super-resolution 3d microscopy of live whole cells using … · 2011-11-29 · nature methods...

Nature Methods

Super-resolution 3D microscopy of live whole cells using

structured illumination

Lin Shao, Peter Kner, E Hesper Rego & Mats G L Gustafsson

Supplementary Figure 1 Simplified diagram of the SLM-based 3D SIM microscope

Supplementary Figure 2 The SLM pixel patterns used in 3D SIM

Supplementary Figure 3 Fourier transform of 3D SIM and conventional wide-field

images

Supplementary Figure 4 3D SIM versus conventional wide-field with depth encoded

in color

Supplementary Figure 5 Deconvolution versus 3D SIM

Supplementary Figure 6 Depth of focus estimation for 3D SIM

Supplementary Figure 7 Simulated 3D SIM images of a moving object

Supplementary Figure 8 The diffraction orders’ strength as a function of the fast

axis’ angle of the half-wave plate

Supplementary Table 1 The function of SLM as a phase modulator

Supplementary Table 2 The function of the polarization rotator

Supplementary Note Multi-color extension of live 3D SIM

Supplementary Discussion Uniformity of the 0-order illumination light

Note: Supplementary Videos 1–8 are available on the Nature Methods website.

Nature Methods: doi:10.1038/nmeth.1734

Supplementary Figure 1: Simplified diagram of the SLM-‐based 3D SIM microscope

Excitation light (488 nm, from a solid-state laser (Sapphire 488-200 CDRH; Coherent)) was coupled into a multimode optical fiber (core size 100 µm, NA 0.12; CeramOptec) after passing through an acousto-optic deflector (AOM-40 AF; Intra-Action) (labeled AOM), here used as a fast shutter and for intensity control. The fiber was coiled and mounted on a high-frequency mechanical shaker to spatially scramble the laser light and hence remove the speckle pattern. The light exiting the fiber was collimated and sent through a pattern generator14 (see Supplementary Fig. 2 and Supplementary Table 1) consisting of a 1024 × 768-pixel ferroelectric-liquid-crystal spatial light modulator (Micron) (labeled SLM), a polarizing beam splitter cube, and a half-wave plate (labeled HWP). The light exiting the pattern generator was diffracted and directed toward the microscope through a polarization rotator14 (Supplementary Table 2), consisting of two switchable ferroelectric-liquid-crystal phase retarders (1/3 wave retardance; Micron) (labeled FLC1, FLC2) and a quarter wave plate (labeled QWP). The polarization rotator was programmed to keep the illumination beams’ polarization perpendicular to the plane of incidence (i.e., s-polarized) in all pattern orientations to maximize the pattern contrast14. A pupil-plane mask (labeled Mask) blocked unwanted diffraction orders caused by the finite-sized pixels of the SLM14. The desired 0 and ±1 diffraction orders were refocused to the center and two points near the opposite edges of the back focal plane of the microscope objective, respectively. After being recollimated by the objective lens (Plan Apo VC 60× WI, N.A. 1.2; Nikon), all three beams approached the sample and interfered to produce a 3D pattern of excitation intensity13. Fluorescent emission light (shown as green) from the specimen was directed toward a camera by a dichromatic beam splitter (labeled DM) as in a conventional fluorescence microscope. Because of a water-immersion objective was used, the highest resolution achievable (120 nm lateral and 360 nm axial) in this article is larger than the originally reported 3D SIM13 (100 nm lateral and 300 nm axial) where an oil-immersion objective was used.


Supplementary Figure 2: The SLM pixel patterns used in 3D SIM

The SLM consists of 1,024 × 768 pixels, each of which can be digitally set to an on or an off state to produce 0 and π phase retardation of the light, respectively, at the output of the beam splitter cube14 (see Supplementary Table 1). The choice of pattern had to satisfy several constraints. To generate efficient 0 and ±1 diffraction orders used for 3D SIM excitation patterns, we used periodic SLM pixel patterns with 30% duty cycle. 3D SIM also requires shifting the phase of the excitation pattern in precise steps of 2π/5, which requires the SLM pixel patterns to have a horizontal or vertical period in pixels divisible by 5. Finally, 3D SIM requires three sets of patterns with similar linespacings but oriented at approximately 60° to each other. Our chosen patterns for the 0° (a) and nominally 60° (b) orientations are shown with on and off pixels drawn in white and blue respectively. The −60° pattern is identical to the +60° pattern except horizontally reflected. The 0° pattern (a) consists of vertically interleaving horizontal patterns of 20% and 40% duty cycle, both of five-pixel period. The mixture of these two patterns produces a five-pixel-linespacing pattern with effectively 30% duty cycle, which is impossible to make directly given the five-pixel period. The pupil mask (Supplementary Fig. 1) blocks the unwanted vertical diffraction orders generated by this pattern. In b, the periodicity is indicated by coloring one pixel in each unit cell red (i.e., the unit cell repeats along the two green-colored vectors: Va = (10, 0) and Vb = (7, 4)). The 60° pattern has an actual orientation angle of θ = arctan(7/4) ≈ 60.25° and a linespacing of 10 × cos(θ) ≈ 4.96 pixels, very close to the target values of 60° and 5 pixels, respectively. It is horizontally periodic with a period of 10 pixels, and thus allows exact 2π/5 phase shifts and 30% duty cycle (3 on pixels per every 10 horizontal pixels).

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Supplementary Figure 3: Fourier transform of 3D SIM and conventional wide-‐field images

Comparison between the Fourier transforms of conventional wide-field (a, b) and 3D SIM images (c, d) shown in Fig. 1. The green circles (a, c) indicate the conventional lateral resolution limit, while the green figure-8-shaped contours (b, d) indicate the conventional axial resolution limit. As can be seen, the extent of the information captured by 3D SIM is enlarged compared to conventional wide-field microscope by almost 2 fold in all three dimensions, i.e., the resolutions are doubled in all three dimensions. Before the 3D Fourier transform was performed, Hamming window was applied in order to minimize artifacts due to edge discontinuities. The residual streak that is still visible along kz axis (b, d) is attributable to overall illumination intensity fluctuation from exposure to exposure. The reason that ky–kz cross-sections (b, d) appear much more pixilated than kx–ky cross-sections (a, c) is that kz pixel size (0.347 µm-1) is about 10 times bigger than kx–ky pixel size (0.039 µm-1). The gray-scale colormap used in this figure is nonlinear with gamma set to 0.4 and range limits set to 0 (lower bound) to 1~2% of the DC amplitude (higher bound).

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Supplementary Figure 4: 3D SIM versus conventional wide-‐field with depth encoded in color

This figure shows maximum-intensity projection of a HeLa cell stained with MitoTracker Green, and is mostly the same as Fig. 2a except that different colors are used to indicate the axial position, or depth, of the fluorophores. The depth-to-color map is shown at the bottom right corner. Scale bar: 2 µm.`

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Supplementary Figure 5: Deconvolution versus 3D SIM

The conventional 3D wide-field microscopy images of the HeLa cell mitochondria were deconvolved using a plug-in to ImageJ (http://www.optinav.com/Iterative-Deconvolve-3D.htm), and are shown here in comparison with 3D SIM. (a) Maximum-intensity projection along z axis; (b) one x–z slice cut through the dashed line. Deconvolution does remove most of the out-of-focus haze typical in wide-field microscopy images. It does not, however, improve either the lateral or the axial resolution.

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Supplementary Figure 6: Depth of focus estimation for 3D SIM

The depth of focus (DOF) of a conventional wide-field microscope can be calculated using this formula (http://www.microscopyu.com/tutorials/java/depthoffield):

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refractive index, NA is the numerical aperture, M is the overall magnification, i.e., the objective’s magnification × magnification between the primary image plane and the detector, and e is the smallest distance that can be resolved by a detector placed in the image plane. The DOF of our SIM microscope under uniform illumination is therefore 0.60 µm. Although an agreed-upon definition of DOF under structured illumination is not available, it is conservative to use the full width at half maximum (FWHM) of the point-spread function’s (PSF) axial profile as a surrogate. For example, the calculated axial FWHM of the conventional PSF is 0.62 µm for our microscope and very close to the calculated DOF of 0.6 µm. We therefore simulated an effective SIM PSF by multiplying a simulated 3D SIM excitation pattern (a) with a simulated conventional 3D PSF using the parameters matching our microscope. The basis for doing so is that the excitation pattern stays axially stationary with respect to the focal plane of the objective while the sample moves through focus13. Depending on where the center of the simulated point source lies in-between the bright and the dark lateral fringes of the excitation pattern (a), the axial profile of the effective SIM PSF (b) can range from the solid blue curve to the purple, green, red, and finally the cyan curve (the conventional PSF axial profile is plotted in the black dashed curve as a reference). Using the peak of the blue profile as the reference maximum, the largest (i.e., the worst) FWHM is found to be 0.4 µm among those profiles that at least partly surpass the half maximum level; the other profiles are not considered. The DOF of our SIM microscope is therefore approximately 0.4 µm.

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Supplementary Figure 7: Simulated 3D SIM images of a moving object

We simulated 3D SIM images of a point-like object that moves during acquisition, to demonstrate the effect of motion artifacts. The exposure time is 35 ms and the speed of the object is 100 nm/s along various directions (b–f; the row of arrows indicates the moving directions, which are within the x–z plane), except for a where the object is stationary. In all simulations, the three lateral SIM pattern orientations (i.e., the directions perpendicular to the lateral SIM fringes) are 0, 60, and 120 degrees from the x-axis. Therefore the moving direction along x-axis simulated here represents the most severe case of motion artifacts. Shown for each example are one x–y and one x–z section that contains the peak pixel of the reconstructed object. As can be seen, the purely z-direction movement causes very little artifacts laterally, and only compresses or stretches the axial profile (b, f); the purely x-direction movement causes appreciable ringing artifacts both laterally and axially (d); and the severity of the artifacts in the 45º movement cases is in-between the cases of purely x- and purely z-direction movement (c, e). While the axial FWHM ranges between 0.5 to 2 times that of the stationary image depending on the moving direction, there is no visibly severe artifact both laterally and axially. We conclude that the 35 ms/ exposure speed, used for acquiring 512 × 512-sized live 3D SIM images, is fast enough to tolerate 100 nm/s sample movement, which agrees with the speed tolerance of 91 nm/s estimated from the depth of focus calculation.

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Supplementary Figure 8: The diffraction orders’ strength as a function of the fast axis’ angle of the half-‐wave plate

The ferroelectric liquid crystal SLM was driven with a direct current electric field, with opposite directions for the on and off pixel states. This field must time-average to zero to avoid slow deterioration of the device through charge migration. Each pixel must thus spend equal time on and off. To this end, each pattern was polarity-switched (switching on pixels to off and vice versa) halfway through each exposure. The 0 diffraction order has different intensities for the two polarities (red and green curves) of the same SLM pattern except when the half-wave plate’s fast axis is at 11.25° from horizontal, which is when the 0 and π phase-retarded light coming off the SLM has the same amplitude. The ±1 diffraction orders always have the same intensities regardless of the polarity (blue), and their maximal strength occurs also at 11.25° half-wave plate angle. The curves shown here were calculated using 5-pixel period and 30% duty cycle, but the same general trend holds for different periods or duty cycles except for the strength ratio between the 0 and ±1 diffraction orders.

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Supplementary Table 1: The function of SLM as a phase modulator

The SLM, half-wave plate (HWP), and the polarizing beam splitter (PBS) work together as a phase modulator (Supplementary Fig. 1). When the SLM is programmed with a pattern of on and off pixels, this phase modulator effectively functions as a diffraction grating. This table illustrates step-by-step the action of the phase modulator on the polarization state of the input light. Each SLM pixel acts as a half-wave plate and can be independently programmed into an off (top row) or on (bottom row) state, with the difference being the orientation of the fast axis: 0° and -45° for the off and on state, respectively. The light entering the PBS is horizontally polarized; by the time it leaves the PBS, it is vertically polarized with π phase difference between the light reflected by the on and off pixels.


Supplementary Table 2: The function of the polarization rotator

The two switchable ferroelectric-liquid-crystal (FLC) phase retarders FLC1 and FLC2 (Supplementary Fig. 1), together with the quarter-wave plate (QWP), act as a polarization rotator. The purpose is to maintain polarization to be perpendicular to the plane of incidence, i.e., s-polarization, regardless of the pattern orientation so as to produce maximal illumination pattern contrast. In this table, the fast axis of the FLC retarders is shown in blue and they can be rapidly (< 100 µs) switched between vertical (off) and 45º (on). The nominal retardance of the FLC devices is 1/3 wave at the excitation wavelength (488 nm). The red arrows indicate the polarization states of the illumination light at various stages, namely before and after FLC1, after FLC2, and after QWP. When vertical polarization is desired (top row), both FLC devices are left in off state, and the incoming vertical polarization passes through unaltered. To produce a linear polarization perpendicular to the -60° orientation (middle row), only FLC2 is switched on, and to produce a linear polarization perpendicular to the +60° orientation (bottom row), both FLC devices are switched on. The angle numbers used in the table refer to the wave vector direction of each pattern; i.e., perpendicular to the lateral fringes of each pattern.


Supplementary Note: Multi-‐color extension of live 3D SIM There are several approaches to multi-color live 3D SIM as listed below. 1. Interleaving different color channels in time. This approach allows slightly different SLM patterns optimized for different excitation wavelengths and therefore optimal utilization of the objective’s NA, i.e., the finest pattern linespacing and thus the greatest possible resolution enhancement, for each wavelength. The temporal resolution would be, however, decreased by a factor equal to the number of colors. 2. Simultaneous acquisition of multiple color channels. Simultaneous image recording would be done with multiple cameras or by splitting one big camera into sub-regions, both with the help of dichromatic beam splitters. The temporal resolution of this scheme would be as high as single-color scenario. 2.a. Single excitation wavelength. Some orange/red fluorophores such as tdTamato can be excited efficiently with 488-nm laser. We can therefore use a single excitation source of 488-nm laser to excite both green and orange/red fluorophores. 2.b. Multiple excitation wavelengths. Because all excitation sources would share the same SLM pixel patterns, the disadvantage would be that optimal NA utilization would be achievable only for the longest wavelength 3. Separate illumination path for each channel and simultaneous image acquisition. In this ultimate but cumbersome solution, multiple copies of the SLM-based illumination path would be built, one for each excitation wavelength. The temporal resolution would be as high as single-color scenario and the spatial resolution would be optimized for all color channels, albeit at the cost of much higher system complexity and higher hardware costs.


Supplementary Discussion: Uniformity of the 0-‐order illumination light

Using only the 0 diffraction order beam for illumination, we acquired a time series of 2D fluorescent images on a thin layer (< 300 nm) of Fluorescein with 10 ms exposure and then corrected it for camera dark level and photobleaching. Shown in Supplementary Video 8 online is a movie of the 100-time-point series. The bright spots in the images were presumably where Fluorescein molecules aggregated. As seen from the movie, there is spatially non-uniform and low-frequency background constantly changing over time, most likely because the fiber shaking mechanism in creating spatially incoherent illumination light is not fast enough (i.e., insufficient sampling in time-averaging of speckle patterns). To determine the level of this non-uniformity in the illumination, we calculated the mean image from the corrected series and subtracted every image of the series by the mean image to obtain an image series representing only the illumination variation plus camera noise and imperfect mean subtraction (i.e., in the mean-subtracted images, we tended to get residual bright or dark spots where the bright spots were in the original images). We calculated the standard deviation of this mean-subtracted series (6.89 in camera counts; the mean is essentially 0) and the uniform illumination level from the mean image’s background mean (132.0 in camera counts). The overall non-uniformity is 6.89/132.0 ≈ 5.2% and it is in small part due to the non-uniformity in the illumination, and largely due to camera noises and imperfect mean subtraction. We therefore conclude that the illumination’s spatial non-uniformity at 10 ms exposure time is << 5%. Furthermore in 3D SIM, each raw image is the sum of five different information components and to separate the components, we need five images taken with the same illumination pattern but with different lateral phases. The separated components, produced before final reconstruction, are therefore an average of the five raw images13 weighted by a set of complex phase factors all of amplitude 1. As a result, the effective non-uniformity in 3D SIM is actually 51/2 times better. In addition, for the conventional or DC component there is another factor of 31/2 improvement because all three pattern orientations contain DC component. When longer exposure time is used, the non-uniformity becomes less by a factor of (Texp/10)1/2, where Texp is exposure time in ms. This low-level of non-uniformity should have negligible effect on SIM reconstruction, as demonstrated by our results.


super-resolution 3d microscopy of live whole cells using … · 2011-11-29 · nature methods...

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