Fast, volumetric live-cell imaging using high-resolution light-field microscopy

Visualizing diverse anatomical and functional traits that span many spatial scales with high spatio-temporal resolution provides insights into the fundamentals of living organisms. Light-field microscopy (LFM) has recently emerged as a scanning-free, scalable method that allows for high-speed, volumetric functional brain imaging. Given those promising applications at the tissue level, at its other extreme, this highly-scalable approach holds great potential for observing structures and dynamics in single-cell specimens. However, the challenge remains for current LFM to achieve subcellular level, near-diffraction-limited 3D spatial resolution. Here, we report high-resolution LFM (HR-LFM) for live-cell imaging with a resolution of 300-700 nm in all three dimensions, an imaging depth of several micrometers, and a volume acquisition time of milliseconds. We demonstrate the technique by imaging various cellular dynamics and structures and tracking single particles. The method may advance LFM as a particularly useful tool for understanding biological systems at multiple spatio-temporal levels.


Introduction
Light-field microscopy (LFM) simultaneously captures both the 2D spatial and 2D angular information of the incident light, allowing computational reconstruction of the full 3D volume of a specimen from a single camera frame [1][2][3][4]. Conventionally, fluorescent imaging techniques acquire 3D spatial information in a sequential or scanning fashion [5][6][7][8][9][10][11][12], inevitably compromising temporal resolution and increasing photodamage for live imaging. The 4D imaging scheme of LFM effectively liberates volume acquisition time (limited primarily by the camera's frame rate) from the spatial parameters (e.g. the field of view (FOV) and spatial resolution), thus making LFM a promising tool for high-speed, volumetric imaging of living biological systems with low photodamage across many spatial levels.
Towards the tissue level, the latest LFM techniques have demonstrated promising results for functional brain imaging with cellular level spatial resolution of several micrometers across a depth of tens to hundreds of micrometers, and at a fast volume acquisition time on the order of 10 milliseconds [4,[13][14][15]. At its other extreme, this highly-scalable approach holds great potential for visualizing delicate structures and dynamics within single-cell specimens. However, the challenge remains for current LFM to achieve subcellular level, near-diffractionlimited 3D spatial resolution.
For the existing LFM techniques, in practice, a microlens array (MLA) is placed at the native image plane (NIP) of a wide-field microscope, and the optical signal is recorded in an aliased manner across the microlenses at the back focal plane of the MLA [1,2]. The development of wave-optics models allows high-resolution reconstruction of densely aliased high-spatial frequencies through point-spread function (PSF) deconvolution [3,4]. However, near the NIP, the sampling pattern of the spatial information becomes redundant, resulting in prohibitive artifacts [3,4]. This limitation causes non-uniform resolution across depth, hindering applications that require visualization of fine 3D information spreading over a large axial range in a sample. Current LFM techniques circumvent the artifacts mainly by imaging on one side of the NIP [3,4,14] or using a coded wavefront [16]. These approaches are feasible for functional brain imaging (e.g. using 20× or 40× objective lenses) despite compromised depth of focus (DOF) or spatial resolution. However, they may be prohibitive for highresolution microscopy, because they would either sacrifice the already tightened DOF (typically <1 µm for a 100×, 1.45NA oil objective lens) or worsen the 3D spatial resolution away from the diffraction limit. Alternatively, the MLA may instead form an imaging relationship between the NIP and the camera sensor, as used in the focused plenoptic camera [17]. While the spatial information at the NIP can thereby be recovered using this scheme, the sampling geometry of the angular information becomes less aliased and redundant, inherently impairing the refocusing (or volumetric imaging) capability for practical applications. Hence, new optical design and computational framework are highly desired for high-resolution lightfield imaging in single-cell specimens.
Here, we develop a HR-LFM method for live-cell imaging by simultaneous, dense sampling of both spatial and angular information. HR-LFM achieves a 3D spatial resolution of 300-700 nm, an imaging depth of several micrometers, and a volume acquisition time down to milliseconds. We demonstrated the technique by imaging various cellular systems and tracking single particles.
In the setup, the MLA forms a defocused imaging relationship as 1/a + 1/b > 1/fml, where a and b denote the distances to the NIP and the camera sensor, respectively, and fml is the focal length of the MLA. This design contrasts with conventional LFM [1] (a = 0 and b = fml) and the focused plenoptic camera [17] (1/a + 1/b = 1/fml) (Appendix 2), and benefits HR-LFM in two main ways. First, the distance a can displace the artifact region away from the DOF by a/M 2 in the object space, where M is the magnification of the objective lens. Second, the distance b facilitates optimum dense sampling of both the spatial and the angular information of optical signals on the camera sensor. In this work, the values of a and b (a = 25 mm and b = 4 mm) were carefully determined using numerical simulations to obtain the optimized spatio-angular distribution for reconstruction of point-emitters distributed in the 3D space (Appendix 3, Eqs. 1-5). Using this scheme, the optical signals imaged by the objective lens can be densely aliased compared to conventional LFM, capturing different perspectives of the sample onto the camera sensor ( Fig. 1b-d). The aliasing of the recorded data can thus effectively suppress the reconstruction artifacts at the NIP, substantially improving the DOF and spatial resolution.

Reconstruction Algorithm
To reconstruct the volumetric data, the Fresnel propagation of light by the distances of a and b, i.e. a defocused PSF, was established using the scalar diffraction theory [18]. Specifically, the final intensity image (x ′′ ) at the camera plane is described by (x ′′ ) = ∫|ℎ(x ′′ , p)| 2 (p) p (Appendix 3, Eq. 5), where x ′′ = ( 1 ′′ , 2 ′′ ) ∈ 2 represents the real coordinates ( 1 ′′ , 2 ′′ ) on the camera plane, p ∈ 3 are the real coordinates of a point source in a volume in the object domain, whose combined intensities are distributed according to (p). ℎ(x ′′ , p) represents the complex-valued PSF, which considers, sequentially, the light propagation through the high-NA objective lens, Fresnel propagation of light by the distance of a, modulation induced by the MLA, and another Fresnel propagation to the camera plane by the distance of b (Appendix 3, Eqs. 1-4). In practice, considering the discrete model, ℎ(x ′′ , p) is represented by the measurement matrix , which elements hkj describe the projection of light arriving at the pixel ( ) on the camera plane from the k th voxel ( ) in the object space. The volumetric information was then reconstructed employing the wave-optics model [3,4] based on an inverse-problem deconvolution framework [19] (Appendix 3 and Supplementary Code). To verify the algorithm, we recorded light-field images of 100-nm fluorescent beads placed on the native object plane (NOP) of the objective lens, where the aggregated beads can be properly reconstructed on the NIP with near-diffraction-limited widths of ~400 nm without artifacts using HR-LFM, compared to conventional LFM (Fig. 1e). Next, to characterize HR-LFM, we imaged 100 nm fluorescent beads and measured the reconstructed PSFs of the system at varying depths ( Fig. 2a,b, Appendices 4 and 5). The numbers of iterations taken for the reconstruction at varying depths were determined based on the distribution of the optical signals across the MLA and the corresponding signal-to-noise ratio (SNR). These numbers were consistently used in this work for other samples (Appendix 4). The full-width at half-maximum (FWHM) values of these reconstructed PSFs at each depth exhibited a near-diffraction-limited 300-700 nm resolution in all three dimensions over a >3 μm range, ~4× larger than the corresponding DOF of wide-field microscopy. Detailed features of the system are shown in Appendix 4. First, when the beads were scanned near the axial position z = a/M 2 = 2.5 µm (a = 25 mm and M = 100; i.e. forming images near the MLA), the optical signals were mainly restrained into a single microlens as in conventional LFM. Thus, HR-LFM performed as a NA-matched single-lens imaging system, exhibiting spatial resolution of ~300 nm and 600 nm in the lateral and axial dimensions, respectively, consistent with the PSF measured in wide-field microscopy using the same 100×, 1.45NA objective lens. Second, when the beads were scanned toward the focal plane z = 0 (i.e. forming images between the MLA and the NIP), the optical signals became broadly distributed on the MLA, which led to higher angular sensitivity, thereby improving the axial resolution (Appendix 5). Notably, the lateral resolution was steadily maintained using the wave-optics model, and thus the system achieved a near-isotropic 3D resolution within this axial range. Lastly, beyond the NIP (z < 0), the optical signals became further broadened on the MLA due to the diffraction of light. While the high axial sensitivity was maintained, the lateral resolution became worse due to the degraded signal detection from an increased number of microlenses. In general, the implementation of wave-optics based reconstruction effectively overcame the tradeoff and maintained a high resolution in both the axial and lateral dimensions. Furthermore, the use of the MLA permits sensitive angular detection of the wavefront (i.e. spatial frequencies), improving axial-resolving capability within a substantial range of the DOF. These features make HR-LFM distinct from a conventional diffraction-limited imaging system, providing a new type of optical engineering scheme for high-resolution microscopy.

Imaging Caliber Structures and Fixed Biological Samples
Further measurements, in good agreement with the reconstructed PSF values, have been obtained using known caliber structures and fixed biological samples. We first imaged surfacestained, 1-µm fluorescent microspheres (F14791, ThermoFisher), which sub-micrometer hollow structure was resolved using HR-LFM (Fig. 2c-e). The corresponding lateral and axial cross-sectional profiles exhibited FWHMs of the stained surface of 300-500 nm in all three dimensions (Fig. 2f), consistent with the measured values in Fig. 2b and Appendix 4.
Next, we imaged immuno-labeled mitochondria in HeLa cells. For sample preparation, HeLa cells were obtained from the American Type Culture Collection (ATCC), maintained in 1× Minimum Essential Medium (MEM) (Corning CellGro) with 10% fetal bovine serum (FBS) (Atlanta Biologicals) and 50 μg/ml gentamycin (Amresco), and incubated at 37°C with 5% CO2. The cells were plated on a 35 mm 2 MatTek glass-bottom dishes (MatTek), incubated at 37°C for 16 hours, and fixed with 4% (vol/vol) formaldehyde (15735, Electron Microscopy Sciences) prepared in phosphate buffered saline (PBS) for 10 mins at 37°C. The cells were then blocked and permeabilized with blocking and antibody dilution buffer (1% (vol/vol) bovine serum albumin (BSA) (Santa Cruz Biotechnologies) and 0.25% (vol/vol) Triton X-100 prepared in PBS) for 1 hour at room temperature. The cells were then incubated with the mitochondrial marker primary antibody mouse anti-Tom20 (Santa Cruz Biotechnologies F10, SC-17764), at 1 µg/ml in blocking and antibody dilution buffer for 2 hours while gently shaking at room temperature. The cells were then washed 3 times with PBS for 5 mins each. Secondary antibody (AlexaFluor 647-conjugated AffiniPure Goat Anti-Mouse IgG, 1 mg/ml, Jackson ImmunoResearch) was diluted 1:1000 in 1% BSA in PBS and incubated with gentle shaking for 1 hour at room temperature. The cells were washed 3 times with PBS for 5 mins. The cells were placed in imaging buffer (20 mM HEPES pH 7.4, 135 mM NaCl, 5 mM KCl, 1 mM MgCl2, 1.8 mM CaCl2, 5.6 mM glucose) before imaging.
As seen, HR-LFM recorded the full 4D light-field information (Fig. 3a), allowing us to synthesize the focal stacks of the entire volume of the specimen (Fig. 3b). Remarkably, HR-LFM captured mitochondria that were out-of-focus and poorly detected by wide-field microscopy due to its limited DOF (Fig. 3c and Appendix 6). The mitochondrial structures were well-resolved by HR-LFM across a ~3-µm axial range in all three dimensions without the need for any sample or focal-plane scanning. Furthermore, as a comparison, conventional LFM can only image cells on one side of the NIP to avoid the prohibitive artifacts, resulting in substantially degraded volumetric imaging capability, especially in the axial dimension such as the DOF and axial resolution (Fig. 3d-f). Furthermore, we imaged the Golgi complex in HeLa cells, immuno-labeled for the Golgi marker GM130 with DyLight 549, where the nearby Golgi structures as close as ~400 nm in all three dimensions were resolved by HR-LFM (Appendix 7).

Imaging Mitochondria in Living Drp1 -/-Mouse Embryo Fibroblasts (MEFs)
To demonstrate live-cell imaging, we first recorded mitochondrial dynamics in living Drp1 -/-MEFs [20], labeled with MitoTracker, a mitochondrial fluorescent tracking dye (Fig. 4). The dynamin-related GTPase (Drp1) mediates mitochondrial division and distribution, playing a critical role in mammalian development [20]; cells lacking Drp1 have low rates of mitochondrial fission and thus have long mitochondria. Drp1 -/-MEFs were generously provided by Hiromi Sesaki (Johns Hopkins University). For sample preparation, Drp1 -/-MEFs were cultured in DMEM + 10% FBS and plated into tissue culture dishes containing sterile coverslips and cultured for 1-2 days until 50-80% confluent. The cells were incubated in medium containing a 1:5000 dilution of MitoTracker Deep Red (M22426, ThermoFisher) for 30 mins at 37°C, washed 3 times with PBS, and then placed back into growth medium lacking MitoTracker.
Using the full sCMOS camera chip (2048 × 2048 pixels), we captured the entire FOV (>100 × 100 µm laterally and >3-5 µm axially) enclosing several cells at a volume acquisition time of 0.1 s (Fig. 4a). The high spatial resolution allows us to visualize fine mitochondrial structures and distributions as close as 500 nm in all three dimensions ( Fig. 4b-g, Visualization 1 and Visualization 2). Without the need for scanning, HR-LFM permits low light exposure (0.05-0.5 W cm -2 ) for time-lapse acquisition over more than thousands of time-points (up to minutes) without obvious photodamage or photobleaching [21]. We observed extension and retraction of mitochondrial tubules, where mitochondrial movements of up to 0.53 μm s −1 were recorded, as well as occasional mitochondrial division (Visualization 1 and Visualization 3). We next imaged Golgi-derived membrane vesicles in living COS-7 cells, labeled with a trans-Golgi marker, mEmerald-Golgi-7 ( Fig. 5 and Appendix 8). These vesicles occasionally undergo rapid movement between the Golgi complex and other intracellular organelles, posing a challenge for capturing their volumetric dynamics using scanning-based imaging methods.
Using the full camera chip, we captured their rapid 3D motions at a volume acquisition time of 0.01 s over hundreds to thousands of camera frames (Fig. 5a). Notably, the high spatiotemporal resolution allowed us to observe the rapid interactions of individual vesicles separated as close as 300-500 nm and moving up to 2.06 μm s −1 in all three dimensions (Fig. 5b-g and  Visualization 4). In addition, the volume acquisition speed can be further accelerated by imaging only a region of interest on the camera chip. We imaged the same samples at a volume acquisition time faster than 5 ms without noticeable degradation in image quality or resolution (Appendix 9). Finally, we tracked HGC nanoparticles suspended in water, labeled with a fluorescent dye Cyanine3 (cy3; Fig. 6). HGC nanoparticles were prepared through the covalent attachment of 5-cholanic acid to glycol chitosan using a previously published protocol [22]. Specifically, 150 mg of 5-cholanic acid dissolved in 60 ml of methanol was activated with 1.5 mol equivalents of N-hydroxysulfosuccinimide (NHS, ThermoFisher) and 1-ethyl-3-(3dimethylaminopropyl) carbodiimide hydrochloride (EDC, ThermoFisher). The activated 5cholanic solution was slowly added to the glycol chitosan solution (500 mg/60 ml, in HPLC water) and stirred for 24 hours at room temperature to ensure complete reaction. The resulting mixture was dialyzed using 10 kDa molecular weight cut-off dialysis cassettes for 24 hours against a water-methanol mixture (1:4 vol/vol), for another 24 hours against water, and lyophilized. For labeling, cy3 dye (Lumiprobe, 1 mg) was dissolved in dimethyl sulfoxide (DMSO, 200 µl) and added dropwise to HGC (100 mg/40 ml, in DMSO) under gentle stirring at room temperature for 6 hours in darkness. The mixture was dialyzed using 3.5 kDa molecular weight cut-off dialysis cassettes for 2 days against HPLC water, and lyophilized. The cy3-HGC nanoparticles were suspended in HPLC water at a concentration of 1 mg/ml and treated with a probe-type sonicator (S-450D Sonifier, Branson Ultrasonics) at 90 W for 6 mins. One drop (5 µl) of cy3-HGC suspension was added to a microscope slide and coverslipped prior to imaging.

Tracking Hydrophobically-modified Glycol Chitosan (HGC) Nanoparticles
At a volume acquisition time of 1 ms, single nanoparticles moving up to 92.81 μm s −1 have been recorded using HR-LFM (Fig. 6a-c and Visualization 5). The 3D positions and trajectories of the nanoparticles were determined by localizing the reconstructed particles using Gaussian fitting with nanometer-level precision in all three dimensions [23] (Fig. 6d). The measurements of the nanoparticles are consistent with the reconstructed PSF values using the fluorescent beads ( Fig. 2b and Appendix 4), showing no compromise in spatial precision as the acquisition is accelerated. The system thus has demonstrated the capability of recording dynamic particle behavior in a volumetric context, which has been a spatio-temporal-limiting step for live-cell imaging.

Conclusion
In summary, we have developed HR-LFM for volumetric live-cell imaging with a spatial resolution of 300-700 nm in all three dimensions, an imaging depth of several micrometers, and a volume acquisition time on the order of milliseconds. Defocusing the MLA effectively mitigates the prohibitive reconstruction artifacts in the previous LFM design, providing fourto five-fold larger DOF than conventional high-resolution wide-field microscopy. In addition, due to its greater axial sensitivity and discrimination, we demonstrated the remarkable resolution improvement especially in the axial dimension (i.e. near-isotropic) within a substantial axial range. These findings may lead to new imaging physics and applications for MLA-facilitied microscopy. Advancing current LFM to the subcellular level, the system enables high-speed, volumetric visualization of dynamics and structures in single-cell specimens with low photodamage. Combining the molecular specificity of fluorescent labeling, great scalability, engineered MLAs and deconvolution algorithms, LFM is becoming a particularly promising tool for imaging diverse anatomical and functional traits, spanning molecular, cellular and tissue levels.

Appendices
Appendix 1: Details on system alignment.
The sCMOS camera was first installed on the camera port of the microscope, and the position of the objective lens was adjusted to form an in-focus image of the sample. Next, the 1:1 relay lens was mounted onto the camera. The camera was placed on a dovetail optical rail (RLA150/M, Thorlabs), aligned to the optical axis, and translated until the same in-focus widefield image was captured. At this point, the camera was conjugated to the NIP. The MLA, mounted in a translational stage, was first inserted near the NIP where the modulation of the MLA (edges of the microlenses) can be observed on the camera. The MLA was then slightly adjusted until the modulation of the MLA disappeared on the camera. At this point, the MLA was aligned to the NIP, and the camera recorded the wide-field images reported in this work. For light-field imaging, the camera was translated away from the sample by the focal length of the MLA (fml = 3.75 mm), where the system formed conventional LFM (Appendix 2; a = 0 and b = fml = 3.75 mm). To establish the design in this work, the MLA was translated away from the sample by a = 25 mm, and the camera, accordingly, by a + bfml = 25.25 mm. At this point, the HR-LFM system was established as reported (a = 25 mm and b = 4 mm) ( Fig. 1a and Appendix 2).   [1,2]. Near the NIP, the sampling pattern of the spatial information becomes redundant (i.e. restrained to one microlens). As a result, the wave-optics based model produces prohibitive reconstruction artifacts across the NIP. (b) For the focused plenoptic camera, the MLA forms an imaging relationship between the NIP and the camera (1/a + 1/b = 1/fml) [17]. The sampling geometry of the angular information becomes less widely distributed, inherently impairing the refocusing (or volumetric imaging) capability. (c) For HR-LFM, the MLA is placed at a defocused position (1/a + 1/b > 1/fml) to facilitate simultaneous, dense sampling of both spatial and angular information. fml, the focal length of the MLA; ftl, the focal length of the tube lens; fobj, the effective focal length of the objective lens; a and b denote the distances from the MLA to the NIP and the camera, respectively; TL, tube lens; OL, objective lens; NOP, native object plane; CP, camera plane. Time-lapse video of reconstructed mitochondria in living Drp1 -/-MEFs (FOV = 133 x 133 µm, volume acquisition rate = 10 Hz). Scale bars, 10 µm (main), 1 µm (insets). Color scale bar, z = -1.0 µm (blue) to 1.5 µm (red).

Visualization 2
Zoomed-in, 3D view of the corresponding region (marked with 'triangle') in Supplementary Video 1 (volume acquisition rate = 10 Hz).

Visualization 3
Zoomed-in, 3D view of the corresponding region (marked with 'cross') in Supplementary Video 1 (volume acquisition rate = 10 Hz).