 2 . In the other figures, fluorescent, i.e. incoherent imaging of a fluorophore distribution s(r) is used to analyze the raw images p m (x,y,φ m ) with phase shift m = 0,1,2 such that L m (r) = I ev,m (r) = I 0,m (x, y) · e −z/d , or correspondingly: Here, the factor σ fl = σ ext · Q fl contains the extinction cross-section σ ext and the quantum efficiency Q fl of the fluorophore. As explained in Eq. (8), the situation becomes more complicated for fluorophores close to an interface.
The modulation contrast C mod of an interference grating can be obtained by the modulation contrast in the image C im mod (r ⊥ , k ev ) = C mod (r ⊥ )·MTF(k ev ), which weights C mod by the modulation transfer function MTF(k ev ) = |FT[PSF(r ⊥ )]|. Both C mod and C im mod can be determined via the extreme values p min and p max inside regions of interest (ROI) with a width 2π/k ev of the intensity pattern at a position r s . However, the approach of analyzing many ROI is impractical and inconvenient when assessing the contrast locally over large field of view. A more direct and user-friendly approach is the local contrast C STD (r ⊥ ) obtained via the normalized standard deviation over typically M = 3 equidistant grating positions φ m = 0 . . . 2π: The standard deviation distribution p STD (x, y) and the mean intensity distribution p mean (x, y) can be obtained by either (coherently) imaging the electric fields at the coverslip onto the camera or by (incoherently) imaging the fluorescence distribution of small beads.
In the case of coherent imaging contrast analysis as shown in Fig. 1, the contrast from the interference pattern |p m (x, y)| 2 = |E 0,m (x, y) * PSF coh (x, y)| 2 ≈ |E 0,m (x, y)| 2 is hardly influenced by the coherent PSF coh (x, y) or transfer function MTF coh (k ev ).
The approach yields a spatially sensitive contrast map, which is shown in Fig. 1(B). The contrast C STD (r ⊥ ) differs from the contrast C mod (r ⊥ ) by a correction factor A corr . Analytically, the

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The standard deviation distribution ( , ) STD p x y and the mean intensity distribution ( , ) mean p x y can be obtained by either (coherently) imaging the electric fields at the coverslip onto the camera or by (incoherently) imaging the fluorescence distribution of small beads.
In the case of coherent imaging contrast analysis as shown in Fig. 1 The approach yields a spatially sensitive contrast map, which is shown in Fig. 1  A does not change for a finite number of phase steps used to sample the grating over the entire period. However, in the experiment, every detector averages the illumination grating over its extent, which renders corr A dependent on the size of the detector, which is evident in the grating image's cross section shown in Fig. 1 (C). If the detector is not radially symmetrical, corr A also depends on the grating's direction relative to the orientation of the detector.
In the case of incoherent imaging of a fluorescent particle acting as a sensor for the measurement of the local intensity, the depth of the evanescent field plays an important role.
For the present analysis, the three dimensional intensity   ,, ev I x y z of the evanescent field was calculated as presented in [23]. Assuming that the particle does not alter the evanescent field in any way, an integration over the volume of the sphere in the evanescent field yields the fluorescence intensity emitted by the fluorescent probe (Born approximation) correction factor is A corr = √ 2 for a sinusoidal grating. A corr does not change for a finite number of phase steps used to sample the grating over the entire period. However, in the experiment, every detector averages the illumination grating over its extent, which renders A corr dependent on the size of the detector, which is evident in the grating image's cross section shown in Fig. 1(C). If the detector is not radially symmetrical, A corr also depends on the grating's direction relative to the orientation of the detector.
In the case of incoherent imaging of a fluorescent particle acting as a sensor for the measurement of the local intensity, the depth of the evanescent field plays an important role. For the present analysis, the three dimensional intensity I ev (x, y, z) of the evanescent field was calculated as presented in [23]. Assuming that the particle does not alter the evanescent field in any way, an integration over the volume of the sphere in the evanescent field yields the fluorescence intensity emitted by the fluorescent probe (Born approximation) The expression above is valid if, the fluorescent response is linear, which is usually the case for linear SIM. For the R=46 nm beads, frequently used in for our experiments, the correction factor is A corr = 1.8784.
In the case of incoherent imaging contrast analysis in Fig. 3(D), the contrast from the interference pattern p m (x, y) is influenced by the incoherent PSF inc (r ⊥ ), or the strongly decaying transfer function MTF inc (k ev ) = AC[MTF coh (k ev )], correspondingly. For inter-bead distances larger than the PSF-width, however, the contrast C mod (r ⊥ ) was hardly influenced by MTF inc (k ev ).
For the approach of directly measuring the inference pattern on the camera chip, the correction factor is determined by the camera's pixel size. Either way, the approach via standard deviation and theoretically determined correction factor enables the access to quantitative contrast maps of the pivotal interference grating.

Noise in the imaging process
According to Eq. (5), the image of a fluorescent sample s(r ⊥ , λ em ), excited at λ ex and emitting at the mean wavelength λ em is illuminated by the intensity I ev,m (r ⊥ , λ ex , φ m ) and blurred by the incoherent detection point spread function PSF(r ⊥ , λ em ). In addition, the image is deteriorated by space variant noise n(r ⊥ ) In Fourier space, the sample spectrumS(k ⊥ ) = FT[s(r ⊥ )] is convolved with the spectrum I ev,m (k ⊥ , φ m ) of the illumination grating, i.e.S(k ⊥ ) is shifted by the wave vector ±2k ev . The convolution with the PSF becomes a multiplication with the incoherent modulation transfer function (MTF), such that the image spectrum reads Neglecting a global phase shift, the illumination spectrum readsĨ ev,m (k ⊥ , φ m ) ≈Ĩ 0 2πδ(k ⊥ ) Therefore, one defines a larger effective MTF eff assembled from nine raw spectraP m,α (k ⊥ , φ m ) with equidistant phases steps m = -1,0,1 and symmetrically distributed azimuthal illumination directions α = 1,2,3 with corresponding wave vectors k ev,α The final super-resolved image p SR (r ⊥ ) is obtained by a deconvolution using the enhanced object spectrumP eff (k ⊥ ) Since, deconvolution is an ill-posed problem, there is no unique solution even in the absence of noise. Usually, a Wiener filterW(k) and an apodisation functionÃ(k) are used to suppress high frequency noise [24]. However, other deconvolution approaches like Richardson-Lucy deconvolution have also been tested [25] For the Wiener filter used in this work, the object's mean power spectral density |S(k)| 2 is unknown and replaced by a parameter w = |Ñ(k ⊥ )| which has to be chosen empiricallyW To assess the amount of noise n(r ⊥ ) in a fluorescent image, the signal-to-noise ratio is a characteristic quantity that can be easily obtained for white noise. Usually, the mean intensity p mean (r ⊥ ) = +1 m=−1 p m (r ⊥ ) and its standard deviation p STD (r ⊥ ) are compared to the dark image's mean value p dark (r ⊥ )

Fast TIRF-SIM setup
The general goal of TIRF-SIM is fast super-resolution imaging of biological, often weakly fluorescent, dynamic samples under a large field of view. We laid further emphasis on costeffectiveness, stability, simplicity and avoidance of diffraction elements. Figure 2 depicts our solution to these requirements. For s-polarized illumination beams, the initial linear polarization is converted to circular polarization with a /4  wave-plate. Then, a custom-built segmented polarizer ("pizza polarizer") [26] filters out the azimuthal component of the circular polarization for each illumination direction. The polarizer eliminates the need for mechanical rotation of a /2  wave-plate, while maintaining high polarization contrast, which is difficult for Liquid Crystal Polarization Retarders or Pockels cells. Moreover, the polarizer contains six pinholes to guarantee homogeneous Gaussian beams.
An inverted microscope (DM-IRB, Leica, Germany) with a NA=1.46 TIRF-objective (HCX PL APO 100x1.46 Oil CORR23°37°, Leica) serves as imaging unit. To permit simultaneous detection of two color channels, a custom-built dual-beam viewer, splits the emission light into two color channels with two dichroic mirrors (H 560 LPXR superflat, AHF) and appropriate emission filters. Two sides of the chip of a Hamamatsu Orca Flash 4.0 CMOS camera image the separated color channels simultaneously.
The selected configuration and components serve the pre-defined purpose of speed, robustness, simplicity and cost-effectiveness. Great care was taken to use stable posts and mounts to avoid thermal drifts. Adjustable mounts were only used, were it could not be avoided. Vibrations are kept minimal, since the two piezo mirrors are the only moving parts of the system.
The reconstruction was performed with the reconstruction algorithm presented in [27,28]. For comparison, the freely available ImageJ plugin fairSIM was applied and provided comparable results. The illumination unit includes illumination sources and beam steering devices (piezo scan mirror). The beam splitting unit comprises a Michelson interferometer with a retro reflector to mirror the beam at the optical axis. The polarization adjustment unit achieves the desired azimuthal polarization through a segmented polarizer ("Pizza polarizer"). In addition to the commercial microscope unit, there is custom-built detection unit, imaging two colors on separate sides of a sCMOS camera chip.

Results: Mapping the interference contrast
An acousto-optic tunable filter (AA Opto-Electronic, Orsay, France) ensures fast on-off switching of the two low noise 50 mW DPSS Lasers (Jive/Calypso, Cobolt, Sweden) with wavelengths of λ 1 = 491 nm and λ 2 = 561 nm, respectively. A piezo scan mirror (S-330.4SL, Physik Instrumente, Germany) displaces the beam from the optical axis to achieve total internal reflection. The time needed to switch between illumination directions is limited by the scan mirror, which needs <5 ms to switch between directions. A large aperture permits large beam diameters resulting in a large FOV, while low dither amplitudes ensures minimal vibrations of the illumination grating.
A Michelson interferometer splits the beam into the two beams needed for interference in the sample plane. A second piezo mirror (S-303.0L, Physik Instrumente, Germany), named "phase shifter" in Fig. 2, shifts the phase of one beam in comparison to the other and hence alters the phase of the illumination grating in steps of ∆ϕ = 2π/3. A retro-reflector mirror (PM1-RR300, Thorlabs, USA) displaces each of the three beams to its opposite side of the propagation axis, yielding illumination patterns in three fixed illumination directions.
For s-polarized illumination beams, the initial linear polarization is converted to circular polarization with a λ/4 wave-plate. Then, a custom-built segmented polarizer ("pizza polarizer") [26] filters out the azimuthal component of the circular polarization for each illumination direction. The polarizer eliminates the need for mechanical rotation of a λ/2 wave-plate, while maintaining high polarization contrast, which is difficult for Liquid Crystal Polarization Retarders or Pockels cells. Moreover, the polarizer contains six pinholes to guarantee homogeneous Gaussian beams.
An inverted microscope (DM-IRB, Leica, Germany) with a NA=1.46 TIRF-objective (HCX PL APO 100 × 1.46 Oil CORR23°37°, Leica) serves as imaging unit. To permit simultaneous detection of two color channels, a custom-built dual-beam viewer, splits the emission light into two color channels with two dichroic mirrors (H 560 LPXR superflat, AHF) and appropriate emission filters. Two sides of the chip of a Hamamatsu Orca Flash 4.0 CMOS camera image the separated color channels simultaneously.
The selected configuration and components serve the pre-defined purpose of speed, robustness, simplicity and cost-effectiveness. Great care was taken to use stable posts and mounts to avoid thermal drifts. Adjustable mounts were only used, were it could not be avoided. Vibrations are kept minimal, since the two piezo mirrors are the only moving parts of the system.
The reconstruction was performed with the reconstruction algorithm presented in [27,28]. For comparison, the freely available ImageJ plugin fairSIM was applied and provided comparable results.

Results: Mapping the interference contrast
The key to high quality imaging with structured illumination is a high modulation contrast C mod (x, y, k ev ) of the illumination interference grating. Stray light, diffraction at edges and imperfections of optical surfaces, back reflections, misalignment, polarization dependence of optical components and the sample itself are just some examples, which may degrade the contrast of the illumination pattern. Consequently, the super-resolved image will contain artefacts, exhibit lower resolution than expected or it even is impossible to reconstruct better-resolved images at all.
In Section 3.2, we introduced a quantitative method to measure the contrast locally over the entire field of view by calculating the standard deviation of several grating positions. The method can be exploited in two ways: First, the illumination grating can be imaged coherently by removing the emission filters (EF) (see Fig. 2). Second, bright fluorescent samples containing small structures like small fluorescent particles can be used as probes to access the contrast directly at the samples position.
With the first method, the dichroic mirror (DM2) still transmits sufficient excitation light so that the totally reflected illumination light coherently images the interference grating on the camera. Contrast maps obtained with this method are shown in Figs. 3(D)-3(J). Here, the contrast C mod (x, y) over the entire illuminated field of view is indicated according to the accompanying color map. Regions of low or zero contrast are shown in blue, while regions of high contrast appear in red. It has to be noted that noisy regions (e.g. dark areas appear in red as well).
With the second method, the exact dimensions of the fluorescent probes are needed to quantitatively calculate the contrast as presented in Section 3.2. Therefore, geometrically well-defined samples like fluorescent beads are required. In addition, dense samples are beneficial to map the contrast over the entire field-of-view.
Hence, coherent images of the illumination grating itself (first method) are a straightforward choice to assess the contrast uniformly without cumbersome sample preparation. However, this way only information about perturbation of the light path is provided, because the light is totally reflected at the coverslip interface. Hence, only fluorescent probes are able provide information about the evanescent field's interference grating itself (second method). Examples are shown in Figs. 3(B) and 3(C).
Both methods yield an interference contrast map C mod (x, y) (see Eq. (2)), which depends on the degree of coherence γ s (∆r = |r 1 − r 2 |, ∆t = t 2 − t 1 ) = e iφ(r 1 ,t 1 ) · e −iφ(r 2 ,t 2 ) , but also on the polarization and phase delays of the electric field of components. It can be expressed as polarization direction as depicted in Fig. 3 (H) and (I) Using a simple plate beam splitter instead of the dichroidic mirror eliminates this deterioration, as well ( Fig. 3 (J).

Results: Image quality hardly depends on wavelength and phase shift
Once the modulation contrast has been optimized, the TIRF-SIM approach presented here offers the expected resolution close to the theoretical limit (Fig. 4).  Misalignment is another critical point, which is a common source of contrast degradation. The two illumination beams have to overlap for all directions at the same position without being tilted or displaced, as it is shown in Fig. 3(G).
Polarization effects of optical components are another source of potential contrast degradation. Especially dichroic mirrors are prone to polarization turning and have to be chosen with great care to avoid significant impairment of contrast depending on the polarization direction as depicted in Figs. 3(H) and 3(I) Using a simple plate beam splitter instead of the dichroidic mirror eliminates this deterioration, as well (Fig. 3(J)).

Results: Image quality hardly depends on wavelength and phase shift
Once the modulation contrast has been optimized, the TIRF-SIM approach presented here offers the expected resolution close to the theoretical limit (Fig. 4). A unique feature of this TIRF-SIM implementation is the simultaneous acquisition of two distinct fluorophores excited at two different wavelengths simultaneously. In this imaging mode, two lasers generate two illumination gratings at the sample at the same time, while the emission light is collected on two different halves of the same camera chip using a dual beam viewer (Fig. 2). This time saving imaging mode is feasible only with a system, which does not contain any diffraction elements like SLMs or wavelength dependent polarization modulators. The only wavelength dependent parameters are the grating's period (  . This does not visibly affect the image quality as shown in Fig. 5 for 92 nm fluorescent beads. Here, a single color sample TIRF-SIM image was acquired with two different phase shifts. Fig. 5 (A)  A unique feature of this TIRF-SIM implementation is the simultaneous acquisition of two distinct fluorophores excited at two different wavelengths simultaneously. In this imaging mode, two lasers generate two illumination gratings at the sample at the same time, while the emission light is collected on two different halves of the same camera chip using a dual beam viewer (Fig. 2). This time saving imaging mode is feasible only with a system, which does not contain any diffraction elements like SLMs or wavelength dependent polarization modulators. The only wavelength dependent parameters are the grating's period |k ev (λ)| = sin θ i · n · 2π/λ and phase shift ϕ n (λ ps ) appearing in the interference term cos(2k ev (λ ex ) · r ⊥ + ϕ n (λ ps )). The phase shift ϕ n (λ ps ) = n 2π 3 = n · 2π/λ ps · d ps is usually altered twice precisely by one third of the wavelength λ to obtain the three raw images along one illumination direction. However since the phase shift mirror can shift correctly for only one wavelength,a precsie 2π 3 grating shift is not possisble for both wavelengths, i.e. for simultaneous acquisitions with two lasers. Therefore, as a compromise, a mean wavelengthλ ps = 1 2 (λ ex1 + λ ex2 ) is chosen and the grating shifted by one third of it, d ps = 1 3λ ps . This does not visibly affect the image quality as shown in Fig. 5 for 92 nm fluorescent beads. Here, a single color sample TIRF-SIM image was acquired with two different phase shifts. Figure 5(A) displays the result for a correct phase shift of 1 3 λ ex1 =163 nm, which is f one third of the wavelength of the illumination laser for each phase step, whereas in Fig. 5(E) a longer, incorrect phase shift 1 3λ ps was used, corresponding to a mean wavelengthλ ps . There are no notable differences visibible in the super-resolved images p SR (r ⊥ , ϕ ex1 ) and p SR (r ⊥ ,φ ps ) and the image's spectra Fig. 5(B), Fig. 5(C) as well as the spectra's averaged radial slices (F), which differ only by less than 5% depending on the frequency, Fig. 5(G) nor in exemplatory line scans in Fig. 5(H). differ only by less than 5% depending on the frequency, (G) nor in exemplatory line scans in Fig. 5 (H). This approach was used for the simultaneous acquisition of TIRF-SIM images in two colors as depicted in Fig. 6 (A). The acquisition of sequential images in Fig. 6 (B) need nearly twice as long. Colocalization of two flurophores emitting light at two different wavelengths cannot not be imparied by sample movement during sequential acquision of the two colors. On the other hand, simultanous imaging may suffer from a compromised phase shift and additional cross-talk between the two color channels. However, a slight loss in contrast (and resolution) for simultaneous imaging is visible in the red channel depicted by in the line scan in Fig. 6 (E). The resolution reduction is very likely due to cross-talk induced by the green fluorescent particles in the red channel, which are not excited during acquisition of the red channel in the sequential imaging mode. During simultaneous acquisition, they emit a non-discardable amount of fluorescence in the red channel, as well and hence the complex reconstruction process yields a lower accuracy. This is not the case in the green channel Fig. 6 (C), yielding no notable difference between simultaneous and sequential TIRF-SIM imaging. This approach was used for the simultaneous acquisition of TIRF-SIM images in two colors as depicted in Fig. 6(A). The acquisition of sequential images in Fig. 6(B) need nearly twice as long. Colocalization of two flurophores emitting light at two different wavelengths cannot not be imparied by sample movement during sequential acquision of the two colors. On the other hand, simultanous imaging may suffer from a compromised phase shift and additional cross-talk between the two color channels.

Results: Image quality depending on sample movement
Optimizing the modulation contrast on the illumination side is the basis of structured illumination imaging. Then, static, bright samples yield the expected gain in resolution as shown above. However, dynamic, low fluorescent biological samples are more challenging. Here, contrast is reduced by averaging a moving point-like object through the grating (period P = /kev) with constant velocity vx over the distance xs = vxt0 during the exposure time t0 of one partial image as sketched in Fig. 7 A. Hence, the intensity depending on vx reads: Hence, for a typical camera integration time of t0 = 0.1s and a grating period of g = 170nm, the velocity perpendicular to the grating should be no more than Fig. 7 (D) indicates this effect exemplarily. A moving fluorophore shows lower modulation contrast due to averaging than a static fluorophore. This is shown theoretically in Fig. 7 (C), corresponding to the sinc-like velocity contrast function of eq.(16).
To investigate this effect also experimentally, we moved the sample with our motorized piezo table at various velocities, while acquiring TIRF-SIM images. As all three directions are reconstructed individually before being combined in one super-resolved image, we used a  However, a slight loss in contrast (and resolution) for simultaneous imaging is visible in the red channel depicted by in the line scan in Fig. 6(E). The resolution reduction is very likely due to cross-talk induced by the green fluorescent particles in the red channel, which are not excited during acquisition of the red channel in the sequential imaging mode. During simultaneous acquisition, they emit a non-discardable amount of fluorescence in the red channel, as well and hence the complex reconstruction process yields a lower accuracy. This is not the case in the green channel Fig. 6(C), yielding no notable difference between simultaneous and sequential TIRF-SIM imaging.

Results: Image quality depending on sample movement
Optimizing the modulation contrast on the illumination side is the basis of structured illumination imaging. Then, static, bright samples yield the expected gain in resolution as shown above. However, dynamic, low fluorescent biological samples are more challenging. Here, contrast is reduced by averaging a moving point-like object through the grating (period P = π/k ev ) with constant velocity v x over the distance x s = v x ·t 0 during the exposure time t 0 of one partial image as sketched in Fig. 7(A). Hence, the intensity depending on v x reads: The time averaged integral can be solved into a form, where a velocity-dependent function C vel (v x ) = sinc(k ev v x t 0 ) describes the modulation contrast of the cosine structure. Assuming an acceptable decrease in contrast to C vel (v x ) = sinc(1) = 84%, the relation between the velocity of

Results: Imaging at low signal-to-noise levels
The signal to noise ratio (SNR) crucially determines the quality of every microscopy image. In TIRF-SIM, the SNR of its raw images affects the image quality of the super-resolved image in many ways: low SNR can obscure an otherwise perfect modulation contrast and induce errors in the reconstruction process. The SNR also affects the choice of user-defined parameters in the reconstruction process, such as the Wiener filter parameter (Eq. (13)). In biological samples, the SNR is often low and further degrades during acquisition of time sequences due to bleaching. Therefore, it is important to test the system's responses including the reconstruction process for robustness to different levels of SNR.
Hence, TIRF-SIM images where reconstructed using raw images with distinct SNRs. To compare distinct sources of noise, SNR levels were altered experimentally and computationally. By reducing the illumination intensity, the SNR of the acquired raw images could be reduced, as well. In addition, Gaussian noise was computationally added to the raw images to control the noise level more specifically. Subsequently, the images were Hence, for a typical camera integration time of t 0 = 0.1s and a grating period of g = 170nm, the velocity perpendicular to the grating should be no more than v x ≤ 170nm π ·0.1s = 541 nm s . Figure 7(D) indicates this effect exemplarily. A moving fluorophore shows lower modulation contrast due to averaging than a static fluorophore. This is shown theoretically in Fig. 7(C), corresponding to the sinc-like velocity contrast function of Eq. (16).
To investigate this effect also experimentally, we moved the sample with our motorized piezo table at various velocities, while acquiring TIRF-SIM images. As all three directions are reconstructed individually before being combined in one super-resolved image, we used a drift correction algorithm between the zero-order images of each direction to highlight the influence of motion on the reconstruction process. Leaving out this step would only lead to simple additional motion blur, as seen in standard microscopy techniques. Without further drift-correction or pre-known parameters, we reconstructed a super-resolved image from these raw images. For a typical acquisition time of a t 0 = 100 ms, which was at the upper end of the acquisition times needed for our biological samples, the reconstruction works surprisingly well even for high sample velocities of up to 500 nm/s and more (Fig. 7). Although this is an idealized setting, the velocities are far above the velocities of the motor driven processes observed in our model system Bacillus subtilis. Therefore, it can be concluded that TIRF-SIM can image cell dynamics of motor driven processes without significant aberrations, as long as the sample velocity is not larger than 1/3 of the ratio between grating period and acquisition time (see Eq. (17)).
The experimental results agree very well with the numerical estimate shown Fig. 7(D) and with the simple velocity estimate based on an averaged illumination grating (Eq. (17)), although the 85nm bead diameter is half the grating period P, i.e. the bead is not a point-like structure.
When the sample moves with velocity v x relative to the grating, an additional phase shift ϕ(v x ) = k ev v x t 0 is introduced, which leads to different shifts exp(imϕ(v x )) of the components of the effective MTF and the effective image spectrum P eff (k ⊥ , v x ) This effect is shown in the image spectra of Fig. 7(D). Hence, these observations suggest that a loss of contrast is the main factor for the observed loss in resolution and image quality in TIRF-SIM.
It should be remarked that this approach is a controlled, artificial way of accessing the influence of motion blur on image quality. When fluorescent objects move randomly, it becomes harder to estimate reconstruction parameters like the grating phase, which lead to serious artefacts [24,27]. Since all objects exhibit the same movement in the approach presented here, the movement can be partially compensated with phase optimization methods used during the reconstruction [27]. Whether this is successful, ultimately depends on the modulation remaining contrast, the fraction of objects moving fast as well as image noise.

Results: Imaging at low signal-to-noise levels
The signal to noise ratio (SNR) crucially determines the quality of every microscopy image. In TIRF-SIM, the SNR of its raw images affects the image quality of the super-resolved image in many ways: low SNR can obscure an otherwise perfect modulation contrast and induce errors in the reconstruction process. The SNR also affects the choice of user-defined parameters in the reconstruction process, such as the Wiener filter parameter (Eq. (13)). In biological samples, the SNR is often low and further degrades during acquisition of time sequences due to bleaching. Therefore, it is important to test the system's responses including the reconstruction process for robustness to different levels of SNR.
Hence, TIRF-SIM images where reconstructed using raw images with distinct SNRs. To compare distinct sources of noise, SNR levels were altered experimentally and computationally. By reducing the illumination intensity, the SNR of the acquired raw images could be reduced, as well. In addition, Gaussian noise was computationally added to the raw images to control the noise level more specifically. Subsequently, the images were reconstructed using different Wiener filter parameters, as the parameter is sensitive to the image noise Eq. (13).
To compare the reconstructed TIRF-SIM images composed of raw images with different SNRs, we use a normalized cross-correlation approach to obtain a similarity parameter σ [18].
Here, the peak of the normalized cross-correlation CC norm (dx = 0, dy = 0) = p 1 (x, y) * p 2 (x, y) of two images p 1 (x, y) and p 2 (x, y) is defined as similarity σ. As the peak of the normalized cross-correlation between two TIRF-SIM images, σ yields one for identical images and 0 for unrelated images. For increasing SNRs, the similarity increases non-linearly as shown in Fig. 8. The Wiener filter deconvolution used in the reconstruction process is superior for Gaussian distributed noise, which is evident in the difference in similarity between artificial and experimentally induced noise of similar SNR.

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reconstructed using different Wiener filter parameters, as the parameter is sensitive to the image noise Eq. (13). Fig. 8 Similarity of TIRF-SIM images reconstructed from raw images with various signal-tonoise ratios (SNR). The SNR were obtained either experimentally by varying the illumination intensity or by computationally adding Gaussian noise to the raw images. Then, the images were cross-correlated, where the similarity parameter  was obtained by extracting the peak value from the cross-correlation. Right: exemplary images p1(x,y) and p2(x,y).
To compare the reconstructed TIRF-SIM images composed of raw images with different SNRs, we use a normalized cross-correlation approach to obtain a similarity parameter  [18]. Here, the zero peak of the normalized cross-correlation , p x y is defined as similarity. One finds 00 1 CC  for identical images and 00 0 CC  for uncorrelated images. For increasing SNRs, the similarity increases non-linearly as shown in Fig. 8. The Wiener filter deconvolution used in the reconstruction process is superior for Gaussian distributed noise, which is evident in the difference in similarity between artificial and experimentally induced noise of similar SNR. Fig. 9 shows the super-resolved TIRF-SIM images ( , ) SR pw  r and spectra ( , ) eff Pw  k for several SNRs and two Wiener filter parameters w. It is visible how the lower Wiener filter parameter (w = 10 -6 top row, w = 10 -8 bottom row) can improve the image quality for lower SNR up to a certain extent. A high Wiener filter parameter reduces the amplification of high frequencies in the side bands of the image spectra, leading to a six-fold geometry in both the spectra in the images (honeycomb structure). Hence, the influence of the SNR on TIRF-SIM image quality cannot be discussed without taking the value of the Wiener filter parameter w into account as shown in Eq. (12) and (13). However, when the SNR becomes very low, other effects like the consequently low modulation contrast and poor phase optimization during the reconstruction process play an increasing role, leading to strong artifacts, making it virtually impossible to distinguish between real structures and artifacts. Following eq. (13), the effective image spectrum reads (19) In general, the results exhibit a slow degradation in image quality -or similarity to an optimal imagefor higher SNRs. Moreover, a smaller Wiener filter parameter yields clearer images at low SNR, but may add overshoot artefacts, which are not an issue for the Wiener parameters chosen here. Therefore, it is advisable to perform TIRF-SIM imaging with raw Fig. 8. Similarity of TIRF-SIM images reconstructed from raw images with various signal-to-noise ratios (SNR). The SNR were obtained either experimentally by varying the illumination intensity or by computationally adding Gaussian noise to the raw images. Then, the images were cross-correlated, where the similarity parameter σ was obtained by extracting the peak value from the cross-correlation. Right: exemplary images p 1 (x,y) and p 2 (x,y). Figure 9 shows the super-resolved TIRF-SIM images p SR (r ⊥ , w) and spectra P eff (k ⊥ , w) for several SNRs and two Wiener filter parameters w. It is visible how the lower Wiener filter parameter (w = 10 −6 top row, w = 10 −8 bottom row) can improve the image quality for lower images of at least 1 SNR  , applying the definition from eq. (14). If SNR drops, image quality can be improved by gradually decreasing the Wiener filter parameter. This approach is especially helpful for time sequences of bleaching samples. However, the similarity already decreases significantly at 10 SNR  , increasing the magnitude and frequency of image artefacts. Consequently, biological samples should be imaged at higher SNRs, to avoid misinterpretation of image artefacts as good as possible.

Imaging of biological samples
Imaging of live biological samples at the highest possible spatial and temporal resolution is one of the main goals in microscopy. TIRF-SIM offers a unique compromise, offering twice the spatial resolution of standard TIRF microscopy at the price of a nine times longer acquisition time. Thus, the technique is suited for biological processes occurring on this timescale and the gain in resolution is need to gain new insights in the interaction of biological structures. This criterion especially applies for filaments and vesicles driven by molecular motors, as they fit well into that category. Examples are the bacterial cytoskeletal protein MreB (Fig. 10, Fig. 11 B), which is essential for the construction of the bacterial cell SNR up to a certain extent. A high Wiener filter parameter reduces the amplification of high frequencies in the side bands of the image spectra, leading to a six-fold geometry in both the spectra in the images (honeycomb structure). Hence, the influence of the SNR on TIRF-SIM image quality cannot be discussed without taking the value of the Wiener filter parameter w into account as shown in Eq. (12) and (13). However, when the SNR becomes very low, other effects like the consequently low modulation contrast and poor phase optimization during the reconstruction process play an increasing role, leading to strong artifacts, making it virtually impossible to distinguish between real structures and artifacts. Following Eq. (13), the effective image spectrum readsP In general, the results exhibit a slow degradation in image quality -or similarity to an optimal image -for higher SNRs. Moreover, a smaller Wiener filter parameter yields clearer images at low SNR, but may add overshoot artefacts, which are not an issue for the Wiener parameters chosen here. Therefore, it is advisable to perform TIRF-SIM imaging with raw images of at least SNR>1, applying the definition from Eq. (14). If SNR drops, image quality can be improved by gradually decreasing the Wiener filter parameter. This approach is especially helpful for time sequences of bleaching samples. However, the similarity already decreases significantly at SNR<10, increasing the magnitude and frequency of image artefacts. Consequently, biological samples should be imaged at higher SNRs, to avoid misinterpretation of image artefacts as good as possible.

Imaging of biological samples
Imaging of live biological samples at the highest possible spatial and temporal resolution is one of the main goals in microscopy. TIRF-SIM offers a unique compromise, offering twice the Eukaryotic cells are usually larger and more complex than bacteria. Here, a large field-ofview is required to image entire cells and long acquisitions with 102-103 images enhance the experiment's significance. These features enable a better understanding of the constant remodeling of the actin cytoskeleton as shown in (Fig. 11). The dense and diffusing background of actin monomers inside the cells produce a significantly higher background than in sparse samples or fixed cells. However, the dynamic rebuilding and formation of filaments (temporally color-coded in Fig. 11) are well resolvable and are the basis of new models and experiments on the cell's cytoskeleton [29,30]. They reveal a unique stopping and reversal behaviour of the green filaments, while the blue filament constantly moves along its track. spatial resolution of standard TIRF microscopy at the price of a nine times longer acquisition time. Thus, the technique is suited for biological processes occurring on this timescale and the gain in resolution is need to gain new insights in the interaction of biological structures. This criterion especially applies for filaments and vesicles driven by molecular motors, as they fit well into that category. Examples are the bacterial cytoskeletal protein MreB (Fig. 10, Fig. 11(B)), which is essential for the construction of the bacterial cell wall and its homolog actin inside eukaryotic cells (Fig. 11). (D) depicts the dynamics of the three visible filaments. The filament indicated with a blue line is moving downwards and the two filaments marked with a green line are moving upwards. (E) and (F) show the kymographs along their tracks as a time representation. They reveal a unique stopping and reversal behaviour of the green filaments, while the blue filament constantly moves along its track.

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Eukaryotic cells are usually larger and more complex than bacteria. Here, a large field-ofview is required to image entire cells and long acquisitions with 102-103 images enhance the experiment's significance. These features enable a better understanding of the constant remodeling of the actin cytoskeleton as shown in (Fig. 11). The dense and diffusing background of actin monomers inside the cells produce a significantly higher background than in sparse samples or fixed cells. However, the dynamic rebuilding and formation of filaments (temporally color-coded in Fig. 11) are well resolvable and are the basis of new models and experiments on the cell's cytoskeleton [29,30].  Here, the twofold increased resolution is essential to differentiate between interacting filaments to better understand the underlying principles [4]. In Fig. 10, the three interacting filaments move on different trajectories, only spatially distinguishable temporally resolvable with TIRF-SIM ( Fig. 10 and Visualization 1 and Visualization 2.

Conclusions
Eukaryotic cells are usually larger and more complex than bacteria. Here, a large fieldof-view is required to image entire cells and long acquisitions with 102-103 images enhance the experiment's significance. These features enable a better understanding of the constant remodeling of the actin cytoskeleton as shown in (Fig. 11). The dense and diffusing background of actin monomers inside the cells produce a significantly higher background than in sparse samples or fixed cells. However, the dynamic rebuilding and formation of filaments (temporally color-coded in Fig. 11) are well resolvable and are the basis of new models and experiments on the cell's cytoskeleton [29,30].

Conclusions
We presented guidelines, methods and implementations to enable super-resolved imaging at several Hertz of low fluorescent biological samples. Our results were achieved by a fast TIRF-SIM system based on piezo scan mirrors, a Michelson interferometer and a segmented polarizer. The setup features fast, simultaneous TIRF-SIM imaging of two colour channels, enabled by a diffraction-less design and a custom-built dual beam viewer to image the two colour channels separately onto a single camera ship. Independent of the specific implementation, a fast TIRF-SIM system's final image quality crucially depends on the time-averaged illumination interference contrast, which itself depends on optimizable optical parameters like laser coherence, polarization and beam displacement. Moreover, the sample itself may deteriorate contrast due to fluorophore dynamics during live cell imaging. We illustrate and discuss these effects in real space and Fourier space and present a practical method to assess and avoid regions of low contrast in the sample plain. Furthermore, we investigated the influence of the signal-to-noise ratio and the Wiener filter parameter on the quality of reconstructed SIM images. The results, we present are not intuitive and may help the community to better understand and adjust important parameters, which define the image quality in structured illumination microscopy. We characterized the limits of a fast TIRF-SIM system, which are sufficient to measure biological dynamics such as molecular motor driven processes. TIRF-SIM imaging without motion blur is demonstrated for dynamics of actin filaments in eukaryotic cells and of MreB filaments in bacteria. We demonstrate that TIRF-SIM offers unequalled spatial resolution close to 110nm with a lens of NA = 1.46. With such a spatio-temporal resolution, new comprehensive insights into intracellular dynamics are possible, which are hardly achievable with conventional microscopy like TIRF.
Our results indicate the necessity to find the best imaging compromise between temporal and spatial resolution together with an optimal photon budget for long acquisition series.