Optical microscopy imaging techniques (e.g., confocal, light sheet, multi-photon, second/third-harmonic generation, and coherent Raman scattering microscopy) [1–7] are indispensable for unlocking comprehensive 3D morphological and chemical information in biotissues, revealing functional and dynamic processes in living cells and tissues (e.g., developmental biology, neuron dynamics, tumor metabolisms, drug deliveries and pharmacodynamics, cancer diagnosis and therapy, and organ functions) [8–13]. Volumetric information of samples is commonly reconstructed by a series of 2D sectioning images captured across various depths through the mechanical movement of either the objective lens or sample stage along the $z$-axis [14]. However, such a scanning approach is hindered by mechanical inertia, resulting in a constrained 3D imaging speed during $z$-direction refocusing [15]. The motion artifacts may also result in unreliable spatial co-registration for 3D image reconstruction, compromising the high-quality volumetric imaging in biological and biomedical systems [16,17]. To overcome the limited imaging speed due to the mechanical $z$-scanning, snapshot 3D imaging technologies such as light-field microscopy (LFM) [18,19], digital holographic microscopy (DHM) [20,21], and point spread function (PSF) engineering microscopy [22,23] have been explored. These technologies enable volumetric imaging through a single 2D projection and the subsequent post-processing, eliminating the need for multiple sequential image acquisitions. However, these methods suffer from limited spatial resolution [24,25], speckle artifacts [26,27], and specific sample constraints (e.g., sparse samples) [28,29] in practical applications.

In this work, we present a novel phase-modulated multi-foci microscopy (${\mathrm{PM}}^3$) technique for snapshot 3D imaging in live tissues. To achieve the mechanical-scanning-free $z$-sectioning in ${\mathrm{PM}}^3$, we apply a spatial light modulator (SLM) to encode the phases of the scattered light from the sample and then project the sharp images from multiple depths onto the predefined areas on a single charge-coupled device (CCD) camera. We provide the theoretical insights and analysis of the working principle of the ${\mathrm{PM}}^3$ technique, and also build the ${\mathrm{PM}}^3$ imaging system to experimentally demonstrate its rapid volumetric imaging capability, showcasing the advantages of large imaging depth and tunable imaging intervals on a variety of samples (e.g., Brownian motion of polystyrene beads and fluorescent beads in water, blood flows and networking among multiple vessels across different tissue depths in zebrafish).

To obtain a sharp image from the out-of-focus position, we utilize an SLM to compensate for the phases of the diverging/converging scattered light collected from the sample. Specifically, we calculate the optical pathlength difference (OPD) between the spherical wavefront of the scattered light and the plane wave. Subsequently, we project an inverse phase onto the SLM to compensate for the OPD and collimate the scattered light from the sample. The correlation between the compensated phase $\mathrm{\Delta }p$ and the distance $\mathrm{\Delta }z$ away from the focal plane of the objective lens can be deduced using the Gaussian thin lens formula [30]: $$\frac{1}{l}+\frac{1}{\mathrm{\Delta }z+f}=\frac{1}{f},$$(1)where $f$ is the focal length of the first lens after the SLM, $l$ is the distance of the point source away from the lens, and $\mathrm{\Delta }z$ is the displacement of the focal spot from the focus of the lens. Thus, the OPD between the spherical and the plane wavefronts can be calculated: $$\mathrm{OPD}=(l-f)-\sqrt{{(l-f)}^2-r_F^2},$$(2)where $r_F$ is the radial coordinate on the Fourier plane. Under the paraxial condition, we can make a Taylor expansion for Eq. (2) and obtain the relationship between $\mathrm{\Delta }z$ and modulation phase $\mathrm{\Delta }p$ (OPD multiplied by wavevector $k$): $$\mathrm{\Delta }z=\frac{2f^2\mathrm{\Delta }p}{r_F^{2}k}.$$(3)

Therefore, the scattered light from the depth $\mathrm{\Delta }z+f$ would be collimated after passing through the SLM and sharply focused on the camera with an imaging lens.

To acquire clear images from multiple tissue depths, the SLM plane is divided into distinct segments, each with a pre-assigned modulation phase $\mathrm{\Delta }{p}_z$ for depth $z$. Additionally, to differentiate the images from various depths, a grating phase $g_z$ is combined with the modulation phase to deflect the image onto the predefined area of the camera. Consequently, the intensity from a specific depth $z$ can be expressed: $$I_z=I_{z0}{e}^{i\mathrm{\Delta }{p}_z}{e}^{ik{r}_F\sin {\theta }_z},$$(4)where $I_{z0}$ is the scattered light from depth $z$, and $I_z$ denotes the image captured by the camera following the phase modulation. ${\theta }_z$ is the deflection angle induced by the grating phase for the scattered light originating from depth $z$.

Figure 1(a) is the schematic of the ${\mathrm{PM}}^3$ system developed for snapshot 3D imaging. In the ${\mathrm{PM}}^3$ system, the sample can be illuminated by using either a light-emitting diode (LED) light (Nikon INTENSILIGHT C-FGFI) or a 532 nm continuous wave (CW) laser light (Verdi-V10, Coherent) through a fiber light guide for label-free bright-field or fluorescence imaging. The scattered or fluorescence light from the sample is collected by an objective lens (Olympus Plan Achromat Objectives, $10\times /0.25\mathrm{NA}$) and is then filtered with a 4 nm bandwidth filter (the combination of SEMROCK FF01-605/64-25 and SEMROCK FF01-565/24-25). Subsequently, the scattered or emitted fluorescence light from the sample is directed onto the SLM (HOLOEYE PLUTO) with a pair of relay lenses and modulated by a specified phase pattern designed. The unmodulated light is obstructed at the focal plane of Lens 3 by an aperture. After modulation with the SLM, the collected light from multiple depths is re-allocated to the specific deflection angles and focused onto a CCD camera (Thorlabs, DCU224C) with another pair of relay lenses.

Figure 1(b) illustrates the working principle of the ${\mathrm{PM}}^3$ technique. To capture a sharp image from an out-of-focus position, an inverse phase [depicted by the green curved line in Fig. 1(b)] is generated by the SLM to offset the spherical wavefront of collected light from the sample. Then, the converging/diverging light is collimated upon passing through the SLM and focused onto the imaging plane sharply. To separate images from multiple depths, the designed grating phases with various deflection angles are combined into the modulation phase, which directs the scattered or emitted fluorescence light from specific depths to the predefined areas on the CCD [Fig. 1(b)]. To simultaneously modulate the scattered or emitted fluorescence light from multiple depths, the SLM plane is divided into several segments, resembling a “pie” shape (for details refer to Fig. 4 in Appendix A), in which the multiple modulation phases and grating phases corresponding to specific tissue depths are pre-assigned to these segments, thereby enabling snapshot 3D imaging.

An example of the phase pattern used in the experiment to capture images from three different depths ($z_1,z_2,z_3$) is depicted in Fig. 1(c). Figure 1(d) is a zoom-in image marked with a red dashed rectangle in Fig. 1(c), where the section highlighted with a red solid rectangle is utilized to compensate and deflect the scattered or emitted fluorescence light from depth $z_1$. Similarly, the green and blue sections are for the depths $z_2$ and $z_3$. Figure 1(e) schematically presents the image acquired on the CCD, incorporating the information from the depths $z_1,z_2$, and $z_3$ marked with red, green, and blue solid circles, respectively. Figures 1(f) and 1(g) illustrate the phase patterns used to capture the 3D image from the 10 different depths with a smaller field of view (FOV) but a larger depth of field (DOF) [Fig. 1(h)]. In practical applications, the numbers and axial positions of imaging planes in ${\mathrm{PM}}^3$ can be tailored for a specific purpose by manipulating the phase patterns on SLM. Figure 1(i) reveals the fit axial intensity profile of a 1 μm polymer bead measured with 10 foci. Figure 1(j) demonstrates the linear relationship between the modulation phase and the measured foci positions at each depth, enabling the prediction of the axial positions of the foci using a specific phase pattern.

The 1 μm polystyrene (PS) beads (Fluka Analytical, 89904) are fixed on microscope slides to assess the relationship between the modulation phase and the axial positions of foci in the ${\mathrm{PM}}^3$ technique. A 1 μL, 2 μm beads suspension liquid (Fluka Analytical, 78452-5ML-F, diluted 1500 times) is sandwiched between the coverslips with a 340 μm thickness chamber for observing Brownian motion. A motor actuator-driven (Thorlabs, Z812B) translation stage moves the chamber along the $z$-axis for wide-range volumetric imaging. A 1 μL, 6 μm fluorescent bead suspension liquid (Polysciences Inc., 19111-2, diluted 5 times) is sandwiched between coverslips within a 510 μm thickness chamber for observing Brownian motion in water. The zebrafish larvae at 5-day post-fertilization are anaesthetized in 80 mg/L MS-222 for about 1 min and then fixed with 3% methylcellulose for ${\mathrm{PM}}^3$ imaging.

A typical pixel dwell time of 45 ms and a frame rate of 15 Hz ($1280\times 1024\mathrm{pixels}$, pixel size of 4.65 μm) are utilized for snapshot 3D imaging. For the Brownian motion of PS beads in water, 10 depths are captured by a single frame of the CCD with an Olympus Plan Achromat Objectives lens ($10\times /0.25\mathrm{NA}$). The size of the 3D volume is $78\mathrm{\mu m}\times 78\mathrm{\mu m}\times 162\mathrm{\mu m}$. For imaging the zebrafish, three tissue depths are imaged with one frame of the CCD using a $20\times$ objective lens (Olympus Plan Achromat Objectives lens, 0.4 NA). The size of the 3D volume is $94\mathrm{\mu m}\times 94\mathrm{\mu m}\times 60\mathrm{\mu m}$. The wavelength of the scattered light is between 573 and 577 nm after passing through a 4 nm bandpass filter. The maximum output power of the LED is about 300 mW, while typically $\sim 20–30\mathrm{mW}$ is used for illuminating the samples. No obvious photodamage effects were observed during the prolonged 3D imaging sessions in living tissue measurements (e.g., zebrafish blood flows in Fig. 3; Visualization 1 and Visualization 2). For observing the 3D Brownian motion of fluorescent beads in water, a 532 nm CW laser with $\sim 10\mathrm{mW}$ is utilized for fluorescence excitation. The filter range is set from 573 to 577 nm. The size of the 3D volume is $208\mathrm{\mu m}\times 208\mathrm{\mu m}\times 200\mathrm{\mu m}$. The frame rate of the SLM is 60 Hz. The switching rate of the motorized translation stage (KVS30, Thorlabs) is 10 Hz under trigger mode.

The image acquired from the CCD camera contains several smaller windows (Appendix B, Fig. 5, and Visualization 1; Appendix C, Fig. 6, and Visualization 2), each corresponding to a specific tissue depth. The 3D image of the sample is reconstructed by stacking these sub-images with MATLAB.

We have applied the ${\mathrm{PM}}^3$ technique to track the Brownian motion of PS beads in water within a larger imaging range compared to the DOF of the objective lens. Figure 2(a) shows the schematic for tracking the 3D distribution of PS beads in water along the $z$-axis, employing the volumetric imaging (10 focal planes with an imaging interval of $\mathrm{\Delta }z$) by ${\mathrm{PM}}^3$. As the beads move along the channel, the imaging volume produced by ${\mathrm{PM}}^3$ dynamically shifts along the $z$-axis. The axial position of the imaging volume is adjusted by varying the phase patterns on the SLM, enabling real-time monitoring of the 3D distribution of PS beads in water. Given the refresh rate of the SLM used ($\sim 5\mathrm{Hz}$ per volume), the ${\mathrm{PM}}^3$ technique can trace the 3D dynamic motions of small particles in water (e.g., the bead’s moving speed of 0.81 mm/s along the $z$-axis is observed in an imaging volume of $78\mathrm{\mu m}\times 78\mathrm{\mu m}\times 162\mathrm{\mu m}$).

Figure 2(b) presents the images of the beads captured at each focal plane within the imaging volume ($\mathrm{\Delta }z=18\mathrm{\mu m}$) by ${\mathrm{PM}}^3$. Figure 2(c) illustrates the 3D snapshot images of PS beads in water, corresponding to different axial positions of the imaging volume. We applied 49 distinct phase patterns and tracked the moving beads [marked by the white dotted rectangle in Fig. 2(c)] over a distance of about 1 mm [Fig. 2(d)], which is $\sim 55$-fold longer than the DOF of the objective lens used (18 μm). Meanwhile, we can also accurately capture the trajectory of two beads [surrounded by the white dashed rectangle in Fig. 2(c)] in the imaging volume [Fig. 2(e)]. The speeds of 3D Brownian motion for these two PS beads in water are estimated to be $\sim 2.58\mathrm{\mu m}/\mathrm{s}$ and $\sim 2.47\mathrm{\mu m}/\mathrm{s}$, respectively. The measured results are close to the theoretical values (2.54 μm/s, time interval of 0.2 s, temperature of 293 K) calculated by the Stokes–Einstein equation [31], demonstrating the feasibility of ${\mathrm{PM}}^3$ in accurately monitoring the particle dynamics in moving objects. Hence, the fast motion dynamics of chemical beads in water across the extended imaging volume can be rapidly captured and quantified by ${\mathrm{PM}}^3$.

To further extend the applicability of the ${\mathrm{PM}}^3$ technique to fluorescence imaging, we switch the LED excitation light source to the 532 nm CW laser excitation to observe the Brownian motion of 6 μm fluorescent beads in water. Figures 2(f)–2(h) present the snapshot 3D images of fluorescent beads within a fixed imaging volume but at different time windows (refer to Visualization 3, Fig. 7, and Appendix D for details). The images of the beads are captured sharply at a volume rate of $\sim 15\mathrm{Hz}$ without blurring (equivalent to the maximum frame rate of the CCD camera used), re-affirming the rapid 3D imaging capability of ${\mathrm{PM}}^3$ in fluorescence imaging applications.

We have utilized the rapid ${\mathrm{PM}}^3$ technique to observe the blood flows across multiple vessels in zebrafish to demonstrate the advantage of a tunable imaging interval in ${\mathrm{PM}}^3$. Figure 3(a) depicts the enlarged view of the phase pattern used to capture the images from three different tissue depths with an identical imaging interval. The area enclosed by a yellow dashed rectangle represents the compensation phase for the scattered light from depth $z=30\mathrm{\mu m}$. Figures 3(b)–3(d) present the snapshot images of blood flows captured at depths of 0 μm, 30 μm, and 60 μm, respectively (refer to Appendix C and Visualization 2). In the trunk artery of the living zebrafish [indicated by a yellow dashed line in Fig. 3(b)], we can clearly observe the blood flow by ${\mathrm{PM}}^3$. Additionally, a single red blood cell in the vein [marked with a red dashed ellipse in Fig. 3(d)] is also evident. However, the image obtained at the focal plane $z=30\mathrm{\mu m}$ is indistinct, making it difficult to monitor the blood flow and blood cells at this depth [yellow dashed line and red dashed ellipse in Fig. 3(c)]. To illustrate the advantages of ${\mathrm{PM}}^3$ with a tunable imaging interval and fast imaging speed, we manipulated the axial position of the imaging plane by modifying the phase compensation at the specific segments on the phase pattern [surrounded by a yellow dashed rectangle in Fig. 3(e)]. Figures 3(f)–3(h) present the clear blood flows (yellow dashed line) and the red blood cells (red dashed ellipse) obtained at $z=0\mathrm{\mu m}$, 10 μm, and 60 μm, respectively, with the modified phase patterns (see Appendix D and Visualization 3) for the same living zebrafish, substantiating the superiority of ${\mathrm{PM}}^3$ with a tunable imaging interval and fast imaging speed.

Conventional 3D image reconstruction by stacking the sequential 2D images captured via mechanical $z$-scanning is widely used in optical microscopy yet encounters the hurdle of constrained imaging speed in tissues and cells. To tackle the challenge, we have developed an innovative ${\mathrm{PM}}^3$ technique for rapid 3D imaging by modulating the phase of the collected scattered or emitted fluorescence light from different tissue depths through an SLM. The ${\mathrm{PM}}^3$ technique enables the simultaneous manipulation of the phase of collected light from multiple depths using a single phase pattern, thereby facilitating the snapshot 3D imaging of tissues and cells. Unlike the LFM technique, the ${\mathrm{PM}}^3$ method encodes the depth information in the Fourier plane of the imaging system. This eliminates the need to capture additional angular information on a limited sensor plane for 3D structure reconstruction, while preserving spatial resolution comparable to that of the objective lens used. Additionally, ${\mathrm{PM}}^3$ captures the incoherent light from the bulk sample, thus avoiding speckle artifacts (e.g., those observed in DHM) and sample constraints (e.g., as encountered in PSF engineering) in 3D imaging. Leveraging on a tunable electronically controlled phase modulator (e.g., SLM), our ${\mathrm{PM}}^3$ provides unique properties of extended imaging depths and adjustable imaging intervals between each focus for biological applications.

We demonstrate the advancement of the extended imaging depths by monitoring the Brownian motion of polymer beads in water (Fig. 2), achieving a substantial enlargement of the volumetric imaging range up to 1 mm. This range is about 55-fold larger than the DOF (18 μm) of the objective lens we used, effectively addressing the trade-off between spatial resolution and DOF in ${\mathrm{PM}}^3$. Conventional long-distance tracking methods employing mechanical $z$-scanning [32,33] can offer higher imaging depth (equivalent to the working distance of the objective lens) and SNR than ${\mathrm{PM}}^3$ when observing the stationary samples without the need for high 3D imaging speed. But the slower 3D imaging speed and less reliable spatial co-registration encountered in mechanical $z$-scanning hamper its wide applications in biological and biochemical systems (e.g., monitoring functional and dynamic processes in live cells and tissues). In contrast, the ${\mathrm{PM}}^3$ technique provides a much higher 3D imaging speed (e.g., simultaneous scanning with at least 10 focal planes [Fig. 2(a)]) associated with mechanical $z$-scanning-free sectioning (only phase pattern variations on the SLM) in a relatively large imaging range, making it highly attractive for rapid, large-scale volumetric imaging applications in living biosystems. One notes that the frame rate of the phase pattern is constrained by the communication time between the SLM and the computer, restricting the tracking speed of ${\mathrm{PM}}^3$ for dynamic processes; and the frame rate of the camera (15 Hz) may also constrain the 3D imaging speed in ${\mathrm{PM}}^3$. To capture faster dynamic processes occurring in various applications (e.g., heart beating dynamics, neural ensemble dynamics, cell sorting in cytometry, and blood dynamics [34–37]), a kHz MEM-based SLM or digital micromirror device (DMD) [38,39] with response time in the millisecond scale together with a kHz-rate scientific complementary metal-oxide semiconductor (sCMOS) camera can be utilized to significantly boost both the axial scanning rate and 3D imaging speed of ${\mathrm{PM}}^3$ for observing rapid functional and dynamic processes in biological and biomedical systems.

We also demonstrate the advantage of a tunable imaging interval in ${\mathrm{PM}}^3$ by observing the blood flows across multiple vessels in zebrafish (Fig. 3). Compared with conventional multi-focal plane microscopy (MPM) involving in specially designed optical elements (e.g., quadratic grating or $z$-splitter prisms) [40,41] with immobilized imaging intervals and depth, the ${\mathrm{PM}}^3$ technique allows for tunable 3D imaging positionings, facilitating the observation of dynamic processes at the multiple depths of interest simultaneously. It is worth noting that ${\mathrm{PM}}^3$ is not limited to the transmission mode in the current study [Fig. 1(a)]. Through modulating the back-scattered or emitted fluorescence light from the multiple tissue depths, ${\mathrm{PM}}^3$ can also operate in epi-detection mode, enabling the real-time monitoring of dynamic and/or functional processes in vivo in live tissues and cells.

In ${\mathrm{PM}}^3$, the scattered light from each tissue depth is modulated by the SLM and sharply imaged by a CCD camera. However, the diffuse scattered light from multiple tissue depths is also modulated by the phase patterns and projected onto the camera, which may degrade the contrast and resolution of the images from different tissue depths. Assuming the number of depths is $N$, then only 1/$N$ of the intensity from a specific depth is projected onto the CCD camera for imaging, while the remaining intensity contributes to the background. Therefore, an increased number of depths may reduce the imaging sensitivity due to the increased crosstalk between different tissue depths and the decreased photon number collected at deeper tissue depths. To mitigate this effect, the deconvolution algorithms [42] can be incorporated into the ${\mathrm{PM}}^3$ technique to enhance the image contrast and resolution in 3D imaging of cells and tissues. On the other hand, the grating structure of the SLM device used in ${\mathrm{PM}}^3$ may introduce a dispersion effect on the collected light from the sample, leading to chromatic aberrations in the image captured by the CCD camera, thereby reducing the resolution of 3D imaging in ${\mathrm{PM}}^3$. To mitigate the dispersion effect, we incorporated a 4 nm bandpass filter into ${\mathrm{PM}}^3$, which maintains a proper imaging resolution necessary for observing fast dynamic processes in the samples or tissues (e.g., Brownian motion of beads in water and blood flow in zebrafish vessels) with an acceptable SNR. To further enhance the SNR of ${\mathrm{PM}}^3$, a broader band filter could be utilized to capture more signal light from the sample with a proper level of imaging resolution. A multi-tile shift-error correction and interpolation algorithm [43] can be integrated into ${\mathrm{PM}}^3$ to eliminate the chromatic aberrations for high-quality dynamic image acquisitions in live cells and tissues.

In summary, we have developed a unique ${\mathrm{PM}}^3$ technique for achieving snapshot 3D imaging in tissues without the need for mechanical $z$-scanning. We have demonstrated the capability of the ${\mathrm{PM}}^3$ technique to rapidly capture dynamic 3D imaging across a variety of samples (e.g., Brownian motion of PS and fluorescent beads in water, as well as blood flows across multiple vessels in zebrafish larvae), spanning the applications from bright-field to fluorescence microscopy. One notes that ${\mathrm{PM}}^3$ can be synergistically integrated with adaptive optics (AO) methods by merging the wavefront correction and depth-modulated phase patterns on the SLM to enable snapshot 3D imaging in deeper tissues [44]. We anticipate that the ${\mathrm{PM}}^3$ technique holds immense promise as a $z$-scanning-free 3D imaging tool for biological and biomedical systems, offering substantial benefits (e.g., rapid 3D imaging capability, extended imaging range, and the adjustable imaging intervals) across a diverse range of biological and biomedical applications.