Three-dimensional live multi-label light-sheet imaging with synchronous excitation-multiplexed structured illumination

: Multiplexed imaging is a powerful tool for studying complex interactions inside biological systems. Spectral imaging methods that capture multiple ﬂuorescent markers synchronously without sacriﬁcing the imaging speed or resolution are most suitable for live imaging. We describe spectral-encoded structured illumination (spectral-SIM) light-sheet microscopy, which enables parallel multi-excitation-channel imaging in 3D. Spectral-SIM encodes the excitation wavelength as the phase of the illumination pattern, and allows synchronous image capture over multiple excitation channels at the same speed and spatial resolution as mono-channel structured light-sheet imaging. The technique retains structured light-sheet microscopy’s ability in removing out-of-focus and scattered emission background, and generates clear 3D multiplexed images in thick tissue. The capability of this technique was demonstrated by the imaging of live triple-labeled transgenic zebraﬁsh to over 300 µm deep with 0.5µm-by-2µm (lateral-by-axial) resolution.


Challenges in hyperspectral light-sheet imaging of live animals
Optical microscopy plays a pivotal role in understanding dynamic processes in biological systems. Light-sheet microscopy [1], which decouples the fluorescence excitation optical path from the emission detection path, employs a thin light sheet to selectively illuminate the layer of interest from the side of the specimen [2], and offers faster 3D optical sectioning and much less photobleaching and photo-damage in comparison to confocal microscopy. Advances in light-sheet microscopy have greatly improved the imaging performance in deep tissue. Scanned light-sheet microscopy [3] improves the illumination efficiency and enables two-photon excitation [4]. Two-sided [5], Bessel beam [6] or Airy beam [7] illumination extends the imaging field-of-view (FOV) without sacrificing the axial resolution. Structured light sheet illumination [6,[8][9][10][11] or slit-confocal emission filter [12,13] removes out-of-focus or scattered fluorescence background and clear up 3D images. With these advances, light-sheet microscopy has become an indispensable technique for in vivo deep-tissue imaging.
This work aims to address the multi-label imaging challenge in the light-sheet mode. In order The laser line illumination c sweeps across the field in synchronization with the confocal slit and generates a diffused line-shape image on the camera d . The effect of slit-detection is simulated by keeping signal within the slit area (red rectangle) and zeroing out signal outside of the slit area. The final image was the sum of multiple frames simulated with the sweeping laser line. A wide slit of 2 µm results in a brighter image e, but more background signal is leaked into the image. The image simulated with a 0.25 µm slit width f contains less background signal, but the desired image signal also drops significantly. (g-i) Light-sheet imaging with the linear SIM (3-frame) method. Multiple laser lines are spaced in narrow spacing within the field, forming a periodic illumination pattern g. After taken 3 frames wide-field exposures h under shifted illumination patterns, SIM image processing yields an image i that is background-free. (j-l) Light-sheet imaging with the NSIM method. Using a wide-spaced periodic illumination pattern j and 11-frame exposures k, the resulting image l has higher signals and better SNR than the 3-frame result, and is still mostly background-free. to study complex interaction inside living organisms, scientists often specifically label proteins or structures inside animals with multiple fluorescence proteins. However, methods for multiplexed light-sheet imaging in live animals are limited. Multiplexed fluorescence imaging of live samples requires a fast method for capture spectral images (λ-stack), followed by spectral unmixing of the λ-stack to quantify spatial distribution maps of individual fluorophore species [14]. Challenges of live hyperspectral light-sheet imaging arise from two facts: first, multiplexed spectral imaging often requires complex instruments and prolonged acquisition; second, light-sheet images taken from thick tissue are often obscured by a diffused background from strong scattering or out-of-focus signals [ Fig. 1(b)], making spectral unmixing maps of multiple fluorophores unreliable.
Traditionally, multi-labeled samples are imaged by sequential exposure with changing optical filters. The approach is time-consuming and could lead to motion artifact. Pierre et al. combined mixed-wavelength two-photon excitation with light-sheet illumination [15]. This method allows three-color imaging without slowing down the imaging speed, but cannot been expanded to more labels. Fast hyper-spectral imaging instruments, such as snapshot imaging systems [16] have been applied to light-sheet imaging. But without a way to remove the background of scattered or out-of-focus signal, these instruments are only suitable for cell cultures not live animals.
At the present, the only light-sheet technique combines background removal with hyper-spectral imaging is based on confocal-slit detection [17]. Wiebke et al. equipped a confocal slit scanning light-sheet imaging system with a line-imaging spectral camera [18]. The system produced high spectral resolution λ-stacks. But its spectral ability came from a significant sacrifice in the imaging speed, which was hundreds of times slower than a color-blind confocal slit-detection light-sheet imaging system. Furthermore, confocal slit-detection cannot fully remove scattering. As demonstrated in Figs. 1(c-f), scattering along the slit detection always leaks into the result. Fig. 1(m) quantifies percentages of detected image signal and residue background signals with an increasing slit width. Since in scanner light-sheet imaging the laser beam is typically loosely focused to >2µm wide to maintain a long sheet, if one desires to achieve a good detection efficiency, the slit width needs to match with the laser width. But with a wide slit, most of the scattering removal ability will disappear [ Fig. 1(e)]. Reducing the slit width will decrease the background but also cause significant signal loss [ Fig. 1(f)]. Hyperspectral light-sheet imaging based on confocal slit detection will always suffer from leaked scattering background, which affects quantitative spectral analysis of the image.

SIM as a solution for background-free hyperspectral light-sheet imaging
Compared with confocal slit-detection, light-sheet imaging with structured illumination (SIM) is more effective in removing the background from scattered or out of focus signal Figs. 1(g-l). In light-sheet SIM, a periodic illumination pattern is formed by incoherently integrating intensities of a laser beam hopping in fixed steps or being modulated the intensity as the laser sweeping across the field. Due to spatial overlapping between profiles of a moving laser beam, the contrast of such incoherently generated pattern decreases as the pattern period decreases, and a pattern with diffraction-limited period will have zero contrast. In comparison, superresolution SIM uses beam interference to coherently generate the pattern. Its pattern contrast can reach 100% regardless the pattern period, and a diffraction limited pattern is possible. In all SIM methods, the pattern contrast decides the signal strength in processed SIM images. Therefore, in light-sheet SIM, the pattern period has to be greater than the diffraction limit in order to ensure an effective image signal recovery. By using a wide pattern, light-sheet SIM loses most of the superresolution ability.
Under a wide incoherently generated illumination pattern, light-sheet SIM also need multiple exposures, each taken with a phase-shifted pattern. The number of exposures depends on the beam width and the pattern period. The rule of thumb is, after multiple exposures, the sum of all patterns needs to be uniform across the field. One can choose a narrow-spaced pattern [ Fig. 1(g)] and taking as minimal as 3 phase-shifted exposures [ Fig. 1(h)] or a wide spaced pattern [ Fig. 1(j)] and taking more than 3 exposures [ Fig.1(k)]. The formal is called the linear SIM method [19], for the method assumes the illumination pattern has a sinusoidal intensity profile containing only the base spatial frequency term. The latter is called nonlinear SIM (NSIM) method [20], for the method considers a more general situation where the intensity profile is a periodic function containing first and higher harmonic frequency terms of the base spatial frequency. Simulation results [ Fig. 1(n)] comparing linear and high-order NSIM show that, under the same total photon-budget as the confocal slit detection simulation, both linear SIM (more laser beams per exposure, less exposures) and high-order NSIM (less number of laser beams per exposure, more exposures) have less residue background than the confocal slit detection, and NSIM is more efficient at recovering the image signal [ Fig.1(l)]. The reason for the difference between linear SIM and NSIM is evident in Fig.1(h) vs. Fig.1(k): when the pattern spacing is narrow and laser beams are dense, a strong background fuses each illumination beams and obscure the desired signal; when the pattern spacing is wide and laser beams are sparse, such fused background does not exist and the overall contrast between illuminated and un-illuminated areas is better, which leads to better signal recovery. The benefit of a wider pattern and more exposures disappears beyond a certain point, depending on the degree of diffusion in the background. In this particular simulation, which mimic the typical background we encounter in live imaging experiments, we found the residue background signal increases slightly as the step number grew larger than 9 and there is no significant image signal improvement beyond 11 steps [ Fig. 1(n)].
The high-order NSIM method does require spreading the same photon budget to more exposures. With state of art cameras capable of taking continues exposures, the speed of light-sheet imaging is mostly limited by the photon budget, i.e. the time needed to accumulate enough total photon counts under a laser power safe for the live animal, not by the number of exposures. Therefore the speed of NSIM is not necessarily slower than 3-step linear SIM or confocal-slit detection.
Background-free images from NSIM provide a solid foundation for hyper spectral light-sheet imaging. Potentially, snapshot hyperspectral imaging can be used with NSIM. However the approach would require a sophisticated instrument and complex image registration correction. Here, we present spectral-encoded structured illumination (spectral-SIM) light-sheet microscopy, a novel structured light-sheet technique capable of imaging multiple excitation spectral channels synchronously through color-blind image capture. The technique retains structured light-sheet microscopy's ability of removing out-of-focus and scattered emission background, and generates clear 3D spectral images of thick specimen under user-adjustable spectral configurations. The technique requires little instrument modification over a mono-channel NSIM light sheet system and captures multi-channel NSIM images at the same speed as mono-channel NSIM.

Theory
The structured illumination microscopy (SIM) method provides a multipurpose theoretical foundation for superresolution imaging [19,20], optical sectioning [21] and scattering removal in deep tissue imaging [10]. The spectral-SIM retains the optical sectioning and scattering removal ability, and extends the original SIM method to spectral imaging. In spectral-SIM imaging, the excitation wavelength information is encoded as the phase of excitation pattern and later decoded during image processing, thus make it possible to perform multi-excitation channel imaging synchronously.

Excitation spectral-coded NSIM
The effective illumination pattern of NSIM [20] can be represented as (1) where f can be any real continuous function, k 0 is the base frequency k-vector of the illumination pattern along the x-axis, φ i is the variable phase term that is stepped between 0 and 2π in the multi-exposure NSIM acquisition process, and φ 0 is the initial phase of sinusoidal pattern. Performing Taylor expansion of the function f allows us to represent the pattern as the sum of a series of harmonics of the base spatial frequency: where a n is the coefficient of the n th order Taylor coefficient of the function f . Captured raw images are where O(x, y) is the object, and PSF is the point spread function of the imaging system. Fourier transform these images yield By changing the illumination phase φ i = 2πi/(2N + 1)(i = −N, ..., N) and acquired 2N + 1 images at different phases, Eq. (4) forms a system of 2N + 1 linear equations, through which 2N + 1 Fourier componentsR n (k x , k y ) can be solved. These components carry information about the object, as well as the initial phase φ 0 of the illumination pattern. Numerically shiftR n (k x , k y ) back by nk 0 yields The possible value of k 0 is constricted by the OT F support. In superresolution NSIM, k 0 is high enough to effectively extend the detectable high frequency information beyond the frequency cutoff of the OT F [20]. When the purpose of NSIM is to remove out-of-focus or scattered light, k 0 is much lower, andR n are mostly overlapping in the Fourier space without significantly increasing the resolution. In such cases, k 0 0, allR n essentially carry the same image informatioñ This redundancy gives the room to carry multi-spectral images inR n . The process starts by encoding the excitation wavelength as the initial phase of illumination pattern. By introducing a phase dispersion φ(λ) between patterns of different excitation laser lines, a phase-encoded multi-wavelength excitation pattern can be generated as: where λ is the excitation wavelength. Using a color-blind camera, the captured image is where O (x, y, λ) is the excitation spectral object. The NSIM reconstruction will yield a set of R n (k x , k y ) that are no longer the same: Equation (10) represents a system of linear equations with a coefficient matrix given by a n exp [inφ(λ)] . Solving it will produce a set of multi excitation spectral images in the Fourier domainÕ k x , k y , λ OT F k x , k y . The coefficient matrix will need to be experimentally determined by taking SIM images of standard dye solutions under single wavelength excitation, which, through Fourier analysis, provide measurements on spatial harmonic strength a n , and the wavelength-dependent pattern phase φ(λ).
The above theory is valid only when the period of the structured illumination is much wider than the diffraction limit, or nk 0 is much smaller that the cutoff frequency of the OTF, so that O k x + nk 0 , k y Õ k x , k y . A period wider than the diffraction limit is also required for effectively detecting the image signal, as shown in Fig. 1. Experimentally, we used pattern periods thirty times of the diffraction limit. Under a such wide period, the effect of superresolution from NSIM is negligible. Other than filtering out the background, multiple exposures under structured illumination does not yield additional spatial information. Spectral-SIM takes full utilization of multiple exposures, and embeds spectral information in each exposure through phase encoding. The image process then decodes the spectral information from 2N + 1 exposures and reconstructs up to 2N + 1 spectral channels.
Unlike spectrometer-based hyper-spectral imaging techniques, whose resolution, spectral span and number of channels are fixed by the spectrometer hardware, the spectral-SIM technique offers flexibility in the spectral configuration. The spectral resolution and spectral span are adjustable through modifying the phase dispersion term φ(λ). The number of spectral channel is freely adjustable without affecting the imaging speed, as long as the number is below the maximal channel capacity 2N + 1. The only compromise is that the noise from all spectral channels are shared by all channels, therefore having more excitation channels are likely cause a decrease in SNR in the decoded spectral image.

Retaining the ability of removing out-of-focus and scattered light
When NSIM is used to remove the background due to out-of-focus emission or scattered emission in deep tissue, Eq. (9) needs to be revised as [10] where O BG (x, y, λ) is the image signal from out of the focus layers or scattered emission, and D (x, y) is the diffusion function due to defocusing or scattering. Consequently,R n (k x , k y ) becomẽ whereD k x , k y , the Fourier transform of D (x, y), is a low-pass filter [ Fig.2(a)]. After numerical shiftingR n (k x , k y ) back by nk 0 , there arẽ Note that the background signalÕ BG k x , k y , λ left a narrow band residue signal through D k x − nk 0 , k y , which is centered at k x = nk 0 [ Fig.2(b)]. When out-of-focus emission or tissue scattering is strong, the residue could generate strip-shape artifacts in final spatial domain images. The phenomenon has been experimentally observed in both superresolution NSIM [22,23] and light-sheet NSIM [10]. Our previous work established the method to remove such artifact in light-sheet NSIM [10]. The method takes advantages of the fact thatD k x − nk 0 , k y is narrowly confined to one side of the frequency span (positive side for n > 0, negative side for n < 0). Applying a half-sided filter onR n (k x , k y ) will remove the background residue [ Fig.2(b)]. Furthermore, because fluorescent targets are real objects, inÕ k x , k y , λ negative and positive spatial frequencies components are conjugated to each other, and only one side of the frequency span is needed to reconstruct the object. The half-sided filter will not affect the reconstruction ofÕ k x , k y , λ . Therefore the spectral-SIM light-sheet method can retain the ability in removing out-of-focus and scattered emission background by applying the same principle to remove the residue background.
By multiplyingR n (k x , k y ) with a unit step filter u(k x ) or u(−k x ), we havẽ Note thatR 0 (k x , k y ) is equivalent to the image taken with a uniform illumination. InR 0 (k x , k y ), the background signal overlaps with the desired imageÕ k x , k y , λ in the Fourier domain, and cannot be filtered out. ThereforeR 0 (k x , k y ) is unusable and has to be discarded. This leaves us 2N frames of complex images [Eq. (14)], whose phases encode excitation spectral information. By throwing outR 0 (k x , k y ), the NSIM process does lose some photon signals. The signal recovery efficiency of NSIM decreases whenR 0 (k x , k y ) is strong, which tends to happen when the background is strong and the pattern period is small [ Fig.1(h)]. Increasing the pattern period will increase the contrast between illuminated and un-illuminated area [ Fig.1(k)], hence decreasẽ R 0 (k x , k y ) and increase the signal recovery efficiency.
We then calculate phase-encoded spectral images fromR n (k x , k y ) and raw images I (x, y, φ i ) by Eq. (15) represents a set of 2N + 1 linear equations with a coefficient array given by a n cos [nφ(λ)].
Solving it will produce a set of multi excitation spectral images of O(x, y, λ) ⊗ PSF(x, y). When the number of excitation channels is smaller than 2N + 1, Eq. (15) is an overdetermined linear system and can be solved through pseudo-inverting the coefficient matrix a n cos [nφ(λ)]. Its redundancy provides better spectral decoding accuracy in low SNR situations. Note in Eq. (15), we add back a case for n = 0, which is the standard deviation of changes in the pixel intensity when the illumination phase φ i steps through a cycle of 2π. The resulting image is the intensity sum of all excitation channels without background signals [21]. In theory, the n = 0 case is not required when the number of excitation channels is less then 2N + 1. But when processing experimental data that contains noise, we found adding the n = 0 case provides better constrain on the spectral decoding process and improves the accuracy of multi-excitation spectral images. Accurately decoding multiple excitation channels also requires precise values of a n and φ(λ), which were experimentally obtained by analyzing images of dye solutions under single wavelength structured illumination.
Also note here in O(x, y, λ), λ refers to the excitation wavelength, whereas most hyperspectral imaging techniques generate a image stack over the emission wavelength. Neither excitation nor emission hyperspectral images are direct representation of fluorophore distributions. Because fluorophores with distinct spectral peaks often have overlapping spectral tails, which causes signal bleedthrough across spectral channels, spectral unmixing of hyperspectral images is needed to quantify contributions of every fluorescent species. Traditionally, spectral unmixing is carried by inverting the linear equation that represents the mixing of multiple emission spectra or excitation spectra [24]. The process can be computing intense and sensitive to noise. Faster and more robust algorithms are being developed for fluorescent hyperspectral imaging [25].

Numerical simulation of spectral-SIM
The image forming, spectral coding and decoding process were verified through simulation first (Fig. 3). The simulation started with a three-channel image and an illumination pattern with three excitation wavelengths [ Fig. 3(a)]. Simulated raw images [ Fig. 3(b)] under 11-step SIM were processed according to Eq. (14), which yielded a set ofR n (k x , k y ). Inverse Fourier transform ofR n (k x , k y ) reveal that these complex images carry intensity images as absolute values and spectral information as phase values [ Fig. 3(c)]. A multi-expiation-channel image was recovered by decoding these complex images [ Fig. 3(d)].
Through the simulation, we found in the present of noise, the spectral decoding process is most reliable when phase differences between adjacent excitation patterns are equally divided in a span of 2π. In the such case, the spectral decoding process, which involves in solving a system of linear equations with a coefficient matrix of a n cos [nφ(λ)], distributes noise equally in all channels. For a triple excitation channel imaging experiment, the optimal condition is φ(λ) roughly differs by 2π/3 between single-wavelength excitation patterns.

Optical setup
To experimentally demonstrate synchronous multiple-excitation imaging with spectral-SIM, we built a Bessel light sheet microscope with multiple excitation lasers [ Fig. 4(a)]. The Bessel beam extends the size of light sheet and supports better uniformity in the pattern contrast over the entire image frame. The system can switch between Bessel beam and Gaussian beam light sheet illumination. If a Gaussian beam were used the field of view would be smaller.
The setup first forms a multi-wavelength achromatic Bessel beam that is later used to generate a structured light sheet with an extended length. The output of combined multiple laser lines is directed to a spatial light modulator (SLM, Hamamatsu X10468-01, 792×600 pixels, 20 µm pitch). With an Axicon phase pattern, the SLM can shape a single wavelength Gaussian beam into a Bessel beam. Due to dispersions in the SLM phase pattern, additional steps are needed to form an achromatic Bessel beam, in which all wavelengths travel at the same beam mode. These steps, which were established by Leach et al [26], are: 1. A grating phase pattern is overlaid with an Axicon phase pattern on the SLM.
2. An iris is placed on the Fourier plane of the SLM to select the first-order diffracted component. 3. A thin prism is placed on the image plane of the SLM to compensated the linear dispersion of the grating. In our case, a 4 • BK7 prism is used. The achromatic Bessel beam used for this study was generated under identical conditions as a previous achromatic Bessel tomography study [27]. The FWHM length of the beam, which sets the width of the light sheet, was 292 µm. The width of the beam, which sets the light sheet thickness and the axial resolution of the system, was 2 µm.
The resulting achromatic Bessel beam is directed to a transmission grating pair (300 lines/mm, Thorlabs GT13-03). The first grating introduces angular dispersion for each laser lines. The second grating compensates the angular dispersion and create linear offsets, which becomes the foundation of spectral encoding. The offset coefficient is adjustable through the distance between two gratings, making the system adaptable to different pattern periods and excitation wavelength combinations. The bundle of multi-wavelength Bessel beams is then delivered to the illumination objective (M plan Apo 20x, Mitutoyo) through a x-y galvo scanner (Thorlabs GVS001) with series of 4f relay lenses. The Bessel beam bundle scans across the sample and excites fluorophores in the extended light sheet. Fluorescent emission is collected by a 40x water immersion objective (LUMPLFLN 40XW, NA 0.8, Olympus) placed orthogonal to the light sheet plane, and imaged through a zooming camera lens (70-300 mm, Sigma Photo) onto a EMCCD (Rolera Thunder, 512-by-512, 16 µm pitch). The lateral resolution of the system is at 0.5 µm, which is set by the 0.8 NA emission collecting objective lens. taken with the EMCCD and 300 mm tube lens focal length while scanning the excitation beam in a dye solution. The periodic excitation pattern is generated by hopping the galvo scanner in fixed steps. The scanner has a 300 µs small step response time, which is negligible compared to the camera exposure time. Patterns from different excitation lasers are parallel and staggered to each other.

Live zebrafish imaging
Live Tg (kdrl:GFP; fli1a:Gal4; UAS:nfsB-mCherry) zebrafish embryos were used to demonstrate double and triple excitation channel imaging. The transgenic embryo expresses GFP and mCherry in vascular endothelial cells. Because they are driven by different promotors, GFP and mCherry expression levels, although mostly co-exist, vary locally. Triple-labeled live embryos were made by staining live transgenic zebrafish embryos with 5 µM Syto60 (Thermofisher, Ex/Em 652/678) in embryo media for 1 hour followed by wash. The procedure adds deep red stain to neuromast and nasal epithelium of live embryos.
Embryos were imaged with 488, 561 and 640 nm multi-channel excitation structured light sheet. A motor translational stage is used to move the sample in z-direction during 3D imaging. The fluorescence emission was imaged to the EMCCD through a stack of 488 nm, 561 nm and 640 nm notch filters with the zooming tube lens set at 300 mm, which allows digital images being captured at a pixel size of 0.25 µm, the Nyqvist sampling size of the 0.5 µm diffraction limit. The 512-by-512 pixel camera was only able to capture roughly a half width of the entire light sheet. A camera with more pixels would allow us to image the entire sheet with 0.5 µm lateral resolution.
The pattern modulation period is set to 14 µm, and 11 frames of stepped exposures were used to capture a image slice. The number of steps and the pattern period were chosen according to previous established guidelines for light-sheet NSIM [10], which are: (1) The pattern period needs to be sufficiently wide to allows effective recovery of the in-focus ballistic signal; (2) The number of pattern shifting steps should be sufficient so that the sum of 2N + 1 shifted patterns is effectively a uniform illumination. The 11-step procedure was chosen to achieve good mono-channel NSIM images. Switching from mono-channel to spectral-SIM does not increase the number of exposures. The 11-step NSIM has a maximal excitation-channel capacity of 11. In this study, double and triple excitation imaging were demonstrated. In both cases, spectral decoding processes were done by solving the overdetermined systems of linear equations represented by Eq. (15).
Because one-photon excitation of Bessel beam induces unwanted out-of-focus emission in side bands of the beam, whereas two-photon excitation of Bessel beam is confined to the center lobe of the beam, the pattern period and number of steps chosen for this one-photon excitation study are larger than what were used in the previous two-photon Bessel NSIM light-sheet study [10]. Similarly, if Gaussian beams, which does not have sidebands, were used, the number of exposure steps needed would be less and the image speed could be faster. However, the field of view supported by Gaussian beam NSIM would be smaller.
Raw structured light sheet images were taken with 35 ms exposures with an EM gain at 50. The total time for a 11-step slice is 0.4 second, regardless the number of excitation channels. Typically, 100 µW 488nm laser power, 60 µW 561nm laser power, and 220 µW 640 nm laser power, measured at the entrance of the illumination objective lens, were used to generate the light sheet.

System testing with dual-excitation imaging
To test the optical system and the imaging reconstruction algorithm experimentally, we first performed dual excitation (488 nm and 561 nm) 11-steps NSIM imaging of a Tg (kdrl:GFP; fli1a:Gal4; UAS:nfsB-mCherry) zebrafish embryo at 2 days past fertilization (dpf). The pattern period was set at 14 µm. was filter out, the absolute value of the image is clear with cellular resolution [ Fig. 5(b)]. The phase value of IFFT R 1 (k x , k y ) contains excitation spectral information [ Fig. 5(c)]. An area with strong GFP expression shows an unique phase value. Fig. 5(d) is the final reconstructed dual-excitation image, plotted in pseudo colors.
We further performed tests on whether there is bleedthrough between excitation channels. Results show that when a laser (488nm or 561nm laser) was turned off, bleedthrough signal in the inactive excitation channel is negligible [Figs. 6(b) and 6(c)], and image signals were assigned to multiple excitation channels accurately.

Triple excitation channel 3D imaging of live zebrafish embryos
The number of channels in the spectral-SIM light sheet system is expandable. Fig. 7 plots results captured with 488, 561 and 640 nm triple-channel excitation light sheet. The image set was taken from the head region of a triple-labeled embryo, made by staining a live Tg (kdrl:GFP; fli1a:Gal4; UAS:nfsB-mCherry) zebrafish embryo with Syto60 at 2dpf. The embryo has genetically labeled GFP and mCherry in vasculature and Syto60 stained neuromast and nasal epithelium. The 3D image extends to 330 µm deep into the tissue with a 1-µm axial step size.
Without structured illumination [Figs. 7(a)-7(d)], the resulting mono-channel image stack cannot distinguish GFP, mCherry and Syto60. Images further contain a diffused background due to out-of-focus excitation and emission scattering. With the 11-step spectral-SIM process [Figs. 7(e)-7(h)], 3D structures of GFP and mCherry labeled vasculature and Syto60 stained nasal epithelium were visualized in parallel at a resolution of 0.5-by-2 µm (lateral-by-axial) without the diffused background. The total acquisition time for the image set is 9 minutes, of which 2 minutes were spent on imaging, and rest of the time was spent on moving the specimen with the motorized translational stage. In the future, the 3D imaging speed could be dramatically improved with an electrical tunable lens [29] or other rapid axial scanning methods.

Discussion
NSIM has long been used in light-sheet imaging to remove background due to tissue scattering and out of focus emission. In such applications, the structured illumination uses a period much wider than the diffraction limit, and each frequency order of the pattern yields redundant image information in a similar Fourier space. The spectral-SIM technique takes advantages such redundancy and use them to convey phase-coded excitation spectral information, and therefore achieves multispectral SIM imaging without adding more exposures.
Comparing with previous hyper-spectral imaging instruments, whose spectral capability came from emission dispersive elements, the spectral-SIM have unique differences and advantages: First, in instruments with dispersive emission elements, the emission spectral resolution and the number of channels are often not adjustable, whereas in spectral-SIM, spectral configurations are fully adjustable without affecting the imaging speed. The flexibility allows users to optimize the spectral configuration for multiplexed imaging; Second, the spectral-SIM technique distinguishes fluorophores by their excitation peaks not emission. It can potentially be combined with emission spectral imaging methods to perform excitation-emission matrix measurements, provide complete spectral characterization of fluorophore mixtures in the imaging mode, and generate rich 5D (excitation, emission, x, y, and z) images for more robust multiplexed image analysis; Third, the spectral-SIM image is free of background.
The spectral channel capacity of spectral-SIM is limited by the number of exposure steps, which is set by the degree of diffusion in the background. Therefore, unlike dispersive hyperspectral imaging, whose channel numbers can be as high as thousands, the number of channels in spectral-SIM is practically limited to 10-20. However, considering live fluorescence imaging always operates at a low photon budget, spreading the budget over hundreds or thousands spectral channel will yield noisy spectra that are unreliable for spectral unmixing analysis. Indeed, previous study on confocal slit hyperspectral light-sheet imaging found, when analyzing a λ-stack images of GFP and YFP, binning down the sub-nanometer resolution λ-stack to a coarse spectral resolution of 20 nm yields the most reliable unmixing result [18]. 20 nm is exactly the difference in emission peaks between GFP and YFP (507 nm vs. 527 nm). The observation confirms the common practice of choosing a low number of channels, each centered at the spectral peak of a fluorescent species, is the most effective way to capture spectral signatures of a multi-labeled fluorescent sample. Spectral-SIM, with its coarse but flexible spectral channels at the user's discretion, is highly suitable in following in this practice. Live imaging results of this work demonstrated, with simple changes on the optical system, a mono-channel SIM light-sheet system can be upgraded to perform multi-excitation-spectral light-sheet image at the same speed as mono-channel acquisition. Background-free excitation spectral images from spectral-SIM are well suited for multiplexed cellular study in live animals.