2.1.

Optical System

We designed our LFM following Levoy et al.⁷ Imaging was performed with a custom-built epifluorescence microscope with an MLA ($125\mu \mathrm{m}$ pitch, $f$/10, RPC Photonics) placed at the imaging plane of a 25×, numerical aperture (NA) = 1.0 water immersion objective lens (XLPLN25XSVMP, Olympus), and 180-mm tube lens (TTL180-A, Thorlabs), shown in Fig. 1(a). The MLA was imaged onto a scientific complementary metal–oxide–semiconductor (sCMOS) camera (ORCA Flash 4 V2 with Camera Link, $2048\times 2048\mathrm{pixels}$, $6.5\mu \mathrm{m}$ pixel size, Hamamatsu) with a 1:1 relay macro lens (Nikon 60 mm f2.8 D AF Micro Nikkor Lens). The MLA was aligned following the advice in Zhang (2010) with a 660-nm light-emitting diode (LED) (M660L2, Thorlabs).²⁵

Fig. 1

(a) Optical system schematic. An MLA is placed at the native imaging plane of a widefield microscope and the back focal plane is imaged onto an sCMOS camera enabling 3D reconstructions from a 2D frame. (b) Example widefield and light-field images from both a single neuron intracellularly loaded with the synthetic calcium dye, CaSiR-1 via a micropipette. Close-up views of the raw light-field images show the circular subimages encoding the 4D spatial and angular information. The light-field is parameterized by a 4D function, $\mathcal{L}(u,v,x,y)$, where each lenslet is $\mathcal{L}(u,v,·,·)$ and the same pixel in each lenslet subimage is $\mathcal{L}(·,·,x,y)$. (c) Example images from bulk-labeled slices where CaSiR-1 AM was bath applied to many neurons. (d) Example widefield and reconstructed light-field images from a $10\mu \mathrm{m}$ fluorescent bead fixed in agarose. (e) The lateral and axial profiles of the bead with widefield (dotted line), synthetic refocusing (dashed line), and RL deconvolution up to 21 iterations (solid lines, iteration number indicated by color code).

The LFM image consists of circular subimages [Fig. 1(b)] which are parameterized by the 4D function $\mathcal{L}(u,v,x,y)$, where each lenslet is $\mathcal{L}(u,v,·,·)$ and the same pixel in each lenslet subimage is $\mathcal{L}(·,·,x,y)$. Each circular subimage represents the angular content of the light at a specific spatial location.

The “native LFM spatial resolution” is given by the microlens pitch divided by the objective magnification. Therefore, an MLA was chosen such that the lateral resolution of our LFM was $5\mu \mathrm{m}$, roughly half the diameter of a cortical neuron ($10\mu \mathrm{m}$). The axial resolution of a LFM is defined by the number of resolvable diffraction-limited spots behind each microlens.⁷ Using the Sparrow criterion and assuming a peak emission wavelength of 664 nm ($\lambda$) for CaSiR-1,²³ the spot size in the camera plane is $7.8\mu \mathrm{m}$. So, with a $125\mu \mathrm{m}$ pitch MLA, we are able to resolve $N_u=16$ distinct spots under each microlens. The depth-of-field when synthetically refocusing is given by Eq. (1), resulting in a depth-of-field of $7.96\mu \mathrm{m}$⁷ compared to $0.9\mu \mathrm{m}$ in a conventional widefield microscope with the same imaging parameters:

2.2.

Brain Slice Preparation

This study was carried out in accordance with the recommendations of the UK Animals (Scientific Procedures) Act 1986 under Home Office Project and Personal Licenses (project license 70/9095). $400\mu \mathrm{m}$ slices were prepared from 33- to 196-day old mice using the “protective recovery” method.²⁶ Slices were cut in Na-aCSF containing (in mM): 125 NaCl, $25{\mathrm{NaHCO}}_3$, 20 glucose, 2.5 KCl, $1.25{\mathrm{NaH}}_2{\mathrm{PO}}_4$, $2{\mathrm{MgCl}}_2$, $2{\mathrm{CaCl}}_2$. After cutting, the slices were transferred for a period of 12 min to a solution containing (in mM) 110 $N$-methyl-d glucamine, 2.5 KCl, $1.2{\mathrm{NaH}}_2{\mathrm{PO}}_4$, $25{\mathrm{NaHCO}}_3$, 25 glucose, $10{\mathrm{MgCl}}_2$, $0.5{\mathrm{CaCl}}_2$, adjusted to 300 to 310 mOsm/kg, pH 7.3 to 7.4 with HCl at 36°C, before being transferred back to the first solution for at least an hour before imaging trials. All solutions were oxygenated with $95\%{\mathrm{O}}_2/5\%{\mathrm{CO}}_2$.

After resting the slices were either bulk-labeled with CaSiR-1 AM-ester dye or used for single-cell labeling with CaSiR-1 potassium salt.

For bulk-labeled slices $50\mu \mathrm{g}$, CaSiR-1 AM (GC402, Goryo Chemicals)²³ was dissolved in $10\mu \mathrm{L}$ of dimethyl sulfoxide (DMSO) with 10% w/v Pluronic F-127 (Invitrogen) and 0.5% v/v Kolliphor EL (Sigma-Aldrich).²⁷ The slices were then incubated for 40 min at 37°C in 2 mL of Na-aCSF with the CaSiR-1 AM/DMSO mixture pipetted onto the surface of each slice, oxygenated by blowing $95\%{\mathrm{O}}_2/5\%{\mathrm{CO}}_2$ onto the surface. After loading, the slices rested in room temperature Na-aCSF for at least 20 min before use.

2.3.

Imaging

For single-cell labeling, cortical cells were patched using 6 to 8 MOhm patch pipettes containing intracellular solution consisting of (in mM): 130 K-Gluconate, 7 KCl, 4 ATP-Mg, 0.3 GTP-Na, 10 Phosphocreatine-Na, 10 HEPES, 0.1 CaSiR-1 potassium salt (GC401, Goryo Chemicals).²³ After sealing and breaking in, the calcium dye was allowed to diffuse into the cell [Fig. 1(b)]. For bulk-labeled slices [Fig. 1(c)], cortical cells were patched containing the same intracelluar solution without the addition of the CaSiR-1 potassium salt.

Cells were patched under oblique LED infrared illumination (peak 850 nm). The signals were recorded with a Multiclamp 700B amplifier (Axon Instruments) and digitized with a Power 1401 (Cambridge Electronic Design).

Imaging trials were taken at 20 frames/s at room temperature. Stimulation consisted of five current pulses for 10 ms at 0.5 Hz where the current was adjusted to stimulate a single action potential. For single cells, this stimulus was applied to the labeled cell with the dye-loading pipette. For bulk-labeled slices, the stimulus was applied to a cell in the field of view causing broader activation of multiple neurons in the local network. Widefield and light-field trials were interleaved by removing and replacing the MLA from a precision magnetic mount (CP44F, Thorlabs). The removal and addition of the MLA shifted the focal sample plane. We calculated this focal plane shift using the thin lens equation to be $\pm 2\mu \mathrm{m}$.

Fluorescence was excited with a 660-nm LED (M660L2, Thorlabs) powered by a constant current source (Keithley Sourcemeter 1401) to illuminate the sample between 2.3 and $14.1{\mathrm{mW}/\mathrm{mm}}^2$. The 660-nm LED was collimated with an $f=16\mathrm{mm}$ aspheric lens (ACL25416U0-A, Thorlabs) and filtered with a 628/40-nm excitation filter (FF02-628/40, Semrock). Collected fluorescence was filtered with a 660-nm long-pass dichroic (FF660-Di02, Semrock) along with a 692/40-nm emission filter (FF01-692/40, Semrock). Imaging data were acquired with Micromanager.²⁸

Single-cell labeled somata laid between 46 and $49\mu \mathrm{m}$ below the slice surface, with a median depth of 47 [IQR, 46.2, 48.6] $\mu \mathrm{m}$. Whereas bulk-labeled somata were between 29 and $36\mu \mathrm{m}$ below the slice surface, with a median depth of 34 [30, 34.8] $\mu \mathrm{m}$.

2.4.

Light-Field Volume Reconstruction

We reconstructed light-field source volumes from the raw light-fields [Figs. 1(b) and 1(c)] using synthetic refocusing⁷ and RL 3D deconvolution.^8,10,11 Images synthetically refocused at a plane $f^{\prime }=\alpha f_0$, where $f_0$ is the native focal plane, were calculated from a light-field image parameterized by $\mathcal{L}(x,y,u,v)$ using the formula derived in Ref. 29 as

Stacks from the same light-field images were also calculated using RL deconvolution. The 3D light-field PSF was calculated using the method described in Ref. 9, by considering how an LFM collects fluorescence from a dipole oscillating with a wavelength of 660 nm. The total PSF was calculated as an incoherent sum of dipoles oriented along $x$, $y$, and $z$. PSF values were calculated on a $5\times 5$ grid relative to the microlens. A low resolution PSF was calculated by averaging over the PSF values weighted by a 2D Hamming window of a width equal to the MLA pitch and coaxial with the lens. The estimated volume, $x$, is recovered from the measured light-field image, $y$, and the PSF, $H$ using the following iterative update scheme in matrix-vector notation:

In addition, to enhance edges and reduce noise, we slightly modified the objective function of RL to include a total variation (TV) term.³⁰ Including a total variation term in the objective function imposes a sparsity constraint on the image gradient. Therefore, an image with low total variation has large regions with close-to-zero gradients (denoised regions) and some with non-zero gradients (edges). To incorporate this regularization prior, we modified the standard RL as follows:

2.5.

Time Series Analysis

2.6.

Statistics

All statistics are reported as median [interquartile range (IQR)]. Wilcoxon matched-pairs signed-rank test was performed between synthetically refocused and 3D deconvolved light-field time series. These reconstructions were generated from the same image series, removing independent variables such as bleaching and changes in dye loading in the case of single-cell labeling. Statistical analysis was performed using Python SciPy.³¹

2.7.

Signal Confinement

3.1.

Synthetic Refocusing Enables Fast, High tSNR Light-Field Reconstruction

We compared the performance of light-field reconstruction techniques on the tSNR of CaSIR-1 signals extracted from both single-cell (intracellularly loaded) and bulk-labeled slices. We reconstructed volumetric light-field time series from four single cells [Fig. 2(a) and Video 1) and four bulk-labeled slices [Fig. 2(b)] with synthetic refocusing and RL 3D deconvolution. For single-cell trials, calcium transients were stimulated by applying suprathreshold current pulses (red lines) to the soma in whole-cell current clamp [Fig. 2(a2)]. Calcium transients from bulk-labeled slices were captured after a single cell was stimulated within the field of view [Fig. 2(a2)]. We interleaved widefield and light-field acquisitions by swapping the MLA in and out of the light path to facilitate comparison of functional signals extracted from matched ROIs. Time courses were extracted from an ROI taken from the top 2 percentile of pixels at the native focal plane. The tSNR, peak signal, and baseline noise were compared between the two light-field reconstruction algorithms and widefield image series.

Fig. 2

A comparison of calcium transient tSNR for widefield (WF) and light fields reconstructed with synthetic refocusing or RL 3D deconvolution. (a1), (b1) The calcium activation maps of planes reconstructed from light fields containing (a1) a single labeled cell and (b1) multiple cells in bulk-labeled slices using synthetic refocusing and RL 3D deconvolution (three-iteration) algorithms. Widefield bulk-labeled images were plotted from single plane activation maps whereas light-field were from maximum intensity projections through z. (a2), (b2) Calcium transient time series were extracted from the mean pixel intensities of the ROIs (outlined in red). As deconvolution iteration number increases, so does (c1) the peak signal and (c2) noise respective to time series reconstructed with synthetic refocusing for matching ROIs, ultimately reducing (c3) the tSNR. The gray traces are from separate single-cell experiments and the red line is the average ($n=4$ cells). (c1)–(c3) Normalized by the signal, noise, and tSNR of signals extracted from the same ROIs in the synthetically refocused planes. (d), (e) Comparison of peak signal (%), noise (%), and tSNR between time series extracted from WF images series, refocused and deconvolved (three-iteration RL) light fields (Video 1, mp4, 8628 KB [URL: https://doi.org/10.1117/1.NPh.9.4.041404.1]).

Iterative 3D deconvolution algorithms including RL are known to amplify noise,³⁰ which increases with iteration number. Therefore, we quantified the effect of iteration number on the peak signal, noise, and tSNR from single-cell trials. Light-field time series were deconvolved with between 1 and 21 iterations. The deconvolution was stopped at 21 iterations, before convergence, to limit noise amplification. Early stopping provides a regularizing effect on the deconvolution.^13,32 The deconvolved time series were normalized to synthetically refocused time series generated from the same raw light-fields. On average, the peak signal (%) increases with iteration number with respect to synthetically refocused light-field time series [Fig. 2(c1)]. As iteration number increases, the deconvolved peak signal increases to a peak signal around 3× greater than that achieved by synthetic refocusing at 21 iterations. In all trials, as iteration number increases, the noise (%) increases compared to synthetically refocused light-field time series [Fig. 2(c2)]. The deconvolved time series noise was on average the same as synthetically refocused light-field time series after 1 iteration increasing to 3× greater with 21 iterations. Therefore, on average, as iteration number increases the tSNR reduces [Fig. 2(c3)]. The tSNR from deconvolved light-field time series after 1 iteration is on average 1.5× larger than that of synthetically refocused light-field time series. The tSNR from deconvolved and synthetically refocused trials is the same around 17 iterations. Next, we compared the performance of light-field reconstruction techniques on the tSNR from all trials for both single-cell and bulk-labeled slices. Three-iteration RL deconvolution was chosen to give the best lateral signal confinement at the highest possible tSNR, as detailed in the next section.

The peak signal from single-cell trials (nine trials, four cells, three mice) was significantly larger when extracted from light-field time series reconstructed with three-iteration RL 3D deconvolution (16.7 [10.9, 23.5]%) compared to synthetic refocusing (11.3 [5.9, 14.7]%; Wilcoxon matched pairs signed rank, $n=9$, $w=36.0$, $p=0.01$) and single-plane widefield time series (3.2 [1.7, 5.6]%; Fig. 2(d1)). The baseline noise did not differ between light-field time series reconstructed with three-iteration 3D deconvolution (0.34 [0.24, 0.44]%), those reconstructed with synthetic refocusing (0.31 [0.20, 0.55]%; Wilcoxon matched pairs signed rank, $n=8$, $w=15.0$, $p=0.4$), and those from widefield time series (0.10 [0.04, 0.26]%; Fig. 2(d2)). The tSNR of times series from three-iteration RL-deconvolved frames (46.0 [35.7, 86.0]) was significantly greater than that of synthetically refocused frames (29.9 [17.8, 49.9]; Wilcoxon rank sum, $n=8$, $w=25.0$, $p=0.01$) and single-plane widefield time series (21.9 [16.8, 86.2]; Fig. 2(d3)).

In bulk-labeled slices (seven trials, six cells, two mice), the peak signal was significantly greater for light-field time series reconstructed with three-iteration RL 3D deconvolution (8.0 [4.7, 15.0]%) compared to synthetically refocused (3.2 [2.6, 8.9]%; Wilcoxon rank sum, $n=7$, $w=0.0$, $p=0.02$) and widefield time series (1.7 [0.8, 5.1]%; Fig. 2(e1)). The baseline noise was significantly larger in three-iteration deconvolved bulk-labeled slices (0.15 [0.09, 0.24]%) compared to synthetic refocusing (0.09 [0.04, 0.10]%; Wilcoxon rank sum, $n=7$, $w=0.0$, $p=0.02$), and widefield time series (0.12 [0.05, 0.22]%; Fig. 2(e2)). The tSNR from light-field time series reconstructed with synthetic refocusing (51.0 [29.5, 112.9]) did not differ from deconvolution-reconstructed trials (40.4 [32.6, 120.7]; Wilcoxon rank sum, $n=5$, $z=14.0$, $p=1.0$) or widefield trials (21.1 [4.9, 51.7]), Fig. 2(e3)).

To enhance edges and reduce noise in bulk-labeled volumes, we modified the objective function of RL to include a TV regularization term (Fig. S1A in the Supplemental Material). Inclusion of the TV term in the RL deconvolution reduced the total variation of the deconvolved stacks from 0.158 to 0.128 after 10 iterations with a regularization factor of 0.01. However, the mean squared error between TV and non-TV reconstructed volumes was very small, resulting in identical peak signal, noise, and tSNR in the extracted calcium time series (Fig. S1B in the Supplemental Material). Increasing iteration number up to 30 increased peak signal, and thus tSNR, for the TV-regularized volume (Fig. S1C in the Supplemental Material).

3.2.

Deconvolution Reconstruction Algorithms Provide Enhanced Spatial Signal Confinement

We compared the lateral and axial signal confinement of single cells intracellularly labeled with calcium dye between widefield z-stacks and 3D light-fields reconstructed with synthetic refocusing [Fig. 3(a2)] and RL 3D deconvolution [Fig. 3(a3) and Video 2]. To assess the impact of deconvolution iteration number on spatial confinement, we measured the FWHM of lateral and axial profiles, normalized to the FWHM the same profiles in synthetically refocused volumes. Both the lateral [Fig. 3(b1)] and axial [Fig. 3(b2)] signal confinement increase with increasing deconvolution iteration number. The red line shows the average for the three cells. The lateral signal confinement [Fig. 3(b1)] for one iteration is around 1.2$\times$ better than synthetically refocused light-field images and plateaus around 10 iterations with a 1.5× improvement. The axial signal confinement [Fig. 3(b2)] for one deconvolution iteration is 1.1× better than synthetic refocusing increasing to 2.2× after 21 deconvolution iterations. Three-iteration RL deconvolution was chosen for further analysis as it maximized lateral confinement while maintaining a high tSNR.

Fig. 3

Deconvolution enhances spatial signal confinement compared to widefield stacks and light-field volumes reconstructed with synthetic refocusing. Lateral and axial single-frame structural profiles from a single-cell filled with CaSiR-1 dye are shown. The lateral profiles are plotted at (a1) the native focal plane from widefield stacks, and light-field volumes reconstructed with (a2) synthetic refocusing and (a3) three-iteration RL deconvolution. The axial profiles have been extracted from the lateral position intersected by the red dashed lines at depths ranging from $-40$ to $+40\mu \mathrm{m}$. Increasing deconvolution iteration number increases both (b1) the lateral and (b2) axial signal confinement compared to synthetically refocused volumes. The deconvolved FWHMs are normalized to that of synthetic refocusing. The gray lines are from three different cells, and the red line is the average. Deconvolved light-fields (three-iteration RL, black solid line, and 21-iteration RL, red dashed line) features better (c1) lateral and (c2) axial spatial confinement than widefield $z$-stacks and synthetically refocused light-field volumes (Video 2, mp4, 8890 KB [URL: https://doi.org/10.1117/1.NPh.9.4.041404.2]).

The 2D spatial profiles [Figs. 3(a1)–3(a3)] clearly show that the light-field images reconstructed with 3D deconvolution have better spatial signal confinement, both laterally and axially compared to both those reconstructed with synthetic refocusing and widefield stacks. The spatial profile for refocused volumes looks similar to widefield, which is expected due to the nature of the reconstruction. A line plot was taken through the lateral and axial profiles, and the FWHM was calculated for each of the imaging configurations from three cells [Figs. 3(c1) and 3(c2)]. The results are summarized in Table 1.

Table 1

Summary of FWHM from single-cell labeled spatial profiles. Reported as median [IQR], n=3.

The lateral signal confinement [$x$ and $y$; Fig. 3(c1)] from light-field images reconstructed with 3D deconvolution (three-iteration RL) was better than that of synthetically refocused or widefield stacks (Friedman’s two-way analysis of variance by ranks; $x$: $n=3$, $w=2.67$, $p=0.26$ $y$: $n=3$, $w=6.00$, $p=0.05$). Moreover, 3D deconvolution significantly improved axial signal confinement [$xz$; Fig. 3(c2)] compared with that of synthetically refocused or widefield stacks (Friedman’s two-way analysis of variance by Ranks; $n=3$, $w=6$, $p<0.05$).

For the bulk-labeled slices, the low contrast of the raw images precluded segmentation of individual cells. The cellular spatial profiles were therefore generated from an activation map (the variance of $\mathrm{\Delta }F/F$ over time). Maximum intensity projections through $xz$ and $yz$ are shown for synthetically refocused [Fig. 4(a)] and deconvolved [three iterations; Fig. 4(b)] volume reconstructions of the variance of the light-field functional time series. The signal confinement for both synthetically refocused and 3D deconvolved light-field volumes enabled resolution of a number of active neurons across different focal planes spanning about $9\mu \mathrm{m}$, which is unachievable with any widefield imaging system. The center of mass of each neuron ranges from depths of $-5$ to $+4\mu \mathrm{m}$. The image contrast is higher for 3D deconvolved than for refocused volumes.

Fig. 4

Reconstructed light-field volumes can distinguish active cells from different axial planes in bulk-labeled slices. Planes from bulk-labeled slices were reconstructed from light-field volumes with (a) synthetic refocusing and (b) 3D deconvolution (three-iteration RL) between $-30$ and $+30\mu \mathrm{m}$ in steps of $1\mu \mathrm{m}$. An activation map was generated from the variance of $\mathrm{\Delta }F/F$ over time to identify active neurons. A maximum intensity projection through $z$ was generated. A $xz$ and $yz$ maximum intensity projection shows multiple active cells in the field of view spanning different axial planes. The lower right plot in each panel shows the $z$-profiles of cellular ROIs circled in the same colors on the image. The center of mass of each neuron ranges in depth from $-5$ to $+4\mu \mathrm{m}$.

In addition, maximum intensity projections through $xz$ and $yz$ were generated with the TV term (Fig. S1D in the Supplemental Material). The TV term at both 10 and 30 iterations did not change the spatial signal confinement.

3.3.

Light-Field Microscopy Resolves Calcium Signals from Neuronal Dendrites in 3D

LFM enables single-frame 3D imaging; therefore, we investigated its application to resolving calcium signals from neuronal processes in three spatial dimensions. We reconstructed 4D ($x,y,z,t$) light-field volumes from time series and extracted temporal signals from ROIs manually defined over dendrites from the $\mathrm{\Delta }F/F$ activation map.

Depth-time plots were extracted from ROIs taken from light-field time series reconstructed with synthetic refocusing [Fig. 5(b)] and 3D deconvolution [three-iteration RL; Fig. 5(c)]. A depth map cannot be produced from widefield images as they are focused on a single axial plane [Fig. 5(a)]. Moreover, in contrast with Fig. 3, which displayed structural data, Fig. 5 shows functional activation maps in which the dendrites feature highest $\mathrm{\Delta }F/F$ and therefore appear bright with respect to the soma. The signals as a function of depth were summed over time for each ROI to generate functional depth profiles [Figs. 5(d1)–5(d3)].

Fig. 5

Calcium signals in dendrites can be observed across axially distinct planes from single-cell light-field volumes. (a) The activation (or variance) map from a widefield image series with time courses extracted from three dendritic ROIs (red, orange, and pink outlines). Depth-time plots are shown from the same ROIs reconstructed from a light-field time series with (b) synthetic refocusing and (c) 3D deconvolution. (d1)–(d3) The sum of the signal over time as a function of depth in the three dendritic ROIs.

The peak dendritic $\mathrm{\Delta }F/F$ signals are greater in deconvolved volumetric light-field time series [Figs. 5(c2)–5(c4)] compared with those synthetically refocused [Figs. 5(b2)–5(b4)], in agreement with the results from Sec. 3.1. From the depth plots, it appears that the center of mass of Area 3 lies near the native focal plane whereas Areas 1 and 2 lie deeper in the slice [Figs. 5(d1)–5(d3)]. This indicates that calcium transients can be resolved from neuronal sub-compartments in axially distinct planes.

The decay time, measured by the FWHM of somatic calcium transients at the native focal plane, is the same between widefield (0.23 [0.20, 0.27]s, $n=3$ cells) and light-field time series reconstructed with synthetic refocusing (soma: 0.24 [0.21, 0.32]s, $n=3$ cells) and 3D deconvolution (soma: 0.22 [0.20, 0.40]s, $n=3$ cells). Moreover, there is no significant difference between the decay time of dendritic signals of synthetically refocused (dendrite: 0.139 [0.136, 0.141]s, $n=3$ cells) or deconvolved (dendrite: 0.132 [0.126, 0.167]s, $n=3$ cells) light-field time series.