2.5D microscopy: Fast, high-throughput imaging via volumetric projection for quantitative subcellular analysis

Abstract

Imaging-based single-cell analysis is essential to study the expression level and functions of biomolecules at subcellular resolution. However, its low throughput has prevented the measurement of numerous cellular features from multiples cells in a rapid and efficient manner. Here we report 2.5D microscopy that significantly improves the throughput of fluorescence imaging systems while maintaining high-resolution and single-molecule sensitivity. Instead of sequential z-scanning, volumetric information is projected onto a 2D image plane in a single shot by engineering the emitted fluorescence light. Our approach provides an improved imaging speed and uniform focal response within a specific imaging depth, which enabled us to perform quantitative single-molecule RNA measurements over a 2×2 mm² region within an imaging depth of ~5 μm for mammalian cells in <10 min and immunofluorescence imaging at a >30 Hz volumetric frame rate with reduced photobleaching. Our microscope also offers the ability of multi-color imaging, depth control and super-resolution imaging.

Graphical Abstract

Introduction

High-throughput and high-content analysis of cells and tissues is invaluable for the screening and profiling of cellular features.^1–2 Since each cell’s response varies under stimulation and during different cell cycles, single-cell resolution is required to analyze biomarkers such as proteins, RNAs and organelles. Imaging-based approaches have been popular in single-cell analysis for studying the expression levels and functions of biomolecules, their interaction networks and the molecular mechanisms of cellular processes.^3–4 These demands have long been fulfilled by high-throughput automated fluorescence microscopy¹ as it provides high spatial resolution (often super-resolution⁵), the ability to perform time-lapse studies⁶ and the versatility to examine tissues as well as cells. In particular, imaging-based transcriptomics using single-molecule RNA fluorescence in situ hybridization (smFISH)⁷ allows hundreds to thousands of transcripts to be measured simultaneously in individual cells by directly visualizing fluorescence spots under a microscope, showing its tremendous power in studying and understanding fundamental biological phenomena and cellular functions.^8–11

However, the fact that the imaging speed of current high-throughput microscopy techniques is two or three orders of magnitude slower than other techniques such as imaging flow cytometry^12–13 has severely limited its widespread adoption. The most time-consuming process in the high-throughput imaging system is serial z-scanning which captures three-dimensional (3D) cell images by mechanically moving the specimens mounted on a piezo-stage (Fig. 1a). This wastes photons emitted by fluorophores residing at out-of-focus regions from wide-field epi-illumination, and can also perturb the samples during the image acquisition.

Figure 1. Working principles of 2.5DM.

(a-e) Focal responses at the x-z plane by different pupil functions from left to right: (a) a clear aperture with NA=1.4, (b) a phase with spherical aberration (SA), (c) a binarized spherical aberration (binary SA), (d) 2.5D phase mask created by binarizing a combination of spherical aberration and defocusing, and (e) a clear aperture with NA=0.45. (f-g) Intensity profiles along the lateral (f) and axial (g) directions for the corresponding pupil functions. The wavelength (λ) is 670 nm and the refractive index (n) of the sample is 1.518. NA=1.4 was used for these simulations unless specified otherwise. All results were obtained by simulation. Scale bar, 1 μm.

To overcome these issues, a variety of approaches have been suggested for fast volumetric imaging toward less or no serial z-scanning.^14–15 For example, the focal plane can be rapidly scanned to obtain either a 3D image stack with a high frame rate or a projected image during a single camera exposure. This has been achieved by using an electrically tunable lens,¹⁶ tunable acoustic gradient (TAG) index of refraction lens,¹⁷ remote focusing¹⁸ or a deformable mirror.^19–20 While these methods generate a near-uniform optical response with uniform lateral resolution over a designed axial range, they have a poor signal-to-noise ratio (SNR) due to a low detection duty cycle, which makes them unsuitable to low-light imaging applications such as single-molecule imaging. Simultaneous 3D imaging by projecting multiple focal planes onto different areas of a camera²¹ or light-field microscopy²² has been reported, but they either inherently exhibited a low SNR²³ or limited spatial resolution. Extended depth-of-field (EDOF) imaging via spherical aberration was shown to be useful for fast 3D imaging; however, it was restricted for use with low numerical aperture (NA) systems.^24–25

In this regard, point spread function (PSF) engineering methods that encode the wavefront at the back focal plane (BFP) of an objective lens^26–27 exhibit several merits compared to other approaches for EDOF imaging. This includes compatibility with high NA objectives, tunability of the imaging depth and the ease of correcting aberrations with the implementation of adaptive optics. One typical PSF engineering approach is to generate an Airy-beam shaped elongated detection PSF using a cubic phase mask.²⁶ However, the result showed a considerable amount of side lobes, requiring a careful deconvolution to reconstruct the original images.²⁸

Here, we report multi-color 2.5D microscopy (2.5DM) that substantially improves the throughput of fluorescence imaging systems while exhibiting high lateral resolution and single-molecule sensitivity. By generating a defocus-invariant PSF within a specific depth via a novel phase pattern, volumetric information is projected onto a 2D image plane by single-shot imaging. The high uniformity of the axial profile and minimal side-lobes allow us to readily interpret the original image without image post-processing. We demonstrate the potential advantage of our 2.5DM by performing quantitative high-throughput smFISH imaging over a 2×2 mm² region in mammalian cells in less than 10 min. We also apply our technique to immunofluorescence imaging to show its versatile use.

Results

Principles of 2.5DM

The 2.5D microscope is based on an epi-illumination widefield imaging system where a PSF engineering module is inserted in the detection pathway (Figure 1S). We are mainly interested in imaging mammalian cells whose thickness is ~4–6 μm via a single-shot volumetric projection without serial z-scanning. Among various approaches for EDOF, a circularly symmetric phase function using controlled spherical aberration and defocus^29–30 attracted our attention because (i) the intensity of the PSF along the optical axis shows excellent uniformity²⁹ unlike other methods showing either a rapid oscillation³¹ or a broad Gaussian response³² that makes it challenging to do quantitative intensity analysis, (ii) the lateral intensity of the PSF is circularly symmetric as contrasted with a cubic phase mask²⁸ and (iii) a phase function ensures high transmission efficiency unlike an amplitude filter.³³ Particularly, we adopted a binary phase function which has shown an EDOF over a certain distance with a relatively sharp focus and well-preserved circularly symmetric intensity distribution around the focal region. However, this has been suggested theoretically only in a low NA imaging system.³⁰

To design a phase function that meets our needs, we simulated a 3D focal response of the collected light through a high NA imaging system (NA = 1.4). We used vectorial Debye diffraction theory to calculate the electric field,^34–35 in which a binary phase modulation was imprinted at the BFP of the objective. The wavelength used was 670 nm which was close to the emission maximum of a common red-emitting fluorophore AlexaFlour 647 (AF647). We first applied a spherical aberration on a pupil plane (Figure 1b). The resulting PSF was elongated but no longer symmetric along the axial direction compared to a tight focus under a clear aperture (Figure 1a). Binarizing this continuous phase function with 0 and π generated two focal spots that were symmetric with respect to the focal plane and effectively further extended the PSF (Figure 1c); however, its intensity distribution was not uniform along the axial direction. To remedy the issue, we additionally introduced a defocus term to the phase function, binarized it, and optimized parameters until we attained a defocus-invariant PSF exhibiting a uniform distribution within a specific depth, for example, 5.5 μm in Figure 1d. (More details found in the Materials and Methods.) Hereinafter, we will call this phase function the 2.5D phase mask, while a clear aperture with NA=1.4 is referred to as widefield (WF).

2.5DM characterization: Simulation

We compared the intensity profiles of the PSF along the lateral (Figure 1f) and axial directions (Figure 1g) for three cases, i.e., a clear aperture (NA = 1.4), 2.5D phase mask (NA = 1.4), and a clear aperture with a low NA system (NA = 0.45) (Figure 1e). The latter aims to generate the same depth of field as a 2.5D phase mask. Compared to WF (NA=1.4), the PSF generated by our 2.5D phase mask showed that the axial focal depth increased by ~8-fold but the lateral width increased only ~1.8-fold whereas for the low NA system the lateral width increases ~2.8-fold. Notably, the 2.5D phase mask exhibited a remarkably uniform axial distribution. To quantify this, we calculated the full-width at 90% of maximum (FW90M) that is commonly used in flat-field illumination.³⁶ The 2.5D phase mask showed 1.8-fold larger FW90M compared to the low NA system given the same axial FWHM. Such a high uniformity will be useful for quantitative imaging. In addition, our method demonstrated superior performances compared to a typical EDOF imaging method using a cubic phase mask (Figure 2S). Importantly, the 2.5D phase mask can achieve an EDOF without compromising the light collection efficiency, which is critical for photon-limited applications. In contrast, the light collection efficiency of the low NA system is 9.7-fold lower than 2.5DM.

Our approach provides tunability of the imaging depth by simply controlling the strength of the aberration term (Figure 2a). In this case, the defocusing was adjusted accordingly based on the strength of the spherical aberration term in order to have a uniform intensity distribution over a designed depth. To elucidate the advantage of the 2.5D phase mask, we plotted an axial FWHM (Δz) as a function of lateral FWHM (Δx) (Figure 2b). Compared to the clear aperture with low NA objectives, our approach minimized broadening of the lateral resolution and provided a uniform axial profile over a larger depth. It should be noted that as shown in a log-log plot (Figure 3S) the slope of the 2.5D phase mask starts to decrease at Δz >7 μm. This may be explained by the fact that as the strength of the spherical aberration increases, the growth rate of the EDOF generated by the 2.5D phase function decreases above a certain threshold DOF. In addition, the flexibility of imprinting different phase functions enables us to create smoother intensity profiles by dithering along the z-axis over ~1 μm without compromising the detection duty cycle (Figure 4S).

Figure 2. Features of the 2.5D imaging system.

(a) Tunable depth-of-field by controlling the spherical aberration strength γ. (b) FWHM of the axial PSF (Δz) as a function of lateral FWHM (Δx) for 2.5D phase function with different depths (red) and various NA cases (black). (c-d) Response of 2.5D imaging to broadband light. Lateral (c) and axial (d) focal responses of the designed binary phase function under monochromatic (dotted blue) and broadband light (solid red). All results were obtained by simulation. Scale bar, 1 μm.

Since the fluorescence emission is not monochromatic, it is necessary to check whether our method can be applied to broadband light. Our simulation showed that degradation in the lateral and axial intensity profiles was almost negligible for the broadband emission (Δλ = 100 nm) compared to that for monochromatic light (Figures 2c and 2d), confirming that our 2.5D phase mask is tolerant to the wavelength variation and can be employed in fluorescence microscopy. When a phase function optimized by scalar diffraction theory is directly applied for a high NA system, the axial intensity of the PSF showed stronger variation within the defined axial distance (intensity dropped below 90% of the maximum intensity) than the desirable case (Figure 5S), indicating that a vectorial Debye diffraction approach was necessitated to correctly design the 2.5D phase mask.

2.5DM characterization: Experiments

To experimentally demonstrate our 2.5DM, an SLM was inserted in the conjugated back focal plane of an objective lens in the detection path (Figure 1S) and the PSF was engineered accordingly by imprinting the 2.5D phase mask onto the SLM. Then, we measured the PSF of the 2.5D imaging system using 80 nm gold nanoparticles dispersed in immersion oil. The gold nanoparticles serve as point source scatterers of the illumination light (λ = 638 nm), which was then collected by an oil immersion objective lens (NA = 1.4). Compared to WF, our 2.5D system demonstrated an elongated focal response along the optical axis with a moderately uniform intensity distribution (Figure 3a), which corresponds well with the simulation presented above. From the intensity profiles (Figure 3b), one can see that 2.5DM changes the FWHM of the PSF along the x-axis from 0.32 μm to 0.51 μm while the FWHM along the z-axis changes from 0.63 μm to 4.50 μm. Thus, our method achieves an axial depth extension of 7.2-fold while only broadening of the lateral width by a factor of 1.6. We obtained similar results from fluorescent beads (Figure 6S). We also confirmed that a low NA system exhibiting an equivalent depth of field to 2.5DM showed a broadening of the lateral FWHM and significant degradation of SNR in single-molecule imaging (Figure 7S).

Figure 3. Experimental characterization of the 2.5D imaging system.

(a-b) PSF measurements using 80-nm gold nanoparticles. (a) Intensity distributions at the x-y and x-z planes with a clear aperture (WF) and a 2.5D phase function. (b) Lateral and axial intensity profiles of WF (black) and 2.5DM (red). (c-d) Single-molecule fluorescence intensity measurements for the surface immobilized AlexaFlour647-DNA. (c) Single-molecule images (left) by WF and 2.5DM. Zoomed-in images from subregions marked by dashed squares (right) at the focal plane and an imaging depth of 1 μm above the surface. Both were recorded at an excitation intensity of 100 W/cm² and an exposure time of 800 ms. (d) Peak intensity histograms of single-molecule spots. Scale bars, 1 μm (a), 10 μm (c, left) and 2 μm (c, right).

It has been noted that the peak intensity of the 2.5D images decreases as the DOF increases. To quantitatively analyze the extent of the intensity reduction, we imaged single-molecule DNAs labeled with AF647 on the glass surface by WF and 2.5DM (Figure 3c). We analyzed >1,000 well-isolated single-molecule spots and plotted background-corrected peak intensity values for each spot in a histogram (Figure 3d). It shows that a mean value of the peak intensity with 2.5DM was ~3-fold lower than a clear aperture case. The ratio of the peak intensity with 2.5DM and WF (commonly called Strehl ratio) indicates that under the same excitation intensity, a ~3× longer exposure time would be needed for 2.5DM if one wants to achieve a comparable peak intensity or SNR as the case with a clear aperture. Note that our WF images were obtained in the presence of a PSF engineering module not directly from a standard WF microscope.

Application of 2.5DM to smFISH

To demonstrate the potential applications of 2.5DM to RNA imaging, we performed smFISH experiments in U2OS cells on EEF2 (Eukaryotic Translation Elongation Factor 2), one of the high-abundance mRNAs in mammalian cells.³⁷ We used 32 FISH probes labeled with AF647. First, we obtained a 3D stack of smFISH images with WF by serial z-scanning over a 5 μm depth with an exposure time of 400 ms per step (25 steps in total) and an illumination intensity of $100\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ (Figure 4a). Then we performed maximum intensity projection (MIP) along the z-axis on the 3D stack to reduce it into a single image that displays location of individual mRNAs in cells (Figure 4b). Next, for the same area we recorded a single snapshot image by 2.5DM with the same excitation intensity as WF (Figure 4c). Each single-molecule spot imaged with 2.5DM corresponded very well with those obtained by MIP (Figure 8S). Transcription active sites were also clearly visible in nuclei. Here an exposure time for 2.5DM was 1 s to achieve comparable image contrast as that with WF. As a result, the total imaging time of 2.5DM was ~10-times shorter than that of WF (~10.5 s). Note that we used the z-step size of 0.2 μm for WF, which is smaller than the Nyquist criterion (~0.3 μm) because the reduced step size minimizes degrading of image contrast.³⁸

Figure 4. Single-molecule FISH images of EEF2 on U2OS cells using 2.5DM.

(a) smFISH images at different focal planes (left) and the corresponding single-shot 2.5D image (right). (b-d) Images obtained by (b) maximum intensity projection (MIP), (c) 2.5DM and (d) average intensity projection (AIP) for the 3D cell volume. Nuclei were stained with DAPI shown in blue. Yellow arrows indicate active transcription sites. 32 FISH probes were labeled with AF647 and an imaging buffer was used to minimize photobleaching. All images were recorded at an excitation intensity of ~100 W/cm² with an exposure time of 400 ms/step (WF) or 1 s (2.5DM). (e) Plots of the number of transcripts found in a single cell (surrounded by a yellow dashed polygon in (b) and (c)) as a function of threshold values for MIP and 2.5DM, where the vertical dashed lines indicate the optimal thresholds. (f) Signal to background ratio (SBR) for different techniques. The error bars denotes the standard deviation from the mean value.

We counted the copy number of mRNAs in a single cell under MIP and 2.5DM (Figure 4e). The number of single-molecule spots was counted for all the possible threshold values (normalized to 1).⁷ A characteristic plateau was observed, where the number of spots reported is less sensitive to the particular threshold chosen within the plateau region and the accurate copy number of mRNAs can be determined. MIP and 2.5D methods detected 617 and 587 mRNAs, respectively, showing a good agreement with each other. We used MIP images instead of 3D stacks because both showed almost the same results (the latter showed the copy number of 609). A slight decrease (~5%) of the detected mRNA number in 2.5DM may be attributed to the overlap of multiple spots (Figure 8S) and photobleaching. The former can be improved by multi-spot fitting.³⁹ Interestingly, a longer plateau was observed with 2.5DM compared to MIP. This may be explained by the uniform intensity along the z-axis for 2.5DM whereas MIP is likely to show nonuniform intensity depending on the relative position of single-molecule spots from a focal plane. We also validated our approach for detecting other mRNA species such as TOP2A (Topoisomerase 2-alpha) (Figure 9S).

Applying average intensity projection (AIP) on the 3D stacks mimics an approach that rapidly moves a focal plane over a certain distance (Figure 4d).^16,40 Since AIP collects not only in-focus fluorescence signals but also out-of-focus background, the signal-to-background ratio (SBR) of AIP was the lowest compared to MIP and 2.5DM (Figure 4f). While 2.5DM compromises the SBR by a factor of 1.7 compared to MIP obtained by 3D stacks, it remarkably reduced the acquisition time by an order of magnitude. We also tested whether MIP and 2.5DM could provide reliable mRNA counting under the same total exposure time. The camera exposure time of 2.5DM and a single z-slice for the 3D stacks were set to 1 s and 40 ms (25 slices × 40 ms = 1 s), respectively. As expected, the MIP image showed lower SNR compared to the 2.5D image and many spots were overwhelmed by noise (Figure 10S), which could result in severe measurement errors,⁷ i.e. false-positive detection and/or missing spots. The much longer exposure time of 2.5DM allowed us to collect more fluorescence emission and led to a higher SNR.

Fast, high-throughput and multi-color smFISH using 2.5DM

We acquired a grid of 26 × 26 smFISH images over a ~ 2 × 2 mm² region within a depth of ~5 μm on U2OS cells (Figure 5a). Each field-of-view (FOV) was ~100 × 100 μm², and a 20% overlap between adjacent images was used to ensure proper stitching. The total acquisition time required for the measurement by traditional high-throughput approach via serial z-scanning was ~64 min; however, our 2.5D imaging system took just 9.2 min (Movies S1 and S2). One can clearly observe the individual transcripts in single cells with high SNR over an entire sample area (Figures 5b and 5c). Total number of imaged cells was ~2,830 and the throughput of conventional WF and 2.5DM was 0.7 cells/s and 5.1 cells/s, respectively. Note that this is two-color imaging; i.e. DAPI and AF647. We segmented well-isolated cells and counted a copy number of mRNAs per cell as a function of nucleus size measured by DAPI images (Figure 5d). Statistical analysis showed a positive linear correlation between the copy number and the nucleus size. This result is similar to a previous study that reveals relationship between the abundance of mRNA, the cell volume and the nucleus size.³⁷ On average, the copy number of EEF2 per cell was 505 ± 2.9 (mean $\pm$ standard error of the mean). By implementing 2.5DM, the throughput efficiency was remarkably improved with a reduced light dose.

Figure 5. High-throughput multi-color 2.5D imaging.

(a) An smFISH image of a 2 × 2 mm region of U2OS cells stained with DAPI (blue) and 32 probes labeled with AF647 for EEF2. 26 × 26 two-colored images with 20 % overlap between adjacent field of views were acquired under epi-illumination at exposure time of 600 ms for AF647 and 20 ms for DAPI. (b) A zoomed image of the rectangular region shown in (a) with an area of 65 × 65 μm². (c) A further-zoomed region represented in (b). (d) Copy number per cell as a function of nuclear size. The total number of cells analyzed was 814. The solid red line indicates the linear fit and r denotes a correlation coefficient. (e) Two color smFISH imaging on EEF2 (labeled with Cy3B) and TOP2A (AF647) on U2OS cells, where green and red represent the Cy3B channel and the AF647 channel, respectively. An illumination intensity of ~100 W/cm² at an exposure time of 600 ms was used. (f) A zoomed image for the rectangular region shown in (e). Scale bars, 200 μm (a), 10 μm (b, e), 2 μm (c) and 1 μm (f).

We also demonstrated the capability of 2.5DM in measuring different mRNA species in individual cells. Multi-color smFISH imaging on EEF2 (Cy3B) and TOP2A (AF647) was performed by illuminating the sample with two lasers at wavelengths of 532 nm and 638 nm. Two distinctive RNA molecules across the entire cell volume were clearly imaged by 2.5DM (Figure 5e). For two-color 2.5D imaging, it was unnecessary to switch the phase pattern of the SLM. Our simulation conducted at two emission wavelengths of Cy3B and AF647 with the same 2.5D phase mask showed that the axial FWHMs of the elongated PSF were 4.7 μm and 5.5 μm, which was larger than our sample thickness (Figure 11S).

Immunofluorescence imaging using 2.5DM

Finally, we employed 2.5DM for immunofluorescence imaging to visualize the distribution of proteins. Vimentin was stained with antibodies labeled with AF647 in U2OS cells. First, images of 25 z-positions within a thickness of 5 μm using an exposure time of 10 ms per frame under epi-illumination ($12\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$) were recorded and projected onto a 2D image by MIP or AIP (Figures 6a and 6b). A single exposure image using 2.5DM was acquired at an integration time of 30 ms (Figure 6d). As expected, the 2.5DM image displayed higher contrast compared to the AIP image. Notably, the 2.5D image exhibited better spatial consistency than the MIP image which displayed discontinuities (Figures 6a and 6c) because MIP highlights variability in sample contrast.⁴¹ However, the contrast of the 2.5D image was worse than that of MIP, as expected due to the broadening effect of the lateral width and lower SBR of 2.5DM. Fortunately, the recent advancement of computation-based super-resolution imaging was able to mitigate this problem. We adopted the super-resolution radial fluctuation (SRRF)⁴² method to our 2.5D image by calculating the radial symmetry. As shown in Figure 6e, SRRF improved not only the spatial resolution but also the SBR, confirming its compatibility with 2.5D images. Microtubules labeled with AlexaFlour 488 showed a similar result to vimentin (Figure 12S). To measure the extent of photobleaching we repeatedly measured fluorescence images over a 3D volume by WF (10 ms/slice) and 2.5DM (30 ms). We observed that 2.5DM had 1.5 times slower photobleaching rate than WF (Figures 6g and 6h), indicating that its lower light dose (8.3-fold) significantly reduces photodamage.

Figure 6. Immunofluorescence imaging of vimentin by 2.5DM.

(a-b) Images obtained by MIP (a) and AIP (b) using 25 z-stacks in an imaging volume of ~100 × 100 × 5 μm³ at an exposure time of 10 ms/slice. (c) A representative frame of the 3D stack at an imaging depth of 2 μm above the surface. (d) A single-shot image using 2.5DM at an exposure time of 30 ms. (e) An SRRF image using 2.5D image in (d). (f) Line profiles along the dashed lines of inset zoom-in regions in (a), (b), (d) and (e). (g) Vimentin images obtained by WF and 2.5DM after specified numbers of image volumes. (h) Photobleaching traces of WF (black) and 2.5DM (red) as a function of the number of image volumes. All images were taken under epi-illumination with an excitation intensity of ~12 W/cm² (a-e) and ~100 W/cm² (g). Scale bars, 10 μm (a-e), 20 μm (g).

Discussion

We presented a fast and high-throughput subcellular imaging platform exhibiting high-resolution and single-molecule sensitivity. To obtain information from 3D cells, unlike traditional methods that mechanically refocus the sample, 2.5DM simultaneously projects axial information onto a 2D focal plane in a single snapshot, demonstrating its great potential in improving the image acquisition rate. In contrast to other PSF engineering approaches for EDOF imaging, our 2.5D phase function showed a uniform focal response along the optical axis over an extended imaging depth and negligible lateral side lobes. Furthermore, controlling the strength of the aberration terms facilitated tunable adjustment of the imaging depth. We employed our technique in quantitative mRNA imaging via smFISH in mammalian cells. The number of mRNAs counted in individual cells corresponded well with the number counted with conventional approaches; however, a single exposure with 2.5DM demonstrated an order of magnitude faster imaging speed. It showed superior SBR to average intensity projections of 3D stack images, which mimics fast volumetric imaging methods via moving of focal planes. The ~3× increase in exposure time of 2.5DM was greatly outweighed by the higher throughput (10x) and more gentle imaging than WF in the end. We also showed that our 2.5DM could be used for imaging proteins which generally have a higher concentration than RNA. While it showed a slightly poorer spatial resolution and higher background than MIP, the 2.5D images robustly displayed all the features shown in conventional imaging with significantly reduced light exposure with a volume imaging rate of >30 Hz.

We note that many fluorescence images obtained in the biology community use a maximum intensity projection to represent a 3D object.⁴¹ This implies that unless 3D structural information is specifically needed, our 2.5DM can be generally used for volumetric imaging of biological samples. For example, assuming that single-molecule spot-analysis is feasible at molecular densities³⁹ of 0.2−1 molecule/μm², the maximum number of countable transcripts by our method amounts to ~1,600 for a U2OS cell whose projected size is ~40 × 40 μm², indicating that our approach will be able to robustly count most RNAs.

Throughput of the current 2.5D imaging system is likely to further increase. The total imaging time of 2.5DM (T_2.5D) can be expressed as T_2.5D = (τ + t_xy) × m², where τ denotes the inverse of the camera frame rate, t_xy the settling time of a motorized xy-stage and m² the number of stitched images. For example, when obtaining Figure 5a, we used τ = 600 ms (AF647) + 20 ms (DAPI), t_xy = 200 ms and m = 26. It is challenging to decrease t_xy because our “stop-and-image” strategy needs a sufficient settling time (>0.1 s). Nevertheless, there are several approaches that can decrease m and τ. For example, if the current objective lens is replaced with a 60×/NA1.4 oil or 60×/NA1.3 silicone objective that displays better field flatness, the imaging FOV will increase 4-fold (~200×200 μm²). A flat-field illumination instead of Gaussian beam illumination will allow us to use a small overlap when stitching images,³⁶ resulting in a decrease of m. The low photobleaching of 2.5DM presented in Figures 6g and 6h indicate that it would be possible to increase the imaging speed using a shorter exposure time with higher excitation intensity while maintaining high SNR. However, it should be noted that the extent of photobleaching of fluorophores and photodamage of samples depends on not only light dose but also the excitation peak intensity.¹⁵ Thus, it is desirable to carefully assess its effects on the imaging performance. Recent powerful computational approaches such as deep-learning based image restoration⁴³ or an sCMOS-related noise correction algorithm⁴⁴ may lower the exposure time by improving SNR. We anticipate that the throughput of our 2.5D imaging system may be able to increase to >200 cells/s, which is comparable to that of imaging flow cytometry.

The total transmission efficiency of the current 2.5D imaging system is ~41%. Since an SLM responds only to light of a certain linear polarization, it is inevitable to discard ~50% of fluorescence light by a polarizing beam splitter (Figure 1S). The optical loss from a knife edge mirror and SLM is attributed to an additional decrease of the transmission efficiency. However, it can be improved by replacing the SLM with a passive phase plate¹⁵ or by using a double-pass SLM arrangement.⁴⁵ The former device can be readily inserted in any microscope with an additional beam relay module, and the latter can fully exploit the advantages of an SLM while maintaining a high transmission efficiency. The SLM can also be used to correct depth aberration (Figure 13S)⁴⁶ and sample-induced aberrations, which minimizes the decrease of the smFISH signal with an increasing imaging depth and within the tissue.

Ideally, 2.5DM can also be applied to high throughput smFISH imaging in tissues. However, one may have to deal with a strong autofluorescence background overwhelming the detected signal, causing difficulty in determining the accurate mRNA count in individual cells. To overcome this issue, signal amplification methods⁴⁷ and/or tissue clearing to suppress the autofluorescence⁴⁸ can be used. Alternatively, selective illumination using a highly inclined beam whose thickness is 3–10 μm could be applied to suppress background.^49–50 This approach is also helpful to reduce side lobes of the effective PSF along the z-axis for 2.5DM. The SLM can also be used to correct aberrations from the specimen, which minimizes the decrease of the smFISH signal within the tissue with an increasing imaging depth.

It is straightforward to combine our method with other techniques, for instance, light-sheet microscopy^16,24 for fast volumetric imaging with high spatial resolution, or multiplexed FISH⁵¹ to increase the number of RNA species that can be measured simultaneously in individual cells and tissues. Since our approach uses a low light dose and obtains single-shot 3D images, it will be possible to capture fast dynamics and rare events from numerous cells by long-term live-cell imaging, which is critical to understand functions and mechanisms of cellular processes such as mitosis and nuclear organization formation.⁵² We expect our simple and versatile technique to advance imaging-based assays in biomedical applications.

Methods

2.5D phase function

We introduced circularly symmetric aberration functions at the back focal plane (BFP) of the objective lens to achieve an EDOF. These circularly symmetric phase functions, i.e. a combination of spherical aberration (P_SA) and defocusing terms (P_DF), named quartic phase mask^29,31 can be written as

$$P_{\mathrm{S}\mathrm{A}}\left(\rho \right)=\text{exp}\left(2\pi i\gamma {\rho }^4\right)$$ (1)

$$P_{\mathrm{D}\mathrm{F}}\left(\rho \right)=\text{exp}\left(2\pi i\psi {\rho }^2\right)$$ (2)

where ρ is the normalized radial coordinate with respect to the maximum radius of the pupil aperture, γ represents the strength of the spherical aberration and determines the extension of axial PSF, and ψ is a parameter to control the position of the focus plane. Then a binarization of the circularly symmetric phase function was induced to convert the continuous phase distribution to a binary phase pattern with only phase 0 and π; otherwise, it yielded an elongated PSF with rapid axial intensity oscillations with a focal shift compared to the original position. The binary phase function of two combined axisymmetric aberration terms can be expressed as:

$$P_{\mathrm{b}\mathrm{i}\mathrm{n}}\left(\rho \right)=\mathrm{B}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{r}\mathrm{y}\left[\text{exp}\left(2\pi i\right(\gamma {\rho }^4+\psi {\rho }^2\left)\right)\right]$$ (3)

where this binarization criterion is defined as³⁰:

$$\mathrm{B}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{r}\mathrm{y}\left[P\left(\rho \right)\right]=\left\{\begin{array}{l}1\text{Re}\left[P\left(\rho \right)\right]\ge 0\\ -1\text{Re}\left[P\left(\rho \right)\right]<0\end{array}\right.$$ (4)

The two parameters γ and ψ were optimized until we attained a defocus-invariant PSF exhibiting an uniform distribution within a specific depth. All of the simulations regarding the intensity distribution in the focal region were based on vectorial Debye diffraction theory^34–35 where the numerical aperture (NA) of the objective was 1.4, the wavelength (λ) was 670 nm and the refractive index (n) of the sample was 1.515, unless specified otherwise. To obtain a focal response from broadband light, we simply assumed a Gaussian emission spectrum with 670 ± 50 nm. The focal response was obtained by incoherently summing the intensity responses at each wavelength with multiplication of a corresponding emission coefficient based on the Gaussian spectrum.

2.5D microscope setup

All images were recorded by a custom-made microscope around Olympus IX73 (See Figure 1S for details). Four continuous-wave lasers (638 nm, 532 nm, 488 nm and 405 nm, Cobolt) were coupled into a single mode fiber (P5–405BPM-FC-2, Thorlabs), and their powers were controlled by a combination of a half-wave plate and a polarized beam splitter. The laser beam exiting from the fiber output was collimated by a lens (L1, f = 80 mm) and further expanded by a telescope composed of two lenses (L2, f = 50 mm; L3, f = 150 mm) to obtain more uniform epi-illumination. An iris was placed between L1 and L2 to control the beam size. The beam then passed through a lens (L4, f = 400 mm), was reflected by a dichroic mirror (DM1, Di03-R405/488/532/635-t1–25×36, Semrock) and delivered to the sample through an objective (UPlanSApo, 100×/1.4, Olympus). Fluorescence emission was collected by the same objective, passed through an emission filter (FF01–446/523/600/677, Semrock) and focused by a tube lens (L5, f = 180 mm). A 1:1 4f system composed of two lenses (L6, f = 200 mm; L7, f = 200 mm) relayed the intermediate image on a scientific complementary metal oxide semiconductor (sCMOS) camera (Zyla 4.2 Plus, Andor), giving an image magnification of 100×. A spatial light modulator (SLM) (PLUTO-2-VIS-097, Holoeye) with 1920 × 1080 pixels was placed at the conjugated BFP to generate the desired phase pattern. A knife-edge mirror was used to redirect the light onto the SLM at a shallow incidence angle (within ±5°) in a compact configuration to ensure proper performance of the SLM. A polarized beam splitter was inserted before the SLM to filter out the orthogonally polarized light which is not modulated by the SLM, avoiding a noisy effect being added to the final image. An automated 3D stage composed of an xy-stage (SCAN IM 120×80, Marzhauser) and a piezo z-stage (Z-insert.100, Piezoconcept) was used for acquiring z-stack images and high-throughput images. In addition, a custom-made z-drift module was inserted in the illumination path to correct z-drift of the sample stage during the high-throughput imaging acquisition. Briefly, a collimated NIR beam (85–2302, Edmund Optics) was passed through a lens (L8, f = 300 mm), then reflected by another dichroic mirror (DM2, FF750-SDi02–25×36, Semrock) and directed onto the sample through the same objective lens. The beam reflected from a coverslip was picked up by a 50:50 beam splitter and focused onto a camera (DMK 23U618, The Imaging Source) by a lens (L9, f = 60 mm). The camera continuously monitored a shift of the NIR beam during the movement of the xy-stage and a feedback signal was sent to the piezo z-stage to correct the drift using pre-calibrated data through a MATLAB script. To sequentially record multi-color images, an Arduino board (UNO R3; Elegoo) was used to digitally modulate on-off states of multiple lasers. All images were 2×2 binned and the FOV was ~100×100 μm². The imaging acquisition was controlled by MicroManager.

Detailed methods for all the sample preparation and imaging analysis used in this work can be found in Supporting Information.

Synopsis:

Single-shot volumetric imaging enables high-resolution subcellular analysis with reduced acquisition time and low light dose.