High-Resolution Fourier Light-Field Microscopy for Volumetric Multi-Color Live-Cell Imaging

This document provides supplementary information to “High-Resolution Fourier Light-Field Microscopy for Volumetric, Multi-Color Live-Cell Imaging , ” https://doi.org/10.1364/OPTICA.419236 . It includes a description of the sample preparation, theoretical models and data processing, as well as the supplementary figures referenced in the main text.

70 °C to avoid condensation.Then we diluted 10 μL 200-nm beads into the agarose solution and mixed them on the vortex mixer.Lastly, the entire bead-agarose solution was added and dried at the center of the dish for observation.

Immunofluorescence staining of mitochondria in COS-7 cells.
Mitochondria in COS-7 cells were immunolabeled with primary antibody TOMM20 (PA5-52843, Thermo Fisher Scientific) and secondary antibody Alexa647 (A-21245, Thermo Fisher Scientific).16% Paraformaldehyde (formaldehyde) aqueous solution (PFA, 15710, Electron Microscopy Sciences) was first warmed to 37 °C.The culture medium in the cell culture dish was then aspirated and 4% PFA was added through the wall of the chamber to cover the bottom of the dish well.The cells were fixed for ~12 minutes in the incubator at 37 °C.After the fixation, the sample was rinsed with a buffer containing 50 mL 1× PBS (10010031, pH 7.4, Thermo Fisher Scientific), 0.25 mL Normal Goat Serum (NGS, 191356, 0.5%, ICN, Biomedicals, Orsay, France), and 250 μL Triton X-100 (85111, 0.05%, Thermo Fisher Scientific) at the room temperature for 5 times at a duration of 30 s, 60 s, 5 min, 10 min, 15 min successively.The cells were then blocked and permeabilized in a permeabilization buffer (5 mL blocking buffer, 100 μL Triton X-100) for 30 min, followed by another two wash steps for 30 s and 5 min successively.After washing the cells, we then prepared the primary antibody solution with the blocking buffer (10 mL 1× PBS, 0.5mL NGS (5%), 0.1 g BSA (Bovine Serum Albumin, BP9703-100 1%, Fisher BioReagents), 50 μL Triton X-100) at a concentration of 1 μg/mL and add 150 μL of the solution into the cell dish.The cells with primary antibody were placed in the dark environment at the room temperature for about 3 hours.After primary antibody labeling, the cells were washed three times for 5 min each time.Then the sample was labeled with the secondary antibody, which was diluted in the blocking buffer at a concentration of 1:1000 for approximately 1 hour.Additional washing steps were taken for three times and 5 min each time.Lastly, the sample was stored in PBS at 4 °C in humidity box until ready for imaging.

Mitochondria and peroxisome labeling in living COS-7 cells.
For single-color live-cell imaging, the thawed cells were grown in a pre-warmed (37 °C) mixed solution containing 3 mL modified DMEM and 15 μL Peroxisome-GFP (CellLight C10604, Thermo Fisher).The GFP was expressed on the peroxisomes in the cells after overnight cell growth.Then the culture medium was removed, and the cells were washed twice with HBSS.Lastly, ~2 mL DMEM (FluoroBrite A1896701, Thermo Fisher) was added into the sample, which was maintained at 37 °C to keep the cells live and active prior to imaging.For multi-color imaging, following the abovementioned peroxisome labeling, we labeled mitochondria with MitoTracker in the live-cell sample.The washed cells were added with pre-warmed (37 °C) staining solution, which was composed of 1.5 μL MitoTracker stock solution and ~2 mL pure DMEM.The MitoTracker stock solution was prepared by dissolving 50 μg lyophilized MitoTracker Deep Red FM (M22426, Thermo Fisher) in 92 μL anhydrous dimethyl sulfoxide (DMSO, BP231-100, Fisher BioReagents).The cells were incubated for 50 minutes at 37 °C and washed twice with HBSS.Then 2 mL FluoroBrite DMEM was added into the sample, which was maintained at 37 °C to keep the cells live and active prior to imaging.

SYSTEM CHARACTERIZATION
The system performance is predicted based on our theoretical framework of Fourier light-field microscopy (FLFM) reported in [1].In particular, we implemented the design parameters in HR-FLFM to the model and characterized the performance in the 3D resolution, depth of focus (DOF) and field of view (FOV).The theoretical results derived as follows showed a good agreement with the experimental measurements.
Lateral resolution.The lateral resolution of the HR-FLFM system can be calculated as: where M is the magnification of the objective lens, λ is the wavelength of the fluorescence emission.NAML is the numerical aperture (NA) of each microlens.The focal lengths of the Fourier lens and the microlenses are represented as fFL and fML, respectively.
In the HR-FLFM system, the magnification of the objective lens is 100× and the peak fluorescence emission wavelengths are 680 nm (dark red) and 510 nm (green).The focal lengths of the Fourier lens and microlenses are fFL = 275 mm and fML = 117 mm, respectively.The NA of each microlens can be calculated as = = × = 0.014, where d = 3250 µm is the pitch distance between two microlenses (Fig. 1(a) and Fig. S1).As a result, the lateral resolution can be obtained to be 575 nm for dark red and 432 nm for green, which are consistent with the measurements (300-700 nm in an axial range of ~4 µm) of the reconstructed images in Fig. 2(f) and biological samples (Figs. 4  and 5).It should be noted that the theoretical model is derived based on elemental images, and as observed, the deconvolution in the reconstruction process provides a moderate enhancement in the resolution.
Axial resolution.The axial resolution of the HR-FLFM system can be calculated as: , given the consideration that the axial positions of the two emitters can be retrieved if they can be resolved laterally in the axial-coupled elemental images [1].In this case, the axial resolution can be obtained as 843 nm for dark red and 632 nm for green, which are consistent with the measurements (0.5-1.5 µm in an axial range of ~4 µm) of the reconstructed images in Fig. 2(f) and biological samples (Figs. 4  and 5).

Depth of focus (DOF).
The DOF of the system can be considered as the full width of the axial PSF (i.e.2× FWHM value in the axial direction), considering the fact that the deconvolution in the reconstruction process is able to retrieve the diffracted information outside of the Rayleigh range of the axial PSF.Therefore, the DOF can be calculated as [1] where Peff is the effective pixel size of the elemental image, which is 153 nm based on the configuration of our setup.Hence, the DOF is obtained as 4.41 μm for dark red and 3.44 μm for green, which are consistent with the measurements (~4 μm) of the reconstructed images in Fig. 2(f) and biological samples (Figs. 4 and 5).It should be mentioned that the retrieval quality of the full axial range can be moderately affected by the SNR degradation as the depth increases.

Field of view (FOV).
The FOV is estimated at the focal plane in the object space of the system [1]: which can be calculated using the system parameters to be 76.39 μm × 76.39 μm, which is consistent with the measurements (~70 μm × 70 μm) using the reconstructed images of biological samples (Figs. 4 and 5).

VECTORIAL DEBYE MODEL
To address the high NA of the objective lens and the corresponding refractive-index mismatch (RIM) between the objective immersion medium and the sample solution, we derived the wavefunction at the native image plane (NIP) using the vectorial Debye theory [2,3].
In brief, we modeled the projection of the 3D object space onto the 2D image space as below: where is the focal length of the objective lens.and are the zeroth and second order Bessel functions of the first kind, respectively; the variables and represent normalized radial and axial coordinates; the two variables are defined by = [( ⁄ − ) + ( ⁄ − ) ] / ( ) and = ( ⁄ ); = ( , , ) ∈ ℝ is the position for a point source in a volume in the object domain; = ( , ) ∈ ℝ represents the coordinates on the NIP; is the magnification of the objective lens; is determined by the minimum of the halfangle of the NA and the critical angle of the total internal reflection = [ ( ⁄ ) , ( ⁄ )] ; the wavenumber , = , / were calculated using the emission wavelength , the refractive index of the immersion medium and the refractive index of the sample solution; and are the refractive (objective side) and incident (sample side) angles at the interface between two media, respectively [3].
In Eq.S5, we defined the aberration function ( ), the Fresnel transmission coefficients and as: ( ) = − ( − ) , ) , where l is the normal focusing position (NFP).In our setup, is 2 mm, M is 100, and is 680 nm and 510 nm according to the peak dark red or green fluorescence wavelengths, respectively.The refractive index of the immersion oil is 1.515, and is 1.46 for glycerol and 1.33 for water solution.Since the fluorescence from the emitters exhibits an isotropic polarization, we set the azimuthal angle of the emitter in the polar coordinates = 90°, so that the light field derived from the vectorial Debye theory only points to the p1 direction for computational convenience [3].
Next, the image at the NIP ( , ) is optically Fourier transformed onto the back focal plane of the Fourier lens, described as [ ( , )], which is then modulated by the MLA.The modulation is described using the transmission function ( ), where = ( , ) ∈ ℝ represents the coordinates on the MLA.Specifically, the aperture of a microlens can be described as a hexagonal amplitude mask ( ⁄ ), combined with a phase mask ‖ ‖ , where = / is the wavenumber in the air.The modulation induced by a microlens is then described as: where = 117 mm is the focal length of the MLA, and = 3250 mm is the diameter of a single microlens (or the pitch of the MLA if the microlenses are tiled in a seamless manner).Thus, the modulation of the entire MLA, composed of periodic microlenses, can be described by convolving ( ) with a comb function △ ( ⁄ ) that corresponds to the three microlenses enclosed in the aperture (e.g.Fig. S1), i.e. ( ) = ( ) ⨂ △ ( ⁄ ), where ⨂ is the convolution operator.
The light field propagating from the MLA to the camera can be modeled using the Fresnel propagation over a distance of [4]: {} is the optical Fourier transform performed by the Fourier lens.In practice, the Fresnel propagation over the distance of is divided and calculated over small steps for computational accuracy.The final intensity image ( ) at the camera plane containing elemental images of each microlens is described by: where ∈ ℝ , as defined in Eq.S5, is the position in a volume containing isotropic emitters in the object space, whose intensity distribution is described by ( ).
) ∈ ℝ represents the coordinates on the camera plane, the exponential term is the Fresnel transfer function, and are the spatial frequencies in the camera plane, and {} and {} represent the Fourier transform and inverse Fourier transform operators, respectively.